Università degli Studi di Pavia - Censimento Centri di ... · Università degli Studi di Pavia Dottorato di Ricerca in Ingegneria Elettronica, Informatica ed Elettrica XXIII Ciclo

Università degli Studi di Pavia

Dottorato di Ricerca in Ingegneria

Elettronica, Informatica ed Elettrica

XXIII Ciclo

The need to coordinate generation and

transmission planning and to ensure

a secure and e�cient reactive power

provision: two key aspects of the

restructured electricity industry

Tesi di Dottorato di:

Ing. Ilaria Siviero

Relatore:

Chiar.mo Prof. Paolo Marannino

Anno Accademico 2009/2010

Contents

1 Introduction 1

1.1 Research motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Generation and transmission planning . . . . . . . . . . . . . . . . . . . . . 2

1.1.2 Reactive support and voltage control . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Research objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.3 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 WTLR and power system planning 9

2.1 Power system planning and electricity market e�ciency . . . . . . . . . . . . . . . 10

2.1.1 Electricity market e�ciency . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1.2 Generation system investments and Social Welfare . . . . . . . . . . . . . . 13

2.1.3 Transmission system expansion and Social Welfare . . . . . . . . . . . . . . 15

2.1.4 General considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Power system planning and network security . . . . . . . . . . . . . . . . . . . . . 16

2.2.1 �Measuring� system security . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.2 Generation expansion and power system security . . . . . . . . . . . . . . . 18

2.2.2.1 Overload mitigation strategy . . . . . . . . . . . . . . . . . . . . . 18

2.2.3 Transmission planning and power system security . . . . . . . . . . . . . . . 20

2.2.3.1 WTLR and transmission planning . . . . . . . . . . . . . . . . . . 21

2.3 Matlab-coded program for WTLR sensitivity calculation . . . . . . . . . . . . . . . 23

2.3.1 Step 1: security analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.2 Step 2: ISDF calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3.2.1 Distribution factor formulation . . . . . . . . . . . . . . . . . . . . 24

2.3.2.2 Post-contingency distribution factor . . . . . . . . . . . . . . . . . 28

2.3.3 Step 3: WTLR calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.3.4 Step 4: WTLR graphical representation . . . . . . . . . . . . . . . . . . . . 29

2.4 Application of the procedure to the CIGRE 63-bus system . . . . . . . . . . . . . . 30

2.4.1 Simulation hypotheses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.4.2 Base case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.4.3 WTLR-based generation expansion and network security . . . . . . . . . . 34

2.4.4 WTLR-based grid development . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.4.4.1 WTLR procedure results . . . . . . . . . . . . . . . . . . . . . . . 39

2.4.4.2 A WTLR-based metric for transmission planning . . . . . . . . . . 41

2.4.4.3 Validation of the WTLR-based metric . . . . . . . . . . . . . . . . 42

2.4.4.4 An index to prioritize transmission planning . . . . . . . . . . . . 43

i

CONTENTS ii

2.5 Changes in the original Matlab-coded procedure . . . . . . . . . . . . . . . . . . . 45

2.5.1 Introduction of the Line Outage Distribution Factors . . . . . . . . . . . . . 45

2.5.1.1 LODF formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.5.1.2 Application to the CIGRE 63-bus system . . . . . . . . . . . . . . 46

2.5.1.3 Using the base ISDFs to compute WTLR sensitivities . . . . . . . 50

2.5.2 Adoption of the distributed slack bus . . . . . . . . . . . . . . . . . . . . . . 51

2.5.2.1 Impact of the choice of the slack bus . . . . . . . . . . . . . . . . . 51

2.5.2.2 Distributed slack bus . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.6 Tests on the Italian EHV system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.6.1 The MVA rating approximation . . . . . . . . . . . . . . . . . . . . . . . . . 57

2.6.1.1 Original procedure results . . . . . . . . . . . . . . . . . . . . . . . 58

2.6.1.2 Check by a standard steady-state security assessment tool . . . . 58

2.6.1.3 Considering the actual voltage magnitudes . . . . . . . . . . . . . 60

2.6.1.4 Considering the actual power �ow limits . . . . . . . . . . . . . . 60

2.6.1.5 Conclusions on the Matlab-coded procedure for WTLR calculation 61

2.6.2 WTLR sensitivity: a tool with several uses . . . . . . . . . . . . . . . . . . 62

2.6.2.1 GENCO viewpoint . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

2.6.2.2 TSO viewpoint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

2.6.2.3 Interchangeability of generation expansion and transmission devel-

opment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

2.7 Chapter conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

3 Reactive power service 91

3.1 Ancillary services . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.1.1 De�nitions in the U.S. markets . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.1.2 Ancillary services in Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.1.3 The Italian ancillary services . . . . . . . . . . . . . . . . . . . . . . . . . . 95

3.2 Reactive power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.2.1 What is reactive power? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.2.2 The need for reactive power . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

3.2.3 Reactive power and blackouts . . . . . . . . . . . . . . . . . . . . . . . . . . 98

3.3 Reactive power support as ancillary service . . . . . . . . . . . . . . . . . . . . . . 99

3.3.1 Technical issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

3.3.2 Policy issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

3.3.3 A challenge for System Operator and Regulatory Authority . . . . . . . . . 101

3.3.3.1 Optimal provision for reactive power service . . . . . . . . . . . . 101

3.3.3.2 The e�ect of reactive power on real power and system security . . 101

3.3.3.3 Reactive power management: dispatch versus procurement . . . . 103

3.3.3.4 Reactive power remuneration schemes . . . . . . . . . . . . . . . . 103

3.3.3.5 Energy price volatility . . . . . . . . . . . . . . . . . . . . . . . . . 103

3.3.3.6 Reactive market power . . . . . . . . . . . . . . . . . . . . . . . . 103

3.4 Reactive power management review . . . . . . . . . . . . . . . . . . . . . . . . . . 104

3.4.1 Reactive power service in di�erent deregulated markets . . . . . . . . . . . 104

3.4.1.1 North America . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

3.4.1.2 Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

CONTENTS iii

3.4.2 Literature on reactive power pricing and management . . . . . . . . . . . . 106

3.4.3 Possible policy solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

3.4.3.1 Decoupling of real and reactive power . . . . . . . . . . . . . . . . 107

3.4.3.2 Zonal reactive power management . . . . . . . . . . . . . . . . . . 108

3.4.3.3 Alternative sources of reactive power supply . . . . . . . . . . . . 108

3.5 Architecture of voltage control system . . . . . . . . . . . . . . . . . . . . . . . . . 108

3.5.1 Hierarchical voltage control system . . . . . . . . . . . . . . . . . . . . . . . 108

3.5.1.1 Basic SVR and TVR concepts . . . . . . . . . . . . . . . . . . . . 110

3.6 Reactive power service in Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

3.6.1 Current regulatory framework in Italy . . . . . . . . . . . . . . . . . . . . . 111

3.6.2 Reactive power service by generators . . . . . . . . . . . . . . . . . . . . . . 114

3.6.3 The Italian network voltage control system . . . . . . . . . . . . . . . . . . 115

3.6.3.1 Selection of pilot nodes, control areas, and control plants . . . . . 116

3.7 Optimal Reactive Power Flow program . . . . . . . . . . . . . . . . . . . . . . . . . 117

3.7.1 Compact reduced ORPF model . . . . . . . . . . . . . . . . . . . . . . . . . 120

3.7.2 Reactive power value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

3.8 Wind energy exploitation and reactive power support . . . . . . . . . . . . . . . . 122

3.8.1 Technical performance requirements for connection of wind farms . . . . . . 123

3.8.1.1 Germany . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

3.8.1.2 Spain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

3.8.1.3 Italy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

3.8.2 Technology solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

3.8.2.1 WTG based reactive power compensation . . . . . . . . . . . . . . 127

3.8.2.2 External reactive power compensation . . . . . . . . . . . . . . . . 128

3.9 Tests on the Italian EHV network . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

3.9.1 Main assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

3.9.1.1 Wind power production . . . . . . . . . . . . . . . . . . . . . . . . 129

3.9.1.2 SVR control areas, pilot nodes, and controlling generators . . . . . 131

3.9.2 Test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

3.9.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

3.9.3.1 Test case 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

3.9.3.2 Test case 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

3.9.3.3 Test case 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

3.9.3.4 Test cases 4 and 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

3.9.3.5 Real losses' variation . . . . . . . . . . . . . . . . . . . . . . . . . 160

3.10 Chapter conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

4 Conclusions 164

A CIGRE-63 bus test system 166

B Power Distribution Factors 169

B.1 Basic distribution factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169

B.2 Impact of changes in network topology and parameter values . . . . . . . . . . . . 171

B.2.1 Outage of a line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

B.2.2 Closure of a line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

CONTENTS iv

C Slack bus modeling in load �ow solutions 174

C.1 Single slack bus power �ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

C.2 Distributed slack bus power �ow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

C.2.1 Participation factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

D Devices for reactive power support 179

D.1 Synchronous generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

D.2 Distributed generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

D.3 Synchronous condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

D.4 Supervar machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

D.5 Shunt capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

D.6 Shunt reactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

D.7 Series capacitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

D.8 Flexible AC Transmission Systems (FACTS) . . . . . . . . . . . . . . . . . . . . . . 182

D.8.1 Static Var Compensators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

D.8.2 Static Synchronous Compensators . . . . . . . . . . . . . . . . . . . . . . . 183

D.8.3 Static Synchronous Series Compensators . . . . . . . . . . . . . . . . . . . . 183

D.8.4 D-var (Dynamic Var) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

D.8.5 Distributed SMES (D-SMES) . . . . . . . . . . . . . . . . . . . . . . . . . . 183

D.8.6 Uni�ed Power Flow Controllers . . . . . . . . . . . . . . . . . . . . . . . . . 183

D.8.7 Interline Power Flow Controllers . . . . . . . . . . . . . . . . . . . . . . . . 184

D.9 Wind generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

D.10 User plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

D.11 Transmission lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

D.11.1 High voltage DC transmission lines . . . . . . . . . . . . . . . . . . . . . . . 185

D.12 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

D.12.1 Transformer taps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

D.12.2 Phase Shifting Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

D.13 Di�erences among equipment types . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

E Italian hierarchical voltage control 188

E.1 Secondary Voltage Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

E.1.1 SART apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

E.1.2 RVR apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

E.2 Tertiary Voltage Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

E.2.1 NVR apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

E.3 Control system algorithms and dynamics design . . . . . . . . . . . . . . . . . . . . 192

List of Figures

2.1 Graph illustrating consumer and producer surpluses . . . . . . . . . . . . . . . . . 11

2.2 Productive e�ciency + Allocative ine�ciency . . . . . . . . . . . . . . . . . . . . . 12

2.3 Productive ine�ciency + Allocative e�ciency . . . . . . . . . . . . . . . . . . . . . 12

2.4 Productive ine�ciency + Allocative ine�ciency . . . . . . . . . . . . . . . . . . . . 13

2.5 E�ects of a capacity expansion investment . . . . . . . . . . . . . . . . . . . . . . . 14

2.6 E�ects of a cost reducing investment . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.7 Technological investments and market e�ciency . . . . . . . . . . . . . . . . . . . . 15

2.8 Overload mitigation strategy using generation . . . . . . . . . . . . . . . . . . . . . 19

2.9 Transmission relief . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.10 Network equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.11 Example of �le with contingency analysis results . . . . . . . . . . . . . . . . . . . 25

2.12 Example of �le with overloaded branches' ranking . . . . . . . . . . . . . . . . . . 25

2.13 Example of �le with WTLR sensitivities . . . . . . . . . . . . . . . . . . . . . . . . 29

2.14 Example of contourf result for WTLR graphical representation . . . . . . . . . . 30

2.15 Example of WTLR graphical representation . . . . . . . . . . . . . . . . . . . . . . 31

2.16 CIGRE 63-bus test system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.17 WTLR graphical representation - Base case . . . . . . . . . . . . . . . . . . . . . . 35

2.18 Node 33V1 WTLR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.19 System overload - New generator at node 33V1 . . . . . . . . . . . . . . . . . . . . 36

2.20 Node 5M1 WTLR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.21 System overload - New generator at node 5M1 . . . . . . . . . . . . . . . . . . . . 37

2.22 Node 66M1 WTLR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

2.23 System overload - New generator at node 66M1 . . . . . . . . . . . . . . . . . . . . 38

2.24 Network reinforcements for CIGRE 63-bus system . . . . . . . . . . . . . . . . . . 39

2.25 Total system overload for all test cases (decreasing order) . . . . . . . . . . . . . . 40

2.26 WTLR algebraic sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.27 Social Welfare for all test cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.28 Impact of the transaction ∆tst . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.29 Density function of the relative errors in line �ow approximations . . . . . . . . . . 48

2.30 Cumulative distribution function of errors in line �ow approximations . . . . . . . 48

2.31 Relative error on WTLR sensitivities using LODFs . . . . . . . . . . . . . . . . . . 50

2.32 ISDF error density function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.33 Scatter plot of the relative errors as a function of the ISDF magnitudes . . . . . . 52

2.34 E�ect of the approximations on WTLR sensitivities . . . . . . . . . . . . . . . . . 52

2.35 WTLR values with di�erent slack buses . . . . . . . . . . . . . . . . . . . . . . . . 54

v

LIST OF FIGURES vi

2.36 Cumulative distribution function of |DSISDF − ISDF | . . . . . . . . . . . . . . . 56

2.37 Impact of adopting a distributed slack bus model on WTLRs . . . . . . . . . . . . 57

2.38 Outaged and overloaded 380 kV lines . . . . . . . . . . . . . . . . . . . . . . . . . . 59

2.39 Impact of the MVA rating approximation on WTLRs . . . . . . . . . . . . . . . . 61

2.40 Geographical and virtual Italian zones . . . . . . . . . . . . . . . . . . . . . . . . . 63

2.41 WTLR map - Italian EHV system (year 2013) . . . . . . . . . . . . . . . . . . . . . 64

2.42 Possible new generation sites (year 2013) . . . . . . . . . . . . . . . . . . . . . . . . 64

2.43 Possible new generation sites (year 2015) . . . . . . . . . . . . . . . . . . . . . . . . 66

2.44 WTLR map - Italian EHV system (year 2009) . . . . . . . . . . . . . . . . . . . . . 69

2.45 Critical grid areas of the current Italian transmission system [23] . . . . . . . . . . 70

2.46 WTLR map - Scenarios A (top) and B (bottom) . . . . . . . . . . . . . . . . . . . 74

2.47 WTLR map - Scenarios C (top) and D (bottom) . . . . . . . . . . . . . . . . . . . 75

2.48 Wind generation capacity installed in Italy at the end of 2009 . . . . . . . . . . . . 76

2.49 Wind generation capacity expected in the medium-term . . . . . . . . . . . . . . . 76

2.50 WTLR map - Scenarios A (top) and B (bottom) without the new wind farms . . . 78

2.51 Network reinforcements considered in the study . . . . . . . . . . . . . . . . . . . . 79

2.52 WTLR algebraic sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

2.53 WTLR map (Benevento-Foggia reinforcement) . . . . . . . . . . . . . . . . . . . . 84

2.54 WTLR map (middle-Adriatic backbone reinforcement) . . . . . . . . . . . . . . . . 84

2.55 WTLR map (new line Montecorvino-Benevento) . . . . . . . . . . . . . . . . . . . 85

2.56 WTLR map (new line Deliceto-Bisaccia) . . . . . . . . . . . . . . . . . . . . . . . . 85

3.1 Example of a synchronous generator loading capability diagram . . . . . . . . . . . 102

3.2 Hierarchical structure for transmission network voltage control . . . . . . . . . . . 111

3.3 Italian regulation for voltage control and reactive exchanges . . . . . . . . . . . . . 112

3.4 Minimum requirement for the network-side reactive power supply - Germany . . . 125

3.5 PQ diagram of the wind energy plant at the grid connection point - Germany . . . 126

3.6 Common WTG electrical topologies . . . . . . . . . . . . . . . . . . . . . . . . . . 128

3.7 Geographic location of the �fteen wind collection substations . . . . . . . . . . . . 130

3.8 SVR areas for the Italian EHV system . . . . . . . . . . . . . . . . . . . . . . . . . 133

3.9 SVR areas and controlling generators - North Italy . . . . . . . . . . . . . . . . . . 133

3.10 SVR areas and controlling generators - Adriatic side . . . . . . . . . . . . . . . . . 134

3.11 SVR areas and controlling generators - Tyrrhenian side . . . . . . . . . . . . . . . 134

3.12 Sensitivities∣∣∣∂QP,k

∂Qj,k

∣∣∣ - Choice of the pilot node of SVR area 7 . . . . . . . . . . . . 135


∂Qj,k



∂Qj,k



∂Qj,k

∣∣∣ - Area 2 (Baggio) . . . . . . . . . . . . . . . . . . . . . . . . . 137


∂Qj,k

∣∣∣ - Generating units of La Casella and Piacenza . . . . . . . . . 137


∂Qj,k

∣∣∣ - Generating units of Torviscosa and Monfalcone . . . . . . . . 138

3.18 Reactive power margins under AVR control (areas of Dolo, Forlì, and Villanova) . 143

3.19 Nodal marginal values of reactive power - Area 1 . . . . . . . . . . . . . . . . . . . 144




LIST OF FIGURES vii






3.28 Nodal marginal values of reactive power - Area 10 . . . . . . . . . . . . . . . . . . 148




3.32 SVR voltage pro�le of pilot nodes - Case 1 and Case 2 . . . . . . . . . . . . . . . . 152

3.33 Reactive marginal values in pilot nodes - Case 1 and Case 2 . . . . . . . . . . . . . 153

3.34 Map of nodal ¿/Mvarh indicators - Case 2 . . . . . . . . . . . . . . . . . . . . . . 154

3.35 Reactive power margins in Central-Southern Italy - Case 1 and Case 3 . . . . . . . 155

3.36 Reactive marginal values in pilot nodes - Case 1 and Case 3 . . . . . . . . . . . . . 156

3.37 Reactive marginal values in wind collector substations - Case 1 and Case 3 . . . . 157

3.38 Reactive marginal values in wind collector substations - Case 1 and Case 4 . . . . 159

3.39 Voltage pro�le of pilot nodes - Case 2 and Case 5 . . . . . . . . . . . . . . . . . . . 160

A.1 CIGRE 63-bus test system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

C.1 Flow-chart of a single slack bus load �ow . . . . . . . . . . . . . . . . . . . . . . . 177

D.1 An example of synchronous generator output capability curve [117] . . . . . . . . . 180

E.1 Hierarchical voltage control for the Italian EHV system . . . . . . . . . . . . . . . 189

List of Tables

2.1 Contingency list (CIGRE 63-bus system) . . . . . . . . . . . . . . . . . . . . . . . 32

2.2 Thermoelectric generation pro�le (CIGRE 63-bus system) . . . . . . . . . . . . . . 32

2.3 Contingency analysis results - Base case . . . . . . . . . . . . . . . . . . . . . . . . 33

2.4 WTLR sensitivities - Base case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.5 Security analysis results for all test cases . . . . . . . . . . . . . . . . . . . . . . . . 40

2.6 Security analysis results - New line 1M1-5M1 or 2M1-5M1 . . . . . . . . . . . . . . 41

2.7 WTLR sensitivities - New line 1M1-5M1 or 2M1-5M1 . . . . . . . . . . . . . . . . 41

2.8 Economic indicators for all test cases (¿/h) . . . . . . . . . . . . . . . . . . . . . . 43

2.9 Index validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

2.10 Contingency analysis results by using LODFs . . . . . . . . . . . . . . . . . . . . . 49

2.11 Contingency analysis results with di�erent slack buses . . . . . . . . . . . . . . . . 53

2.12 Participation factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.13 Contingency analysis results using the distributed slack bus power �ow . . . . . . . 55

2.14 Contingency analysis results (original procedure) . . . . . . . . . . . . . . . . . . . 58

2.15 WTLR sensitivities (original procedure) . . . . . . . . . . . . . . . . . . . . . . . . 59

2.16 Check by a standard steady-state security assessment tool . . . . . . . . . . . . . . 60

2.17 Contingency analysis results (considering the actual voltage magnitudes) . . . . . . 60

2.18 Contingency analysis results (considering the actual power �ow limits) . . . . . . . 61

2.19 OPF results (year 2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

2.20 OPF results (year 2015) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

2.21 Contingency analysis results (without doubling the Adriatic backbone) . . . . . . . 67

2.22 Priority list of the new generation sites (year 2015) . . . . . . . . . . . . . . . . . . 68

2.23 Contingency analysis results (year 2009) . . . . . . . . . . . . . . . . . . . . . . . . 69

2.24 Scenarios for assessing Italian EHV development plan bene�ts . . . . . . . . . . . . 71

2.25 Main grid reinforcements (2010 development plan) . . . . . . . . . . . . . . . . . . 71

2.26 Contingency analysis results - Scenario A . . . . . . . . . . . . . . . . . . . . . . . 72

2.27 Contingency analysis results - Scenario B . . . . . . . . . . . . . . . . . . . . . . . 73

2.28 Contingency analysis results - Scenario C . . . . . . . . . . . . . . . . . . . . . . . 73

2.29 Contingency analysis results - Scenario D . . . . . . . . . . . . . . . . . . . . . . . 73

2.30 Contingency analysis results (Benevento-Foggia reinforcement) . . . . . . . . . . . 80

2.31 Contingency analysis results (middle-Adriatic backbone reinforcement) . . . . . . . 80

2.32 Contingency analysis results (new line Montecorvino-Benevento) . . . . . . . . . . 81

2.33 Contingency analysis results (new line Deliceto-Bisaccia) . . . . . . . . . . . . . . . 82

2.34 Summary of the contingency analysis results . . . . . . . . . . . . . . . . . . . . . . 83

2.35 Contingency analysis results (New CCGT power plants) . . . . . . . . . . . . . . . 87

viii

LIST OF TABLES ix

2.36 WTLR values at some nodes in Central-South Italy . . . . . . . . . . . . . . . . . 87

3.1 Payments by Italian consumers for excess withdrawal of reactive energy . . . . . . 113

3.2 Bonus/penalty for reactive power as percentage of reference tari� - Spain . . . . . 127

3.3 Wind power collection substations . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

3.4 Generation marginal costs of di�erent thermoelectric technologies . . . . . . . . . . 131

3.5 OPF results (maximum wind power generation) . . . . . . . . . . . . . . . . . . . . 131

3.6 Sensitivities∣∣∣ ∂QP,k

∂QA,h

∣∣∣ - Decoupling requirement . . . . . . . . . . . . . . . . . . . . . 139

3.7 Diagonal-dominance of the matrix∣∣∣ ∂QP,k

∂QA,k

∣∣∣ . . . . . . . . . . . . . . . . . . . . . . . 139


∂Qj,k

∣∣∣ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140

3.9 Pilot node voltages and reactive power productions - Case 1 . . . . . . . . . . . . . 142

3.10 Losses' gradient and nodal marginal value in pilot nodes . . . . . . . . . . . . . . . 151





3.15 Real losses and their variations with reference to Case 3 . . . . . . . . . . . . . . . 161

A.1 Generator buses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

A.2 Load buses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

A.3 Transmission lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

D.1 Characteristics of voltage-control equipment [43] . . . . . . . . . . . . . . . . . . . 186

Chapter 1

Introduction

1.1 Research motivations

Electricity markets around the world were for a long time either formed by vertically-integrated,

state-owned companies, or private �rms subject to governmental regulation that were often monop-

olies within their supply area. By the end of the century liberalization processes had been initiated

in many countries all over the world, although the process slowed after the dramatic failure of the

California market in 2000-2001.

The change to free markets is based on several economic and policy motivations that di�er strongly

from country to country. The primary reason for introducing competition in the developed coun-

tries (e. g. North America and Western Europe) is to increase the competition, and thereby also the

economic e�ciency in the operation of the electrical power system. For fast developing countries

(e. g. China and India), the typical reason is to create a more level playing �eld to attract private

investment, thereby relieving the government in funding the electric sector's growth that is cru-

cial to economic development. In addition the technological advancement of gas-�red turbines, in

particular highly e�cient combined cycle turbines, have broken the dominance of coal and nuclear

plants and signi�cantly lowered barriers to entry for private investors in generation.

Several approaches and measurements have been taken, including:

� restructuring: reorganizing the roles of market participants (including regulators and insti-

tutions), not necessarily a �deregulation� of the market;

� liberalization: synonym of restructuring with the aim of obtaining competitive markets;

� corporatization: make state-owned institutions act like private ones;

� privatization: selling state-owned assets to private stakeholders;

� deregulation: removing or simplifying government rules and regulations that constrain the

operation of market forces.

Successful liberalization generally requires: sector restructuring, implementation of competitive

wholesale markets and retail supply, incentive regulation of the grid, independent regulation, and

privatization.

Nevertheless, these processes have given rise to various issues in both planning and operating the

electric energy systems.

1

CHAPTER 1. INTRODUCTION 2

1.1.1 Generation and transmission planning

In the past, the electricity industry featured vertically integrated utilities. As a consequence,

transmission planning was closely coupled to generation planning. Utilities, because they owned

generation and transmission, could optimize investments across both kinds of assets considering

their interchangeability. With respect to operations, utilities routinely scheduled generation day-

ahead and re-dispatched generating units in real-time to prevent the occurrence of congestions.

The costs of such scheduling and re-dispatch were spread across all customers and re�ected in

retail rates. In addition, utilities had good data and forecasting tools to estimate current and

future loads and generating capacity. Because each utility was the sole provider of retail electricity

services, it had considerable information on current and likely future load levels and shapes. Since

each utility was the primary investor in new generation, it had considerable information on the

timing, types, and locations of new generation and corresponding information on the retirement

of existing units. Finally, the amount of wholesale electricity commerce was much less than it is

today and it was much simpler.

In today's electricity industry, generation and transmission are increasingly separated, either

through functional unbundling of these activities or through corporate separation. This de-

integration, combined with the competitive nature of electricity generation, makes it much harder

for transmission planners to coordinate their activities with those of generation owners. Speci�-

cally, transmission planners need detailed information on the timing, magnitudes, and locations of

new generating units; the developers of these facilities are unwilling to share competitive informa-

tion until required to do so (e. g. for environmental permits and for transmission-interconnection

studies).

One critical outcome of the de-integration of generation and transmission, the advent of many

new players (brokers, marketers, and power producers), and the consequent increasing number

of commercial transactions is the more frequent stressing of the transmission grid due to the

occurrence of congestion situations. One of the main reasons for the increasing frequency of

congestion is that the transmission network investments have not kept pace with the increasing

demand for transmission services. In the short-term, the only way to deal with the congestion

problem is through e�ective congestion management, i. e. through deploying e�cient procedures

to coordinate all participants' actions to maintain system reliability. Of necessity, congestion

management is no longer an internal matter, but it involves a system operator, transmission owners

(if di�erent from the system operator), power producers, and load-serving entities. But congestion

has rather serious long-term market e�ects, and consequently impacts the decisions regarding new

investments in both transmission and generation.

Congestion impacts market players in many di�erent ways. Congestion may prevent the use of

lower-priced generators to meet the load and consequently may result in a generation/demand

schedule with higher total costs and entailing losses of market e�ciency. Also, congestion facilitates

the opportunities to exercise market power through gaming by some players to increase their pro�ts.

Since in a competitive electricity market framework the grid is the interface where buyers and

sellers interact with each other, one of the main objectives of network planning is to provide a

nondiscriminatory competitive environment for all stakeholders while maintaining power system

reliability. Therefore, increasing transmission capacity is likely to be necessary to encourage and

facilitate competition among electric market participants, to provide nondiscriminatory access

to cheap generation for all consumers, to alleviate transmission congestion, and to mitigate the


possible exercise of local market power, as well as to increase the network reliability and security.

Although generation and transmission planning is no longer an integrated process, as it used

to be in the past, generation expansion decisions may be a�ected by decisions on transmission

expansion and vice versa. For instance, a transmission project may take �ve or ten years, longer

than two years or so for building a gas turbine or a combined cycle power plant. A generation

project may be initiated after the transmission project has commenced, potentially altering the

�nancial assumptions used to justify the transmission project. There is also the substitution e�ect

of transmission, that is, the transmission expansion can cause the substitution (in production)

of some expensive power plants, originally dispatched because of binding network constraints.

So generators are a�ected by transmission enhancements which will either expand their market

opportunities (if they are low-cost) or reduce their market opportunities (if they are high-cost and

have captive customers).

Producers' expansion investments and transmission development plans may con�ict because of

the diversity of their respective interests: on one hand, generation capacity expansion may worsen

existing network congestions and even compromise the e�ectiveness of a planned grid reinforcement;

on the other hand, the development plan of the transmission system can in�uence the planning

decisions taken by power producers, even discouraging the construction of new power plants, and

moreover transmission capacity increase may be not su�cient to allow existing and planned power

plants to be fully exploited.

Furthermore, the competitive business environment of generation pushes investors to faster plan-

ning, shorter deployment times, and less sharing of commercially sensitive information. The reg-

ulated business environment of transmission pushes it to slower planning and longer deployment

times (to accommodate an inclusive public process) and the wide sharing of information.

In conclusion, the split and di�erences between competitive generation and regulated transmis-

sion can lead to investment decisions in both sectors that are sub-optimal from a broad societal

perspective.

1.1.2 Reactive support and voltage control

The main function of an electrical power system is to transport electrical power from generators

to loads. In order to function properly, it is essential that the voltage is kept close to the nominal

value, in the entire power system.

Voltage control is in fact necessary because of the capacitance, resistance, and inductance of trans-

formers, lines, and cables. Since branches have a capacitance, resistance, and inductance, a current

�owing through a branch causes a voltage di�erence between the ends of the branch (i. e. between

the nodes being connected by the branch). However, even though there is a voltage di�erence

between the two ends of the branch, the bus voltage is not allowed to deviate from its nominal

value in excess of a certain value (normally 5% to 10%). Appropriate measures must be taken to

prevent such deviation. Voltage control refers to the task of keeping the bus voltages in the system

within the required limits and of preventing any deviation from the nominal value to become larger

than allowed.

The node voltage is a local quantity, as opposed to system frequency, which is a global or system-

wide quantity. It is therefore not possible to control the voltage at a certain bus from any point in

the system, as is the case with frequency. Instead, the voltage of a certain node can be controlled

only at that particular node or in its direct vicinity.


This is achieved di�erently for transmission networks and for distribution grids because of the

di�erent characteristics of the branches in transmission networks and distribution grids and the

divergent numbers and characteristics of the generators connected to both. Transmission networks

mainly consist of overhead lines with very low resistance. The voltage di�erence between two ends

of a line with a high inductive reactance X when compared with its resistance R (i. e. with a low

R/X ratio) is strongly a�ected by what is called the reactive power �ow through the line.

Owing to the characteristics of transmission networks and the connected generators, voltages are

controlled principally by changing the reactive power generation or consumption of large-scale

centralized generators connected to the transmission network. They are very �exible in operation

and allow a continuous control of reactive power generation over a wide range, according to their

loading capability diagram. Sometimes, dedicated equipment is used, e. g. capacitor banks or

technologies referred to as �exible AC transmission systems (FACTS). These are, in principle,

controllable reactive power sources.

In contrast, distribution grids consist of overhead lines or underground cables in which the resis-

tance is not negligible when compared with the inductance (i. e. that have a much higher R/X

ratio than transmission lines). Therefore, the impact of reactive power on bus voltages is less

pronounced than in the case of transmission networks. Further, the generators connected to dis-

tribution grids are not always capable of varying their reactive power output for contributing to

voltage control. So voltages in distribution grids are controlled mainly by changing the turns ratio

of the transformer that connects the distribution grid to the higher voltage level and sometimes

also by devices that generate or consume reactive power, such as shunt reactors and capacitors. In

general, distribution grids o�er fewer possibilities for voltage control.

By using large-scale power plants to regulate voltages in the transmission network and by using

dedicated devices in distribution grids to regulate the voltages at the distribution level, a well-

designed, traditional power system can keep the voltage at all nodes within the allowed band

width.

This was the approach traditionally adopted, when vertically integrated utilities operated power

generating units, on the one hand, and power transmission and distribution systems, on the other

hand. They also handled the voltage control issue, both short-term (day-to-day dispatch of units)

and long-term (system planning).

Owing to recent developments, this situation has been however changed. The liberalisation and

restructuring of the electricity industry has resulted in the unbundling of power generation and

grid operation. These activities are no longer combined in vertically integrated utilities as they

used to be. As a consequence, voltage control is no longer a �natural part� of the planning and

dispatch of power plants. Now, independent generation companies carry out the planning and

dispatch, and, in the long term, conventional power stations that are considered unpro�table will

be closed down without considering their importance for grid voltage control. In addition, the

grid companies have to solve any voltage control problem that may result from the decisions

taken by generation companies. In the short term, this can be done by requiring the generation

companies to re-dispatch. In the long term, additional equipment for controlling the voltage can

be installed. Moreover, the voltage control and the reactive power support are now considered an

ancillary service that grid companies often have to remunerate. Another recent development is that

generation is shifted from the transmission network to the distribution grid. As a result of these

two developments (unbundling and decentralisation), it is becoming more di�cult to control the

voltage in the entire transmission network from conventional power stations only. Grid companies


respond by installing dedicated voltage control equipment and by requiring generation equipment

to have reactive power capabilities independent of the applied technology. This means that no

exception is made for wind power or other renewables any longer, as has often been the case until

now.

In particular, among the recent developments that challenge the traditional approach to voltage

control, there is the increasing exploitation of wind energy for generating electricity. Until few

years ago, most wind turbines have been erected as single plants or in small groups and connected

to distribution grids. Now the attention is shifted towards large-scale wind farms to be connected

to the transmission network. The wind farm a�ects the power �ows and hence the bus voltages. As

regards the transmission network, voltages are controlled mainly by large-scale conventional power

plants. If their capability to control voltages throughout the transmission grid is not su�cient to

compensate for the impact of the wind farms on the node voltages, the voltage at some buses can

no longer be kept within the allowed range around its nominal value and appropriate measures

have to be considered and taken.

Concerning this, two issues are particularly important. The voltage control capabilities of wind

turbines are becoming an increasingly important consideration regarding grid connection to ensure

appropriate voltages at their connection point. So grid codes often include some kind of reactive

power requirement for wind farms, usually expressed in terms of power factor range. Moreover, it

is likely that, thanks to its dispatching priority, the wind power production will replace the power

generation of conventional plants so reducing their voltage control capability. The problem will be

more serious if the wind farms are far from the big load centers, even in remote areas or o�shore.

So it may be inevitable to take additional measures to control the grid voltage.

1.2 Research objectives

The research work presented in this thesis investigates the two issues discussed in the preceding

section.

The above considerations have made clear that in liberalised electricity markets there is the need

to better coordinate generation and transmission expansion in order to achieve a more coherent

development of the whole power system, that will favourably a�ect both system operation and

market e�ciency. The �rst part focuses on this issue. A methodology based on the nodal index

called Weighted Transmission Loading Relief, recently proposed in literature, is de�ned. The

WTLR sensitivity seems to be suited to attain the above-mentioned purpose since it is capable of

�measuring� the impact of real power injections into the grid on system security. In particular, its

basic concept is that an injection may help to mitigate the overload on a grid branch by creating

a counter-�ow, so suggesting the importance of strategic generation siting (i. e. of determining

geographic locations where new generation would enhance the system security by creating post-

contingency counter-�ows that would mitigate overloads under contingency conditions). The use

of this tool by a generation owner to assist the de�nition of its expansion plan may thus favour

the system security enhancement. But this is not a task pertaining to power producers in the

restructured electricity industry. Nevertheless, as explained in the previous section, also generation

owners may bene�t from strategic generation siting because network bottlenecks may limit the

dispatchability of new power plants and thereby advantage less e�cient ones. The �rst objective of

the research work is to show this use of the WTLR tool, while the second purpose is to demonstrate

that it can be helpful also to transmission planners. Consequently, the WTLR methodology could


allow both generation and transmission planning goals to be reached, even though they are di�erent

and sometimes in disagreement in a liberalised environment. Moreover, since the WTLR main

objective is the network security enhancement, that can be achieved also thanks to an appropriate

generation expansion, the whole power system and especially its operation could bene�t from

adopting this approach.

The second part of the research work deals with the reactive power management in post-deregulation

electricity industry. As results from the preceding section, this topic has become much more impor-

tant after the electricity market liberalisation and especially after the unbundling process, that has

led to the de-integration of generation and transmission. There are many important and crucial

aspects concerning this topic, some deriving from the peculiarities of reactive power supply, some

due to the new liberalised environment, some resulting from the increasing interest in renewable

technologies and particularly in wind power exploitation. The research focuses on three chief is-

sues: the optimal reactive power provision that �ts the needs of system operators, the de�nition

of a possible remuneration scheme for reactive power providers, and the impact of wind power on

voltage control and reactive power support. The main tool used in the analysis is an Optimal

Reactive Power Flow (ORPF) program, designed for hierarchical voltage regulation structures,

such as that developed for the Italian EHV system by its past monopolistic utility. Some nodal

indicators are calculated allowing both economic and security aspects to be investigated. On one

hand, they provide the economic value of VAR sources at a certain bus in the system, so suggesting

a suitable �nancial compensation scheme for reactive power service and the implementation of a

zonal reactive market based on the Secondary Voltage Regulation (SVR) areas; on the other hand,

they identify the network locations (nodes or areas) that are poor in terms of reactive sources,

so giving the transmission planner useful indications about the additional measure to be taken to

control the voltages. The technical requirements for grid connection of wind farms and especially

their possible utilization under primary and secondary voltage regulation are examined to assess

the impact of wind generation on voltage control and the bene�ts resulting from wind farms' par-

ticipation in reactive power support. Finally, the e�ects of the planned network reinforcements are

investigated.

In view of the above discussions, the main objective of this research work is therefore to present

suitable approaches for achieving more coordination between generation expansion and transmis-

sion development, on one hand, and for ensuring a secure and e�cient reactive power provision and

for favouring the integration of wind farms in power systems, on the other hand, in the context of

the new planning and operating paradigms of deregulated electricity industry.

1.3 Thesis outline

This thesis is organized in two main parts which refer to the two topics considered in the research

work.

Chapter 2 deals with the methodology based on the Weighted Transmission Loading Relief sensi-

tivities and its application to power system planning. After investigating the relationship between

generation expansion and transmission planning in a liberalised environment and their respective

e�ects on both electricity market e�ciency and power system security (Sections 2.1 and 2.2), the

WTLR-based methodology is described, and the MATLAB procedure implemented for the cal-

culation and graphical representation of WTLRs is presented in Section 2.3. First, it is applied

to the CIGRE 63-bus test system in order to check the outcomes' correctness and then to de-


�ne a possible metric for prioritizing transmission planning (Section 2.4). Some changes made in

the original MATLAB procedure, including the introduction of Line Outage Distribution Factors

(LODFs) and the adoption of the distributed slack bus, are described, and their impact on the

procedure results are analysed in Section 2.5. Finally, in Section 2.6 the methodology is used to

carry out some analyses on the Italian EHV electric system at di�erent projection horizons, with

the aim of demonstrating the potential applications of the WTLR tool for power system planning.

In particular, as regards the producers' viewpoint, some simulations are performed considering a

possible set of new generation sites in order to de�ne a priority list. Instead, as regards trans-

mission planning, the tests on the Italian system presented in the chapter show that the WTLR

procedure can be used to identify the weakest grid areas and elements, to demonstrate the develop-

ment plan bene�ts, to assess the impact of an increasing wind penetration on network security, to

rank a set of planned transmission reiforcements, and to propose new grid reinforcements. Finally,

the interchangeability of generation and transmission investments, in terms of system security

enhancement, is demonstrated.

Chapter 3 looks at the reactive power support and voltage control ancillary service in the restruc-

tured and liberalised environment. First, it brie�y introduces the concept of ancillary services and

proposes a summary of their de�nition in di�erent markets, including the Italian one (Section 3.1).

Then it reviews the essential and basic principles of reactive power support and voltage control,

giving an interesting overview of the main general issues, both technical and regulatory, related

to the procurement and management of these services, and showing the various challenges with

which the System Operator and the Regulatory Authority have to deal, especially concerning the

provision mechanism and the remuneration scheme (Sections 3.2 and 3.3). Section 3.4 presents a

detailed review of the reactive power management topic, brie�y describing the approach to reac-

tive power provision in di�erent deregulated markets in North America and Europe, and making

a summary of the literature on reactive power pricing and management. In Section 3.5 the ar-

chitecture of the voltage control system is considered with particular regard to its organization

into three-level hierarchy, which is the voltage regulation structure set up for the Italian electric

system by its past monopolistic utility (ENEL). In particular, the basic principles of Secondary

and Tertiary Voltage Control are described. Section 3.6 deals with the reactive power service in

Italy, providing an outline of the current regulatory framework and of the main characteristics of

its network voltage control system. The Optimal Reactive Power Flow program (ORPF), that has

a fundamental role in hierarchical voltage control scheme since it computes the optimal voltage

pro�les and reactive levels, is presented in detail, and how to derive an economic value of reactive

power from its solution is delineated (Section 3.7). Section 3.8 investigates the impact of wind

power on voltage control and reactive power procurement, and a summary of some regulatory

requirements with regard to reactive power control in steady-state conditions for wind plants and

of some existing technology solutions is provided. The results of the tests on the Italian EHV

system are presented in Section 3.9. Firstly, the generation pro�les at the �fteen wind collection

substations, connected to the 380 kV network, considered in the analysis, are de�ned by means

of an Optimal Power Flow program. Then the control areas, pilot nodes, and controlling gener-

ators are selected according to some speci�c criteria. The test cases are de�ned considering the

following aspects: what kind of generators operates under voltage control (synchronous generators

and/or wind farms), planned transmission reinforcements in service or not in service, presence of

the large-size wind farms connected to the 380 kV network.

Finally, the main characteristics of the CIGRE 63-bus network will be described in Appendix A.


Appendix B will treat the theory of Power Distribution Factors, which has been the basis for deriv-

ing the approximate Injection Shift Distribution Factors (ISDFs), in normal and post-contingency

conditions, and the Line Outage Distribution Factors (LODFs), both implemented in the MAT-

LAB program for WTLR calculation. In Appendix C the issue of slack bus modelling in load �ow

solutions will be discussed, with particular regard to the basic concepts of the distributed slack

bus model and its di�erences with respect to the traditional power �ow formulation. Appendix D

and Appendix E will analyse two aspects of reactive power supply and voltage control thoroughly:

they will describe the devices capable of providing reactive power support and the main technical

features of the Italian hierarchical voltage control system.

Chapter 2

WTLR and power system planning

The evolution of the electricity industry from the past vertically integrated utilities to the nowadays

deregulated and unbundled structures has introduced deep changes in the planning and operation of

electric energy systems. In this new environment the coordination between transmission planning

and generation expansion is no longer assured as it used to be in vertically integrated structures,

where both transmission network and generation power plants belonged to the same utility com-

pany. Traditionally the integrated planning of generation and transmission systems was in fact

the responsibility of vertically integrated utilities under state regulatory oversights. In today's

increasingly competitive electricity markets, self-interested players and competitors participate in

the planning and operation of power systems. Generation companies (GENCOs), as independent

and for-pro�t market entities, are freely and actively making plans for generation expansion, which

could dramatically impact existing transmission �ows and congestions. Customers can also select

their own electric energy suppliers based on economics, power quality, and security. Instead, the

transmission system continues to be regarded as a regulated monopoly. As a consequence, the

transmission system planning is facing credible challenges for managing its operation economics

and security. So the con�ict between these two aspects is inevitable in the restructured electricity

industry planning.

In the VIU (Vertically Integrated Utility) arrangement, the aim of the integrated planning of

generation and transmission systems was to minimize both investment and operation costs, while

supplying demand for energy over a time horizon, keeping the quality and reliability standards

of the network. In the competitive electricity market, as demand grows and new power plants

are installed, increasing transmission capacity is likely to be necessary also to improve market

competition and mitigate the possible exercise of locational market power. In particular, the

Transmission System Operator (TSO) has to de�ne �strong and �exible� transmission expansion

plans to face the numerous uncertainties which can characterize the planning process. The analysis

of present and forecast scenarios of the electric system allows the TSO to determine where, when,

and what kind of network reinforcements need to be built in order to avoid both security and

economic ine�ciencies in the future.

One of the main uncertainties that the Transmission System Operator has to consider in transmis-

sion planning, to ensure a secure, reliable, and uninterrupted electricity supply, is the generation

system development (i. e. size and location of new power plants). In competitive electricity mar-

kets GENCOs' objective for generation resource planning is to maximize expected payo�s over

planning horizons. Such generation system development, which is not necessarily correlated to the

9

CHAPTER 2. WTLR AND POWER SYSTEM PLANNING 10

network planning, could also reduce the electricity market e�ciency: it could lead to a bad location

of the cheapest power plants, whose generation would be substituted by that of more expensive

units, because of the occurrence of network congestions. Moreover, it could reduce the expected

e�ectiveness of a grid reinforcement planned by the TSO.

Therefore, a better exploitation of both existing and planned network facilities would be attained

if there were a more coherent development of generation and transmission systems. More coordi-

nation would be justi�ed by the strong interrelationship between these two systems. The planning

decisions taken by power producers can in fact in�uence the development plan of the transmission

system, and vice versa.

Finally, besides being interdependent, generation investments and transmission expansion may be

equivalent in terms of both improving electricity market e�ciency and enhancing power system

security, that is, generation and transmission may be interchangeable.

The chapter will investigate these issues, and then it will describe a methodology, based on a nodal

index called Weighted Transmission Loading Relief (WTLR), capable of assessing the impact of

generation on network security. A MATLAB program for the calculation of this indicator and its

application to a test system (CIGRE 63-bus system) will be presented. Finally, some simulations

on the Italian EHV electrical system will be shown in order to demonstrate the tool usefulness for

generation and transmission planning and especially for attaining a more coherent development of

the whole power system.

2.1 Power system planning and electricity market e�ciency

2.1.1 Electricity market e�ciency

According to an economic de�nition, the Social Economic Welfare is the di�erence between a

product's value to the consumer and its cost of production. It is also the sum of producer pro�t

and consumer surplus in a free market economy. The producer surplus is the amount that producers

bene�t by selling at a market price mechanism that is higher than they would be willing to sell for.

Instead, the consumer surplus is the amount that consumers bene�t by being able to purchase a

product for a price that is less than they would be willing to pay [1].

On a standard supply and demand (S&D) diagram, consumer surplus is the triangular area above

the price level and below the demand curve, since intramarginal consumers are paying less for the

item than the maximum that they would pay. On the contrary, producer surplus is the triangular

area below the price level and above the supply curve, since that is the minimum quantity a

producer can produce (Figure 2.1).

Economic e�ciency is a general term in economics describing how well a system is performing, in

generating the maximum desired output for given inputs with available technology.

A system can be called economically e�cient if:

� no one can be made better o� without making someone else worse o�;

� more output cannot be obtained without increasing the amount of inputs;

� production proceeds at the lowest possible per unit cost.

Productive e�ciency occurs when production of one good is achieved at the lowest possible cost,

given the production of the other good(s). Equivalently, it is when the highest possible output


Figure 2.1: Graph illustrating consumer and producer surpluses

of one good is produced, given the production level of the other good(s). In other words, it

is the optimum organization of production: �rms produce the demanded quantity of goods or

services (electric energy in our case) at the minimum cost, considering the current best-practice

technological and managerial processes.

Allocative e�ciency occurs when consumers get the maximum quantity of goods or services (elec-

tric energy in our case), given the current production costs. In other words, it is the optimum

management of commercial exchanges.

Necessary and su�cient condition for the Social Welfare maximization is that productive and

allocative e�ciencies are jointly ful�lled. This condition is represented by Figure 2.1, in which

both produced and consumed quantities are the highest possible at the lowest possible cost.

The other market conditions that can occur are the following:

� Productive e�ciency + Allocative ine�ciency (Figure 2.2)

Production costs are the lowest possible, but the market quantity is not the highest possible,

because of ine�ciencies in electric energy exchanges. By causing a di�erence between the

price received by producers and that paid by consumers, the Transmission System Operator

secures the area labeled Congestion Revenue, which comes at the expense of the consumer

surplus and producer surplus that would have existed in case of allocative e�ciency. The

�gone� triangle of Deadweight Loss (DWL) goes to no one because those transactions are

prevented by transmission limits.

� Productive ine�ciency + Allocative e�ciency (Figure 2.3)

Both produced and consumed quantities are the highest possible, given the current production

costs. But the given output could be produced at a lower cost.

� Productive ine�ciency + Allocative ine�ciency (Figure 2.4)


Figure 2.2: Productive e�ciency + Allocative ine�ciency

Figure 2.3: Productive ine�ciency + Allocative e�ciency


Figure 2.4: Productive ine�ciency + Allocative ine�ciency

The market quantity is not the highest possible and also the production costs are not the

lowest possible.

2.1.2 Generation system investments and Social Welfare

From the viewpoint of Social Welfare, the most relevant investments are those in �xed assets, which

include machinery, buildings and land, and in technology [2].

For our purposes, it is enough to consider only two types of investments in power generation system:

� capacity expansion;

� cost reducing.

Capacity expansion investments enable a �rm to expand the amount of its production volume

that is produced at minimum unit costs. There are two types of �rms which undertake these

investments:

� a �rm already in the sector (left side of Figure 2.5);

� a new �rm, if the market system is competitive.

The e�ects of generating capacity investments are:

� if the investment is made by a new �rm and the market system is non-competing, the market

will become more competitive and the market power will decrease;

� the competitive o�er is expanded for the same price (right side of Figure 2.5);

� the investment can allow capacity/reliability constraints to be ful�lled: for instance, in the

face of demand uncertainty in the short-run, it allows a reserve capacity to be available.


Figure 2.5: E�ects of a capacity expansion investment

Figure 2.6: E�ects of a cost reducing investment

Cost reducing investments consist in adopting new equipments to modernize the production cycle

or in replacement and extraordinary maintenance of existing facilities: from the viewpoint of a

�rm, these investments have the main purpose of reducing the unit costs, as shown by the left side

of Figure 2.6. The consequences on the sector supply are instead represented on the right side of

Figure 2.6.

In conclusion, the e�ects of technological investments on Social Welfare are (Figure 2.7):

� Cost minimization: both expansion capacity and cost reducing investments allow the produc-

tive e�ciency to be improved because the total costs are reduced, tending more and more to

the long-run costs. More precisely, the sector supply will tend to the long-run supply curve,

when the most e�cient �rms have been imitated (by new ones or competitors), while the

least e�cient ones have changed their production and cost structure.

� Market power mitigation: if a new �rm enters the market, there will be more competition

and the allocative ine�ciency will be reduced.


Figure 2.7: Technological investments and market e�ciency

2.1.3 Transmission system expansion and Social Welfare

Transmission system investments consist in developing new network assets and in upgrading the

existing ones. Their main objectives are:

� to develop the interconnections among national areas to reduce grid bottlenecks and network

congestions;

� to increase the transmission capacity of the interconnection corridor between two neighbour-

ing countries;

� to connect new power plants or new loads to the electricity network.

In competitive electricity markets, an increase in transmission capacity can have two di�erent

e�ects on Social Welfare, named [3]:

� substitution e�ect, which was the only economic e�ect of the transmission expansion in

vertically integrated structures;

� strategic or competition e�ect.

On one hand, the transmission expansion can cause the substitution (in production) of some

expensive power plants, originally dispatched because of binding network constraints, by cheaper

ones, so reducing the total generation costs and improving the productive e�ciency (substitution

e�ect).

On the other hand, an increase in transmission capacity can allow market participants to sell/buy

power demanded/produced far away, which encourages competition among �rms, so mitigating the

possible exercise of market power and improving the allocative e�ciency (strategic e�ect).

2.1.4 General considerations

According to the preceding subsections, in competitive electricity markets an increase in transmis-

sion capacity may have the same e�ect of a generation system investment on Social Welfare and

market e�ciency.


The substitution e�ect can allow low-cost power to be produced in greater quantities so improving

the productive e�ciency. In this case, an increase in transmission capacity is equivalent to a

generation investment aimed at expanding the total production capacity (generation expansion

investment) or at reducing the total generation costs (cost reducing investment).

The strategic e�ect can encourage competition among producers and improve the allocative e�-

ciency. In this case, an increase in transmission capacity has the same e�ect of the entry of new

�rms into the market.

Therefore, these brief remarks highlight that generation investments and network expansion may

be equivalent in terms of electricity market e�ciency and Social Welfare improvement.

The next section will also demonstrate that system security may bene�t from an appropriate choice

of new power plants' sites, besides from transmission planning.

2.2 Power system planning and network security

The bulk power system is made up of three main parts: generation, transmission, and load (i. e.

customer electric demand). The electric industry uses terms such as reliable, unreliable or system

reliability as qualitative measures of the relative strength or balance of the bulk electric system.

Reliability is the term used by the electric industry to describe and measure the performance of the

bulk power system. It is the degree to which the performance of the elements of that system results

in power being delivered to consumers within accepted standards and in the amount desired. The

degree of reliability may be quantitatively measured by the range of operating conditions under

which the system performs within acceptable parameters.

For instance, NERC (North American Electric Reliability Corporation) de�nes the reliability of

the interconnected bulk power system in terms of two basic and functional aspects [4]:

� Adequacy: the ability of the bulk power system to supply the aggregate electrical demand

and energy requirements of the customers at all times, taking into account scheduled and

reasonably expected unscheduled outages of system elements.

� Security (or operating reliability): the ability of the bulk power system to withstand sudden

disturbances such as electric short circuits or unanticipated loss of system elements from

credible contingencies.

In plain language, adequacy implies that su�cient generation and transmission resources are avail-

able to meet projected needs plus reserves for contingencies. Instead, security implies that the

power system will remain intact even after outages or equipment failures.

From the static viewpoint, network security can be summarized to include the following conditions:

no loss of load, bus voltages within power quality bounds, line �ows not exceeding thermal limits,

and the system operating away from the point of static voltage collapse.

2.2.1 �Measuring� system security

The transmission system security for a given scenario can be assessed by means of contingency

analysis simulations. Contingency analysis [5] de�nes a set of plausible contingencies that represent

events such as failure or disconnection of network devices. A �contingency list� contains each of the

elements that will be removed from the network model, one by one, to test the e�ects for possible

overloads of the remaining grid elements. In its basic form, contingency analysis executes a power


�ow calculation for each potential problem that is de�ned by the contingency list: the failure or

outage of each element in the contingency list (e. g. a loss of a transmission line) is simulated in

the network model by removing that element. The resulting network model is solved to calculate

the new power �ows, voltages, and currents for the remaining elements of the model.

The outcomes can be tabulated in order to detect the contingencies that may lead to severe or

critical operating conditions, and to decide remedial actions, such as re-dispatch or load shedding.

They can be also used to determine the transmission lines or transformers that present severe

violations for one or multiple outages, and to rank grid branches according to their relative �weak-

ness�. So this analysis supplies some useful information not only about the need to upgrade the

transmission system, but also about the way of designing its expansion to avoid thermal overloads

under speci�c conditions.

There are several metrics that can be adopted to rank weak grid elements: for example, the

number of contingencies that cause overloads in a speci�c branch or its maximum percentage

overload. Nevertheless, the former does not consider the overload severity, while the latter does

not take into account the number of overloads.

An indicator that captures both the contingency severity and the presence of multiple violations

can be derived as follows [6]. Let:

� PCO% be the branch percentage overload that appears in a line when a contingency occurs;

� PACO% be the sum of all overloads in a particular branch.

In other words, the aggregate contingency overload for a given line (or transformer) jk is calculated

as:

PACO%,jk =∑c

P cCO%,jk c ∈ Contingency List (2.1)

This quantity is expressed in percentage and it is not able to discriminate among voltage levels:

for instance, a 10% overload in a low voltage element would have the same rank as a 10% overload

in a higher voltage element. So it is useful to convert it to MW:

PACO,jk = PACO%,jk ·MVAratingjk (2.2)

The previous expression is based on the approximation that the line MVA rating is a MW limit.

This is commonly done in linear methods and in the DC power �ow.

The PACO expressed in MW is a better index compared to the percentage quantity because it

retains information about the line MVA �ow, e. g. a 20% overload in a 132 kV line should have

lower severity than a 20% overload in a 400 kV line.

The PACO index has the following properties that make it useful for assessing the �weakness� of a

branch:

� if a branch is not overloaded for any contingencies (belonging to the contingency list), then

its PACO will be equal to zero;

� if a branch is either heavily overloaded for a few contingencies or lightly overloaded for lots

of contingencies, its PACO will be high;

� if a branch is heavily overloaded for numerous contingencies, its PACO will be very high;

� the higher the PACO, the �weaker� the branch.


One measure of system security is the amount of thermal overloading that occurs during a set of

simulated contingencies or forced outages. The level of contingent overloading may be expressed as

the sum of MW overloads in all monitored transmission elements and for all simulated contingen-

cies. Since the PACO can be computed for every branch, a system aggregate contingency overload

can be calculated as:

OverloadSY S =∑jk

PACO,jk jk ∈ Overloaded branches (2.3)

For a given line jk and a given contingency c the contribution to the OverloadSY S would be the

amount of MW that the real power �ow on line jk exceeds its rating, when the contingency c

occurs. If the line operates within its limits for all contingencies, then its contribution to the

OverloadSY S will be equal to zero.

Although the OverloadSY S provides a metric of the security of the overall grid, it will tend to be

higher not only for highly stressed systems but also for large systems. In order to make the metric

independent of the network size, it can be divided by the number of branches Nbranches, resulting

in the Thermal Security Index (TSI) of the system:

TSISY S =OverloadSY S

Nbranches(2.4)

Given a contingency set, this metric represents the average MW overload expected in a line in case

of contingency.

2.2.2 Generation expansion and power system security

The continuing growth in demand for electric power, decreased investment in transmission facilities,

and widespread implementation of electricity markets will continue to place increased stress on the

electric transmission network. So, as previously said, there is an increasing need for systematic,

integrated planning processes that, while ensuring energy adequacy, are able to identify the broader

impact of new resources on grid security. These processes would permit utilities to strategically site

power plants based on system security goals, allowing the grid to move toward healthier operating

conditions. The following paragraph will describe a methodology able to capture how generation

impacts system reliability and security, based on a nodal index proposed in literature few years

ago [6].

2.2.2.1 Overload mitigation strategy

The proposed methodology is based on the overload mitigation strategy illustrated in Figure 2.8,

which shows an overloaded line and an injection that helps to mitigate the overload by means of a

counter-�ow. So the goal of strategic generation siting is to determine geographic locations where

new generation would enhance the system security by creating post-contingency counter-�ows that

would mitigate overloads under contingency conditions.

As injections at any place in the system will at least marginally a�ect the �ows everywhere in the

system, the aim is to look for a mechanism to simultaneously maximize the contingency overload

mitigation in multiple congested elements and minimize new overloads in the system.

Since the new generation will be connected to a bus, it is necessary to relate information regarding

weak elements (the problem) to bus injections (the solution). This can be accomplished by calcu-


Figure 2.8: Overload mitigation strategy using generation

lating the Injection Shift Distribution Factors1 (ISDFs). This sensitivity is de�ned as the change

in a branch MW �ow with respect to the change in a bus MW injection, assuming a �xed sink for

a transfer whose source is the proposed generation:

ISDF bus ibranch jk =

∆MWFlowbranch jk

∆MWInjectionbus i(2.5)

Denoting by n the number of buses in the system, it is clear that for each weak element an n-size

array of sensitivities can be determined. So the ISDFs with respect to multiple weak elements

form a matrix in the bus and weak element dimensions. The highest negative ISDF in this array

corresponds to the bus where a power injection results in the highest reduction of the normal

operation �ow on that element.

Electricity system policy though does not de�ne security based on normal operation �ows, but

rather on contingency conditions (i. e. following the outage of a given line st). Thus post-contingency

ISDFs are required:

ISDF bus ibranch jk,contingency c =

∆PostContMWFlowbranch jk,cont c

∆MWInjectionbus i(2.6)

Note that when contingency conditions are studied, there will be one ISDF for each source bus,

to mitigate each weak branch, under each contingency. The post-contingency sensitivities form a

large three-dimensional object in the bus, weak branch, and contingency dimensions, and they can

be used to design strategies to mitigate contingency overloads.

Since a single locational value is needed for each bus, both the contingency and weak branch

dimensions need to be collapsed to the bus dimension. As a power injection will simultaneously

a�ect several branches under several contingency conditions, it is possible to de�ne an Equivalent

Transmission Loading Relief (ETLR) sensitivity, which corresponds to the impact of injecting

power at a given bus on all branches and under all contingency conditions. The ETLR is simply

the sum of the ISDFs computed for a bus:

ETLRbus i =∑jk

∑c

ISDFbus i,branch jk,cont c (2.7)

1In [6] this sensitivity is called TLR (Transmission Loading Relief).


where jk ∈ Overloaded branches and c ∈ Contingency List.Although the ETLR represents the simultaneous e�ect of injection, it does not take into account

the severity of the overloads, something that is fundamental for strategic overload mitigation. In

order to consider this important aspect, a weighting mechanism is introduced. So the severity of

the overloads can be incorporated by computing a WTLR (Weighted Transmission Loading Relief)

sensitivity:

WTLRi =Nviol

OverloadSY S

∑jk

ISDF ijkPCO,jk +

∑jk

∑st

ISDF ijk(st)P

stCO,jk

(2.8)

where:

� Nviol is the number of overloads;

� OverloadSY S is the system overload;

� PCO,jk, P stCO,jk are the overloads on branch jk in intact system conditions and following the

outage of the line st respectively;

� ISDF ijk, ISDF

ijk(st) are the Injection Shift Distribution Factors of branch jk with respect

to the injection at bus i in intact system conditions and following the outage of the line st

respectively.

The WTLR represents the locational impact of generation on network security: it corresponds to

the total expected MW contingency overload reduction (in all branches and under all contingencies)

if 1 MW is injected at that particular bus. More precisely, the WTLR of a bus is an indicator which

approximates the total change in the system overload (OverloadSY S) that would be obtained with

a 1 MW injection at that particular bus.

The WTLR sensitivity represents the locational value of the security bene�t obtained with new

generation and it is measured in OverloadSY S per megawatt installed.

Thus the approach allows comparing the reduction of the overall system overload for generation

located at di�erent WTLR locations and it allows ranking the sites where new generation injections

would enhance system security.

Note that the highest negative WTLRs are located at the receiving end of the overloaded elements.

Clearly, injections at these buses will produce counter-�ows in the overloaded elements, which will

reduce their PACO. On the other hand, injections at buses with positive WTLR will produce power

�ows that would worsen the overloads. So if overload mitigation is the goal, then new generation

should be installed at buses that have the lowest WTLR.

2.2.3 Transmission planning and power system security

Maintaining power system security is one of the major challenges that TSOs (Transmission System

Operators) have to face today. In fast moving and de-regulated electricity markets, transmission

companies across the globe often have a dual and con�icting responsibility for maintaining system

security and for achieving high transmission performance levels. So the objective in market-based

transmission planning is to maintain system security within an acceptable level while maximizing

the social welfare (or minimizing the investment and operation costs).

According to the Ministerial Decree D.M. April 4, 2005 [7], the Italian TSO has to de�ne the

development plan of the transmission network to achieve the following objectives:


� to ensure the security of electricity supply and to meet the demand growth;

� to upgrade the interconnection capacity with neighbouring countries;

� to meet the grid connection requests by the entitled parties;

� to minimize the risk of network congestions;

� to guarantee a secure operation of the network.

According to the Italian grid code [8], the planning process starts from collecting, sorting, and

analysing the data about:

� load prediction;

� new power plants' size and location;

� national power balance and electric power exchanges with foreign countries.

With reference to the projection horizon, some probable scenarios are de�ned and on the basis of

them some reference cases are built and analysed to detect possible critical operational situations

and above all to determine the network reinforcements necessary for their enhancement. Then the

TSO carries out a steady-state security analysis applying the N-1 criterion,2 to set up the initial

development programme of the transmission network, while meeting the following conditions:

� with reference to some typical operational situations, considering the predictable generation

schedules, the power supply must be guaranteed without any violation of security constraints

(limitations on currents in lines and transformers and on voltage magnitudes in grid nodes)

in normal state, i. e. in intact system conditions;

� the outage of single network equipment must not result in thermal overloading of branches,

deterioration of voltage pro�les below permitted range, loss of load.

Obviously, besides the need to maintain power system security, the TSO also checks the di�erent

development options from a techno-economical viewpoint by comparing the estimated construction

costs with the expected bene�ts in terms of reducing the overall system cost. If that is possible,

such assessment considers the costs due to: network congestions, grid losses, risk of loss of load,

predictable tendency of the electricity market, opportunity to increase the transmission capacity

with neighbouring countries.

2.2.3.1 WTLR and transmission planning

The Weighted Transmission Loading Relief sensitivity is based on the overload mitigation strategy

illustrated in Figure 2.8, which exploits the potential e�ect of strategic generation siting on system

security. Even if this is its original application, the approach can be a useful tool for transmission

planning.

A desirable goal of any network upgrade or reinforcement would be to improve the system security

as measured by OverloadSY S . As well explained before, negative WTLR values correspond to sites

where injections will tend to enhance grid security by reducing OverloadSY S , while locations with

positive WTLRs are �poor� for network security, since they will worsen the contingency overloads.

2The N-1 criterion essentially says that an outage of any grid element shall not result in the overloading andsubsequent failure of other elements in the system.


Figure 2.9: Transmission relief

In particular, considerable changes from positive to negative values reveal the presence of congested

grid elements: the region with negative WTLRs is at the receiving end of an overloaded branch,

whereas locations with positive WTLRs are at the sending end. So information supplied by these

sensitivities can be successfully used to identify the most critical grid elements and sections, that

are to be reinforced.

Besides these fundamental indications, the bus WTLR value can be also applied to each end of a

proposed transmission line to linearly estimate the total expected OverloadSY S change consequent

on the addition of a new branch. To enhance system security, new lines should be added to produce

counter-�ows on the lines and transformers that experience contingency overloads as illustrated in

Figure 2.9.

Assume that the power �ow expected from bus j toward bus k is Pjk. If the system is supposed to

be loss-less and linear within a range de�ned by the incremental �ow on the proposed line, then

adding the proposed line will be equivalent to place a generator at bus j with an output of −Pjk

and a generator at bus k with an output of +Pjk, as illustrated in Figure 2.10.

The bus-based WTLR values may then be applied to estimate the impact of a new transmission

line on system security by calculating the following index:

Pjk (−WTLRj +WTLRk) (2.9)

The expected Pjk can be evaluated by adding the line jk to the system and quantifying Pjk with

a full non-linear power �ow calculation.

The simulations on a test system, which will be presented after the description of the procedure

for WTLR calculation coded in the Matlab programming language, will be also used to validate

the above index and particularly to show that, given a set of new transmission lines, it can supply

helpful information to prioritize grid planning.


Figure 2.10: Network equivalents

2.3 Matlab-coded program for WTLR sensitivity calculation

A procedure has been implemented in the Matlab programming language [9] to calculate WTLR

sensitivities and above all to obtain their graphical representation, that shows the grid areas ade-

quate to the installation of new power plants and those requiring network reinforcements.

The computational procedure operates in the following main steps:

1. N and N-1 security assessment to �nd possible branch overloads and consequently the total

system overload OverloadSY S ;

2. calculation of the Injection Shift Distribution Factors in both pre-contingency and post-

contingency conditions;

3. calculation of Weighted Transmission Loading Relief sensitivities by equation (2.8);

4. graphical representation of WTLR factors.

The original procedure is based on these main assumptions:

� the security assessment is performed by means of AC power �ow calculations according to a

traditional contingency analysis;

� the overloads are determined assuming the approximation that the line MVA rating is a MW

limit;

� the ISDFs are calculated considering a single slack bus, i. e. concentrated slack bus.

2.3.1 Step 1: security analysis

As above said, N and N-1 security assessment is performed by means of a sequence of AC load

�ow calculations. According to a standard contingency analysis, the procedure executes a power

�ow calculation in intact system conditions and for each outage included in the contingency list:

the failure or outage of each element in the contingency list (in our case, the trip of a transmission

line) is simulated in the network model by removing that element.

The procedure calls one of the power �ow solvers that are included in MATPOWER package [10]

and can be accessed via the runpf function, so performing a load �ow calculation in N security


conditions. More precisely, the procedure exploits the default power �ow solver, which is based on

a standard Newton's method using a full Jacobian, updated at each iteration.3

To carry out the security assessment considering the N-1 criterion and so to simulate a transmission

line outage, it has been necessary to make suitable changes in the original runpf function. The

procedure is also able to simulate the system operation following the outage of a line with two

parallel circuits carried by the same pylon (the so called �N-1.5� security criterion). In these cases

it is possible to consider higher power �ow limits: for instance, the user can choose to put 20% on

all line thermal limits.

After each load �ow, the branch overloads (MW) are calculated as:

Overloadjk = Powerflowjk − Limitjk (2.10)

where:

� Limitjk = MVAratingjk =√

3VnIn in intact system conditions;

� Limitjk = k ·MVAratingjk = k ·√

3VnIn in N-1 security conditions (with k ≥ 1, default:

k = 1.2, which puts 20% on all line thermal limits).

The contingency analysis results are organized by contingency and then saved in a �le: as shown

in Figure 2.11, each row lists the contingency that caused at least one overload, together with the

overloaded branch, the violating �ow and percentage, the overload in MW.

The overloaded branches are also organized according to their criticality measured by their total

overload, i. e. the sum of all overloads on that particular branch. This ranking, which is useful to

identify the weakest grid elements, is then saved in a �le: as illustrated in Figure 2.12, each row

lists the overloaded branch, the number of violations, and the total overload.

2.3.2 Step 2: ISDF calculation

The second main step of the procedure is the calculation of Injection Shift Distribution Factors,

�rst in intact system conditions and then considering those transmission line outages that caused

at least one overload.

The following paragraphs have the aim of explaining how to derive the Injection Shift Distribution

Factors in both N and N-1 security conditions, considering a single slack bus [11, 12].

For the sake of simplicity, the DC approximation of the distribution factors has been adopted in

the procedure for the calculation of WTLR sensitivities.

2.3.2.1 Distribution factor formulation

The basis for the distribution factor formulation begins by considering linear circuits with voltage

and current sources interconnected by impedances [11, 15].

Consider an n-bus plus ground network modeled with the admittance matrix referenced to ground.

For a given schedule of constant power bus loads and slack bus 1, a base case A solution satis�es:

3The ENFORCE_Q_LIMS option is set to 1 (default is 0): then, if any generator reactive power limit is violatedafter running the AC power �ow, the corresponding bus is converted to a PQ bus, with the reactive output set tothe limit, and the case is re-run. The voltage magnitude at the bus will deviate from the speci�ed value in order tosatisfy the reactive power limit.If the generator at the reference bus reaches a reactive power limit and the bus is converted to a PQ bus, the �rst

remaining PV bus will be used as the slack bus for the next iteration. This may result in the real power output atthis generator being slightly o� from the speci�ed values.


Figure 2.11: Example of �le with contingency analysis results

Figure 2.12: Example of �le with overloaded branches' ranking


IA1...

IAn

=

Y11 . . . Y1n...

...

Yn1 . . . Ynn

V A1

...

V An

(2.11)

with each bus injection current IAi coming from the ground through a path not included in [Y ].

The [Y ] matrix may include any line, transformer, load admittance connected between any two

buses or between a bus and ground. For a generator, this injection current is the generator

current. For a load (not included in [Y ]), this injection current is the negative of the load current.

All quantities are in per unit. For this analysis, let slack bus 1 be an ideal voltage source with

voltage �xed as:

V1 = V 01 (2.12)

Eliminating the slack bus current from the network model gives:IA2...

IAn

=

Y22 . . . Y2n...

...

Yn2 . . . Ynn

V A2

...

V An

+

Y21...

Yn1

V 01 (2.13)

Solving for the case A voltages gives:V A2

...

V An

=

Z22 . . . Z2n

......

Zn2 . . . Znn

IA2 − Y21V 0

1

...

IAn − Yn1V 01

(2.14)

The line currents for case A are:

IAjk =V Aj − V A

k

zjk(2.15)

where zjk is the primitive line jk impedance.

Now consider changes in injection currents from case A to case B. The case B network equations

(for unchanged impedances) are:V B2

...

V Bn

=

Z22 . . . Z2n

......

Zn2 . . . Znn

IB2 − Y21V 0

1

...

IBn − Yn1V 01

(2.16)

The line currents for case B are:

IBjk =V Bj − V B

k

zjk(2.17)

From equations (2.14)-(2.17) the change in voltages and line jk current between cases B and A

are: ∆V2...

∆Vn

=

Z22 . . . Z2n

......

Zn2 . . . Znn

∆I2...

∆In

(2.18)


∆Ijk = IBjk − IAjk =

n∑i=2

[Zji − Zki

zjk

]∆Ii (2.19)

where: ∆Ii = IBi − IAi . In cases where bus j or k equal 1, the entries of [Z] are de�ned to be zero.

This change can be written as:

∆Ijk =

n∑i=2

T ijk∆Ii (2.20)

where

T ijk =

Zji − Zki

zjk(2.21)

is the so called Current Transfer Distribution Factor (CTDF).

When the slack bus is represented as a voltage source with loads and other generation represented

as current sources, the solutions given by equations (2.18) and (2.19) are exact. The solution is

instead approximate when constant power loads or additional voltage controlled buses are present.

In power �ow studies, it is customary to convert these to power distribution factors by considering

loss-less conditions and assuming voltages to be near unity:

ISDF ijk =

Xji −Xki

xjk= −bjk (Xji −Xki) (2.22)

where xjk and bjk are the primitive line jk reactance and susceptance respectively.

Introducing the susceptance matrix [B] of DC load �ow, the Injection Shift Distribution Factor

(ISDF) can be written as:

ISDF ijk = Bjk (Xji −Xki) (2.23)

So the change in line real power �ow in response to real power injection changes can be approxi-

mated as follows:

∆Pjk 'n∑

i=2

ISDF ijk∆Pi (2.24)

Given a network with n buses and L branches, the complete ISDF-matrix Ψ can be obtained by

the following matrix calculation [13, 14], which is implemented in the Matlab-coded procedure:

Ψ = BdAX (2.25)

where:

� Bd ∈ RL×L is the diagonal matrix whose elements are the branch susceptances (branch

susceptance matrix);

� A ∈ RL×(n−1) is the branch to node incidence matrix whose row l (with 1 at column j and −1

at column k) is[

0 · · · 0 1 0 · · · 0 −1 0 · · · 0](reduced incidence matrix);

� X = B−1 ∈ R(n−1)×(n−1) is the reactance matrix, which is the inverse of the susceptance

one (reduced nodal reactance matrix).


It is clear that the sensitivity matrix Ψ is strictly dependent on the choice of the slack bus (i. e.

DC load �ow reference bus) in the system.

2.3.2.2 Post-contingency distribution factor

For the calculation of the Injection Shift Distribution Factors in post-contingency conditions, it is

necessary to determine the inverse of the new susceptance matrix because of the grid topological

changes as a result of the line outage. To do this in a numerically cheap way, we can apply the

Woodbury Matrix Identity (also called the matrix inversion lemma), which generally says that the

inverse of a rank-k correction of a matrix can be computed by doing a rank-k correction to the

inverse of the original matrix [16].

In the special case where we have to calculate the inverse of a rank-1 correction of a matrix (that is

the case of the calculation of the reactance matrix in post-contingency conditions), we can use the

so-called Sherman-Morrison formula [17], which computes the inverse of the sum of an invertible

matrix M and the dyadic product, uvT , of a column vector u and a row vector v:

M−1NEW =

(M + uvT

)−1= M−1 −M

−1uvTM−1

1 + vTM−1u(2.26)

In our case, the new susceptance matrix BNEW following the line st outage is:

BNEW = B + uvT = B − astbstaTst (2.27)

where ast =[

0 · · ·s1 · · · 0 · · ·

t−1 · · · 0

]T(with 1 at column s and −1 at column t),

u = −ast and vT = bsta

Tst.

The new reactance matrix XNEW can be calculated by the following matrix calculation, which is

implemented in the Matlab-coded procedure:

XNEW = B−1NEW = B−1 +B−1ast

[1− aT

stbstB−1ast

]−1bsta

TstB

−1 (2.28)

Therefore, the generic element of XNEW is:

XNjk = Xjk +

(Xsj −Xtj) (Xsk −Xtk)

βst(2.29)

with

βst =1

bst− (Xss − 2Xst +Xtt) (2.30)

2.3.3 Step 3: WTLR calculation

The contingency analysis and the ISDF calculation provide all the data necessary for the WTLR

computation by using equation (2.8).

The procedure allows the user to select the set of grid buses that will be considered for the

calculation of both ISDFs and WTLRs. For instance, if the analysis regards the Italian transmission

system (380 and 220 kV), the user can choose among three di�erent options: all 380 kV nodes, all

220 kV nodes, or the node set included in a �le by the user, which will be read and loaded by the

procedure. The resulting WTLRs are then saved in a �le, as shown in Figure 2.13.


Figure 2.13: Example of �le with WTLR sensitivities

2.3.4 Step 4: WTLR graphical representation

The last step of the procedure is the graphical representation of WTLRs. A preliminary work is

indispensable: since each WTLR factor refers to a single node, which has its own location in the

grid, it is necessary to load an image �le with the �gure of the network considered in the analysis

(using the imread4 function), to display it in a �gure window (using the image5 function), and

then to select the sequence of points [x, y] in the plane, corresponding to the chosen set of grid

nodes, with the ginput function, that enables the user to select points from the �gure using the

mouse for cursor positioning and returns the coordinates of the pointer's position (when a mouse

button is pressed). To avoid repeating these operations whenever the user is going to apply the

procedure on a particular network, it is better to save the selected coordinates in a MAT-�le and

to load them when necessary.

To obtain the WTLR graphical representation, �rst the procedure has to associate each index

(included in a vector z) to the corresponding node, i. e. to its location in the grid and so to its

coordinates x, y in a two-dimensional Cartesian space.

Since the data are not conveniently spaced evenly on a grid, in fact x and y are unevenly spaced

vectors and are not vertices of a rectangular array, the procedure has to use the meshgrid6 function

to create an evenly spaced grid around the range of the data: this can be considered the X-Y

�interpolation space�. Using the original data and the X-Y �interpolation space�, the griddata7

4A = imread(filename, fmt) reads a grayscale or colour image from the �le speci�ed by the string filename. Ifthe �le is not in the current directory, or in a directory on the Matlab path, it is necessary to specify the fullpathname. The text string fmt speci�es the format of the �le by its standard �le extension. The return value A isan array containing the image data. The class of A depends on the bits-per-sample of the image data, rounded tothe next byte boundary.

5The function image creates an image graphics object by interpreting each element in a matrix as an index intothe �gure's colormap or directly as RGB values, depending on the data speci�ed.

6[X, Y] = meshgrid(x, y) transforms the domain speci�ed by vectors x and y into arrays X and Y , which can beused to evaluate functions of two variables and three-dimensional mesh/surface plots. The rows of the output arrayX are copies of the vector x, while the columns of the output array Y are copies of the vector y.

7Z = griddata(x, y, z, X, Y, method) �ts a surface of the form z = f(x, y) to the data in the (usually) nonuniformlyspaced vectors (x, y, z). It interpolates this surface at the points speci�ed by (X,Y ) to produce Z. The surfacealways passes through the data points. X and Y usually form a uniform grid (as produced by meshgrid). Themethod de�nes the speci�ed interpolation method and so the type of surface �t to the data.


Figure 2.14: Example of contourf result for WTLR graphical representation

function calculates the interpolated Z data. Then, the contourf8 function provides a �lled contour

plot that displays isolines calculated from matrix Z, i. e. from the interpolated WTLR values, and

�lls the areas between the isolines using constant colours (an example is shown in Figure 2.14). To

get the �nal WTLR map as in Figure 2.15, the user has to superimpose the grid image on that

produced by the procedure by means of a suitable graphic software.

2.4 Application of the procedure to the CIGRE 63-bus sys-

tem

The above described procedure is �rst applied to the CIGRE 63-bus system [18].

The objective of the application to a small electric system is to demonstrate the e�ectiveness of

the proposed procedure to choose the adequate generation and transmission investments. The

results are also used to de�ne a metric to classify the transmission reinforcements according to

their positive impact on network security and electricity market e�ciency [19, 20].

The main features of the test system, illustrated in Figure 2.16 are summarized in Appendix A.

2.4.1 Simulation hypotheses

The main hypotheses for the simulations regard the contingency list for N-1 security assessment

and the thermoelectric generation pro�le.

8[C, h] = contourf(X, Y, Z, v) draws a contour plot of matrix Z with contour levels at the values speci�ed in vectorv, using X and Y to determine the x- and y-axis limits. When X and Y are matrices, they must be the same size asZ, in which case they specify a surface. X and Y must be monotonically increasing. The colour of the �lled areasdepends on the current �gure's colormap.


Figure 2.15: Example of WTLR graphical representation

Figure 2.16: CIGRE 63-bus test system


Table 2.1: Contingency list (CIGRE 63-bus system)

Table 2.2: Thermoelectric generation pro�le (CIGRE 63-bus system)

The set of contingencies includes the outages of every 220 and 150 kV line (Table 2.1); if a line is

made up by more than one circuit, the procedure will simulate the trip of one of them only. In N-1

security conditions the real power limits are increased by 20%. In order to assess the transmission

system adequacy, the thermoelectric generation pro�le considered in the analysis results from a

dispatch procedure which does not take into account any network constraints and so does not

introduce any power adjustments (i. e. re-dispatching actions). In this way the security assessment

is able to identify the most critical operation conditions and the weakest grid elements. Table 2.2

summarizes the thermoelectric generation pro�le.

2.4.2 Base case

Table 2.3 summarizes the security analysis outcomes for the base case described in the previous

paragraph. There are 37 transmission limit violations and the total system overload amounts to


Table 2.3: Contingency analysis results - Base case

1562.4 MW. The line 1M1-3M1 is the weakest grid element with 31 violations and a total overload

of 1226.6 MW; in particular, it is already overloaded in intact system conditions. This is due to

the real power �ow from the low-cost generators at bus 11R3, owned by a self-producer, to the load

buses in area V, which has not enough generation capacity to meet its local demand and whose

generators at bus 92V3 are the most expensive in the system.

Table 2.4 shows the WTLR indices calculated for all grid buses (except for the slack bus 41M3). The

nodes with the smallest WTLR sensitivities, which are the most adequate to host new generating

capacity according to the index de�nition, are situated in areas V and T; instead, adding new

power plants in area R will result in the largest overload increase. Therefore, importing areas are

the best locations for new generating capacity because a power injection at negative-WTLR bus

is able to produce counter-�ows which relieve overloads (for instance, on the line 1M1-3M1).

Figure 2.17 illustrates the WTLR graphical representation: a green or red area corresponds to


Table 2.4: WTLR sensitivities - Base case

the lowest or highest indices respectively. Changes from negative to positive values (from green

to yellow/red on the map) reveal the presence of congested elements (for instance, the lines 1M1-

3M1 and 75T2-775T2), so identifying the weakest grid sections or areas where new transmission

facilities should be realized.

2.4.3 WTLR-based generation expansion and network security

Considering the basic concept of the WTLR methodology (i. e. overload mitigation strategy using

generation), the most obvious use is strategic generation siting.

Among the set of negative-WTLR buses, three possible new generation sites are selected:

� node 33V1 (base WTLR = -17.07);

� node 5M1 (base WTLR = -10.89);

� node 66M1 (base WTLR = -4.73).

The aim is to evaluate the bene�ts for power system operation resulting from the new real power

injection at each of the above buses and thus to check the correctness of the information provided

by the WTLR values. The tests are carried out considering one site at a time. For example, a

new generator connected to the node 33V1 is added to the network model, its size is increased by

50 MW at a time until the corresponding WTLR becomes positive, and the total system overload

is calculated in each case. The production cost of the new unit is assumed low enough to allow it

to be fully dispatched.

The variations of the index value at the new generation sites and of the system overload are

displayed in Figures 2.18-2.19 (bus 33V1), 2.20-2.21 (bus 5M1), and 2.22-2.23 (bus 66M1).

The di�erences among the three cases are likely to be due to larger or shorter electrical distance

from the most critical grid element, i. e. the line 1M1-3M1.

The results make it evident that:

� the installation of new generating capacity in a negative-WTLR bus allows the total system

overload to be reduced;

� raising the installed capacity, the WTLR value increases while the system overload decreases;


Figure 2.17: WTLR graphical representation - Base case

Figure 2.18: Node 33V1 WTLR


Figure 2.19: System overload - New generator at node 33V1

Figure 2.20: Node 5M1 WTLR


Figure 2.21: System overload - New generator at node 5M1

Figure 2.22: Node 66M1 WTLR


Figure 2.23: System overload - New generator at node 66M1

� at a certain value of the new generating capacity, the WTLR becomes positive and corre-

spondingly the total system overload starts to increase again;

� the smaller the WTLR in the base case, the quicklier the total system overload decreases by

raising the new generating capacity;

� on one hand, the nodes with the smallest WTLR can be considered the most adequate sites

for installing new units resulting in an e�ective system security enhancement, on the other

hand, these buses might be able to host a smaller generating capacity.

2.4.4 WTLR-based grid development

According to what said for the base case simulation and for the possible use of the information

supplied by the WTLR sensitivities, the realization of a new line connecting the exporting areas

R and F to the importing area V can produce a substantial congestion alleviation, so resulting in

global system security enhancement.

The most obvious choice is to double the connection between the nodes 1M1 and 3M1, since the

existing line is the most critical grid element, as shown by the contingency analysis results in

Table 2.3. The other network reinforcements are selected according to the following criterion:

� from bus → negative-WTLR bus;

� to bus → positive-WTLR bus.

The new line will be an alternative path for power transmission from the exporting areas (yellow-red

colour/positive WTLR) to the importing ones (green colour/negative WTLR).

The set of nodes selected to de�ne the grid reinforcements includes:

� from bus: 9V1, 5M1 (WTLR = -12.24, -10.89 respectively);


Figure 2.24: Network reinforcements for CIGRE 63-bus system

� to bus: 1M1, 2M1, 8M1 (WTLR = +7.67, +3.63, +3.23 respectively).

So the set of network reinforcements considered in the study comprises the following transmission

lines: 1M1-3M1, 1M1-9V1, 1M1-5M1, 2M1-9V1, 2M1-5M1, 8M1-9V1, and 8M1-5M1 (Figure 2.24).

To make the comparison easier, all new lines are assumed to have the same features of the line

1M1-3M1.

2.4.4.1 WTLR procedure results

The realization of a new line is simulated in the network model by adding that element. The

procedure is then applied to the new grid model in order to calculate the new total system overload

and the new WTLR values.

The security assessment outcomes concerning all test cases are summarized in Table 2.5, which

shows the change in the total system overload and in the number of congestions consequent on the

realization of each of the new transmission lines.

The simulations demonstrate the correctness of the information supplied by the WTLR indices:

adding a new line from a green-coloured area to a yellow/red-coloured one can contribute to

congestion alleviation. All the new lines considered in the analysis have in fact a positive e�ect on

system security.

As shown in Figure 2.25, the lines 1M1-5M1 and 2M1-5M1 are the most e�ective in terms of

network congestion alleviation. They both produce the same redistribution of power �ows on grid

branches and so the security analysis provides the same outcomes (Table 2.6). There are only the

three violations that are caused by the export from area R (1M1-1R1) and by the import into area

T (75T2-775T2, 65T2-665T2) respectively, and that are not a�ected by the network reinforcement.

All the WTLR sensitivities (Table 2.7) are equal to zero except for the nodes of area R, which are


Figure 2.25: Total system overload for all test cases (decreasing order)

Table 2.5: Security analysis results for all test cases


Table 2.6: Security analysis results - New line 1M1-5M1 or 2M1-5M1

Table 2.7: WTLR sensitivities - New line 1M1-5M1 or 2M1-5M1

still positive but lower than in the base case, and for some nodes in area T, that are still negative

but higher than in the base case (lower absolute value).

2.4.4.2 A WTLR-based metric for transmission planning

The simulation results described in the previous paragraph have highlighted that:

� a network reinforcement, if properly chosen, can reduce the occurrence and/or the size of

branch overloads;

� consequently, the WTLR sensitivities vary according to the security analysis outcomes, re-

sulting in a more or less considerable decrease in their absolute values.

The second consideration suggests the possibility of de�ning a global index or a metric which can be

used to classify the network reinforcements based on their impact on overall system security. This

metric is the WTLR algebraic sum. The bar charts of Figures 2.25 and 2.26 show an interesting

analogy: the more the total system overload decreases, the more the metric diminishes.

So the global index calculation con�rms that the two lines 1M1-5M1 and 2M1-5M1 are the best

grid reinforcements in terms of security enhancement. On the basis of that, the WTLR algebraic

sum can be considered a measure of system security, as well as the total system overload, i. e.

the amount of thermal overloading that occurs during a set of simulated contingencies or forced

outages.


Figure 2.26: WTLR algebraic sum

2.4.4.3 Validation of the WTLR-based metric

In competitive electricity markets, transmission capacity expansion is necessary to increase Social

Welfare and market e�ciency, besides ensuring a secure, reliable, and uninterrupted electricity

supply.

To validate the WTLR-based metric de�ned in the previous paragraph and so to demonstrate that

the new lines 1M1-5M1 and 2M1-5M1 are the most e�ective also in terms of market e�ciency

improvement, an Optimal Power Flow procedure is applied to each test case and two standard

economic indicators (Social Welfare and Congestion Revenue) are calculated as follows:

� Producer revenue (Pgen i is the production of generator i and pgen i is the nodal marginal

price at the bus to which the generator i is connected):

Revenuegen i = Rgen i = pgen i · Pgen i (2.31)

� Generation cost (according to the hourly cost function of generator i):

Costgen i = Cgen i = C0i + C1iPgen i + C2iP2gen i (2.32)

� Producer surplus:

Πtot =∑i

(Rgen i − Cgen i) (2.33)

� Consumer surplus9 (dj and pj are the load and the nodal marginal price at bus j respectively):

Sc =∑j

(pref − pj) · dj (2.34)

9The demand is supposed inelastic and so it is necessary to �x a reference price for the consumers (pref= 150¿/MWh).


Table 2.8: Economic indicators for all test cases (¿/h)

� Social Welfare:

W = Πtot + Sc (2.35)

� Congestion Revenue:

CR =∑j

pj · dj −∑i

Rgen i (2.36)

As shown in Table 2.8, all the new lines produce a Social Welfare increase and a consequent Conges-

tion Revenue reduction compared with the base case. More precisely, four network reinforcements,

including the lines 1M1-5M1 and 2M1-5M1, produce practically the same increase in Social Welfare

(about 20200 ¿/h). It follows from this that the grid reinforcements with the largest impact on

network congestion mitigation are also among the most e�ective ones from the point of view of the

electricity market functioning (Figure 2.27).

2.4.4.4 An index to prioritize transmission planning

The preceding paragraphs have described the de�nition and validation of a WTLR-based metric

which could be used to classify network reinforcements on the basis of their impact on both system

security and electricity market e�ciency. Its calculation follows the application of the WTLR

procedure to the new test case, resulting from the addition of the new line to the base case: so

this process has to be repeated for all candidate lines. Compared to this, the methodology brie�y

outlined in subsection 2.2.3 has some advantages: in particular, the index calculation needs only

the WTLR values corresponding to the base case and the estimate of the expected power �ow

on the new line in intact system conditions (see equation (2.9)). The method, which has been

automated and implemented in the Matlab programming language, can be summarized as follows:

� de�ne a list of potential transmission lines;

� perform a standard contingency analysis to calculate the total system overload with reference

to the existing transmission network (base case);


Figure 2.27: Social Welfare for all test cases

� calculate the WTLR sensitivities (base case);

� quantify the expected real power �ow on the new lines in intact system conditions;

� calculate the indicator with reference to each of the new lines.

The main problem is the evaluation of the power �ow on the new lines. It can be solved by adding

the new line jk to the system and then quantifying Pjk with a full non-linear power �ow simulation.

This process has to be performed for each line.

The list of candidate lines considered for the method validation includes: 1M1-5M1, 1M1-9V1,

2M1-5M1, 2M1-9V1, 8M1-5M1, and 8M1-9V1. Table 2.9 summarizes the results: from and to bus

WTLRs, real power �ow, and index value. According to the index de�nition, a minus sign means

a positive e�ect on system security, i. e. a decrease in total system overload: the lowest values

correspond to the best network reinforcements in terms of security enhancement. Apart from a

few exceptions, the outcomes con�rm the priority order already made clear by applying the WTLR

procedure to calculate the system overload and the WTLR-based metric. The discrepancies, above

all that regarding the lines 2M1-9V1 and 8M1-5M1, are probably due to the approximations (loss-

less system and linearity) considered in the index de�nition.

Therefore, the validation rati�es that the indicator can give a good indication of the impact of a

potential transmission line on total system overload and consequently on overall system security.

Thanks to its main features, especially the easiness of its calculation, it could be adopted to evaluate

new transmission connections and to help the selection of those that provide the most e�ective

improvements to overall system security.

This WTLR-based methodology enables an easily automated process for comparing the e�ects of

new lines on total system overload and above all it can estimate which new connection will have the

greatest marginal bene�t to system security. Thus it has proved to be a fast-screening tool to allow

a transmission system planner to evaluate a given set of alternatives. This fact demonstrates the


Table 2.9: Index validation

importance of the approach. The ability to screen a certain number of alternatives to determine a

subset of promising ones for further evaluation (e. g. economic analysis) can be very important.

2.5 Changes in the original Matlab-coded procedure

This section will describe the modi�cations made in the original Matlab-coded program for the cal-

culation of WTLRs by introducing the Line Outage Distribution Factors, with the aim of reducing

the number of mathematical operations to be performed and consequently the total computational

time, and by adopting the distributed slack bus in order to remove the ISDF dependence on the

choice of the slack bus.

2.5.1 Introduction of the Line Outage Distribution Factors

As described in section 2.3, given a certain scenario, the basis for the WTLR calculation is a

standard contingency analysis carried out by a sequence of AC load �ow calculations to �nd possible

branch overloads. This step is quite time-consuming, especially for large networks, because the

Matlab-coded procedure performs a power �ow in intact system conditions and for each outage

included in the contingency list. In order to improve this process and above all to reduce the

total computational time, the original procedure is modi�ed in the following way: it performs an

AC load �ow to evaluate the real power �ows in N security conditions, while the real power �ows

following a line outage are determined by means of the so called Line Outage Distribution Factors

(LODFs).

2.5.1.1 LODF formulation

The formulation of the Line Outage Distribution Factors can be derived examining how the outage

impacts may be simulated by net injection and withdrawal changes [21].

First of all, it is necessary to de�ne the so called Power Transfer Distribution Factor (PTDF),

which measures the sensitivity of line MW �ows to 1 MW transfer. So the impact of a ∆tst-

MW transaction from node s to node t on the real power �ow Pjk on the line jk is ∆Pjk and is

determined by:

∆Pjk = PTDF stjk∆tst (2.37)

where the PTDF is de�ned as:

PTDF stjk = ISDF s

jk − ISDF tjk (2.38)


Figure 2.28: Impact of the transaction ∆tst

The line st outage changes the real power �ow in the post-outage network on each line connected

to s by the fraction of Pst. This impact can be simulated by introducing a transaction ∆tst in the

pre-outage network (Figure 2.28). The injection ∆tst adds a change PTDF stst ∆tst on the line st

�ow and a net �ow change of (1− PTDF stst ) ∆tst on all the other lines but st that are connected

to node s. By selecting ∆tst to satisfy:

(1− PTDF st

st

)∆tst = Pst (2.39)

the transaction ∆tst changes the �ow Pjk, jk 6= st, by:

∆Pjk = PTDF stjk∆tst =

PTDF stjk

1− PTDF stst

Pst (2.40)

The term

PTDF stjk

1− PTDF stst

(2.41)

is the Line Outage Distribution Factor of the line jk with respect to the line st outage.

Consequently, the real power �ow on the line jk following the line st outage can be approximated

as:

Pjk(st) ≈ Pjk + LODF stjkPst (2.42)

2.5.1.2 Application to the CIGRE 63-bus system

According to what said in the previous paragraph, after carrying out a load �ow in intact system

conditions and after computing the ISDFs with reference to the original network, the procedure

determines the real power �ows on grid branches in N-1 security conditions by means of the

LODFs. Instead of a sequence of AC load �ow calculations, the procedure thus performs this

matrix computation only:P (1)

...

P (Nout)

=

P...

P

+

LODF (1)

...

LODF (Nout)

. ∗ [ P (out) · · · P (out)]

(2.43)


where:

� all the matrices ∈ RNout×Nb (Nout is the number of line outages in the contingency list and

Nb is the number of grid branches);

� .∗ is the Matlab arraywise multiplication;10

� the n-th row P (n) of the �rst matrix is the vector of the real power �ows following the line

outage n;

� all rows of the second matrix are equal to the vector P of the real power �ows in intact

system conditions;

� the n-th row LODF (n) of the third matrix is the vector of LODFs with respect to the line

outage n: in particular, the element corresponding to the line to be outaged, which cannot

be calculated by equation (2.40), is set at -1 so zeroing the post-contingency power �ow on

that particular line;

� all columns in the fourth matrix are equal to the vector P (out) =[P(1) · · · P(Nout)

]Tof

the real power �ows on the lines included in the contingency list in N security conditions.

The new procedure is applied to the base case of the CIGRE 63-bus system and the new outcomes

are compared with the original ones. The approximations used in the derivation of the Line Outage

Distribution Factors11 introduce an error in the calculation of Pjk(st): the absolute value of the

relative error is computed as: ∣∣∣∣∣Pjk(st) − Exact Pjk(st)

Exact Pjk(st)

∣∣∣∣∣ (2.44)

where Exact Pjk(st) is the real power �ow determined using the AC load �ow (i. e. the exact

method) and Pjk(st) is the result obtained using the distribution factors.

To investigate the quality and robustness of the distribution factors for congestion modelling, the

absolute values of the errors (calculated for every real power �ow) are collected and then their

density function is constructed. The plot in Figure 2.29 shows that the frequency for the relative

errors is high for very small values but rather low for large errors. The corresponding cumulative

distribution function is displayed in Figure 2.30: the plot indicates that the relative errors are

smaller than 2% for more than 90% of the cases, while they are above 1% in about 20% of the

cases.

We, therefore, conclude that the linearization approximation in the derivation of the distribution

factors introduces these errors, but at least for a test system as the CIGRE 63-bus one its e�ect

on the calculation of the real power �ows in N-1 security conditions is very small.

The contingency analysis results obtained using the approximate method are summarized in Ta-

ble 2.10: each row lists the contingency (line st outage), together with the overloaded branch jk,

the LODF, the real power �ows on the lines jk and st in intact system conditions, the post-outage

line jk power �ow,and the relative error (in per cent) on Pjk(st). So, regarding the overloaded

branches, the highest absolute value of the relative error on Pjk(st) amounts to about 3.1%. Ob-

viously, the approximations also a�ect the overloads detected by the contingency analysis: for the

10A. ∗B is the element-by-element product of the arrays A and B.11They are the assumptions used in the derivation of DC power �ow models.


Figure 2.29: Density function of the relative errors in line �ow approximations

Figure 2.30: Cumulative distribution function of errors in line �ow approximations


Table 2.10: Contingency analysis results by using LODFs

most part, the �LODF overload� is smaller than the �exact� one. So the total system overload,

which amounts to 1521 MW, is lower than that computed by adopting the original procedure

(1562.4 MW).

In the light of these di�erences, though small, it is interesting to estimate the impact that the

approximate method for congestion modelling has on WTLR sensitivities. Figure 2.31 illustrates

the relative errors on WTLRs. It is clear that the error is small for most nodes (lower than 2%),

except for the buses of area T (3÷10%). The absolute errors are however not considerable and so

the qualitative indications provided by WTLRs are still good. We can conclude that, in spite of

the approximations in the derivation of LODFs, the outcomes of the new procedure are acceptable.

The simulations also demonstrate that introducing the distribution factors to detect possible branch

overloads allows the total computational time to be reduced notably. This improvement to the

original procedure allows simulating the line outages by changing the network topology and carrying

out a sequence of AC power �ow calculations to be avoided, since it needs the computation of

LODFs and the matrix calculation in equation (2.43) only.


Figure 2.31: Relative error on WTLR sensitivities using LODFs

2.5.1.3 Using the base ISDFs to compute WTLR sensitivities

To further speed up the Matlab-coded program, another simpli�cation can be introduced: using the

base Injection Shift Distribution Factors, calculated in intact system conditions, to determine the

WTLR sensitivities. In this way, the procedure has not to compute the post-contingency reduced

reactance matrix XNEW , given by equation (2.28), and then the new complete ISDF-matrix Ψ

for each outage.

We �rst investigate the ISDF errors introduced by the changes in the network topology. For each

line outage the original procedure calculates the ISDF for every node in the system. We compute

the relative error for each ISDF by comparing it to the corresponding reference value determined

in N security conditions: ∣∣∣∣∣ISDF post − ISDF base

ISDF base

∣∣∣∣∣ (2.45)

We collect the errors and construct the density function shown in Figure 2.32. This plot demon-

strates that, although the topology changes in the network may result in major impacts on the

value of some particular ISDFs, the fraction of ISDFs which are signi�cantly impacted is relatively

small. The scatter plot in Figure 2.33 shows the size of relative error as a function of the corre-

sponding ISDF magnitude: it reinforces the notion that large errors are associated primarily with

small magnitude ISDFs. These results suggest using the base ISDFs to calculate WTLR sensi-

tivities, since the errors on the distribution factors are relatively small and so this approximation

should not a�ect the resulting indices very much.

The chart in Figure 2.34 displays the WTLRs computed: 1) by applying the original procedure, 2)

by using the base ISDFs, and 3) by using both the LODFs and the base ISDFs. The simulations

indicate that the WTLR errors stay in an acceptable range.

To conclude, the results highlight that the simpli�cations (i. e. using the LODFs for the contingency


Figure 2.32: ISDF error density function

analysis and the base ISDFs for calculating the WTLRs) do not compromise the quality of the

information supplied by WTLR sensitivities. Furthermore, they allow performing an AC load �ow

calculation and determining the modi�ed ISDF matrix for each outage to be avoided, so resulting

in a notable reduction of the total computational time.

2.5.2 Adoption of the distributed slack bus

Besides being quite time-consuming, especially for large networks, which may not be a real problem

since the WTLRs are useful indices for power system planning, the original procedure has an

e�ective limit: it considers a single slack bus, i. e. concentrated slack bus, in the power �ow

calculations and above all in the ISDF computation.

2.5.2.1 Impact of the choice of the slack bus

We �rst investigate the impact of the selection of the slack bus on the power �ow calculations

and especially on the branch overloads detected by the contingency analysis. The simulations are

performed by applying the original procedure which, as explained in section 2.3, uses a single slack

bus load �ow analysis. Table 2.11 shows the total overload system with reference to �ve di�erent

slack buses: 41M3 (the original one), 11R3, 43F3, 61T3, and 92V3. More precisely, the congestions

are the same for all test cases and there are not big di�erences in the size of the overloads: so the

impact of the system overload errors on WTLR values should be quite small.

As explained in subsection 2.3.2, the ISDF matrix is instead strictly dependent on the selection

of the slack bus in the system. So now we look into the e�ects of changing the slack bus on the

determination of the distribution factors and consequently of the WTLR sensitivities.

Just to investigate this aspect, the choice of the �ve slack buses considered in the simulations is

made in such a way that each of the �ve areas of the CIGRE 63-bus system, one at a time, is


Figure 2.33: Scatter plot of the relative errors as a function of the ISDF magnitudes

Figure 2.34: E�ect of the approximations on WTLR sensitivities


Table 2.11: Contingency analysis results with di�erent slack buses

the �sink area� (41M3-area M; 11R3-area R; 43F3-area F; 61T3-area T; 92V3-area V). Figure 2.35

clearly shows that the WTLRs depend strongly on where the slack bus is in the grid. In particular,

the arithmetic mean of the WTLR values is very di�erent in the �ve test cases:

� �41M3 case�: WTLR arithmetic mean = -3.57;

� �11R3 case�: WTLR arithmetic mean = -14.68;

� �43F3 case�: WTLR arithmetic mean = -3.49;

� �61T3 case�: WTLR arithmetic mean = +1.21;

� �92V3 case�: WTLR arithmetic mean = +8.73.

In the original network the slack bus is 41M3, which has been selected because of its baricentric

position in the system. Besides demonstrating the e�ectiveness of the WTLR methodology, the

results described in section 2.4 highlight the quality of the information supplied by the WTLRs

and so, on the light of the above considerations, the correcteness of selecting the node 41M3 as the

slack bus.

The diagram in Figure 2.35 shows that the �43F3 case� is the only similar to the base one and we

thus conclude that the two nodes 41M3 and 43F3 act in like manner as slack bus: they are in fact

�electrically� close, since the high voltage generator bars (44F1 and 4M1) are connected by a double

circuit line. All the WTLRs related to the �11R3 case� are negative because an injection at any

node in the system, which is withdrawn from the slack bus in area R, would produce a counter-�ow

on the lines 1M1-3M1 and 1R1-1M1 so resulting in a large total system overload decrease. On the

contrary, nearly all the WTLRs corresponding to the �92V3 case� are positive: the reasons are just

the opposite of the previous case.

2.5.2.2 Distributed slack bus

Even though the simulations described in the previous paragraph show that the results of the

contingency analysis are little a�ected by the selection of the slack bus, the distributed slack

bus concept is introduced in the power �ow model used by the Matlab-coded procedure. The

traditional Newton-Raphson formulation of the load �ow problem is properly modi�ed introducing

the so called participation factors in order to distribute the real power mismatch due to uncertain

system losses to a particular set of generation units. The complete treatment of this subject is in

Appendix C.

Obviously, the participating sources, chosen to act as the slack bus, are the generators connected

to the �ve nodes considered in the previous paragraph, namely: 41M3, 11R3, 43F3, 61T3, and

92V3. The participation factors ρs are calculated as follows (Table 2.27):


Figure 2.35: WTLR values with di�erent slack buses

Table 2.12: Participation factors

ρs =Pmax s∑

s∈DsPmax s

(2.46)

where Ds is the set of generation units that function as the slack bus and Pmax s is the maximum

real power by generation unit s.

The contingency analysis results are summarized in Table 2.13. It is clear that removing the

concentrated burden of the slack bus does not cause remarkable changes with respect to the �only

one slack bus� test cases. The outcomes demonstrate that, in case of a single slack bus, selecting

the node 41M3 is correct for the load �ow analysis: the security assessment results in Tables 2.3

and 2.13 are practically the same.

Now we investigate the e�ect of assuming the distributed slack bus on the distribution factors and

consequently on the WTLR values.

We de�ne the Distributed Slack Injection Shift Distribution Factor (DSISDF) as the change in


Table 2.13: Contingency analysis results using the distributed slack bus power �ow


Figure 2.36: Cumulative distribution function of |DSISDF − ISDF |

a line real power �ow in response to 1 MW injection at a particular bus and a corresponding

withdrawal at the distributed slack buses assuming participation factor control. The DSISDF

mathematical formulation12 is [22]:

DSISDF ijk = −bjk (Xji −Xki) + bjk

∑s∈Ds

ρs (Xjs −Xks) (2.47)

To evaluate the impact of adopting the distributed slack bus on the distribution factors, we compute

the absolute error for each DSISDF by comparing it to the corresponding reference value (ISDF)

determined by using a single slack bus model:

|DSISDF − ISDF | (2.48)

The cumulative distribution function is displayed in Figure 2.36: the plot indicates that the absolute

errors are smaller than 0.06 for more than 90% of the cases. Since by de�nition the distribution

factors may be at most equal to unity, these di�erences might be even non-negligible.

The WTLR sensitivities are now calculated as follows:

WTLRi =Nviol

(∑jkDSISDF

ijkPCO,jk +

∑jk

∑stDSISDF

ijk(st)P

stCO,jk

)OverloadSY S

(2.49)

Figure 2.37 shows the indices calculated by equation (2.8), i. e. considering a single slack bus

(41M3), and by equation (2.49), i. e. adopting the distributed slack bus, respectively. It is clear

that the di�erences between the ISDFs and the DSISDFs a�ect the WTLR sensitivities which are

in general smaller in case of removing the concentrated burden of the slack bus. However, from a

12The DSISDF formulation is obtained considering the assumptions used in the derivation of DC power �owmodels.


Figure 2.37: Impact of adopting a distributed slack bus model on WTLRs

qualitative viewpoint there are not substantial changes.

We can conclude that in any case the most correct choice is to assume a distributed slack bus

model, so making the ISDFs and the WTLRs completely indipendent of the selection of the slack

bus. But the simulations highlight that the results can be little a�ected by the �only one slack

bus� assumption on condition that the slack bus is suitably chosen.

2.6 Tests on the Italian EHV system

To assess the performances of the WTLR approach and of the Matlab-coded program on large

systems, some tests are carried out on detailed models of the Italian EHV network (380 kV and

220 kV). This section will �rst investigate the impact of assuming the approximation that the line

MVA rating is a MW limit in determining the branch overloads. Then the simulations will show

that the WTLR methodology can be used with di�erent purposes for power system planning.

2.6.1 The MVA rating approximation

As described in section 2.3, the original methodology assumes the approximation that the line

MVA rating is a MW limit and so it ignores both the actual voltage magnitude and the power

factor cosϕ. We now investigate the e�ect of this assumption on security assessment results and

on WTLR sensitivities.

The procedure is applied to the Italian EHV electric system with reference to a summer peak load

condition at the projection horizon of the year 2013. Such a kind of scenario is chosen since the line

current limits allowed in summer are lower than in winter and so it may represent a very stressed

operation condition for the Italian network. The nodal loads, the available power plants, and the

amount of the electricity import refer to what published by the Italian TSO in its development

plan [23] for the projection horizon considered in the study.


Table 2.14: Contingency analysis results (original procedure)

The main hypotheses assumed in the analysis are:

� the power productions of the thermoelectric plants refer to an unconstrained clearing market

point: in other words, the schedule is the result of a λ-dispatching procedure that takes into

account the economic merit order only, while ignoring any transmission system constraint.

As result of the unconstrained market, the Italian transmission system may be harmfully

stressed in peak load conditions, since the main power plants are not always close to the load

areas;

� the N-1 security assessment is carried out including in the contingency list the outages of all

380 and 220 kV lines;

� unlike what we previously assumed for the CIGRE 63-bus system tests, the power �ow limits

considered in N-1 security conditions are not increased by 20% of their rating; so in both N

and in N-1 security conditions they are calculated as:13

Limitjk = MVAratingjk =√

3VnIn (2.50)

2.6.1.1 Original procedure results

The contingency analysis performed by the original Matlab-coded program gives the results sum-

marized in Table 2.14. The Italian 380 kV network at the year 2013, according to the grid devel-

opment plan, is represented in Figure 2.38, which helps us to locate the geographical position of

the outaged and overloaded lines. Some 380 kV bus WTLRs are shown in Table 2.15.

2.6.1.2 Check by a standard steady-state security assessment tool

To control the correctness of the results obtained by assuming the MVA rating approximation,

a standard steady-state security assessment tool is applied to the Italian test case. This tool,

which performs a load �ow calculation for each outage in the contingency list, determines the line

currents and compares them to the corresponding current limits so detecting the actual overloads.

The outcomes are summarized in Table 2.16, which clearly shows that assuming the MVA rating

approximation introduces some errors in the contingency analysis results. All the power �ows ex-

pressed in per cent of the corresponding limits in Table 2.14 are higher than the per cent currents

13The coe�cient k, which allows the line thermal limits to be increased in N-1 security conditions, is set to unity.


Figure 2.38: Outaged and overloaded 380 kV lines

Table 2.15: WTLR sensitivities (original procedure)


Table 2.16: Check by a standard steady-state security assessment tool

Table 2.17: Contingency analysis results (considering the actual voltage magnitudes)

in Table 2.16. Moreover, six violations detected by the original procedure are not con�rmed by

the standard security assessment tool: actually the outage of the 380 kV lines Ferrara Focomorto-

Ferrara Nord, Lonato-Nogarole Rocca, Sermide St.-Crevalcore, Valmontone-Presenzano, and Avel-

lino Nord-Bisaccia (one at a time) do not cause any network congestions, while the outage of the

380 kV line Ariano Irpino-Benevento overloads the 380 kV line Gissi St.-Villanova only.

2.6.1.3 Considering the actual voltage magnitudes

On the basis of the results described in the preceding paragraph, it is appropriate to modify the

original methodology used to calculate the branch overloads in order to take into account the actual

voltage magnitudes instead of their rated values. The power �ow limits are now computed as:

Limitjk =√

3VjIn (2.51)

where it is assumed that the power �ow is from bus j to bus k. The new contingency analysis

outcomes are summarized in Table 2.17: the new method allows only the e�ective overloads to be

detected, even if the per cent power �ows are little smaller than the actual ones.

2.6.1.4 Considering the actual power �ow limits

As well as the bus voltage magnitudes, the load �ow calculations by using the MATPOWER

package allow us to determine the power factors cosϕ and so the actual power �ow limits on grid


Table 2.18: Contingency analysis results (considering the actual power �ow limits)

Figure 2.39: Impact of the MVA rating approximation on WTLRs

branches. So we can compute the e�ective per cent power �ows and the e�ective MW overloads

(Table 2.18).

The diagram in Figure 2.39 shows the impact of the approximations adopted to calculate the

branch overloads on WTLR sensitivities. It clearly demonstrates that considering the rated voltage

magnitudes, instead of the actual ones, produces the largest errors: the bigger the WTLR absolute

value, the larger the error. On the contrary, ignoring the power factors does not compromise the

quality of the information provided by the indices.

2.6.1.5 Conclusions on the Matlab-coded procedure for WTLR calculation

On the basis of the tests on the Italian EHV system, we can conclude that the MVA rating

approximation is not suitable especially for the operation conditions in which the bus voltage

magnitudes diverge from the corresponding rated values, since in these cases it produces non-

negligible errors in the contingency analysis results and in the WTLR calculation.


Consequently, in the simulations in which it is better not to use this simpli�cation, it is impossible

to adopt the Line Outage Distribution Factors to compute the approximate branch power �ows in

N-1 security conditions, because the actual voltage magnitudes are not calculated by this method.

Moreover, the tests on the Italian EHV network demonstrate another limit of adopting the LODF

simpli�cation: it is not able to detect the line outages that cause the non-convergence of the load

�ow algorithm. For instance, this is the case of the outage of the 380 kV line Dugale-Montecchio in

the North-East: the power �ows, that have to reach the 380/132 kV substations of Montecchio and

Sandrigo to meet the demand of the big load areas in the province of Vicenza, have to cover a long

electrical distance, which produces considerable voltage drops and leads to the system collapse due

to the lack of adequate reactive power resources in the area.

2.6.2 WTLR sensitivity: a tool with several uses

Other simulations aimed at showing several uses and applications of the WTLR methodology are

performed on the Italian EHV network at di�erent projection horizons: the tests will demonstrate

that this methodology could be a useful tool for both generation and transmission planning and

particularly for achieving a more coherent development of the whole power system.

All the simulations, whose results will be presented in the next paragraphs, are carried out con-

sidering the main assumptions described in subsection 2.6.1, except for the fact that the branch

overloads are calculated with reference to the e�ective real power �ow limits.

2.6.2.1 GENCO viewpoint

The WTLR methodology is founded on the basic concepts described in subsection 2.2.2.1. The

obvious use of this tool is thus the strategic generation siting, that is, to determine the geographic

locations where new generation would enhance the system security by creating post-contingency

counter-�ows that would mitigate overloads under contingency conditions. According to this, it

seems that the only advantage of the strategic generation siting is the system security improvement,

which is one of the chief tasks of a System Operator, but which does not involve the Generation

Companies. Also a producer can however bene�t from an exact and appropriate selection of the

sites for new power plants.

In a liberalised electricity market, where there can be a strong competition among power producers,

the transmission system limits have a key role in the clearing of the market. For instance, in Italy

the violation of one or more inter-zonal limits14 produces the separation of the Italian system in

two or more zones during the day-ahead market (the so called �Mercato del Giorno Prima�) and the

network constraints thus a�ect the market results and above all what producer o�ers are accepted.

In the Italian ancillary service market (the so called �Mercato del Servizio di Dispacciamento�) the

intra-zonal transmission constraints are taken into account and a generation re-scheduling occurs

in case of network congestions [24].

Therefore a GENCO, whose main purpose is to maximize its expected pro�ts, may gain some

advantages from an appropriate generation siting. Besides envisaging the supply concentration

and the possible competition with other producers, its expansion plan should consider the areas

14The Italian network is divided in the following zones: six geographical zones (North: Val d'Aosta, Piedmont,Lombardy, Trentino Alto-Adige, Veneto, Friuli Venezia Giulia and Emilia Romagna; Central-North: Tuscany, Um-bria and Marche; Central-South: Latium, Abruzzi and Campania, excepting the Gissi production area; South:Molise, Apulia, Basilicata and Calabria, plus the Gissi production area; Sicily, Sardinia), seven virtual foreign zones(France, Switzerland, Corsica, Corsica AC, Austria, Slovenia, Greece) and �ve limited production areas (Monfalcone,Foggia, Rossano, Brindisi, Priolo), as shown in Figure 2.40.


Figure 2.40: Geographical and virtual Italian zones

which are not limited by existing network bottlenecks or those where the TSO has planned some

grid reinforcements, so that its future power productions will not su�er heavy restrictions due to

some network constraint. The WTLR methodology can give a GENCO some useful indications

about this issue.

The simulations on the Italian EHV network at the year 201315 provide the WTLR graphical

representation in Figure 2.41.

First of all, it can be used to qualitatively identify the best areas and locations for new power

plants so that they should not be heavily limited by the occurrence of network congestions. As

already highlighted by the contingency analysis results, the most critical grid element is the middle-

Adriatic backbone, particularly between the electrical substations of Gissi St. and Villanova: it is

clear that at the projection horizon the least appropriate sites are situated in Southern Italy and

especially on the Adriatic side, where there is already a strong competition and where new power

plants will be installed in the next few years.

Always with reference to a GENCO's expansion plan, the WTLR values pertinent to a given

scenario can be used to rank a set of possible new generation sites. For instance, consider the

following six candidates for a new 800 MW CCGT power plant16 (Figure 2.42):

1. 380 kV node of Acciaiolo;

2. 380 kV node of Marginone;

3. 380 kV node of Suvereto;

4. 380 kV node of Fano;

5. 380 kV node of Villavalle;

6. 380 kV node of Presenzano.

According to the WTLR indications, the six candidates can be ranked in the following way:

15The simulations to which Figure 2.41 refers are carried out by using the modi�ed Matlab-coded program thatconsiders the actual power �ow limits and not the MVA rating approximation.

16The list reports the 380 kV nodes to which the new power plant could be connected.


Figure 2.41: WTLR map - Italian EHV system (year 2013)

Figure 2.42: Possible new generation sites (year 2013)


1. Fano (WTLR = -0.32);

2. Acciaiolo (WTLR = -0.07);

3. Marginone (WTLR = -0.06);

4. Suvereto (WTLR = -0.03);

5. Villavalle (WTLR = -0.02);

6. Presenzano (WTLR = +0.29).

In particular, it follows that the best location for a new power plant is the node of Fano, while the

worst one is the bus of Presenzano. Considering these suggestions in the de�nition of the expansion

plan, the risk of possible limitations due to some network constraint should be reduced. Moreover,

the whole power system will gain some advantages in terms of security enhancement.

This situation may change in consequence of the reinforcement of the Adriatic backbone as planned

by the Italian TSO within 2013-2015:17 the WTLR di�erences may become less notable, but in

any case the node of Presenzano may be still the least attractive because of the strong competition

among the power producers in the area.

A standard Optimal Power Flow, that provides the real power dispatch at the minimum generation

cost, is applied to six new test cases, each of which is derived from the base scenario by adding

one of the six new power plants. The outcomes are then compared to the indications given by

the WTLRs to con�rm (or not) the above-mentioned ranking and to estimate the overall system

bene�t in each case.

The simulations are carried out considering the e�ective generation costs of the thermoelectric

power plants assumed in service, so that no conjecture is made about the producers' o�ers in the

electricity market.

The analysis performed by means of the OPF procedure and considering the N-1 security criterion

highlights that the most critical grid element is the middle-Adriatic backbone, so con�rming that

the new generation sites to the north of this grid section are favoured by their geographical position.

The ranking of the generation sites are validated by evaluating two parameters: the dispatched

power of the new power plants, which �xes their utilization hours, and the variation of the real

power losses, that a�ect the total generation cost and thus the system operation economy. Ta-

ble 2.19 summarizes the OPF outcomes pertinent to the six test cases. So di�erent values of the

dispatched power in the second column are due to the distance (both geographical and electrical)

of the new generation sites from the load areas and also to the concentration of more or less com-

petitive power producers in the zone. The smallest value pertinent to the power plant connected

to the 380 kV node of Presenzano con�rms that it will be disadvantaged by its location because it

will cope with the strong competition in Southern Italy and more precisely in Campania.

The comparison between the outcomes of the two procedure makes it evident that there is an

exact correspondence between the WTLR ranking and the results in Table 2.19. In particular, the

realization of a new CCGT power plant connected to the 380 kV node of Fano will yield the greatest

bene�ts in terms of both system security enhancement, as suggested by the corresponding WTLR,

and reduction in power losses and total generation costs, as highlighted by the OPF calculations.17In the last development plan [23], to overcome the existing power limitations on the production areas in Southern

Italy, the Italian TSO has scheduled to double and reinforce the middle-Adriatic backbone by implementing a seconddouble-circuit line between the existing substations of Villanova and Foggia by 2013-2014. Furthermore, to makethe 380 kV network more meshed and to improve the system reliability and the security of supply, the Italian TSOhas planned to construct a new 380 kV line between the existing substations of Fano and Teramo by 2015.


Table 2.19: OPF results (year 2013)

Figure 2.43: Possible new generation sites (year 2015)

This approach can be used also to evaluate the e�ect of a delay in the completion of the grid

development plan. For instance, consider the Italian EHV electric system with reference to a

summer peak load condition at the projection horizon of the year 2015 and the following set of

possible new generation sites (Figure 2.43):

� 380 kV node of Udine Ovest;

� 380 kV node of Forlì;

� 380 kV node of Teramo;

� 380 kV node of Aliano.

As regards the base 2015 scenario, the steady-state security assessment, on the basis of which

the WTLR sensitivities are calculated, does not detect any network congestions: thanks to the

network reinforcements scheduled by the Italian TSO within 2015, the transmission system is able

to transfer the power �ows generated by the power plants in service towards the load areas without

overloading any grid element. Consequently, it is impossible to determine the indices and to get


Table 2.20: OPF results (year 2015)

Table 2.21: Contingency analysis results (without doubling the Adriatic backbone)

useful information concerning the sites chosen for the installation of a new 800 MW CCGT power

plant.

The OPF procedure applied to four new test cases, each of which is derived from the base scenario

by adding one of the four new power plants, gives the results in Table 2.20.

Further analyses, using the WTLR tool and considering less positive assumptions about the com-

pletion of the transmission system development plan, are carried out. For example, suppose that

the doubling of the middle-Adriatic backbone between the nodes of Villanova and Foggia is not

completed by 2015, contrary to what is planned by the Italian TSO. The corresponding contin-

gency analysis results are shown in Table 2.21: for the given scenario the only network congestions

regard just the existing 380 kV line Gissi St.-Villanova. According to the resulting WTLR indices,

the four candidates can be ranked as follows:

1. Teramo (WTLR = -2.10);

2. Forlì (WTLR = -1.23);

3. Udine Ovest (WTLR = -1.03);

4. Aliano (WTLR = +2.50).

It is clear that, if the doubling of the middle-Adriatic backbone was not completed by 2015, the

site of Aliano would be the least suitable for installing a new CCGT power plant, as it could be

limited by the occurrence of congestions.

Considering the data in Table 2.20, resulting from the study on the most favourable scenario in

terms of network upgrades, and the WTLR-based ranking, pertinent to the base scenario without

the reinforcement of the middle-Adriatic backbone, we can derive the priority list in Table 2.22.

As pointed out by the second column, any power plants should not be limited by the occurrence of

network congestions, if the grid development plan was completed according to what is scheduled

by the Italian TSO [23]. Indeed, the limitation on the power production at the node of Aliano,


Table 2.22: Priority list of the new generation sites (year 2015)

to which the lowest dispatched power in Table 2.22 refers, is especially due to a very high supply

concentration in Southern Italy.

To conclude, the analysis suggests that, from the producer's viewpoint, the 380 kV node of Udine

Ovest is the best site for a new CCGT power plant since it has the highest dispatchability. More-

over, it produces the largest bene�ts for the system not only in terms of decrease in real power

losses (-20 MW), but also in terms of security enhancement. Concerning this, suppose that the

main grid reinforcements planned by the Italian TSO in the North-East (i. e. the 380 kV line

Volpago-Venezia Nord and the 380 kV double circuit line Udine Ovest-Udine Sud-Redipuglia) are

not completed by 2015. The outage of the 380 kV line Dugale-Montecchio does not cause any

overloads, but leads to notable voltage drops in the area (see subsection 2.6.1.5). The installation

of a new power plant connected to the 380 kV node of Udine Ovest allows the maintenance of an

adequate voltage pro�le thanks to a better distribution of the real power �ows in the network and

to a larger availability of reactive resources which compensate for the reactive power losses.

2.6.2.2 TSO viewpoint

One of the main tasks of a Transmission System Operator is the system security maintenance. So

one of the main objectives of the grid development plan is to reduce the risk of network congestions

and the existing limitations on the production areas.

Besides being helpful for strategic generation siting, the WTLR methodology can be successfully

used by the TSO to guide transmission planning. Some of its potential applications are:

1. to identify the weakest grid areas, where new transmission facilities have to be installed;

2. to demonstrate the bene�ts of realizing the entire development plan within the prearranged

time limit and thus the consequences of a possible delay;

3. to assess the impact of the generation system expansion on network security;

4. to assess the e�ectiveness of a single grid reinforcement planned by the TSO in terms of

security enhancement and so to rank a set of grid upgrades in order to prioritize transmission

planning;

5. to determine new network reinforcements, to be included in the transmission system devel-

opment plan.

Determination of the most critical grid elements. To prove that the WTLR tool can be

used by the TSO to determine the weakest grid sections, the Matlab-coded program is applied

to the Italian EHV system with reference to a peak load condition of summer 2009. In order to


Table 2.23: Contingency analysis results (year 2009)

Figure 2.44: WTLR map - Italian EHV system (year 2009)

validate the outcomes, they will be compared with the data published by the Italian TSO in its

last development plan [23].

The contingency analysis results are summarized in Table 2.23, while the WTLR graphical repre-

sentation is illustrated in Figure 2.44.

As expected, the correctness of the outcomes is rati�ed by what reported in [23] about the most

critical grid areas of the current Italian grid (Figure 2.45): more precisely, the procedure results

show the inadequacy of the 220 kV network, especially in the area of Milan (overload of the

line Milano Porta Venezia-Milano Porta Volta), in Campania (overload of the line Frattamaggiore-

Starza Grande), in the North-East (overload of the line Dolo-Camin), and also the critical operation

condition of the 380 kV lines Foggia-Benevento and Gissi St.-Villanova. Obviously, the test case

does not highlight all the operation problems that involve the Italian transmission system: this is

just an example of application to demonstrate the tool usefulness.

The information provided by the WTLR map also prove the need to realize some of the network

reinforcements planned by the Italian TSO: for instance, the transmission capacity increase of the


Figure 2.45: Critical grid areas of the current Italian transmission system [23]

existing 380 kV line Foggia-Benevento (target year: 2012), the doubling of the 380 kV middle-

Adriatic backbone (target year: 2013/2014), the realization of a new 380 kV double circuit line

between the substations of Camin and Dolo in the North-East (target year: 2011/2013), and the

reinforcement of the network in the area of Milan (target year: 2012).

Assessment of development plan bene�ts. Besides identifying the most critical grid ar-

eas [19, 20], so providing interesting information for transmission planning, the WTLR tool can

be used to demonstrate the bene�ts of completing the realization of all the network reinforce-

ments included in the development plan within the prearranged time limit and thus to assess the

consequences of a possible delay due to some impediment [22].

First a medium-term summer scenario of the Italian EHV system (Scenario A) is considered. A

second scenario (Scenario B) is derived from this one by removing all the network reinforcements

scheduled by the TSO for the �ve-year period 2010-2014. Other simulations are then carried out on

a long-term summer scenario (Scenario C), from which, by eliminating all the grid reinforcements

planned for the �ve-year period 2014-2019, a fourth scenario (Scenario D) is obtained.

Table 2.24 summarizes the main features of the scenarios de�ned to assess the bene�ts of the ten-

year grid development plan [23], while the most important grid upgrades (from north to south)

included in it are listed in Table 2.25.

Tables 2.26 and 2.27 reports the contingency analysis results concerning the medium-term scenar-

ios.

In Scenario B, where the transmission system has the present structure, the major operation

problems, some of which are already in intact system conditions, regard the current inter-zonal


Table 2.24: Scenarios for assessing Italian EHV development plan bene�ts

Table 2.25: Main grid reinforcements (2010 development plan)


Table 2.26: Contingency analysis results - Scenario A

section between Central-South and South, and precisely: the 380 kV lines Benevento-Foggia and

Matera-S. So�a and the Adriatic backbone, through which a large part of the power production

of Southern Italy �ows towards the big load areas in Campania and in Central Italy. Also the

380 and 220 kV transmission system between the North-West and the North-East is a�ected by

considerable power �ows which cause some overloads in N-1 security conditions, so making the

network reinforcements necessary.

The WTLR graphical representation on the bottom of Figure 2.46, pertinent to Scenario B, and

the WTLR map in Figure 2.44, concerning the current Italian EHV system, can be compared to

assess the impact of the medium-term generation expansion on network security. It is clear that,

if the main points of the development plan were not realized by 2014, so making some existing

critical situations worse, the system operation would be very di�cult: the most critical areas

would be Southern Italy, a�ected by a great generation expansion in recent years and where new

thermoelectric power plants and the largest part of the new wind farms expected in the medium-

term will be installed, and to a lesser extent Piedmont.

The comparison of the two maps in Figure 2.46 qualitatively shows the e�ectiveness of the main

network reinforcements planned by the Italian TSO in terms of system security enhancement: their

completion within 2014 will result in an overall congestion alleviation.

As regards the year 2019, the installation of new generation power plants and the electricity

demand growth could give rise to some operation problems, as shown by Table 2.29 and Figure 2.47

(bottom), above all in Central-Southern Italy, despite the medium-term transmission expansion.

The network reinforcements planned for the �ve-year period 2014-2019 will result in a general

improvement, even though the 380 kV line Matera-S. So�a may be still critical because the current

grid development plan does not include the transmission capacity increase of this line.

Assessment of the impact of an increasing wind penetration on network security.

Given the concepts on which the WTLR indices are based, the most obvious use of this tool

by a Transmission System Operator is the assessment of the generation expansion impact on

system security. For instance, consider the medium-term scenario of the preceding paragraph (i. e.

Scenario A). The Italian EHV system model is de�ned taking into account the wind generation

expansion expected in the next few years.

Figure 2.48 shows the geographical distribution of the total wind generation capacity installed in

Italy at the end of 2009.

To get an idea of the wind power capacity that is expected to be in service in the next two years

(2011/2012), the Italian TSO considers the wind farms for which the investors have already taken a

�nancial commitment to cover the grid connection charges. To outline a possible expansion scenario

with reference to the projection horizon 2014/2015, the TSO takes into account the wind farms

for which the grid connection solution has been accepted and a commitment for the preliminary


Table 2.27: Contingency analysis results - Scenario B

Table 2.28: Contingency analysis results - Scenario C

Table 2.29: Contingency analysis results - Scenario D


Figure 2.46: WTLR map - Scenarios A (top) and B (bottom)


Figure 2.47: WTLR map - Scenarios C (top) and D (bottom)


Figure 2.48: Wind generation capacity installed in Italy at the end of 2009

Figure 2.49: Wind generation capacity expected in the medium-term


plan has been undersigned (Figure 2.49).

Most of the wind power plants will be in the south of Italy and in the two major islands: nearly

6500 MW of wind generation capacity are expected in the short-medium term. The long-range

situation in Sicily, Sardinia, Apulia, Calabria, and Campania is particularly signi�cant: they are

the most favourable areas in terms of wind availability, where about half of all Italian wind farms

will be installed. Note that the wind power plants connected to the medium voltage distribution

network are not displayed in Figure 2.49.

To assess the impact of an increasing wind penetration on system security in terms of network

congestion increase, consider two new test cases derived from the medium-term scenarios of the

previous paragraph (i. e. Scenarios A and B) by removing the wind farms that will be realized

within 2014 and that are supposed to be in service [25-27]. A new scheduling of the thermoelectric

units, still resulting from a merit order dispatch, needs to be introduced. For the most part the

wind power generation is replaced by the most competitive CCGT power plants, which may be

located not only in Southern Italy.

As shown on the top of Figure 2.50, the completion of the grid development plan will lead to a

general improvement in terms of congestion alleviation. The security assessment, on which the

WTLR calculation is based, does not detect any power limit violations in Central-Southern Italy,

mainly thanks to the doubling of the middle-Adriatic backbone, the transmission capacity increase

of the 380 kV line Benevento-Foggia, and the new 380 kV line between the future substations of

Deliceto and Bisaccia.

The comparison between Figures 2.46 and 2.50 shows that the installation of the new wind farms

could increase the occurrence of network congestions: this demonstrates, even more clearly, the

need to carry out the development plan of the Italian transmission system, also considering the

increasing wind penetration.

Ranking of grid reinforcements. Consider Scenario B again. Some new test cases are derived

from it by adding one of the main network reinforcements included in the grid development plan

(one for each test case). The goal is to assess the e�ectiveness of the single network reinforcement,

with reference to the scenario chosen for the simulations, and then to outline a possible �ranking�.

The analysis focuses on Central-Southern Italy. Only the most signi�cant tests and results in terms

of congestion alleviation will be described (see Figure 2.51).

� Case B1: transmission capacity increase of the 380 kV line Benevento-Foggia.

The power plants in the area between the regions Apulia and Molise are now limited because

of the insu�cient transmission capacity of the 380 kV network that does not enable them to

be fully exploited to meet the considerable electricity demand of the neighbouring areas. In

anticipation of the new power plants which are expected to be installed in these regions in

the next few years, the transmission capacity of the existing 380 kV line Benevento-Foggia

needs to be increased. For this reasons, the line will be rebuilt by using higher capacity

wires. Table 2.30 summarizes the contingency analysis outcomes pertinent to the new test

case, resulting from the original one, i. e. Scenario B, by increasing the current limit of the

above-mentioned line (from 1600 A to 2400 A). The main e�ect of this grid reinforcement is

to solve the operation problems that a�ect the existing line Benevento-Foggia: the security

assessment does not detect any overload on it. Consequently, there is a notable decrease in

the indices of the nodes in Southern Italy, though they are still quite high, especially on the


Figure 2.50: WTLR map - Scenarios A (top) and B (bottom) without the new wind farms


Figure 2.51: Network reinforcements considered in the study

Adriatic side between the substation of Gissi and the south of Apulia. On the contrary, the

WTLRs of the 380 kV buses of Villanova, Teramo, Rosara, Candia, and Fano decrease. In

particular, the highest and the smallest values refer to the nodes of Gissi St. and Villanova

respectively, since the most critical grid element is the line between these two substations.

� Case B2: doubling of the middle-Adriatic backbone.

The recent development of the electrical system in Southern Italy has led to the limitation of

some power plants, particularly in the areas of Brindisi and Foggia. To overcome these prob-

lems and to avoid further ones in the future, the Italian TSO has planned the reinforcement

of the middle-Adriatic backbone by building a second double circuit line between Foggia and

Villanova. Table 2.31 reports the contingency analysis results concerning this new test case.

It is clear that the doubling of the middle-Adriatic backbone is very important to enhance

the network security. The number of congestions decreases in Central-Southern Italy: the

security assessment detects one violation in the 220 kV transmission system in Campania and

two overloads on the 380 kV line Matera-S. So�a. Therefore, besides solving the operation

problems that a�ect the existing line between the substations of Foggia and Teramo, the grid

reinforcement in question also avoids the congestions on the 380 kV line Benevento-Foggia,

as there is another path to transfer the power production of the generators in Apulia.

� Case B3: new 380 kV double circuit line Montecorvino-Avellino N.-Benevento.

The authorization of new power plants in Calabria, Apulia, and Campania makes the rein-

forcement of the transmission system necessary to remove the limitations on the present and

future power productions due to the occurrence of congestions in the EHV grid in Campania.

The Italian TSO has planned the realization of a new 380 kV double circuit line between


Table 2.30: Contingency analysis results (Benevento-Foggia reinforcement)

Table 2.31: Contingency analysis results (middle-Adriatic backbone reinforcement)


Table 2.32: Contingency analysis results (new line Montecorvino-Benevento)

Montecorvino and Benevento, together with a new 380/150 kV substation to the north of

Avellino that will be connected to both the new line and the existing 380 kV line Matera-S.

So�a. The contingency analysis results are given in Table 2.32. First of all, the construction

of the new line, which makes the 380 kV network more meshed, solves the congestions on the

380 kV line Benevento-Foggia in consequence of the outage of the 380 kV line Avellino Nord-S.

So�a. This is the main e�ect, even if the size of all the other overloads in Central-Southern

Italy diminishes. Nevertheless, this improvement yields only a small decrease in the positive

WTLR values, especially on the Adriatic side, which re�ects the operation problems of the

middle-Adriatic backbone and of the line Benevento-Foggia.

� Case B4: new 380 kV line Deliceto-Bisaccia.

The Italian TSO has planned the construction of a new 380/150 kV substation near Deliceto

in Apulia that will be connected to the existing 380 kV line Foggia-Candela and that will

collect the power productions of the wind farms expected in the area. It will be connected

also to the future substation of Bisaccia and thus to the existing 380 kV line Matera-S. So�a.

The goal is to make the 380 kV grid more meshed and to reduce the risk of congestion, so

removing the probable limitations on the new power plants in Apulia and on the Adriatic

side, including the wind power production in the area of Candela. As shown by the security

assessment results in Table 2.33, the grid reinforcement in question produces an overall

congestion alleviation. The most evident improvement refers to the 380 kV line Benevento-

Foggia which is not overloaded by the outage of the 380 kV lines Teramo-Villanova and Gissi

St.-Villanova any longer: the power �ows that reach the node of Foggia cannot be conveyed

by the middle-Adriatic backbone; in this case they can �ow not only on the line Benevento-

Foggia, but also on the new line Deliceto-Bisaccia and then on the line Matera-S. So�a. Some


Table 2.33: Contingency analysis results (new line Deliceto-Bisaccia)

operation conditions however get worse. For instance, the size of the overloads on the line

Benevento-Foggia following the outage of the line Avellino Nord-S. So�a increases, as the

power �ows on the line Matera-S. So�a, once the substation of Bisaccia has been reached,

can be transmitted by the new line towards the bus of Foggia. Moreover, in case of the

outage of the line Benevento-Foggia, besides the congestion on the line Gissi St.-Villanova,

the security assessment detects also the overload on the line Bisaccia-Avellino Nord: the

power �ows, arrived at the bus of Foggia, have to be conveyed partly by the middle-Adriatic

backbone, partly by the new line Deliceto-Bisaccia, since they cannot �ow on the outaged

line Benevento-Foggia.

To de�ne a priority list of the above grid reinforcements, �rstly we can consider the variation of the

total system overload with respect to the base case (Scenario B), which measures the e�ectiveness

of each transmission upgrade in terms of congestion alleviation with reference to the scenario

considered in the study. A summary of the contingency analysis results is given in Table 2.34.

The number of violations and the system overload provide a clear indication of the e�ects of each

transmission reinforcement. As already shown by the detailed description of each test case, the

largest bene�ts derive from doubling the middle-Adriatic backbone, that will indeed a�ect a grid

section on which the TSO has detected some congestions in certain present operation conditions

and which may become more and more critical in the future in view of the expected generation

system development in South Italy and especially considering the growing utilization of wind power.

Furthermore, compared to the other grid reinforcements, it does not consist in constructing a single

line, or in increasing the current limit of an existing one, but in realizing a set of new lines according

to a well-designed scheme so increasing the available transmission capacity of the grid section and

making it more meshed. Also the calculation of one of the two metrics de�ned and validated for


Table 2.34: Summary of the contingency analysis results

Figure 2.52: WTLR algebraic sum

the CIGRE 63-bus system, that is, the WTLR algebraic sum, strengthens the above conclusions

since it re�ects the size of the reduction of the WTRLs (in absolute value) and consequently of

their algebraic sum in each case (Figure 2.52).

Though the above results provide quantitative data concerning the bene�ts of each transmission

reinforcement, one of the main advantages of the WTLR indices is their ability to be graphically

represented and to supply interesting qualitative information about the most severe congestions

and the most critical grid sections. The next �gures (Figures 2.53-2.56) show the WTLR maps

resulting from the analysis of each test case.

The comparison between the maps before (i. e. relative to Scenario B, see Figure 2.46 on the bottom)

and after adding a grid reinforcement highlights the e�ectiveness of the transmission upgrade in

reducing network congestions in Central-South Italy. This analysis suggests the following priority

order, which is also con�rmed by the total overload values and by the WTLR-based metric:

1. doubling of the middle-Adriatic backbone (12 congestions; total overload = 967.8 MW;

WTLR algebraic sum = +30.49);

2. transmission capacity increase of the line Benevento-Foggia (17 congestions; total overload


Figure 2.53: WTLR map (Benevento-Foggia reinforcement)

Figure 2.54: WTLR map (middle-Adriatic backbone reinforcement)


Figure 2.55: WTLR map (new line Montecorvino-Benevento)

Figure 2.56: WTLR map (new line Deliceto-Bisaccia)


= 2173.5 MW; WTLR algebraic sum = +106.21);

3. new double-circuit line Montecorvino-Avellino Nord-Benevento (21 congestions; total over-

load = 2663.1 MW; WTLR algebraic sum = +137.67);

4. new line Deliceto-Bisaccia (23 congestions; total overload = 2943.1 MW; WTLR algebraic

sum = +155.68).

We can conclude that the transmission planner can get useful information for de�ning a priority

list of a set of grid reinforcements by comparing all the WTLR maps which are immediately

comprehensible to everyone, considering the meaning of the indices.

De�nition of new grid reinforcements. The WTLR methodology has been demonstrated

to be a useful tool for determining the most critical grid elements and sections, given a certain

scenario. Therefore, it can be used to de�ne new network reinforcements to be included in the

development plan.

The contingency analysis results (Table 2.28) and the WTLR map (on the top of Figure 2.47) in

Scenario C, which refers to the projection year 2019, indicate that, considering the scenario under

study, the only overloads are on the 380 kV line Matera-S. So�a between the future substations of

Bisaccia and Avellino Nord in case of the outage of one of the two lines Ariano Irpino-Benevento and

Aliano-Matera. These congestions are probably due to some existing limitations obliging the TSO

to operate the line with a current limit of 1920 A, as well as the development of generation and load

expected in the next decade. To solve these operation problems the transmission planner should

take into proper consideration the transmission capacity increase of the line in question, including

it in the development plan. To simulate the realization of the grid upgrade by 2019, the current

limit of the line Matera-S. So�a is increased from 1920 A to 2400 A in the network model used

for the tests (Scenario C). Since the contingency analysis does not detect any congestion, all the

WTLRs in the long-term are equal to zero and the corresponding map is entirely white-coloured.

2.6.2.3 Interchangeability of generation expansion and transmission development

Considering the basic concept of the WTLR methodology, that is, the strategic generation siting

in favour of system security, and the indications given by the WTLR values concerning the most

suitable grid areas for installing new generating capacity, two 800 MW CCGT power plants are

added to the network model in Scenario B and connected to the lowest WTLR buses in Central-

Southern Italy (Villanova = -1.60 and Benevento = -1.78) [22]. The aim is to evaluate the bene�ts

of the new power injections and their e�ects on grid congestion alleviation. The new generators are

dispatched at their rating, while the power production of Apulia and Abruzzi regions is reduced

by the same amount (Case B5).

The above sites are chosen according to their WTLR so that the power injections of the new CCGT

plants help in alleviating the overloads on the lines Ariano Irpino-Benevento and Gissi St.-Villanova.

Negative-WTLR regions are in fact at the receiving end of at least one congested grid element,

while positive-WTLR areas are at the sending end. Real power injections at a negative-value bus

will therefore produce counter-�ows which will contribute to congestion alleviation.

The security assessment results in Table 2.35 are alike to those obtained by realizing the doubling

of the middle-Adriatic backbone (see Table 2.31). Obviously, the network in Northern Italy is

not a�ected by the power production of the new plants, which instead solve all the congestions


Table 2.35: Contingency analysis results (New CCGT power plants)

Table 2.36: WTLR values at some nodes in Central-South Italy

on the lines Ariano Irpino-Benevento and Gissi St.-Villanova. Also the remaining overloads in

Central-South Italy (on the 220 kV line Frattamaggiore-Starza Grande in Campania region and on

the 380 kV line Teramo-Rosara in Marche region) are practically the same.

The WTLR values of some 380 kV nodes in Central-Southern Italy are in Table 2.36 with refer-

ence to Scenario B, Case B2 (i. e. doubling of the middle-Adriatic backbone), and Case B5 (i. e.

installation of new CCGT plants).

The comparison between the second column and the last one shows that the installation of new

generating capacity at Villanova and Benevento buses signi�cantly improves the network security.

The third and fourth columns con�rm the above considerations on the outcomes of the contingency

analysis. The WTLRs are in fact nearly the same, as the security assessment results are alike.

The tests on Case B2 and Case B5 demonstrate the interchangeability of generation and trans-

mission expansion and especially that, if appropriately located, the real power injection of a new

generating unit may have the same e�ect of a grid reinforcement in terms of system security en-

hancement. Moreover, they prove that the WTLR methodology can be useful to achieve a more

coherent development of the whole power system thanks to a more coordination between generation

expansion and transmission development.


2.7 Chapter conclusions

Restructuring have introduced competition in the generation and, in some cases, in the retail

segments of the electric power industry. A common element of restructuring is the unbundling of

generation and transmission, with the latter being opened for use by all eligible market participants

under the so called open-access regime. This has greatly transformed the traditional power industry

and introduced many new challenges in all aspects of generation, transmission and system operation

and planning.

The unbundling of generation, transmission, and distribution has resulted in multiple parties in

the business. To foster competition and pre-empt market power abuse, some jurisdiction required

generation divestiture to create more independent generation owners. The generation enterprises,

unlike the integrated utility of the regulated world, have di�erent and sometimes con�icting ob-

jectives. The presence of new structures and the diversity of the many new players in electricity

markets have fundamentally invalidated some assumptions and relationships of the traditional

planning process, bringing new challenges especially to the transmission planning problem.

In the restructured industry, generation expansion decisions are made by individual generation

companies, often not completely known to the authority responsible for transmission planning.

Indeed beyond the �ve- or ten-year horizon, generation scenarios are largely unknown. Moreover,

generation expansion decisions may be a�ected by decisions on transmission expansion and vice

versa. All these aspects resulting from the electricity industry restructuring and liberalisation

may cause a con�ict between generation owners' investments and transmission planners' decisions,

especially because of the diversity of their interests and objectives. This lack of coordination in the

planning process may be a serious problem for the operation of power systems, that are large-scale,

integrated, and complex engineering systems, which intrinsically need a certain level of centralized

coordination to function. In particular, it may have heavy repercussions on network security and

hence on electricity market e�ciency and social welfare.

The chapter has shown the interchangeability of generation and transmission investments and

particularly it has highlighted that generation expansion may have the same (positive) e�ect of

a transmission reinforcement on power system security. The WTLR methodology is based just

on this concept, which suggests the advantages of strategic generation siting not only for network

security enhancement, but also for better and more e�ciently exploiting the available generation

park.

A procedure for the calculation and graphical representation of WTLRs has been implemented

in the Matlab programming language and described in detail in the chapter. It has been applied

to a test system (CIGRE 63-bus network) in order to check the outcomes' correctness. Besides

identifying the most suited network sites for installing new generating units, which is the basic

idea of the WTLR methodology, the contingency analysis results and the consequent WTLR map

provide useful information also about the most critical grid areas and elements. Some simulations

have been performed considering a possible set of new transmission lines for the CIGRE network.

The choice of the grid reinforcements and in particular the selection of the new lines' endings have

been based on the WTLR values: the �from bus� has a negative index, while the �to bus� has a

positive one, so that the new line will certainly alleviate grid congestions and improve network

security. Then a priority list of the new lines has been de�ned according to the total system

overload decrease achieved thanks to each new grid element. This ranking has been validated from

an economic perspective by calculating the social welfare increase by means of an Optimal Power


Flow procedure. Two simple indicators, which can be used to prioritize transmission planning,

have been proposed: the algebraic WTLR sum, which can be considered a �measure� of overall

system security, as well as the total system overload, and an index that can estimate which new

connection will have the greatest marginal bene�t to network security.

The tests on the CIGRE 63-bus system have suggested some possible modi�cations to be made in

the proposed procedure coded in the Matlab programming language.

The �rst objective has been the reduction of the total computational time. The most time-

consuming phases are the standard contingency analysis, carried out by a sequence of AC load

�ow calculations (one for each line outage), and the calculation of ISDFs in N-1 security condi-

tions. The Line Outage Distribution Factors (LODFs) have been introduced in the determination

of the real power �ows on grid branches in post-contingency conditions, so substituting the stan-

dard contingency analysis. To further speed up the Matlab-coded program, another simpli�cation

has been considered: using the base ISDFs to compute the WTLR indices. The e�ect of these two

approximations has been investigated, showing that they do not cause large errors. The second

objective has been to remove the WTLR dependance on the selection of the slack bus in the grid.

The concept of distributed slack bus has been introduced in both load �ow calculations and ISDF

computation. The simulations have shown that in any case the most correct choice is to assume

a distributed slack bus model, but at the same time they have highlighted that the results can be

little a�ected by the �only one slack bus� assumption on condition that the slack bus is suitably

selected among the grid nodes.

The second part of the chapter refer to the tests on the Italian EHV electric system. First,

the most important limit of the original methodology has been pointed out. The impact of the

MVA rating approximation (i. e. the approximation that the line MVA rating is a MW limit,

so disregarding both the actual voltage magnitude and the power factor) on security assessment

results and WTLR sensitivities has been investigated by means of a standard steady-state security

assessment tool. The check has shown that the MVA rating approximation introduces notable

errors in the contingency analysis results. Therefore, the original Matlab-coded program has been

suitably modi�ed by considering the actual power �ow limits in the calculation of the branch

overloads. The WTLR tool has been then applied to di�erent test cases in order to demonstrate

its usefulness for generation and transmission planning. Although the basic idea of the WTLR

methodology is the strategic generation siting to improve power system security, it can be a helpful

tool also for generation owners, that can bene�t from an appropriate selection of the locations for

installing new power plants: considering the suggestions given by WTLRs in the de�nition of the

expansion plan, the risk of possible limitations due to some network constraint could be reduced.

Moreover, given a certain set of possible new generation sites, the WTLR indices can be used to

de�ne a priority list. Since the fundamental objective at which the WTLR methodology aims is

power system enhancement and this is one of the main tasks of system operators, the obvious

application of the tool is transmission planning. The tests on the Italian EHV network have shown

some of its potential uses. The transmission planner can make use of it to identify the weakest

grid sections and elements, to demonstrate the bene�ts of the grid development plan, to assess the

impact of generation expansion on network security, to de�ne possible priority lists of planned grid

reinforcements, and to determine new network enhancements.

The WTLR sensitivities have therefore proved to be a simple, but e�ective instrument for both

generation and transmission planning. It is based on simple concepts since it is founded on load

�ow calculations and sensitivity computations. But at the same time it is e�ective especially thanks


to the graphical representation of WTLRs which, though provides only qualitative information, is

extremely intelligible. We can conclude that its main advantage is to allow a more coherent devel-

opment of the whole power system to be attained, since it exploits the concept of interchangeability

of generation and transmission.

Chapter 3

Reactive power service

Traditionally, electric utilities have been vertically integrated monopolies that have built gener-

ation, transmission, and distribution facilities to serve the needs of the customers. For the past

decade, the electric power industry has been going through a process of transition and restruc-

turing by moving away from vertically integrated monopolies and towards competitive markets.

This has been achieved through a clear separation between transmission and generation activities

(unbundling), as well as by creating competition in the generation sector. The restructuring pro-

cess has created certain class of services such as frequency regulation, voltage and reactive power

control, energy imbalance, and generation and transmission reserves, which are essential to the

power system in addition to the basic energy and power delivery ones. This class of services is

referred to as ancillary services, and they are indispensable to ensure system security, reliability,

and e�ciency. Ancillary services are no longer an integral part of the electricity supply, as they

used to be in the vertically integrated power industry structure, since they are now unbundled and

also priced separately. So the main issues are to identify what kind of services are indispensable to

ensure the electricity supply with certain quality standards, to de�ne the most suitable methods

for their acquisition, to evaluate the exact amount of each service that is necessary to operate the

system reliably, and �nally to set up the proper remuneration mechanisms for the suppliers, if the

regulation provides for this eventuality.

In a competitive environment, the provision of these services must be carefully managed so that

the power system requirements and market objectives are adequately met. The System Operator

is the entity entrusted to their acquisition through commercial transactions with ancillary services

providers. Currently, there is not a single international classi�cation of ancillary services, but each

electricity market has its own de�nition. There are however similarities in the de�nition of the

ancillary services in the di�erent contexts, at least regarding their functions. The main di�erences

are usually in the methods adopted for their provision and remuneration.

Reactive power and voltage support is recognized as ancillary service, since it is essential to ensure

a secure power system operation. From this perspective, the objectives are essentially the main-

tainance of appropriate voltage pro�les in all grid nodes, so guaranteeing certain standards of power

quality, and of su�cient, well-distributed reactive power margins to compensate for disturbances

in case of contingency.

But, in the competitive electricity market environment, the provision of such a service must take

into account the economics in addition to the technical and physical considerations and so depends

on the market players and the electricity market rules. In particular, competition in generation

91

CHAPTER 3. REACTIVE POWER SERVICE 92

makes it important to consider the development of a reactive power market that complements the

existing energy market. Although the cost of reactive power production is much less than that of

real power, reactive power is critical to system reliability since its su�cient provision is necessary

to avoid an extremely costly system collapse. Moreover, under stressed system conditions, reactive

power requirements from some generators are only met at the expense of reducing their real power

output, and hence they signi�cantly increase the cost associated with reactive power production.

Besides this new aspect deriving from the restructuring and liberalisation of the electricity industry,

the increasing attention towards renewable sources and especially towards wind energy has raised

another important issue for power system operation and in particular for reactive power provision.

Wind farms that are large enough to be connected to the transmission system tend to be erected

in remote areas or even o�shore because of their dimension and impact on the scenery. Given that

the bus voltage is a local quantity, it can be di�cult to control the voltage at these distant places

by use of conventional power stations elsewhere in the grid. Therefore, wind turbines are required

to have voltage control capabilities. The voltage control capabilities of wind turbines are becoming

an increasingly important consideration regarding grid connection and also the turbines' market

potential. Furthermore, large-scale wind farms may make it necessary to install voltage control

devices in the transmission network, irrespective of the voltage control capabilities of the wind

turbines themselves: even if the wind turbines have exactly the same voltage control capabilities

as the conventional synchronous generators whose output they replace, there will be no guarantee

that they can ful�l the voltage control task of these generators. Therefore, it may be unavoidable

to consider and take additional measures to control the grid voltage.

These issues will be investigated in the chapter, and in particular an approach, based on an

Optimal Reactive Power Flow (ORPF) procedure, aiming at solving the optimal reactive power

provision problem, considering the di�erent views of buyers and sellers (i. e. the System Operator

and the producers), will be considered. It will allow the determination of the value of VAR support

required to the generation buses for the ful�lment of the constraints imposed by a secure and

economic system operation, while suggesting a suitable �nancial compensation scheme for reactive

power service and above all the implementation of a zonal reactive market based on the Secondary

Voltage Regulation areas. The simulation analyses will focus also on the perspective impact of large

wind power injections on the voltage control performances in the Italian EHV electrical system.

In particular, the outcomes will evaluate the economy and security level achievable in the Italian

system at 2014 peak-load under optimal reactive power schedules. Finally, the tests will allow the

e�ects of the planned network reinforcements to be assessed.

3.1 Ancillary services

As anticipated, the identi�cation of the ancillary services can be di�cult because there is not

a single de�nition internationally recognized. In fact, di�erent approaches can be adopted for

de�ning them.

3.1.1 De�nitions in the U.S. markets

In its Order 888 [28], the Federal Energy Regulatory Commission of the United States of America

(FERC) de�nes ancillary services as �those services necessary to support the transmission of electric

power from seller to purchaser given the obligations of control areas and transmitting utilities within


those control areas to maintain reliable operations of the interconnected transmission system�.

FERC Order 888 requires transmission providers to include six ancillary services in an open-access

transmission tari� to maintain reliability within and among the control areas a�ected by the

transmission service. These six services are divided into the following two categories:

� Services that FERC requires transmission providers to o�er and customers to accept from

the transmission provider, and these include:

� scheduling, system control, and dispatch: this service is required to schedule the move-

ment of power through, out of, within, or into a control area in order to maintain

supply-demand balance;

� reactive supply and voltage control from generation sources: the System Operator re-

quires generators to produce (or absorb) reactive power in order to maintain the system

bus voltages within some desired limits.

� Services that FERC requires transmission providers to o�er but which customers can accept

from the transmission provider, third parties, or by self-supply, and these include:

� regulation and frequency response: the use of generation equipped with governors and

automatic generation control (AGC) to follow the instantaneous change in the load in

order to maintain continuous generation-load balance within the control area, and a

scheduled interconnection frequency at 60 Hz;

� energy imbalance: the use of generation to correct for hourly mismatches between actual

and scheduled delivery of energy between suppliers and their customers;

� operating reserve - spinning: spinning reserve service is provided by unloaded generating

units that can respond immediately to correct for generation-load imbalance in the event

of a system contingency;

� operating reserve - supplemental: supplemental reserve service is provided by unloaded

generating units, by quick-start generation, or by interruptible load to correct for

generation-load imbalance in the event of a system contingency; however the response

does not have to be immediate, as in case of spinning reserve, but rather within a short

period of time.

FERC does not specify technical details of the services, and the costing methods for the services

remain ad hoc, varying widely from one provider to another.

Some organizations, including the North American Electric Reliability Council (NERC), do not

agree with the de�nition given by FERC and especially with the name �ancillary services�, since

these services are not auxiliary, but an integral part of the transmission utilities.

In their technical report [33] Hirst and Kirby presents a survey based on the work of several others,

including FERC [28], Houston Lighting & Power [34], the Michigan Public Service Commission [35],

the New York Power Pool [36], and the North American Electric Reliability Council [37]. This

technical report de�nes the ancillary services as those functions performed by electrical generating,

transmission, system-control, and distribution system equipment and people to support the basic

services of generating capacity, energy supply, and power delivery. The authors thus develop the

set of ancillary services by identifying those services that are essential to maintain electric system

reliability, are required to e�ect a transaction, or are a consequence of a transaction. They instead


exclude the services that are optional, long-term in nature, too cheap to warrant the costs of

metering and billing, naturally bundled with other services, or very location speci�c. The set of

services comprises scheduling and dispatch and several generating services, such as load following,

reliability, and supplemental reserves, as well as loss replacement and energy imbalance. Finally,

it includes system voltage control, which requires both generating units and transmission system

equipment.

NERC follows up on FERC's initiative by conducting its own more technical study to identify

ancillary services. In particular, NERC refers to ancillary services as Interconnected Operation

Services (IOS) [37], so emphasizing their essential role in the reliable operation of interconnected

bulk electricity systems as the U.S. one. Together with the Electric Power Research Institute

(EPRI), NERC de�nes twelve IOS that are necessary to support the transmission of power at an

adequate level of reliability and security; some of these services are similar to the six ancillary

services required by FERC. They are:

� regulation: using generation or load in order to maintain a minute-to-minute generation-load

balance within the control area;

� load following: the provision of generation and interchange capability required to maintain

the hour-to-hour and daily load variations not covered by regulation service;

� energy imbalance;

� operating reserve - spinning;

� operating reserve - supplemental;

� back-up supply: electric generating capacity used to replace a generation outage or the failure

to deliver generation due to an outage of transmission sources, and to serve a customer's load

that exceeds its generation;

� system control: activities that are required to ensure the reliability of the North American

interconnections, to minimize transmission constraints, and to guarantee the recovery of the

system after a contingency or disturbance;

� reactive power and voltage control from generation sources;

� network stability services from generation sources: using special equipment or devices, such

as power system stabilizers and dynamic braking resistors, at the generating plants to meet

NERC reliability requirements and maintain a secure transmission system;

� system black start capability: the availability of generating units that can start without an

outside electrical supply to take part in the restoration plan after a system blackout;

� real power transmission losses: the provision of capacity to replace energy losses on a trans-

mission system;

� dynamic schedule: the provision of the real-time monitoring, telemetering, computer software,

hardware, communications, engineering, and administration that are needed to electronically

move real energy services associated with generation or load out of its Host Control Area

and into a di�erent Electronic Control Area.

NERC IOS Working Group also identi�es an Ancillary Services Market Framework consisting of

two distinct parts: a resource supply market and an ancillary service delivery market [29].


3.1.2 Ancillary services in Europe

The European Directive 2003/54/EC [30] says: �ancillary services means all services necessary for

the operation of a transmission or distribution system�. Among the tasks of Transmission System

Operators, it indicates the responsability for �ensuring a secure, reliable and e�cient electricity

system and, in that context, for ensuring the availability of all necessary ancillary services insofar

as this availability is independent from any other transmission system with which its system is

interconnected�.

European UCTE Operation Handbook [31] gives the following de�nition: �Ancillary services are

Interconnected Operations Services identi�ed as necessary to e�ect a transfer of electricity between

purchasing and selling entities (transmission) and which a provider of transmission services must

include in an open access transmission tari��.

Ancillary services are de�ned by the Union of the Electricity Industry - EURELECTRIC [32]

as �all services required by the transmission or distribution system operator to enable them to

maintain the integrity and stability of the transmission or distribution system as well as the power

quality. Ancillary services are procured by the system operators and are provided by network

users (generators, customers) or system assets�. Acknowledging that several further ancillary

services can be and currently are de�ned in di�erent countries, this report discusses the following

ancillary services: frequency control, voltage control, spinning reserve, standing reserve, black-start

capability, remote automatic generation control, grid loss compensation, and emergency control

action.

A possible general cathegorization is:

� interconnection services:

� frequency response;

� special protection schemes: generator tripping and load shedding;

� generation-demand imbalance services:

� regulation;

� load following;

� contingency reserves: spinning and non-spinning reserves;

� local services:

� reactive support;

� black-start.

3.1.3 The Italian ancillary services

As regards the Italian situation, the ancillary service topic has been treated according to the

guidelines of the European Directive 96/92/EC [38], which have been formally acknowledged by

the Italian Regulatory Authority (Autorità per l'Energia Elettrica e il Gas - AEEG) in [39].

The de�nition of ancillary services accepted in Italy is the following: �set of all the activities

that need to be performed to support the power transmission while maintaining a reliable system

operation and ensuring the required standards of quality and security� [40].


The provision of ancillary services by the System Operator is regulated by the regulatory order

168/03 [41], that says:

� in the market for ancillary services, according to its own needs, the System Operator provi-

sions the resources necessary:

� for congestion management;

� to create su�cient reserves;

� to maintain the supply-demand balance in real-time.

� the System Operator organizes the market for ancillary services, which is subdivided into

several phases, consistent with the following objectives and criteria:

� to minimize the costs and to maximize the revenues resulting from the provision;

� to give market participants a clear signal of the economic value of the resources indis-

pensable to the electric system operation;

� to allow market participants to bid according to their cost structures through an appro-

priate de�nition of resources' typologies, market mechanisms, and bids' format;

� to allow the provision costs of the di�erent resources to be clearly identi�ed.

The fourth chapter of the Italian Grid Code [8] deals with the so called �dispatching rules� and in

particular it identi�es the resources indispensable to ensure a secure system operation and certain

standards of power quality:

� resources for congestion management;

� resources for primary reserve: they are used to automatically correct for the istantaneous

generation-load imbalance in the whole European interconnected grid;

� resources for secondary reserve: they are used to compensate the generation-load imbalance

within the Italian system;

� resources for tertiary reserve: they are used to constitute adequate capacity margins;

� resources for energy imbalance in real-time: they are used to maintain the supply-demand

balance, to solve the network congestions, and to restore the necessary margins of secondary

reserve;

� reactive reserve for primary voltage regulation;

� reactive reserve for secondary voltage regulation;

� black-start service;

� load-rejection service, that is, a generation group must maintain its stability in the case of

its disconnection from the grid;

� interruptible load service: it consists in the disconnection of load from the synchronous elec-

tric system, usually performed automatically, to control the system frequency in emergency

situations, and it can be used by the System Operator if the provision of resources in the

market for ancillary services is insu�cient to ensure a secure system operation.


3.2 Reactive power

3.2.1 What is reactive power?

Almost all bulk electric power is generated, transported, and consumed in alternating current

networks. Elements of AC systems supply (or produce) and consume (or absorb or lose) two kinds

of power: real and reactive power. Real power accomplishes useful work, while reactive power

supports the voltages that must be controlled for system reliability.

In an AC electrical system, voltage and current pulsate at the system frequency and thus are

described mathematically by sine waves. Voltage is a measure of the potential energy per electric

charge, and current is a measure of the average velocity at which electrons are moving.

Although AC voltage and current pulsate at the same frequency, they peak at di�erent times.

Power is the algebraic product of voltage and current. Over a cycle, power has an average value,

called real power, measured in watts. There is also a portion of power with zero average value that

is called reactive power, measured in vars. The total power is called apparent power, measured in

volt-amperes.

Reactive power has zero average value because it pulsates up and down, averaging to zero; reactive

power is measured as the maximum of the pulsating power over a cycle. Reactive power can be

positive or negative, depending on whether current peaks before or after voltage. By convention,

reactive power, like real power, is positive when it is �supplied� and negative when it is �consumed�.

Absorbing reactive power lowers voltage magnitudes, while producing reactive power increases

voltage magnitudes.

Reactive power in an electric transmission system is just the pulsating transfer of stored energy

between various kinds of electrical components in the system. Because voltage and current are

pulsating, the power on a transmission line also pulsates. In a transmission system, this pulsating

transfer of stored energy results in a loss of power called line losses. Real and reactive power are

in quadrature (90 degrees out of phase) and hence the letter Q is commonly used to designate

reactive power. Real power is commonly designated as P.

Reactive power takes up space on transmission lines. For a transmission line, the square of the real

power plus the square of the reactive power must be less than the square of the thermal capacity

(measured in volt-amperes) of the line. When thermal capacity is exceeded signi�cantly for a

long time, the line will sag, possibly into vegetation, causing a short circuit, or anneal, resulting

in structural damage. Real power losses in transmission lines are proportional to the current in

the line. Because power is the algebraic product of voltage and current, the same power at high

voltages has a lower current, and hence, has lower losses.

Reactive power is di�cult to transport. At high loadings, relative losses of reactive power on

transmission lines are often signi�cantly greater than relative real power losses. Reactive power

consumption or losses can increase signi�cantly with the distance. Transmission losses lead to the

expression that reactive power does not travel well. When there is not enough reactive power

supplied locally, it must be supplied remotely, causing larger currents and voltage drops along the

path [43].

3.2.2 The need for reactive power

Reactive power is directly associated with voltage, and thus voltage control is achieved in electric

power systems by absorbing/delivering reactive power. Voltage control, which implies maintaining


the voltage at each bus in the system within de�ned limits, is important for proper operation

of electric power equipment to prevent damage such as overheating of generators and motors, to

reduce transmission losses, and to maintain the ability of the system to withstand disturbances,

such as system faults, loss of generation, or transmission line outage, and prevent voltage collapse.

In general terms, decreasing reactive power causes voltages to fall, while increasing reactive power

causes voltages to rise. A voltage collapse occurs when the system is trying to serve much more

load than the voltage can support.

Inadequate reactive power supply lowers voltage; as voltage drops, current must increase to main-

tain the power supplied to the loads, hence causing the lines to consume more reactive power and

the voltage to drop further. Moreover, if current increases too much, transmission lines will trip,

overloading other lines and eventually causing cascading failures. If voltage drops too low, some

generators will automatically disconnect to protect themselves. Voltage collapse occurs when an

increase in load or loss of generation or transmission facilities causes dropping voltage, which leads

to a further reduction in reactive power from capacitors and line charging, and still further voltage

reductions. If the declines continue, these voltage reductions cause additional elements to trip,

leading to further reduction in voltage and loss of load. The result is a progressive and uncontrol-

lable decline in voltage, because the power system is unable to provide the reactive power required

to supply the reactive power demand.

Insu�cient reactive power at key locations in the system can also result in the inability to transfer

active power beyond a level that is often well below other system limits. As regards this issue, in

order to ensure a secure power system operation, the System Operator has to check the technical

feasibility of potential transactions resulting from energy market clearing; only the transactions

that are within the grid transfer capabilities are allowed. This is particularly important since

currently, electricity markets are usually operated under stressed loading conditions due to the

increased demand and power transfers, so increasing the risk of stability problems. Under such

conditions, system stability limits can be approximated through voltage stability limits.

Finally, reactive power is not only necessary to operate the transmission system reliably, but it can

also substantially improve the e�ciency with which real power is delivered to customers. Increasing

reactive power production at certain locations (usually near a load center) can sometimes alleviate

transmission constraints and allow cheaper real power to be delivered into a load pocket [43].

3.2.3 Reactive power and blackouts

Insu�cient reactive power supply can result in voltage collapse, which has been one of the reasons

for some major blackouts worldwide.

Voltage collapse occurred in the United States in the blackouts of July 2, 1996, and August 10,

1996, on the West Coast. Voltage collapse also factored in the blackouts of December 19, 1978,

in France; July 23, 1987, in Tokyo; March 13, 1989, in Québec; August 28, 2003, in London;

September 23, 2003, in Sweden and Denmark; September 28, 2003, in Italy [43].

While the August 2003 blackout in the United States and Canada was not due to a voltage collapse

as that term has been traditionally used, the �nal report of the U.S.-Canada Power System Outage

Task Force said that �insu�cient reactive power was an issue in the blackout�: dynamic capacitive

reactive power supplies were exhausted in the period leading up to the blackout. The Task Force

also recommended strengthening the reactive power and voltage control practices in all NERC

Regions [44].


3.3 Reactive power support as ancillary service

As explained in the preceding section, reactive power needs to be managed in a way to ensure

su�cient amounts are produced to meet demand and so that the electric power system can operate

e�ciently. If reactive power is not properly managed, signi�cant problems such as abnormal

voltages and system instability can occur. Appropriate regulatory policies are thus necessary to

ensure an adequate supply of reactive power at reasonable cost. The rules for procuring reactive

power can a�ect whether adequate reactive power supply is available, as well as whether the supply

is procured e�ciently from the most reliable and lowest-cost sources.

In the past vertically integrated framework, the reactive power management had three main ob-

jectives: maintaining a proper voltage level throughout the network under both normal and post-

contingency operating conditions, minimizing the real power losses, and reducing the risk of current

and voltage violations. In this environment both investment and operation costs regarding reactive

power management were included in transmission and ditribution tari�s and then charged to end

users. The precise knowledge of the power system status and in particular of the generators' avail-

ability allowed the vertically integrated utilities to take the optimal management decisions and to

ful�l all operating requirements. Moreover, the planning and development of reactive resources

were related to that concerning the active ones in the medium-long term.

The restructuring of the electricity industry makes it necessary to revise, from both technical

and economic viewpoint, the methodologies adopted for power system planning, operation, and

control. As regards reactive power service, the general guidelines are still substantially good, while

the provision mechanisms by the System Operators may change.

Currently, most System Operators procure reactive power services from available providers based

on operational experience and expected voltage problems in the system. In real-time, most System

Operators use power �ow programs to dispatch reactive power from the already contracted gen-

erators. There are however several issues and concerns associated with the current procurement

practices and pricing policies for reactive power which call for further systematic procedures to

have more e�cient service management and su�cient reactive power support for a more reliable

power system. Some of these issues are technical limitations associated with power system opera-

tion, while others are policy issues related to the rules under which the electricity market operates

in a certain jurisdiction. These issues have to be carefully examined in de�ning correct provision

and remuneration mechanisms. New policy solutions need to be proposed that �t into the new

shift of paradigm of power system operation. In a competitive electricity market, the objective of

the System Operator should be to provide reactive power ancillary services from possible service

providers at the least cost, while ensuring a secure operation of the power system. Appropriate

pricing structures and payment mechanisms are necessary to achieve such an objective.

An overview of the main general issues related to the procurement and management of reactive

power and voltage support services is proposed in the following subsections [43].

3.3.1 Technical issues

Technical issues include the following:

� The high losses associated with transferring reactive power require that it should be provided

locally. The reactive power procurement therefore depends on the availability of local reactive

power sources. This may result in fewer suppliers generally available to provide the reactive


power needed at any individual location. These suppliers are likely to have signi�cant market

power. Moreover, such characteristics imply that reactive power cannot be treated as a

commodity of the same type as real power.

� The value of 1 Mvar support with respect to voltage control and system security varies across

the system. The bene�ts of reactive power from generators, with respect to system security,

have to be considered in the provision of reactive power.

� It is necessary to consider the e�ect of reactive power production of a synchronous genera-

tor on its real power generation. In particular situations reactive power requirements from

a generator can only be met at the cost of reducing its real power output (the so called

opportunity costs1).

� Spot energy market prices are volatile, and they a�ect reactive power prices. This will be a

signi�cant issue if reactive power is managed in the same time frame of real power, since in

this case reactive power prices will be highly a�ected by the energy market prices.

� There are two ways of providing reactive power service: short-term dispatch versus long-term

procurement. If reactive power is provided based on a short-term dispatch, several issues such

as energy market price volatility and the e�ect of reactive power on real power and system

security will arise. On the other hand, long-term procurement can solve most of these issues,

but it does not consider real-time operating conditions.

3.3.2 Policy issues

Policy issues include the following:

� Optimal procurement of reactive power is not always achieved since the System Operators

do not always purchase reactive power at least-cost. In a competitive market environment,

reactive power services should be e�ciently provided from the most reliable and lowest-cost

sources.

� Reactive power ancillary services are not provided by considering all available sources; only

reactive power from generators is considered as an ancillary service and is eligible for �nancial

compensation. This decreases competition due to a lower number of market participants, and

allows the market power to be exercised by certain service providers.

� Poor �nancial incentive and discriminatory payments may result in generators not being

equally compensated. Unless reactive power suppliers are encouraged to participate in fair

agreements, they will not be willing to provide these services. This may impede adequate

and su�cient provision of reactive power support, and it may result in limited number of

service providers, leading to an ine�cient market operation.

1A generator's capacity constraint, which is usually called the loading capability diagram (see Appendix E), playsan important role in calculating its opportunity cost. The capacity constraint is the restriction on the operation ofa generator, which is limited by the synchronous generator armature current limit, the �eld current limit, and theunderexcitation limit. Because of these limits, the production of reactive power may prevent some other alternativecapacity usages. The highest value of the alternative capacity usage is de�ned as the opportunity cost of reactivepower. Assume that the capacity of a generator is used only for producing P and Q and the markets for buying andselling P and Q are always available. According to the de�nition of opportunity cost, the value of the alternativecapacity usage for Q is the pro�t of P that can not be achieved by producing Q [45].


� There is a lack of transparency and consistency in planning and procurement process for

reactive power services. This may result in an ine�cient supply of reactive power support,

since reactive power needs and reserves are not clearly de�ned by existing standards.

� Interconnecting standards are assumed to be insensitive to local needs, i. e. without consid-

ering that reactive power needs may vary from one location to another.

3.3.3 A challenge for System Operator and Regulatory Authority

3.3.3.1 Optimal provision for reactive power service

As already explained, in a liberalised electricity market framework the System Operator has to

ensure the same standards of quality and security guaranteed by the past vertically integrated

utilities, but it may have di�culties in meeting these requirements because electricity generation

and distribution do not fall under its competence any longer. This situation is even more compli-

cated with regard to voltage control, considering the di�culties of reactive power to be conveyed

over long distances, the variety of resources and equipments that can be exploited to provide the

reactive power service,2 and the resulting di�culties of their well-coordinated management.

Reactive power provision by the System Operator should be achieved in an optimal manner, and

the choice of an appropriate optimization criterion is essential for the development of competitive

reactive power provision mechanisms. But: what is the best optimization criterion to be adopted

by the System Operator? What is the optimization objective to determine the system reactive

power schedules? Should it be system loss minimization, as has been the usual practice, or should

it be system security maximization or reactive power cost minimization?

3.3.3.2 The e�ect of reactive power on real power and system security

The main function of a synchronous generator is to generate real power to meet the system demand.

Under critical conditions, the System Operator may request or instruct a generator to increase its

reactive power output, which may require a reduction in its real power production. The reactive

power capacity of a synchronous generator is determined by its capability curve, representing its

ability to simultaneously produce real power and generate/absorb reactive power (Figure 3.1).

The boundary of the feasible operating region of the generator is formed by the intersection of

four physical limiting relationships: the minimum loading, the �eld current (�eld heating limit),

the armature current (armature heating limit), and the under-excitation of the generator (under-

excitation limit) [46].

A possible partitioning of the area contained by the generator capability curve into three regions to

represent speci�c operation regimes of the generator has been proposed in [47]. The three-region

model consists of:

1. the obligation to serve region within the capability curve area delimited by the regulatorily

mandated constraints, such as lead/lag power factor or reactive power limits, under which

service is provided;

2. the boundary region speci�ed by the capability curve with the operation of the generator at

its reactive power limits;

2See Appendix E.


Figure 3.1: Example of a synchronous generator loading capability diagram

3. the remaining region in the area contained by the capability curve and not belonging to either

of the two regions above.

Operation in the obligation to serve region is not eligible for any additional payment. The operation

in the boundary region may receive payment to compensate for the reduction in the real power

generation so as to allow the required change in the reactive power. Such a change incurs a

loss of opportunity to generate real power and should be, therefore, eligible for opportunity cost

payments for this loss [48]. So any reactive power generation requested by the System Operator

in the boundary region will require a decrease in the real power generation from the already

dispatched levels. Such an e�ect on real power dispatch should be considered when modeling the

reactive power dispatch problem.

The re-scheduling in real power generation associated with an increase in the reactive power re-

quirements may result in an insecure operation of the power system. Hence, the System Operator

needs to check the technical feasibility of the resulting solution after reactive power dispatch pro-

cedures are completed. Therefore, in order to ensure a reliable and secure system operation, it is

important to incorporate system security in the reactive power provision procedures by including

appropriate transmission security constraints, and to consider the e�ect of reactive power dis-

patch on real power dispatch and system security. Transmission security constraints are typically

represented by voltage, thermal, and stability limits.


3.3.3.3 Reactive power management: dispatch versus procurement

Reactive power provision can possibly be managed as a short-term provision in which it is dis-

patched from available generators based on real-time system operating conditions. It may be also

managed as a seasonal provision in which it is procured based on long-term agreements between

the System Operator and the service providers. If reactive power is managed concurrently with

the energy market clearing process, some problems may arise such as price volatility and the e�ect

of reactive power on real power and system security.

Currently, most System Operators sign long-term contracts with reactive power service providers,

based on operational experience and knowledge of the system and the expected voltage problems.

In real-time, most System Operators run power �ow programs to determine the required reactive

power dispatch levels from contracted providers. The System Operator has to check if the solution

of the power �ow is not violating any of the security limits. In the case when generators are

operating in the opportunity region, where they are required to back-up their real power generation

to meet the reactive power requirements, the System Operator needs to check if the resulting

operating point after re-scheduling of real power is secure or not.

3.3.3.4 Reactive power remuneration schemes

In a competitive market environment, if reactive power service providers are not properly compen-

sated for their service, they will not have enough incentive to provide the required reactive power

support, which will a�ect the power system operation and security. An important issue that arises

with regard to reactive power markets is then the choice of an appropriate remuneration mecha-

nism. Should it be a market-based auction mechanism where the suppliers provide their reactive

power bids to the System Operator, which in turn determines the best reactive power price using an

appropriate objective function? If so, should it then be a uniform price market for reactive power

with a single reactive power price for the whole system, or a zonal level reactive power auction

market where the system is divided into zones, and separate reactive power prices are determined

for each zone? Should a Locational Marginal Price (LMP) market, in which reactive power price

varies across each bus, be used? If there is no auction market, then reactive power payments could

be set on a contractual basis, with the System Operator entering into bilateral agreements with

the service providers and signing long-term contracts for the required reactive power services.

3.3.3.5 Energy price volatility

Energy prices can be highly volatile under certain system conditions, such as demand spikes or

outages. In a short-term operational time-frame, volatile energy market conditions might have an

impact on reactive power procurement and dispatch procedures.

3.3.3.6 Reactive market power

One of the primary obstacles to the implementation of a competitive market for reactive power

is the possibility of market power arising because of the limited number of reactive power service

providers at a given location. Furthermore, reactive power is a �local� service, and so it must be

procured and provided as close to the demand buses as possible because of the technical issues

associated with transporting reactive power over long distances. Thus in a reactive power market,

it is plausible that some �well-located� suppliers may try to exercise market power by submitting


excessively high price o�ers or by withholding reactive power supply in an attempt to increase the

reactive power market price to their own advantage [49].

3.4 Reactive power management review

Reactive power management and payment mechanisms di�er from one electricity market to an-

other, and no uniform structure or design has yet de�ned. There is no fully developed structure

for competition or pricing of reactive power services in any system. Moreover, there is no uni�ed

framework, universally acceptable, for reactive power management. In some cases the pricing is

based on �xed contractual payments, and in other cases based on gross system usage (embedded

cost), while in other markets there is no mechanism for payments. Even the classi�cation of the

obligatory reactive power requirements does not follow any well-de�ned criterion, apart from the

operator's experience [43].

3.4.1 Reactive power service in di�erent deregulated markets

While in current deregulated power systems, provision of real power is fully competitive, no fully

competitive market-approach to reactive power provision exists. It means that the reactive power

service is based on a regulated provision and not a reactive power.

The System Operator generally �xes mandatory requirements for reactive supply by generators,

which can be summarized as follows:

� the generators shall keep power factor to be equal to a certain value: the mandatory reactive

power production (or consumption) decreases according to the reduction of real power;

� the generators shall deliver (or absorb) at least a minimum amount Qmin of reactive power;

� the generators shall maintain voltage level at delivery points to be equal to a certain value;

� a reactive power thresold is de�ned as a percentage of the maximum producible (or consum-

able) according to the capability curve.

Moreover, if the System Operator needs an additional reactive supply (or consumption) to maintain

the security standards, it can:

� impose the generator to supply (or consume) this additional amount according to its capa-

bility curve, while taking into account and respecting the concept of opportunity cost;

� allow the generator to supply or not this additional amount. In case of participation, an

economic agreement between the System Operator and the producer is stipulated.

3.4.1.1 North America

Currently, according to NERC's Operating Policy 10 [50], only synchronous generators are com-

pensated for reactive power provision.

The New York ISO (NYISO) uses an embedded cost based pricing to compensate generators for

their reactive power services, and it also imposes a penalty for failing to provide reactive power.

Generators are also compensated for their lost opportunity costs if they are required to produce

reactive power by backing down their real power output [51].


Such opportunity cost payments also exist in PJM Interconnection [52] and California ISO (CAISO).

Provision of reactive power services in the California system is based on long-term contracts be-

tween CAISO and reliable must-run generators; generators are mandated to provide reactive power

within a power factor range 0.9 lagging to 0.95 leading. Beyond these limits, the generators are

paid for their reactive power including a lost opportunity cost payment [53].

The Independent Electric System Operator (IESO) in Ontario, Canada, requires generators to

operate within a power factor range of 0.9 lagging to 0.95 leading and within a +/-5% range of its

rated terminal voltage. The IESO signs contracts with generators for reactive power support and

voltage control, and generators are paid for the incremental cost of energy loss in the windings due

to the increased reactive power generation. The generators are also paid if they are required to

generate reactive power levels that a�ect their real power dispatch, receiving an opportunity cost

payment at the energy market clearing price for any power not generated [54].

3.4.1.2 Europe

In the United Kingdom, the TSO National Grid Electricity Transmission (NGET) invites half-

yearly tenders for both �obligatory reactive power services� which correspond to the base reactive

power that each generator is required to provide, and �enhanced reactive power services� for gen-

erators with excess reactive power capabilities. There are two payment mechanisms: a default

payment agreement, where both the generator and NGET enter into an agreement for service

provision and payments, and a market-based agreement, where generators submit their reactive

power bids to the NGET [55].

Sweden follows a policy wherein reactive power is supplied by generators on a mandatory basis and

without any �nancial compensation. The goal is to keep reactive power �ow on the transmission

system close to zero, especially at certain interfaces. Some large generators are seldom used for

voltage control and are operated at a constant reactive power output. Hydro and thermal units

are required to maintain a capability to inject reactive power of one third the amount of real power

injection (a power factor of approximately 0.90).

Also in Norway reactive power is provided by generators on a mandatory basis and without any

�nancial compensation: all generators is required to supply reactive power within a power factor

range of 0.93 lagging to 0.98 leading. Additional reactive power supply is individually imposed to

generators. The remuneration of these additional provisions is yearly negotiated by the System

Operator and the producers' representatives.

In the Netherlands, individual network companies have to provide for their own reactive power,

usually through bilateral contracts with local generators, who are only paid for the reactive capacity

but not for reactive energy [56].

In Spain the voltage regulation service is provided by both generators (with a net power higher

than 30 MW) and consumers (> 15 MW). There are a compulsory service, which has not any

�nancial compensation, and an optional one. As regards generators, they must have a minimum

margin of reactive power at cosφ = 0.989 (both lagging and leading), equal to 15% of the maximum

real power of the group. Consumers are required to ful�l some obligations depending on the time

band: they shall consume reactive power with cosφ ≥ 0.95 during peak hours, while they are

not allowed to inject reactive power into the grid during o�-peak hours. Besides the compulsory

service, generators and consumers can o�er additional reactive power resources, that are instead

remunerated [57].


3.4.2 Literature on reactive power pricing and management

Traditionally, reactive power dispatch has always been viewed by researchers as a loss minimization

problem, subject to various system constraints such as nodal real and reactive power balance,

bus voltage limits, and power generation limits [58-61]. Another approach has been to dispatch

reactive power with the objective of maximizing the system loadability in order to minimize the

risk of voltage collapse [62, 63]. Furthermore, multi-objective optimization models have also been

proposed for the reactive power dispatch problem. In these models, reactive power is dispatched

to achieve other objectives, in addition to the traditional loss minimization, such as maximizing

voltage stability margin [64], or minimizing the voltage and transformer taps deviation [65].

Researchers have been working at reactive power pricing and management in the context of the

new operating paradigms in competitive electricity markets. Both technical and economic issues

associated with pricing of reactive power, along with its optimal provision, have received signi�cant

attention.

Several approaches have been reported in the literature for identifying and analysing the di�erent

cost components associated with reactive power production from synchronous generators. In [45]

Lamont and Fu have provided a comprehensive analysis of the various economic costs of reactive

support from both generation and transmission sources. The cost of reactive support has been

shared in explicit and implicit costs: the former are related to the capital cost of the facilities

and to the operating cost of production, while the latter refer to the Opportunity Costs (OCs).

Luiz da Silva et al have discussed in [66] the practical issues related to the de�nition of a suitable

cost structure for reactive power production, as well as the development of appropriate payment

mechanisms for reactive power providers. Costs of reactive power production are divided into

�xed capital costs and variable costs. A detailed analysis have been carried out for di�erent

variable costs associated with reactive power production from various sources, including generators,

synchronous compensators, static compensators, and shunts capacitors. The authors have proposed

that payments for generators operating as synchronous compensators should be determined based

on the operating time and real power consumption, rather than on reactive power production

or absorption. They also have argued that certain reactive power sources, such as capacitors

and on-load tap changers, should be considered as part of the transmission network and not

as ancillary services' providers. Gross et al have examined in [48] the variable costs of reactive

power production/absorption by a generator, identifying the most dominant cost component, which

is determined as the foregone pro�t of a generator in the real power market consequent to the

obligation to reduce the real power sales for the provision of additional reactive power.

Reactive power pricing policies have been typically based on power factor penalties. With the de-

velopment of real-time or spot pricing theory, there has been signi�cant interest in their application

in the context of competitive electricity markets.

Baughman and Siddiqi have introduced real-time pricing for reactive power in [67], based on the

hourly marginal costs of providing real and reactive power at a given bus. These marginal costs,

which correspond to the added operating expense incurred by the utility to serve an incremental

demand, are obtained by solving a modi�ed optimal power �ow (OPF) that minimizes the total

generation cost subject to operation constraints that include load �ow equations, real and reactive

generation limits, bus voltage limits, and transmission system limits.

In [68] Hao and Papalexopoulos have presented two pricing methods based on reactive power unit

cost measure. In the �rst structure, reactive power production limits are determined by perfor-


mance requirements and standards; in this structure, penalties are proposed for service providers

that violate these performance standards, and credits are given for providing extra reactive power

generation beyond the speci�ed standards. The second structure is based on a local reactive power

concept, where the Indipendent System Operator (ISO) procures reactive power services from gen-

erators based on the cost of their reactive power capacity, and then recovers these payments from

load customers according to their demand.

The model proposed by El-Keib and Ma in [69] is based on the calculation of the Short Run

Marginal Costs (SRMCs) by means of a decoupled OPF algorithm: one related to the real sub-

problem, the other related to the reactive sub-problem. In particular, the reactive power optimisa-

tion provides the calculation of the reactive marginal costs, considering the additional real power

generating cost for an increase of the reactive power demand: in this way, also the synchronous

generators operating inside their capability limits are compensated.

In [70], pertinent to the English market, the authors have presented a method for the simulation

and analysis of the reactive power market based on combined capacity and energy payments.

The authors of [71] have focused on the Spanish electric system. The reactive support is divided

in two di�erent services: the reactive energy market and the reactive capacity market.

All these papers are based on the marginal cost theory, supposing that marginal cost can recover

all the costs involved to produce, transport, and deliver reactive power.

An innovative approach for pricing the reactive power ancillary service is presented in [72]. A two-

step approach is proposed. First of all the TSO determines the marginal bene�t of each reactive bid

from an OPF problem, whose objective is to minimize the system transmission losses subject to the

operational constraints. Then the marginal bene�ts are included in a composite objective function,

the Societal Advantage Function (SAF), together with the price bid o�ers of the producers. The

SAF is maximized, seeking contribution to the system performance (in terms of loss reduction)

from reactive power providers with lowest possible cost.

A �rst attempt to de�ne the impact of the existence of a SVR (Secundary Voltage Regulation)

scheme in the EHV system on the reactive pricing structure can be found in [73].

In [47] Zhong and Bhattacharya set up a market-approach in which generators submit bids for

their reactive support and a uniform market price is determined through an auction. Generators

submit their bid for four di�erent types of capacities, one of which is the operating range where

Lost Opportunity Costs (LOCs) are imposed on the generator and another is for the absorption

component. A market price is then determined for each separate component. A composite objective

function containing three di�erently weighted terms is minimized. The ISO performs his choice

balancing three di�erent objectives: minimum cost of reactive power provision, losses minimization

and minimum deviation from the contracted transactions. This approach has been extended by

Zhong et al in [74] by using the concept of voltage control areas to determine a zonal market price

to reduce the possibilities of market power exploitation by generators with strong market position.

3.4.3 Possible policy solutions

3.4.3.1 Decoupling of real and reactive power

On the basis of the discussions in section 3.3, and in particular considering the problems that

arise when both real and reactive power are simultaneously managed and priced by the System

Operator, a possible solution is to decouple these two markets from each other. Decoupling of real

and reactive power markets is possible by placing them in two entirely di�erent operating time


frames. This methodology has been suggested in [69, 75]. Such a decoupling implies that the OPF

problem can be separated into two sub-problems. The real power sub-problem essentially provides

the real power dispatch and prices in real-time based on a cost minimization (or social welfare

maximization) market settlement model. The reactive power sub-problem, operating on di�erent

time frames, provides reactive power contracts, prices, and dispatch levels based on appropriate

optimization criteria.

3.4.3.2 Zonal reactive power management

Given the localized nature of reactive power and the common practices amongst most electric

utilities in regards to splitting the whole system into zones or voltage control areas, zonal reactive

power management and pricing might be an appropriate approach. In the case of a system-wide

uniform price, market ine�ciencies resulting from market power being exercised by some reactive

power service providers, anywhere in the system, will a�ect all other providers in the system.

Zonal reactive power pricing, on the other hand, helps isolate and con�ne any existing market

ine�ciencies within the zone. These market ine�ciencies may arise from some service providers

trying to exercise market power by increasing their reactive power price o�ers. In terms of service

provision, zonal reactive power management allows for having additional reactive power reserves for

each zone; this reserve can be called upon by the System Operator in emergency cases associated

with severe contingencies in the system. In general, zonal reactive power management can be

achieved by splitting the system into di�erent voltage control areas [76].

3.4.3.3 Alternative sources of reactive power supply

One of the main challenges associated with reactive power provision is that, so far, only reactive

power support from synchronous generators has been considered as an ancillary service and eligible

for �nancial compensation. With a more liberal reactive power ancillary service provision struc-

ture, there would be more competition due to an increased number of providers. It is important

to examine how other reactive power providers, such as capacitor banks and FACTS controllers,

could participate in the reactive power ancillary service markets to help develop a fully competitive

reactive power market. This particular issue is not studied in this thesis, since the characteristics of

these reactive power resources make them essentially di�erent from generators; hence, appropriate

policies will be required to determine how these resources can be properly compensated for pro-

viding reactive power as an ancillary service. In this thesis, only reactive power from synchronous

generators is considered as an ancillary service [49].

3.5 Architecture of voltage control system

The architecture of the voltage control system can be fully centralized or decentralized or hier-

archical. Here we will describe in detail only the latter scheme, since it is the voltage regulation

structure set up for the Italian electric system by its past monopolistic utility (ENEL).

3.5.1 Hierarchical voltage control system

The voltage control system can be organized into a three-level hierarchy [77, 78]. In short:

1. Primary voltage and reactive power control level.


It consists in automatic actions on individual or a limited number of power system equipment

based upon local measurements. It is a local automatic control that maintains the voltage

at a given bus (at the stator in the case of a generating unit) at its set-point. Automatic

voltage regulators (AVRs) ful�l this task for generating units. Other controllable devices,

such as static voltage compensators, can also participate in this primary control. It faces up

to local perturbations such as short circuits close to generating units. The typical response

time scale is between a few milliseconds up to about one minute.

2. Secondary voltage and reactive power control level.

It consists in coordinated actions of control resources within a de�ned part/area of the power

system aimed at maintaining system security. It is a centralized automatic control that

coordinates the actions of local regulators in order to manage the injection of reactive power

within a regional voltage zone. The typical response time scale is between one minute and

up to a few minutes.

3. Tertiary voltage and reactive power control level.

It consists in coordinated global economy and/or security optimization on utility, pool, or

country levels based upon real-time measurements. The typical response time scale is around

10 minutes or longer.

Hierarchical systems based on network area subdivision and automatic coordination of reactive

power resources were �rst studied in Europe for achieving network voltage control. These innova-

tive solutions, named Coordinated Voltage Regulation (CVR) or Secondary and Tertiary Voltage

Regulations (SVR and TVR), depending on their hierarchical level, have been studied in Italy [79-

81], France [82, 83], Belgium [84, 85], and Spain [86, 87]. Some of them operate in real systems

and are extended at the national level. As a result of changes in the organization of European

utilities and the resulting energy markets' deregulation, hierarchical voltage control systems are

increasingly being appreciated and reinforced. In fact, system operators recognize that SVR and

TVR permit both simpli�cation of automatic control of overall transmission network voltages and

recognition of the contributions of di�erent participants to the voltage ancillary service.

Progress and trends in transmission network voltage control require major development and inno-

vation through use of simple, e�ective, automatic control systems, managed and supervised directly

by system operators. Moreover, because voltage control is prevalently a local problem, potential

solutions must consider automatic coordination of local reactive power resources, primarily those

of generators and compensators but also shunt capacitors and reactors, OLTCs, SVCs, and STAT-

COMs. For this reason, the goals (quality and security improvements in network operation) of

voltage ancillary service can be pursued through a decentralized voltage control system, by in-

troducing local coordination in each area/region of the power system. Such coordination requires

exchange of data and signals between the regional dispatcher and local plants/substations: the

more data are exchanged in real-time, on the basis of power system dynamics, the more the volt-

age control system can improve performance and e�ectiveness. The bene�ts of network voltage

control in terms of grid e�ciency, on the other hand, are more strongly linked with inter-area

coordination, requiring e�ective exchange of data and signals among regional dispatchers and the

central/national system operator. In particular, the exchange of measurements with the neigh-

bouring utilities (e. g. boundary bus voltages and tie-line reactive power �ows), as well as the

coordination of mutual control actions, are very important for reducing system losses. The on-line


and real-time monitoring of actual EHV control system performance also represents a challeng-

ing opportunity for indubitable correct recognition of power plants' contributions to the voltage

service, in the framework of energy sector liberalization and ancillary market competition. The

main reasons supporting coordinated �automatic� real-time voltage regulation can therefore be

summarized as follows [88]:

� the quality of power system operation is improved, in terms of reduced variation around the

de�ned voltages pro�le across the overall transmission network;

� the security of power system operation is enhanced, in terms of reactive power reserves kept

available by generating units for dealing with emergency conditions;

� the transfer capability of power system is improved, in terms of increased transmissible real

power levels, with reduced voltage instability and collapse risks;

� the e�ciency of power system operation is enhanced, in terms of minimization of real power

losses, reduction of reactive �ows and better exploitation of reactive resources;

� the controllability and measurability of voltage ancillary service is simpli�ed, in terms of

de�nition of functional requirements and performance monitoring criteria.

3.5.1.1 Basic SVR and TVR concepts

The basic concepts of SVR are summarized to permit understanding of the proposed control

system's structure, performance, and advantages:

� the idea of automatic real-time control of hundreds of transmission bus voltages is too com-

plex, very critical, not reliable, and therefore unrealistic and uneconomical;

� the generating units' reactive power is, obviously, the main resource already available in the

�eld, low-cost, and simple to control for network voltage support;

� a realistic simple voltage control system should consider the dominant buses only (a small

amount), thus allowing a sub-optimal but feasible and reliable control solution;

� in order to easily realize the dominant bus (pilot node) idea we call joint-buses those having

high electrical coupling to form a �control area� with voltages close to each other;

� the control structure, based on the subdivision of the grid into several control areas, auto-

matically and, as much as possible, independently regulates each area pilot node voltage;

� the control resource is essentially based on the reactive powers of the largest generating units

in the area (control plants), which mainly in�uence the local pilot node voltage.

The basic idea of TVR comes from the need to increase the system operating security and e�ciency

through centralized coordination of the decentralized SVR structure:

� the pilot nodes' voltage set-points must be adequately updated and coordinated with slower

dynamics than SVR, considering the actual condition of the overall grid and avoiding useless

and con�icting inter-area control e�orts;

� the pilot nodes' voltage set-points can be computed and updated in real-time, considering

the global control system structure and its real-time measurements;


Figure 3.2: Hierarchical structure for transmission network voltage control

� the pilot node' voltage set-points have to be optimized to minimize grid losses while still

preserving control margins.

It is necessary to point out that, notwithstanding the goal of minimizing control system complexity,

the e�ort involved in achieving an e�ective control system is in any case considerable when a large

transmission network is involved, as con�rmed by past experience and existing applications. On

one hand, a new power plant apparatus is needed to control the reactive power production of

generating units, as well as of synchronous compensators, according to the local bus-bar or remote

pilot node voltage regulator and taking into account the instantaneous available capability of

the plant generators. On the other hand, a speci�c regional dispatcher regulator is necessary to

automatically maintain pilot node voltages at their scheduled values, controlling the new power

plant apparatus via rapid telecommunications, turning on/o� reactor banks and shunt capacitors,

and ordering OLTCs and FACTS controller set-points. Lastly, a new voltage and reactive power

optimizing regulator is required at the national/utility control level, to coordinate and update all

the pilot node voltage set-points on-line and in real-time (Figure 3.2) [88].

3.6 Reactive power service in Italy

3.6.1 Current regulatory framework in Italy

This subsection brie�y introduces the current legislative, regulatory, and technical framework with

respect to voltage control and to �reactive requirements� for producers and consumers connected

to the Italian grid. Most relevant regulatory orders and technical standards are mentioned in

Figure 3.3.

According to the grid code [8], conventional (i. e. thermal and hydro) power plants shall be able

to operate at over-excitation power factor 0.85 or 0.9 (the value depends on the size and type

of generator) and at under-excitation power factor 0.95. All generating units connected to the

transmission and sub-transmission grids shall contribute to the primary voltage control, that is,

the machines have an automatic voltage regulator and simply regulate the voltage on the generator


Figure 3.3: Italian regulation for voltage control and reactive exchanges

bus-bars.

Generating units below 10 MVA can be allowed to provide �xed power factors. It is envisaged

that, in the future, generators unable to provide primary voltage control will have to pay a fee for

it. A complex secondary voltage regulation, including a regulator of reactive power and voltage in

the power plants and the communication systems with the regional voltage regulator, is installed

on all generators and is coordinated by the Italian National Control Center with the objective of

controlling voltages in some selected network buses (called pilot nodes) based on the de�nition of

network control areas. The choice of generators' participating to SVR depends on their capabilities

and system characteristics.

For generating units connected to medium voltage (MV) grids, the standard of Italian Electrotech-

nical Committee CEI 0-16 [89] states that the reactive injection/withdrawal shall allow to operate

medium and low voltage (LV) grids within their nominal voltage +/- 10%. Therefore it shall

be agreed with the local distribution system operator (DSO) and be ruled within the individual

contract of connection.

For consumers and DSOs, the regulatory order 348/07 (electricity tari� regulation for the period

2008-2011) [90] introduced a mandatory framework for payments related to excess reactive energy

withdrawals. All consumers with contractual power higher than 16.5 kW have to pay in case

their average monthly reactive consumption is higher than 50% of their average monthly active

consumption. In case their power factor is below 0.8 (reactive consumption > 75%), an increase

of payments applies as described in Table 3.1. In case the consumer is equipped with a meter

allowing to read hourly withdrawals, the payments are set to zero in light load hours.

The Italian TSO applies the payments of Table 3.1 in case of excess reactive withdrawals at

the connection points with DSOs (except than in light load hours) and takes into account such

payments for de�ning the remuneration of dispatching resources. Further, according to the grid


Table 3.1: Payments by Italian consumers for excess withdrawal of reactive energy

code, the TSO can impose to DSOs the power factor in their connection points for voltage quality

and losses reasons. Similarly, DSOs apply the same payments to interconnected DSOs in case of

excess reactive withdrawals (except than in light load hours). DSOs have to transfer the payments

which they collected from grid users and interconnected DSOs to a fund for promotion of energy

e�ciency measures.

The de�nition of the economic value of payments is based on a Decree of Interministerial Committee

on Prices of December 1993, CIP 15/93 [91]. Before the regulatory order 348/07, the application

of payments for excess reactive withdrawals was optional for DSOs, which however had to take

into account their amounts within the cap for distribution revenues (tari� options were subject

to regulatory approval). In the consultation process towards the third regulatory period 2008-

2011, the Italian Regulatory Authority explicitly stated the objective of encouraging consumers to

prevent signi�cant voltage drops in distribution grids and contribute reducing grid losses by means

of mandatory �reactive payments�. Stakeholders were consulted on the opportunity to introduce

a mandatory scheme and were invited to suggest how to size the economic value of payments. Six

respondents out of six agreed with the opportunity to implement a mandatory framework, whereas

there was less consensus on the de�nition of values. Indeed, one respondent suggested to use

the values de�ned by CIP 15/93, one respondent to slightly modify CIP 15/93 values for sake of

simplicity, one respondent to have increasing payments for lower power factors, one respondent to

consider incentive possibilities for consumers with their power factor signi�cantly higher than 0.9,

one respondent to size the payment referring to capital expenditures for compensating equipment,

taking into account a proper pay-back period [92]. The Italian Regulatory Authority started, with

the regulatory order Electricity 48/09 issued in April 2009, the process to review regulation of

reactive energy transits in transmission and distribution grids.

The ultimate aspect related to reactive energy injections and withdrawals is the voltage pro�le

in electricity grids, i. e. the magnitude of voltage provided to customers at all voltage levels. In

Europe, the most important standard regarding voltage characteristics of electricity supplied by

public distribution networks is EN 50160 issued by CENELEC (Comité Européen de Normalisation

Électrotechnique) [93]. It de�nes, describes, and speci�es the main characteristics of the voltage

at a network user's supply terminals in networks below 35 kV. As for supply voltage variation

limits, EN 50160 states that under normal operating conditions, during each period of one week,

95% of the 10 minutes root mean square values of the supply voltage shall be within the range of

contractual voltage +/- 10%. EN 50160 is currently under revision after three years of cooperation

between CEER (Council of European Energy Regulators) and CENELEC. In Italy, minimum and

maximum voltages for transmission and sub-transmission are de�ned yearly, according to provisions

in the quality chapter of grid code. For 380 kV nominal voltage, they are 375 kV-415 kV to be


ful�lled 95% of time and 360 kV-420 kV to be ful�lled 100% of time in normal and alert security

state. Further, the Italian Regulatory Authority introduced by its order 333/07 (electricity quality

regulation for the period 2008-2011) a guaranteed quality standard for checking voltage magnitude

and supply voltage variations by the involved DSO upon request of a LV or MV grid user.

3.6.2 Reactive power service by generators

In the Italian power system in the '80s ENEL, the state-owned vertically integrated utility in force

up to 1999, set up a hierarchical structure for network voltage control [79], which is presently

updated, enlarged, and managed by TERNA, the current Italian Transmission System Operator.

According to this, the grid code [8] de�nes two di�erent reactive power services, as anticipated in

the preceding subsection:

1. reactive resources for Primary Voltage Regulation (PVR);

2. reactive resources for Secondary Voltage Regulation (SVR).

The reactive power support for primary voltage regulation is divided into:

� reactive power reserve for primary voltage control of the single generation unit:

it consists in controlling the reactive power production of a generation unit by an automatic

regulation device (AVR - Automatic Voltage Regulator3) capable of modulating the reactive

power delivered by the group considering the variation of the voltage magnitude at its ter-

minals with respect to a certain reference value. Only generating units below 10 MVA can

be allowed to provide �xed reactive power amounts or power factors, subject to the TSO

agreement.

� reactive power reserve for primary voltage control on the high-side bus-bar of a power plant:

it consists in subjecting the reactive power production of all groups in a power plant to

an automatic regulation device (power plant voltage and reactive power regulator4) that is

able to modulate the reactive power delivered by each generation unit based on the voltage

variations on the high-side bus-bar of the power plant with respect to a suitable daily voltage

trend or an operator-de�ned set-point. All power plants with at least one generating unit

above 100 MVA are required to provide this service.

The primary voltage control is a mandatory service, without any �nancial compensation.

The reactive power support for secondary voltage regulation consists in controlling the reactive

power production of all groups in a power plant by a centralized automatic regulation device

capable of modulating the reactive power delivered by each generating unit based on the voltage

variations at some buses selected by the TSO and called pilot nodes. The reactive power regulation

is made according to the reactive level received by a Regional Voltage Regulator (RVR).5

The secondary voltage regulation is now a voluntary service. Therefore, it is important to analyse

possible rules and �nancial compensations related to such voltage regulation service, as well as

their consequences on the performances provided by this structure in a deregulated market.

3In Italian it is called RAT - Regolatore Automatico di Tensione.4In Italian it is called SART - Sistema Automatico per la Regolazione della Tensione di centrale. It can operate

in two di�erent control modes: local operation for primary voltage control on the high-side bus-bar of a power plant,and telecontrol for secondary voltage regulation.

5In Italian it is called RRT - Regolatore Regionale di Tensione.


3.6.3 The Italian network voltage control system

The Italian hierarchical voltage control system regulates the voltages of the main EHV buses (pilot

nodes) in a closed loop through real-time control of the reactive resources which most in�uence

these buses. This permits secure transmission network operation, very close to the highest voltage

limits, through rapid control of the main generators (control plants), coordinated by a reactive

power level within the same grid portion (control area) and automatically forced to their limits

only when needed. The Regional Voltage Regulators (RVRs) close the control loops of the pilot

node voltages, providing each area with a speci�c reactive power level which controls the local

power plants' voltage and reactive power regulators (named SART). In turn, the SART closes the

reactive power control loops of the plant units, directly acting on the set-points of the generators'

automatic voltage regulators (AVRs). RVR also controls capacitor banks, shunt reactors, OLTCs,

and SVCs to avoid saturation of area generators. AVR rapid control is referred to as Primary

Voltage Regulation (PVR). The combination of SART [94] and RVR [95] implements the SVR. At

the highest hierarchical control level, a Tertiary Voltage Regulator (TVR) coordinates the RVRs

in a real-time closed loop.

It establishes, on the basis of the actual �eld measurements, the current pilot node voltages which

achieve the minimum feasible grid losses, by slow RVR set-point correction, keeping the system

under control at all times. To achieve this aim, an Optimal Reactive Power Flow (ORPF) for Losses

Minimization Control (LMC) computes, in short (the day ahead) or very short (minutes ahead)

terms, the forecasted optimal voltages and reactive levels, starting from the foreseen/current state

estimation. TVR therefore minimizes the di�erences between the actual �eld measurements and

the optimal forecasted references. This computed �compromise� represents the maximum tenable

voltages plan at any instant. The combination of TVR [96, 97] and LMC [98, 99] forms the National

Voltage Regulator (NVR), which so links ORPF forecasting with real-time optimization of SVR

set-points.

The hierarchical voltage control system has di�erent operation modes, according to its implemen-

tation progresses, maintenance interventions and transient or persistent failures:

� without plant telecommunications, or when the RVR is not operating, SART automatically

regulates the local EHV bus voltage (high-side voltage regulation), according to de�ned

daily trends or the plant operator's voltage set-points, agreed by phone with the regional

dispatcher;

� without system operator's telecommunications or when TVR is not operating, the RVR

autonomously regulates the pilot node voltages of its controlled areas, according to stored

daily trends or the regional dispatcher's chosen set-points, agreed by phone coordination with

national control center;

� when the LMC is not operating, the TVR autonomously coordinates the RVRs, assuming,

as a reference for the optimization of pilot node voltages and reactive power margins, the

available long term forecasted optimal plan or the national control center operator's manual

reference.

The following subsection will consider one of the basic issues for designing the voltage control

system. Other technical characteristics are described in detail in Appendix E.


3.6.3.1 Selection of pilot nodes, control areas, and control plants

The three hierarchical levels consist of overlapped closed-loop controls, whose coordination in space

and time requires a careful design of their stability and dynamics to achieve adequate performance

even when faced with contingencies. The design starting point requires proper subdivision of the

overall grid into control areas around the selected pilot nodes, and correct choice of the most

appropriate control plants.

The selection of pilot nodes is based on the intuitive idea that such buses must be chosen among

the strongest ones, able to impose voltages on the other electrically close buses. The design crite-

ria, based on short-circuit capacities and sensitivity matrix computations, also requires electrical

coupling between pilot nodes to be su�ciently low to avoid possible problems of dynamic inter-

action between secondary control loops. With this constraint, in fact, excessive reactive power

exchanges among adjacent control areas, determined by even slight di�erences between the pilot

node voltages imposed by the regulating system, are basically prevented. If network operational

requirements condition pilot node selection by determining excessive electrical coupling between

control areas, the secondary control law should de-couple the dynamic interactions between con-

trol loops. The analytic procedure of selection of pilot nodes consists of a successive re-ordering

of the sensitivity matrix, expressing the dependence of the grid bus voltages on reactive power

injections, with primary voltage regulation operating. The method assumes the load or generation

bus, having the strongest short-circuit capacity, as the �pilot node 1�. All buses with the highest

coupling coe�cient with �pilot node 1� are assumed belonging to �control area 1� and excluded

from subsequent pilot node choices. This procedure, progressively applied, identi�es the other

pilot nodes which are the strongest of the remaining buses and therefore gradually weaker, until

the procedure stops due to insu�cient short-circuit capacity.

The choice of control plants is based on the simple criterion that they must operate in the control

area and have the largest reactive power capability and the highest electrical coupling with the

selected pilot node. Selection of control plants also permits advance recognition of control areas

with consistent reactive power resources, as well as those where the reactive power reserves are

critical and pilot node voltage regulation could more easily reach saturation. The analytic proce-

dure for the choice of control plants requires successive re-organization of the sensitivity matrix,

expressing the dependence of the pilot node voltages on the reactive power injections by generators.

The method assumes all the generators belonging to the �control area i� and having their highest

coe�cient placed in the �pilot node i� row, as potential �control plants i�. All potential plants

with the highest product of sensitivity coe�cient by rated reactive power capability are de�nitely

assumed as �control plant i�.

These simple methods are not computationally heavy and give satisfactory results, once some

threshold values have been re�ned, taking particular network characteristics into account.

For instance, accepting a higher electrical coupling increases the number of pilot nodes but also

requires more complex control laws to deal with closed-loop interaction and dynamic instability

risks. Moreover, frequent re-selection of pilot nodes, even in the case of small network changes, is

required. On the contrary, excessively low electrical coupling reduces the number of pilot nodes

and signi�cantly de-couples their control loops, but at the same time worsens voltage quality.

Similarly, accepting excessively low products of sensitivity coe�cients by rated reactive powers

increases the number of control plants and the corresponding reserve margins, but could require

more unnecessary control infrastructures to permit the participation and coordination of small


generators.

The subdivision of the whole system into control areas must be robust and conservative, to prevent

control system recon�guration from becoming too frequent in response to minor network changes.

Relevant structural changes, however, must be analysed to determine their impact on pilot nodes,

control areas and control plant selection, and to adequately re-tune regulation parameters [88].

3.7 Optimal Reactive Power Flow program

As explained in the preceding subsection, the optimal voltage pro�les are determined by an Optimal

Reactive Power Flow program [96]. The ORPF mathematical model is compact reduced:

minF (u) (3.1)

subject to

Xmin ≤ X (u) ≤ Xmax (3.2)

umin ≤ u ≤ umax (3.3)

where u = [vg, qg, rt, qb] is the vector of the reactive control variables and X = [V, Qg] is the

dependent variable vector.

The reactive control variables, on which the optimization algorithm acts, are:

� terminal voltages of the control generation buses that are reactive slack buses, i. e. P-V and

θ-V buses (vg);

� reactive power injections (or withdrawals, if under-excited) by control generators at P-Q

buses or at θ-Q bus6 (qg);

� transformation ratios of OLTC transformers (rt);

� reactive power injections by compensation devices (qb).

The dependent variables, whose values are determined by a load-�ow calculation, after solving the

optimization problem and �nding the optimal values of the control variables, are:

� voltages at P-Q or θ-Q buses, including the so called �sentinel buses�, that are load buses

where it is important to maintain an appropriate voltage pro�le since they characterize the

voltage pro�le of the EHV network7 (V );

� reactive power injections (or withdrawals) by control P-V or θ-V generators (Qg).

The constraints (3.2)-(3.3) represent the technical and operational limitations. Xmin, Xmax, umin,

umax are the lower and upper bounds of dependent and control variables. The dependent variables

X are expressed as linear functions of the control variables u by means of sensitivity relations.

The control variables u have to comply with some technical constraints, including:

� the minimum and maximum voltages of control P-V or θ-V generators;

6This case is uncommon because the real slack bus is usually also a reactive one.7If the operational limits are ful�lled by the �sentinel buses�, also the other load nodes will comply with them.


� the minimum and maximum reactive power injections (or withdrawals) by control P-Q or

θ-Q generators, within their capability limits;

� the minimum and maximum transformation ratios of OLTC transformers;

� the maximum reactive power injections by compensation devices.

The dependant variables X have to satisfy some functional constraints, including:

� the minimum and maximum reactive power injections by control P-V or θ-V generators,

within their capability limits;

� the minimum and maximum voltages at P-Q or θ-Q buses;

� the minimum and maximum voltages at sentinel buses;8

� the maximum real power produced by the Q-V bus within its capability limits.

The ORPF program can emphasize the security aspect or the economic one by selecting one of the

following objective functions:

� security: equal distribution of reactive power margins;

� economy: minimum real power losses.

As a usual practice, the second one is considered and in the objective function F (u) a quadratic

function is assumed for the network losses PL (or the real power injection PS by the slack bus).

The introduction of SVR involves the de�nition of:

� pilot nodes of SVR areas (they are of sentinel type);

� generating units belonging to each SVR area;

� alignment constraints for reactive power production by generators of each SVR area.

In each SVR controlled area Ak, the reactive power productions of the Ngk controlling units[qg1 , qg2 , . . . , qgNgk

]must satisfy the alignment constraints (the variable qAk

is the area Ak reactive

level):

qpugj =qgj

qgj max=

QAk

QAk max= qAk

j = 1, . . . , Ngk (3.4)

if the pu level qAkis positive (over-excited area Ak),

qpugj =qgj

qgj min=

QAk

QAk min= qAk

j = 1, . . . , Ngk (3.5)

if the pu level qAkis negative (under-excited area Ak),

where

QAk=

Ngk∑i=1

qgi (3.6)

8The selection of the most signi�cant P-Q buses (sentinel buses) allows functional constraints (3.2) to be stronglyreduced.


QAk min=

Ngk∑i=1

qgimin (3.7)

QAk max=

Ngk∑i=1

qgimax(3.8)

are the reactive power production of area Ak and its lower and upper bound.

The variable qAktakes the place of the Ngk reactive productions of the controlling units in the

new formulation of the problem.

If the reactive power �ows between SVR areas (Qrs) are included in the dependent variable vector,

the problem will consider also the functional constraints that they have to satisfy (i. e. minimum

and maximum reactive power �ows between SVR areas).

The ORPF model for the de�nition of the optimal reactive power levels (of each SVR area) and

of all the reactive control variables is given by (Problem P1):

minPS (vg, rt, qA, qg, qb) (3.9)

subject to

Vmin ≤ V (vg, rt, qA, qg, qb) ≤ Vmax (3.10)

Qgmin ≤ Qg (vg, rt, qA, qg, qb) ≤ Qgmax (3.11)

Qrsmin ≤ Qrs (vg, rt, qA, qg, qb) ≤ Qrsmax (3.12)

qpugj = qAkj = 1, . . . , Ngk k = 1, . . . , Nar (3.13)

vgmin ≤ vg ≤ vgmax (3.14)

rtmin ≤ rt ≤ rtmax (3.15)

qAmin ≤ qA ≤ qAmax (3.16)

qgmin ≤ qg ≤ qgmax (3.17)

qbmin ≤ qb ≤ qbmax (3.18)

where qA is the vector of the reactive levels of the Nar SVR controlled areas.

In such a way, the number of the control variables is reduced. The variables vg and qg are pertinent

to the generators not controlled by SVR.

The set of constraints (3.10) contains the limitations on the voltages at P-Q and θ-Q generation

buses (including the generating units belonging to the SVR areas) and at the sentinel buses (in-


cluding the pilot nodes). Constraints (3.11) include the capability limits of P-V and θ-V generation

buses; in the adopted model for each bus i these limitations are quadratic functions of Pgi and vgi .

Constraints (3.12) are the limitations on the reactive power interchanges between neighbouring

areas.9 Equalities (3.13) are the area alignment constraints. Finally, constraints (3.14)-(3.18) are

the lower and upper bounds of the control variables.

3.7.1 Compact reduced ORPF model

Starting from a base case solution of the load-�ow equations, the slack power variation ∆PS with

respect to the control variables displacements ∆u is expressed as a second order function of the

variables:

∆PS = ∇PTS ∆u+

1

2∆uTHS∆u (3.19)

where ∇PS and HS are the gradient and the Hessian matrix of PS (u).

The constraints on the dependent variables of the load-�ow equations are linearized at the base

case solution. Therefore the limitations on the voltages at P-Q buses and on the reactive power

productions of P-V buses are expressed by the following linear inequality system:

A∆u ≤ b (3.20)

where A is the sensitivity matrix of the dependent variables with respect to the control variables.

The system (3.20) contains the linearization of the inequality constraints (3.10)-(3.12) and of the

equalities (3.13).

The algorithm used for solving the ORPF problem consists in the iterative solution of quadratic

problems, like the following (Problem P2):

min

(∇PT

S ∆u+1

2∆uTHL∆u

)(3.21)

subject to

A∆u ≤ b (3.22)

∆umin ≤ ∆u ≤ ∆umax (3.23)

HL is the the Hessian matrix of the Lagrangian function of Problem P1. A load-�ow solution

veri�es the satisfaction of constraints (3.10)-(3.12) in P1 and allows the updating of the gradient

vector ∇PS , the matrix of the coe�cients A and the lower and upper bounds of the constraints

in P2.

3.7.2 Reactive power value

The solution of Problem P1 gives the optimal reactive level of each area, the associated pilot

node voltage reference, and the voltage set-points of the other units not operating in the SVR

scheme. Besides the Lagrange Multipliers (LMs) of the equality constraints (3.13) and of the active

inequality constraints (3.10)-(3.12) are available. It is known that the LM gives the variation of the

9This set of constraints is included in the ORPF model only if the secondary voltage regulation operates.


objective function when an active constraint experiences a unitary relaxation. The marginal costs

(bene�ts) of the reactive power consumption (production) in the network buses are determined

by a linear combination of the real losses and of the active constraints' sensitivities to the nodal

reactive power injections at the ORPF solution point [100, 101].

The marginal losses' variation consequent to a nodal reactive injection in the bus i is given by:

dPL

dQ=∂PL

∂Qi+

Nar∑k=1

Ngk∑j=1

λAkj∂Qkj

∂Qi+

NQ∑p=1

λV p∂Vp∂Qi

+

NV∑l=1

λQl∂Ql

∂Qi(3.24)

where:

� PL are the real losses in the system (in MW);

� Qi is the reactive power injection at P-Q or θ-Q bus i (in Mvar);

� NQ is the number of P-Q or θ-Q buses in the network;

� NV is the number of P-V or θ-V generation buses in the network;

� λA is the matrix of the LMs of the alignment constraints (3.13);

� λQ are the LMs associated to the NV binding constraints in the inequality set (3.11) (gener-

ators hitting their capability limits);

� λV are the LMs associated to the NQ active constraints in the inequality set (3.10) (voltage

of P-Q buses hitting lower or upper bounds).

Therefore:

� the �rst term is the real losses' variation consequent to a nodal reactive injection Qi in the

bus i (losses' grandient);

� the second term is the real losses' variation consequent to a nodal reactive injection Qi in

the bus i, that would occurr if the alignment equality constraints were relaxed;

� the third term is the real losses' variation consequent to a nodal reactive injection Qi in the

bus i, that would occurr if the constraints on the voltage at P-Q or θ-Q were relaxed;

� the last term is the real losses' variation consequent to a nodal reactive injection Qi in the

bus i, that would occurr if the constraints on the reactive power production/absorption at

P-V or θ-V generation buses were relaxed.

The resulting marginal cost (bene�t) at bus i (in ¿/Mvarh) will depend on the system marginal

price of the electric energy CMWh (¿/MWh):

CMvarhi = CMWh

dPL

dQ(3.25)

In conclusion, this nodal indicator provides the marginal reduction of the hourly cost of real losses

(¿/Mvarh) obtained by the additional injection of 1 Mvar in the selected bus.

The reactive power value in each bus is tightly connected to the technical limitations a�ecting the

system operation and to the operational constraints de�ned by the TSO.

The constraints included in the ORPF program can be classi�ed according to their nature and

to the possibility to be slightly violated (if they are not due to technical or security limitations).


The constraints that cannot be violated in any way are de�ned hard constraints. Capability

chart limitations (3.11), depending on the synchronous generator characteristics and on the AVR

design, are hard constraints as well as the alignment constraints (3.13) deriving from SVR. The

limitations on the voltages at the EHV network buses (pilot or sentinel nodes) included in (3.10)

are operational constraints (not necessarily hard) depending on the TSO operational choices and

not strictly related to technical limitations. So they are de�ned soft constraints and their possible

contribution to reactive power marginal value can be disregarded.

3.8 Wind energy exploitation and reactive power support

The voltage control in the network is rendered more di�cult if conventional power stations which

are involved in the voltage control with synchronous generators are replaced by wind energy plants,

and no new devices are provided for reactive power supply.

Wind power plants have in fact certain characteristics that distinguish them from conventional

power generation technologies. Among those, the most impacting reactive power control consider-

ations are [102]:

� Intermittency.

The lack of dispatchability, high variability of power output over time, and lower capacity

factors are in striking contrast with conventional generation sources. Unlike these, the planner

must anticipate that the wind plant may operate anywhere from zero to rated real power

output at any time, without regard to daily or seasonal load patterns.

� Lack of geographic correlation with load.

Another important issue is the low level of geographic correlation between existing transmis-

sion capacity and prime wind resource areas. Consistent high wind speeds are unattractive

for commercial and residential development, so these areas tend to be very sparsely popu-

lated with little electric load. The consequence of this is that, in most cases, wind power

development will occur at weak (i. e. high source impedance) locations in the transmission

network. It follows that these locations would be the most challenging with regard to voltage

regulation and transient stability.

� Asynchronous generation technology.

Up to now, wind turbine generators have, for the most part, utilized asynchronous generator

technology. In the case of variable speed wind turbines, it is able to provide for aerodynamic

e�ciency optimization by adapting the turbine rotor speed to the wind speed. In addition,

it provides for the structural load mitigation necessary to provide acceptable life expectance

in turbulent wind regimes. From a reactive power control standpoint, however, these tech-

nologies perform very di�erently than conventional wound-�eld synchronous generator with

exciters under voltage regulator control.

These three factors frequently create unique local voltage regulation issues not ordinarily encoun-

tered with dispatchable synchronous generating sources.

Initially, wind turbine generators were exempted from contribution to the reactive power. Now

grid codes in an increasing number of contries requires that wind farms take their share in reactive

power balance. The requirements vary from a demand to keep to near zero (unity power factor)


to speci�cally de�ned leading and lagging requirements at rated output. The point at which these

requirements are de�ned typically depends on the ownership of the interconnector between the

wind farm and the grid.

The reactive power capability of wind turbines vary widely from that of induction generators

compensated with switched capacitors to generators with full AC/DC converters, with full vector

control, o�ering a variable dynamic response. When available, the capability can be used to control

the reactive power at the terminals of the wind farm, but only at a remote connection point to the

grid if it is electrically very close. Some wind farms operate with secondary voltage control, provided

by a wind farm controller, providing target reactive power set points for individual turbines.

Increased requirements for reactive power controllability will lead to changes in the wind farm

design and/or lead to the application of switched/controlled reactive power compensation. The

application of switched capacitors may have some limitations as capacitor switching tends to have

negative impact on wind turbine gear boxes. Power electronics provide sophisticated means to

dynamically supply reactive power.

It should be noted that the wind generator reactive power control ancillary services may not always

be available as typically wind generators are disconnected when the wind speed is below the cut-

in wind speed. For this reason separate substation based reactive compensation may o�er an

advantage.

Wind farms will typically be connected to the network using one or more radial high-voltage

transmission lines or cables. In the case of AC overhead lines the reactive power characteristics

vary from capacitive to inductive as a function of line loading. In the case of an underground or

undersea AC cable connection, reactive power is supplied to the system and it needs to be absorbed

to avoid overvoltage. For large wind farms planned today, hundreds of kilometres of high-voltage

cables will be connected to the network which will require signi�cant reactive power compensation

installations and will lower the system resonnace frequency. For HVDC connections there are

no reactive power issues between the two terminals, and the reactive power requirements at the

connection point to the grid will typically be determined either by the grid code, or by speci�c

connection agreements [103].

3.8.1 Technical performance requirements for connection of wind farms

In the past, the technical requirements for connecting a generating plant were speci�ed in terms

of large-size synchronous machines due to their exclusive use and dominant impact on the grid.

However, large-scale wind farms are now playing an increasingly important role in many networks,

and their fundamentally di�erent operational characteristics when compared with sinchronous

machines need to be re�ected in modern grid codes. Grid code requirements are tipically neutral

as far as possible, but some have to be speci�c because of the characteristics of wind generation.

A summary of some regulatory requirements with regard to reactive power control in steady-state

conditions for wind plants follows [102].

3.8.1.1 Germany

According to the TransmissionCode 2007 and the subsequent SDLWindV [104, 105], each new

wind energy plant to be connected to the network must meet within the rated operating point the

requirements at the grid connection point according to a variant of Figure 3.4. The transmission

grid operator selects one of the potential variants on the basis of the relevant network requirements.


The agreed reactive power range must be able to be completely cycled through within maximum

four minutes and is to be provided at the operating point. Changes to the reactive power speci�ca-

tions within the agreed reactive power range must be possible at all times. The network operator

must specify one of the three variants according to Figure 3.4 by the time of the grid connection

of the wind energy converter on the basis of the relevant network requirements. If the network

operator later requires a variant other than the one agreed, the claim for the system service bonus

will remain una�ected by this.

Apart from the requirements as to the reactive power supply at the rated operating point of the

wind energy plant, there are also requirements concerning operation with an instantaneous real

power, which is less than the operational installed real power. In this case, it must be possible to

operate the wind energy plant at every possible working point in accordance with the generator

output diagram. Figure 3.5 shows the minimum requirement for the reactive power supply from

generating units operating at less than full output at the grid connection point. The highest re-

active power range to be covered and the associated voltage band are indicated in these �gures.

The abscissa indicates the reactive power to be provided in relation to the amount of operational

installed real power in percent. The ordinate indicates the instantaneous real power (in the con-

sumer meter arrow system negative) in relation to the amount of operational installed real power in

percent. Every point within the bordered areas in Figure 3.5 must be able to be started up within

four minutes. The requirement for this can result, depending on the situation, in the network and

denote a supply of reactive power taking priority over the real power output. The operating mode

is coordinated between the operators of the wind energy plant and the operator of the transmission

grid.

3.8.1.2 Spain

Operation of the high voltage transmission system in Spain is under the central control of Red

Eléctrica de España (REE). The Spanish Royal Decree 436/2004, in force till 2007, stated that

the wind plants were not required to participate in steady-state voltage regulation, but were in-

centivized to operate at or above speci�ed power factors by premiums and penalties applied to

the feed-in tari�. A new regulatory system, de�ned in the Spanish Royal Decree 661/2007, has

the aim of further favouring the wind integration in the power system. The incentives/penalties

associated to reactive power service are still e�ective, but now the wind farms above 10 MW may

be required to temporarily change their power factor by the TSO according to necessity.

As incentive to supply reactive power, a bonus or penalty is calculated as a percentage of a reference

tari� which presently has a value of 78.441 ¿/MWh. The percentage rates are shown in Table 3.2.

Alternatively, operators of wind power plants can participate in a reactive power market which,

as of yet, has not been implemented. During peak load, there is an incentive to supply capacitive

power, during o�-peak load there is an incentive to supply inductive power [106].

3.8.1.3 Italy

The Italian Regulatory Authority, with the regulatory order Electricity 98/08 of 25 July 2008 [107],

issued new rules for wind turbine generators (WTGs). It approved a new annex A17 of Italian Grid

Code [108], which requires new WTGs to have the capability to regulate their injection/withdrawal

of reactive power in the range 0.95 inductive power factor - 0.95 capacitive power factor at generator

terminals. The power factor can be kept �xed at a certain value agreed by both the TSO and the


Figure 3.4: Minimum requirement for the network-side reactive power supply - Germany


Figure 3.5: PQ diagram of the wind energy plant at the grid connection point - Germany


Table 3.2: Bonus/penalty for reactive power as percentage of reference tari� - Spain

wind farm's owner.

According to the AEEG Consultation 25/09 [109], the Italian TSO requires to update all pre-

existing WTGs in Southern Italy, Sicily, and Sardinia in order that they have the reactive regulation

capabilities de�ned in Annex A17. This would allow the de�nition - in the future - of reactive power

schedules for WTGs, based on local reactive needs. The Italian Regulatory Authority asked the

TSO to perform a technical survey of existing WTGs, including an estimation of costs for adapting

them to the �reactive requirements� of Annex A17. The resulting technical survey envisages that

costs for �reactive requirements� have an average value of about 5400 ¿ per installed MW.

3.8.2 Technology solutions

A wide range of steady-state and dynamic reactive power control solutions exists for wind plants,

and the proper solution depends not only on the speci�c electrical characteristics of the transmission

system in the area of the plant, but also on the wind turbine generator topology. Most modern

wind turbines utilize one of the three electrical topologies shown in Figure 3.6 [102]:

� line connected induction machines, either cage or wound rotor with slip (rotor resistance)

control (Figure 3.6 A);

� doubly fed induction machines with line connected stators and power converter controlled

rotors (Figure 3.6 B);

� synchronous or induction machines with stators connected through fully rated power con-

verters; induction machines include active recti�ers, while synchronous machines may utilize

either active or passive recti�cation (Figure 3.6 C).

3.8.2.1 WTG based reactive power compensation

The line connected induction machine consumes reactive power for excitation and due to reactive

losses in the stator and rotor winding leakage inductances. Mechanically switched power factor

correction capacitors are frequently applied at the wind turbine terminal to raise the e�ective


Figure 3.6: Common WTG electrical topologies

power factor of the machine under steady-state conditions. However, these mechanically switched

capacitors are of limited use in maintaining terminal voltage (and, hence, restraining torque) during

transmission system faults due to the inherent operational delays of the switches.

The doubly fed induction machine has inherent continuously-acting reactive power control capabil-

ity. The rotor side inverter is used to control the �ux producing component of the generator rotor

currents to sink or source reactive power through the stator winding by under or over excitation

of the rotor. When transformed to the rotating reference frame, the rotor currents are DC, and

the machine behaves similar to a conventional wound �eld synchronous machine. A second sink

or source of reactive power is the line-side inverter. The phase angle of the line-side currents with

respect to the line-side voltages is also continuously variable, and the line-side inverter's reactive

power capability remains available even if the wind turbine is not producing real power, e. g. un-

der low wind conditions. Under both steady-state and transient conditions, the reactive current

capability of the wind turbine is limited only by the current ratings of the two inverters.

Likewise, wind turbine generators with full conversion also have inherent continuous-acting reactive

power control capability. The line-side inverter carries the entire real and reactive components of

current, with the desired power factor, under either steady-state or transient conditions, achieved

by commanding appropriate direct and quadrature axis components of line current. Again, the

reactive current capability is limited only by the thermal limits of the power converter or by other

control limits imposed the wind turbine manufacturer [102].

3.8.2.2 External reactive power compensation

For wind plants utilizing turbines without reactive power control capability, or as supplemental

capability where the wind turbines' reactive power capacity is insu�cient to meet steady-state

or dynamic voltage regulation criteria, a number of external solutions are available. For reasons


of economy, the external solutions are normally applied at a single location in the wind plant

(typically the medium voltage bus in the plant's collector substation).

The simplest steady-state solutions are combinations of mechanically switched capacitors and reac-

tors. These solutions su�er from a lack of granularity that can only be overcome through reduced

step sizes (increased costs), limited dynamic response due to mechanical switching times, possible

power quality issues due to inrush currents, and signi�cant maintenance costs resulting from the

high number of operations subjected on the switches. Still, where the primary objective of the

reactive power compensation system is to satisfy steady-state voltage regulation concerns, this

remains a viable solution.

3.9 Tests on the Italian EHV network

3.9.1 Main assumptions

Taking into account the objective of assessing simultaneously economy and security, the tests are

carried out on extreme peak load conditions of the Italian EHV system. Economic evaluations

should be intended only to derive locational di�erences of marginal costs of reactive power, as it is

obvious that economic assessments have to be based on several load conditions (in particular, fre-

quent �mid-peak� conditions) or multi-scenario analysis. However, the choice of studying �extreme

peak� is justi�ed by the aim of having a proper assessment of system security under challenging

conditions.

The ORPF procedure is thus applied to a detailed model of the Italian continental electrical system

(380 and 220 kV). A baseline future scenario is de�ned with reference to a peak load condition of

the winter 2014. Fifteen 380 kV wind power collection substations,10 with a total installed capacity

of 5000 MW, are considered in the study [110]: there are nine in Apulia (Troia, S. Severo, Deliceto,

Manfredonia, Cerignola, Spinazzola, Castellaneta, Erchie, and Latiano), two in Campania (Ariano

Irpino and Bisaccia), one in Basilicata (Irsina), and three in Calabria (Carlopoli, Maida, and

Marcedusa). Their geographical location is displayed in Figure 3.7, while Table 3.3 summarizes

their main features:11 the 380 kV lines to which the wind collection substations will be connected

(second column), the amount of the generation capacity installed and connected to each collectors

(third column), and some notes concerning the authorization process (fourth column).

3.9.1.1 Wind power production

Assuming in operation the second 380 kV link between Rizziconi in Calabria and Sorgente in Sicily,

according to the 2010 transmission system development plan, a power exchange of 500 MW from

Calabria to Sicily is supposed, even though actually other values of the exchange (-500 MW, 0 MW)

have been considered and investigated. This choice indeed allows a larger dispatchability of the

wind power generation in Southern Italy.

A traditional SCOPF (Security Constrained Optimal Power Flow), which determines the real power

dispatch at the minimum cost while ful�lling the transmission constraints (i. e. inter-zonal power

limits and current limits on grid branches), is used to estimate the maximum amount of wind

generation consistent with the maintenance of an adequate level of system security. In particular,

10The collector is a 380/150 kV substation which will collect the electric power production by the wind farmsconnected to it.

11All the wind power collection substations, except for Troia, Deliceto, Bisaccia, and Maida, are under authoriza-tion as works related to production initiatives according to the Legislative Decree 387/03.


Figure 3.7: Geographic location of the �fteen wind collection substations

Table 3.3: Wind power collection substations


Table 3.4: Generation marginal costs of di�erent thermoelectric technologies

Table 3.5: OPF results (maximum wind power generation)

regarding the production costs of the main generation technologies, the ranges in Table 3.4 are

assumed. To simulate the dispatching priority of wind generation, a lower marginal production

cost is considered for this technology so that any wind power curtailment is exclusively due to

binding transmission limits.

In order to estimate the maximum amount of wind generation consistent with the maintenance of

an adequate level of system security, the minimum power that can be produced by some CCGT

plants in Central-South Italy, namely one generating unit of Termoli, Gissi, Modugno, Enipower

Brindisi, Altomonte, Scandale, Simeri Crichi, Rizziconi, and the power plant of Candela, is assumed

to be equal to zero. Therefore, the OPF procedure can exclude them from service and at the

same time allow the wind farms to produce more power. In any case, this assumption takes into

due consideration the need to ensure a su�cient spinning reserve, supposed equal to 50% of the

dispatched wind power, on the thermoelectric units (both coal-�red and CCGT) in service.

The optimization in N-1 security conditions considers the possible outage of the 380 and 220 kV

lines whose trip may lead to exceed the operational limit of at least one grid element with particular

regard to the macro areas Central-South and South.

The OPF results are summarized in Table 3.5 with reference to the maximum amount of wind power

generation that can be produced according to the N and N-1 security criteria. In both cases the

value is lower than the total installed capacity (5000 MW) because of the active network constraints

in the third column. The OPF calculations in N-1 security conditions, that preventively take into

account the possible outage of each of the lines included in the contingency list, make remarkable

changes to the optimal generation schedule in intact system conditions. The active constraints limit

the wind power production which �ows on the 380 kV line Matera-S. So�a, especially between the

future substations of Bisaccia and Avellino Nord.

The baseline scenario is de�ned supposing the real power productions to be �xed and considering

the above OPF results.

3.9.1.2 SVR control areas, pilot nodes, and controlling generators

The selection of SVR control areas, pilot nodes, and controlling generators is made according to

the criteria described in subsection 3.6.3.1.


The pilot nodes, whose voltages re�ect the voltage pro�les of neighbouring buses, are suitably

chosen among the sentinel nodes. The selection strategy follows these main requirements [111]:

� generators assigned to a certain area must be capable of highly a�ecting the voltage of the

corresponding pilot node (sensitivity requirement);

� SVR areas should be decoupled as much as possible from the viewpoint of reactive power

support (decoupling requirement);

� reactive power provisions by the controlling generators of a certain area, expressed in p.u.

(the so-called reactive power level), must be as like as possible (alignment requirement).

In order to meet the above conditions, the de�nition of SVR areas is performed by adopting some

speci�c voltage/var sensitivity criteria. Pilot nodes are chosen among the sentinel buses with the

highest short-circuit power. Their selection is based on the sensitivity matrix∣∣∣∂V∂Q ∣∣∣: the lower is

its value, the higher is the short-circuit power.

As regards the sensitivity requirement, the pilot nodes are assumed as P-V buses, while the gener-

ators under SVR are modelled as P-Q ones. For each area k the sensitivity matrix∣∣∣∂QP,k

∂Qj,k

∣∣∣ providesa measure of the e�ectiveness of the remote control action obtained by an additional supply of 1

Mvar by generator j, compared with a possible local control by a SVC (Static Var Compensator)

in the pilot node k: the nearer to unity is this value, the more adequate is the assignment of

generator j to area k.

Taking into account the alignment constraints imposed to the generators included in each SVR

area, the computation of the square matrix∣∣∣ ∂QP,k

∂QA,h

∣∣∣, where QA,h is the reactive power level of

area h, allows the ful�lment of the decoupling constraints to be veri�ed. In a right design of

the SVR areas, the diagonal entries∣∣∣ ∂QP,k

∂QA,k

∣∣∣ should be as nearer as possible to unity, while the

o�-diagonal terms should be as small as possible.

As described in [100, 101, 112], to de�ne a suitable zonal reactive power market, a further re-

quirement should be considered: the marginal values of reactive power produced by generators in

a certain area, calculated by the ORPF, should be similar.

According to these requisites, the Italian continental EHV system is divided into thirteen SVR

areas, as shown in Figure 3.8, where pilot nodes are also highlighted. The controlling generators

assigned to each area are displayed in Figure 3.9 (North Italy: Casanova, Baggio, S. Rocco al

Porto, S. Fiorano, Ostiglia, and Dolo), 3.10 (Adriatic side: Forlì, Villanova, and Brindisi Sud), and

3.11 (Tyrrhenian side: Calenzano, S. Lucia, S. So�a, and Laino).

Other schemes with di�erent SVR areas and/or pilot nodes have been investigated to de�ne the

most appropriate one.

Selection of the pilot node of area 7 (Forlì or Porto Tolle). The pilot node of area 7 is

selected between the buses of Forlì in Emilia Romagna and Porto Tolle in Veneto. The comparison

is made considering the absolute value of the sensitivities∣∣∣∂QP,k

∂Qj,k

∣∣∣ with reference to the controlling

generators in the area (Enipower Ravenna and Porto Corsini). The diagram in Figure 3.12 clearly

shows that the bus of Forlì is the most suitable for being the pilot node of area 7.

Selection of the pilot node of area 8 (Calenzano or Poggio a Caiano). The pilot node

of area 8 is chosen between the buses of Calenzano and Poggio a Caiano, both in Tuscany. The

comparison is made considering the absolute value of the sensitivities∣∣∣∂QP,k

∂Qj,k

∣∣∣ with reference to the


Figure 3.8: SVR areas for the Italian EHV system

Figure 3.9: SVR areas and controlling generators - North Italy


Figure 3.10: SVR areas and controlling generators - Adriatic side

Figure 3.11: SVR areas and controlling generators - Tyrrhenian side


Figure 3.12: Sensitivities∣∣∣∂QP,k

∂Qj,k

∣∣∣ - Choice of the pilot node of SVR area 7

controlling generators in the area (La Spezia, Roselectra, Bargi, and S. Barbara). Since, according

to Figure 3.13, the bus of Bargi St., to which the hydroelectric groups are connected is electrically

closer, to the node of Calenzano, this one is selected as the pilot node in the area.

Selection of the pilot node of area 13 (Laino or Rossano Calabro). The pilot node

of area 13 is chosen between the buses of Laino and Rossano Calabro, both in Calabria. The

comparison is made considering the absolute value of the sensitivities∣∣∣∂QP,k

∂Qj,k

∣∣∣ with reference to

the controlling generators in the area (Altomonte, Scandale, Simeri Crichi, and Rizziconi). The

diagram in Figure 3.14 makes it evident that the bus of Laino is the most suitable for being the

pilot node of area 13, since all the controlling groups are electrically closer to this bus than to the

other.

De�nition of area 3 (pilot node: S. Rocco al Porto). Initially, a scheme, including only

12 SVR areas (i. e. without the area of S. Rocco al Porto), is considered. In this con�guration

the generating units of Piacenza and La Casella are assigned to the area of Baggio. The relevant

sensitivities∣∣∣∂QP,k

∂Qj,k

∣∣∣ are displayed in the diagram of Figure 3.15, which shows that the values

relative to the above-mentioned power plants are the lowest (about half of the sensitivities of the

groups Enipower Ferrera and Turbigo) because of their longer electrical distance from the node of

Baggio and their smaller in�uence on its voltage. These considerations suggest the de�nition of a

new SVR area with the bus of S. Rocco al Porto as pilot node and with the groups of Piacenza

and La Casella as controlling generators. Figure 3.16 con�rms the correctness of this choice.

SVR scheme with 14 areas. The pilot node of area 6 is chosen between the buses of Dolo

in Veneto and Redipuglia in Friuli Venezia Giulia. The computation of the absolute value of the

sensitivities∣∣∣∂QP,k

∂Qj,k

∣∣∣ with reference to the controlling groups in the area (Fusina, Edison Marghera,



∂Qj,k



∂Qj,k




∂Qj,k

∣∣∣ - Area 2 (Baggio)


∂Qj,k

∣∣∣ - Generating units of La Casella and Piacenza



∂Qj,k

∣∣∣ - Generating units of Torviscosa and Monfalcone

Torviscosa, and Monfalcone) indicates that the choice of Dolo as pilot node is correct, except for

the generators of Torviscosa and Monfalcone, which are electrically closer to the bus of Redipuglia,

as shown by the diagram in Figure 3.17.

These considerations suggest the de�nition of a new SVR area with the bus of Redipuglia as pilot

node and with the groups of Torviscosa and Monfalcone as controlling generators. But in this

con�guration the decoupling requisite is not ful�lled by the two areas of the northern Adriatic side

(i. e. Dolo and Redipuglia), as shown by the computation of the sensitivity matrix∣∣∣ ∂QP,k

∂QA,h

∣∣∣:∣∣∣∣∂QP,Dolo

∂QA,Dolo

∣∣∣∣ = 0.742Mvar

Mvar

∣∣∣∣ ∂QP,Dolo

∂QA,Redipuglia

∣∣∣∣ = 0.0847Mvar

Mvar∣∣∣ ∂QP,Dolo

∂QA,Redipuglia

∣∣∣∣∣∣ ∂QP,Dolo

∂QA,Dolo

∣∣∣ = 0.11

Ful�lment of decoupling and sensitivity requirements by the adopted SVR scheme.

The ful�lment of the decoupling constraints can be checked by calculating the sensitivity matrix∣∣∣ ∂QP,k

∂QA,h

∣∣∣ (Table 3.6): in a right design of the SVR areas, in fact, the diagonal terms should be as

nearer as possible to unity, while the o�-diagonal ones should be as small as possible.

For further veri�cation of the matrix diagonal-dominance the Euclidean norm ne of the k-th row

vector (k = 1, . . . , Nar) can be calculated and then compared with the in�nity norm ni, i. e. the

diagonal term. The results are summarized in Table 3.7, which highlights the e�ectiveness of the

proposed SVR scheme with the only exception of a weak coupling between the areas of Casanova

and Baggio.

Table 3.8 shows the values of the sensitivity∣∣∣∂QP,k

∂Qj,k

∣∣∣ for all the generators under SVR. It allows

the ful�lment of the sensitivity constraints to be veri�ed: in fact, the nearer to unity is this value,


Table 3.6: Sensitivities∣∣∣ ∂QP,k

∂QA,h

∣∣∣ - Decoupling requirement

Table 3.7: Diagonal-dominance of the matrix∣∣∣ ∂QP,k

∂QA,k

∣∣∣


Table 3.8: Sensitivities∣∣∣∂QP,k

∂Qj,k

∣∣∣


the more adequate is the assignment of generator j to area k. Considering the unhomogeneity of

the indices in certain SVR areas, the generating units with the lowest sensitivities (for example,

the power plant of Ponti sul Mincio in the area of Ostiglia) could be excluded from the secondary

voltage control.

3.9.2 Test cases

The de�nition of the test cases aims at assessing the perspective impact of large wind power

injections on the voltage control performances in the Italian EHV electrical system and the bene�ts

that may be achieved thanks to the network reinforcements included in the development plan,

evaluating the economy and security level achievable in the Italian system at 2014 peak-load under

optimal reactive power schedules.

The test cases are therefore de�ned considering the following aspects:

1. what kind of generators operates under voltage control (synchronous generators and/or wind

farms);

2. planned transmission reinforcements in service or not in service;

3. presence of the wind farms connected to the �fteen collection substations in Table 3.3.

They can be summarized as follows:

1. Case 1: only synchronous generators operating under voltage control-transmission reinforce-

ments in service-wind farms' power factor equal to unity.


ments not in service-wind farms' power factor equal to unity.


ments in service-no wind farms.

4. Case 4: synchronous generators and wind farms operating under voltage control-transmission

reinforcements in service.

5. Case 5: synchronous generators and wind farms operating under voltage control-transmission

reinforcements not in service.

All the simulations consider the operation of AVR only and the operation of both AVR and SVR.

Obviously, the use of the ORPF program will also allow the determination of the optimal reac-

tive power schedules that �t the needs of the system operator, and the de�nition of a possible

remuneration scheme for reactive power providers.

3.9.3 Results

3.9.3.1 Test case 1

The test case 1 considers the transmission network reinforced as planned by the Italian TSO for

the year 2014 and a wind farms' power factor equal to 1.

Table 3.9 summarizes some ORPF results for Case 1 for both AVR and SVR: voltage magnitudes

in pilot nodes and the total reactive power production of each area calculated as the ratio between


Table 3.9: Pilot node voltages and reactive power productions - Case 1

the actual value Q and the maximum QREF . These results show that the Eastern Adriatic coast,

i. e. areas of Dolo, Forlì, and Villanova, is characterised by a relatively high utilization (0.67-

0.79 p.u.) of its reactive resources, which are however relatively poor compared to other areas,

especially in the area of Forlì and Villanova. In the case of generators under SVR, there is a small

decrease. Voltage values are within their acceptable limits, with minimum voltage 388 kV in S.

So�a (South-West of Italy).

Under primary voltage control, the ORPF procedure, which calculates the optimal voltage refer-

ence for each generation unit while minimizing the real power losses, generally raises the voltage

magnitude at the grid buses with respect to the pre-optimization condition. Nevertheless, the

exploitation of the controlling groups may not be optimal because of their di�erent utilization

and consequently some generators may have very small reactive power margins. In fact, the main

objective of AVR is to raise the voltages as much as possible, thus reducing the real power losses

in the system, by reducing the line currents and by compensating for the reactive losses thanks to

the increase of the reactive production of the line capacitances. Figure 3.18 shows some signi�cant

examples with reference to the areas of Dolo, Forlì, and Villanova.

The additional constraints on the controlling generators under SVR has just the aim of aligning

their reactive power productions with the reactive level of the corresponding area, thus ensuring

the reactive margins being uniformly distributed among the groups. These constraints usually

increase the control capability, so increasing the network security level also in case of disturbances

that may require considerable amounts of reactive power to be available. Therefore, while gen-

erally reducing the real power losses in the system, the Secondary Voltage Regulation primarily

pursues the goal of security maintenance through the ful�lment of the alignment constraints. For

this reason, the voltage magnitudes are usually lower than under AVR only. As shown in Ta-

ble 3.9, the biggest reductions refer to the pilot nodes Dolo (AVR: 401.81 kV; SVR: 395.21 kV)

and Forlì (AVR: 408.10 kV; SVR: 403.02 kV). The Primary Voltage Regulation increases the volt-

ages compared to the pre-optimization condition, but the distribution of the reactive margins

within the above-mentioned areas is quite irregular. The introduction of SVR and especially of

the alignment constraints reduces the voltage in the pilot nodes by about 5-6 kV, while reducing

the total reactive power production and hence increasing the reactive margin with respect to both

the pre-optimization condition and PVR operation only.


Figure 3.18: Reactive power margins under AVR control (areas of Dolo, Forlì, and Villanova)

As explained before, though the objective function of the ORPF procedure is the minimization

of the real power losses in the grid, the optimization under SVR has a second goal, that is, the

alignment of the reactive power generations in each control area to increase the system security.

In fact, the real losses amount to 469.37 MW under AVR and 475.74 MW under SVR. Their

variations with respect to the pre-optimization condition are -3.87% and -2.57% respectively.

The results show the bene�ts of determining the reference values for voltage regulators, also under

AVR only, by using an appropriate reactive power optimization procedure. First, the system

operation economy takes advantage from it since it allows the real losses to be reduced. Also the

system security is improved because the voltage magnitudes in the system are usually increased

under both AVR and SVR compared to the pre-optimization condition. This is an important

e�ect above all in the case of particularly stressed operating conditions. Moreover, the outcomes

demonstrate the importance of adopting the Secondary Voltage Regulation since it allows the

reactive resources to be better exploited, increasing the available reactive power margins and

hence the system controllability.

Besides these technical aspects, that are important for the System Operator, another issue, con-

cerning the de�nition of a suitable remuneration scheme for reactive power providers, can be

investigated and a possible solution can be proposed on the basis of the ORPF procedure results.

As described in subsection 3.7.2, the optimization tool calculates an economic indicator that indi-

cates the value of the reactive resources in a node: the nodal marginal value of reactive power. It

is determined by the in�uence of the reactive injection on the real power losses (MW/Mvar) and

their cost (in this study: 100 ¿/MWh) and it is based on the calculation of some sensitivity coef-

�cients that, for a particular system condition, can be given by the ORPF dispatching procedure.

So this nodal indicator provides the marginal reduction of the hourly cost of real losses (¿/Mvarh)

obtained by the additional injection of 1 Mvar in the selected node.

Figures 3.19-3.31 show the nodal marginal values of reactive power in each control area with


Figure 3.19: Nodal marginal values of reactive power - Area 1



















reference to the pilot nodes12 and the high-voltage bus-bars of the P-Q controlling generators.

These indicators are generally smaller when only AVR operates, while they are usually increased

under SVR because of a larger contribution of the losses' gradient and the presence of the alignment

constraints. Table 3.10 shows the contribute of the losses' gradient and the nodal marginal value

of reactive power in the pilot nodes under both AVR and SVR.

Figures 3.19-3.31 make it evident that the reactive power value is higher in those areas where the

grid is less meshed (for instance, in Southern Italy), the load is big (for example, in the areas of

Baggio, Dolo, and S. So�a), and the reactive resources are poor (for instance, in the areas of Forlì

and Villanova). This means that the adopted methodology is able to evaluate the importance of

the reactive resources for system operating security and above all to introduce di�erentials among

the grid buses according to their location in the network: the more indispensable the reactive

source, the higher its economic value and remuneration.

Apart from a few exceptions, regarding in particular the generators of Ponti sul Mincio in the area

of Ostiglia and Modugno in the area of Brindisi Sud, the nodal marginal value of reactive power in

a pilot node can be assumed as representative of the others. The variability of the nodal marginal

costs is strictly related to the variability of the sensitivity∣∣∣∂QP,k

∂Qj,k

∣∣∣: the greater is the homogeneity of

these sensitivities, that is, the better is the position of the pilot node with respect to its controlling

groups, the smaller is the variability of the nodal marginal values of reactive power.

We can conclude that the adoption of a hierarchical voltage control architecture and especially of

the secondary regulation level can be the basis for implementing a suitable remuneration scheme

for reactive providers, which are compensated for their service according to their position in the

grid. In fact, the subdivision of the network into SVR areas, if appropriately de�ned, can be a good

way to implement a regional (zonal) reactive power market. The selection of the control areas and

of the generators under SVR must thus take into account also the homogeneity among the nodal

12The pilot node in each �gure is labelled with *.


Table 3.10: Losses' gradient and nodal marginal value in pilot nodes


marginal values of reactive power within a certain area.

3.9.3.2 Test case 2

The test case 2 is de�ned as Case 1, except for the assumption that the transmission system has

its present structure. The simulations have in fact the aim of assessing the consequences of a

possible delay in the completion of the grid development plan and thus the bene�ts deriving from

the transmission system reinforcement.

Table 3.11 summarizes some ORPF results for Case 2 for both AVR and SVR: voltage magnitudes

in pilot nodes and the total reactive power production of each area.

In Case 2 there is a signi�cant reduction of reactive power margins in all Central-Southern areas

(Villanova, S. Lucia, Brindisi, S. So�a, and Laino), where the overall increase of reactive injection is

1115 Mvar under AVR and 1088 Mvar under SVR, while it is 1539 Mvar under AVR and 1488 Mvar

under SVR in the whole Italy. Further, there is a signi�cant reduction of voltages in Villanova and

S. So�a, that drop to very low values (Figure 3.32):

� Villanova

396.57 kV → 370.50 kV under AVR only;


Figure 3.32: SVR voltage pro�le of pilot nodes - Case 1 and Case 2

393.96 kV → 367.28 kV when also SVR operates.

� S. So�a

388.12 kV → 372.83 kV under AVR only;

388.12 kV → 372.01 kV when also SVR operates.

Indeed, under SVR, saturation of reactive capabilities occur in Villanova control area, causing the

drop of Villanova voltage to 367 kV. Also the reactive margins of the areas of S. Lucia, S. So�a,

and Laino decrease, with a reactive zonal production of about 0.75, 0.70, and 0.79 p.u. respectively

under SVR. Only the area of Brindisi Sud in Southern Italy is not critical, although also its reactive

power production increases: it is in fact �rich� in terms of available reactive resources compared to

its load.

This test case, which refers to a very stressed operating condition, as shown by the low voltage

values in Central-Southern Italy and on the Adriatic side, demonstrates even clearlier the need to

use an ORPF procedure to determine the set-points for voltage regulators. At present the grid in

these areas is poorly meshed and hence the reactive power resources need to be exploited as well

as possible.

Besides these indications about power system management, the results highlight the need for the

completion of the transmission system development planned by the Italian TSO for the year 2014.

In particular, the saturation of reactive resources in Villanova area underlines the importance of

doubling the Adriatic backbone between the substations of Villanova and Foggia. In case of delay in

the authorization and realization of this network upgrade, it would be necessary to install adequate

reactive compensation devices, e. g. capacitor banks, in view of the power system expansion in the

medium term.

Figure 3.33 displays the values of the economic indicator ¿/Mvarh: as already explained, the

greater is the value, the more critical is the corresponding area. Reactive power injections and


Figure 3.33: Reactive marginal values in pilot nodes - Case 1 and Case 2

withdrawals in the areas of Villanova, S. So�a, and Laino have the highest marginal costs:

� Case 1

Villanova AVR - SVR: 1.641 - 1.795 ¿/Mvarh;

S. So�a AVR - SVR: 1.376 - 1.776 ¿/Mvarh;

Laino AVR - SVR: 1.286 - 1.614 ¿/Mvarh.

� Case 2




These economic indicators are characterized by signi�cant regional variations, ranging from 0.2

¿/Mvarh in Northern Italy up to 4.1 ¿/Mvarh on the Adriatic side of Central Italy. Moreover,

the economic indicators demonstrate the improvements achievable thanks to the major grid rein-

forcements, as they double in the most critical areas in Case 2 without grid reinforcements.

A map of ¿/Mvarh indicators for the Italian EHV system is shown in Figure 3.34: the highest

values (blue-green coloured regions) refer to Central-South Italy, because of its poorly meshed grid,

if not properly reinforced, and the large-size wind farms that are expected in the medium term

and whose power production is likely to substitute the thermoelectric one. The map con�rms

the considerations at the ending of the preceding paragraph about the possible implementation

of a regional-based reactive power remuneration mechanism: the subdivision in homogeneously

coloured zones respects the division of the Italian EHV system into the SVR areas in Figure 3.8,

so demonstrating the usefulness and the e�ectiveness of the proposed methodology [113].

Since the ¿/Mvarh indicators and hence their graphical representation identify the grid locations

where the reactive resources are more valuable from an economic point of view because of their


Figure 3.34: Map of nodal ¿/Mvarh indicators - Case 2

indispensability for power system operation, the information provided by the map can be also used

by the transmission planner to easily identify the poorest grid areas in terms of reactive capability

where additional measures have to be taken to control grid voltages.

3.9.3.3 Test case 3

A third case (named Case 3) is analysed to assess the impact of wind generation on voltage

pro�les and reactive power margins essential to preserve the system security and controllability

in case of contingency. The wind power production is assumed to be zero and it is substituted

by an equivalent amount produced by combined cycle gas turbines (CCGT) in Southern Italy.

Transmission reinforcements are supposed in service.

Table 3.1213 gives the voltage magnitudes in pilot nodes and the total reactive power production

of each area in Mvar and in p.u..

In Case 3 the reactive power margins in Central-Southern Italy are higher than in Case 1 (-

576 Mvar under AVR and -434 Mvar under SVR), especially in Villanova control area, as shown

in Figure 3.35, which displays the Mvar still available in each control area.

Figure 3.36 compares the marginal costs of reactive power in pilot nodes in Case 3 vs. Case 1, while

Figure 3.37 considers the 380 kV wind power collection substations. The presence of wind power

generation with �xed power factor (equal to unity) in Case 1 (and maybe real power re-dispatching

13The reactive power margins in per unit are calculated considering the reference values QREF of the base case(Case 1) to allow the comparison with the other test cases, although the maximum reactive power capabilities inSouthern Italy in Case 3 are higher because the wind farms are substituted in production by thermoelectric unitswhich can participate to reactive power support and voltage control.



Figure 3.35: Reactive power margins in Central-Southern Italy - Case 1 and Case 3


Figure 3.36: Reactive marginal values in pilot nodes - Case 1 and Case 3

as well) causes a substantial increase in marginal costs of reactive power in Central-Southern Italy,

especially in the areas of Villanova, S. So�a, and Laino:

� Villanova

0.702 ¿/Mvarh under AVR only;

0.926 ¿/Mvarh when also SVR operates.

� S. So�a



� Laino



The reactive control in the area of Brindisi is less critical than in the areas of Villanova, S. So�a,

and Laino, as witnessed by the nodal marginal costs in its three 380 kV wind power collection

substations (Erchie, Latiano, and Castellaneta), because its reactive resources are greater than

in the neighbouring areas. The nodal marginal cost of reactive power in Castellaneta is higher

than the values in Erchie and Latiano, which are closer to Brindisi large thermoelectric generation

units. Nodal reactive marginal costs in Carlopoli, Maida, and Marcedusa are somewhat lower than

the value in Laino, which is their pilot node. Nodal reactive values in all other wind collection

substations are similar to the value in Villanova. The results of Case 3 show that, even with the

same system and generation external conditions and real power market price (cost of losses), actual

very high or very low production of wind power can lead to signi�cant di�erences of nodal reactive

values in the most critical network areas.


Figure 3.37: Reactive marginal values in wind collector substations - Case 1 and Case 3

3.9.3.4 Test cases 4 and 5

Finally, two analyses are performed considering di�erent hypotheses about the �reactive charac-

teristics� of WTGs (capability to control their power factor in the range 0.95 over-excited/0.95

under-excited), according to the provisions of annex A17 of the Italian Grid Code [108]. The pos-

sible participation of WTGs to voltage control, both AVR and - more theoretically - SVR (thanks

to the exploitation of suitable power electronics devices) is studied in Case 4 with all grid reinforce-

ments and in Case 5 without reinforcements. A new control area (area of Foggia) is de�ned and

some wind power generators in Apulia and Campania (Deliceto, S. Severo, Manfredonia, Cerignola,

and Troia) are assigned to it. The others are instead assigned to the areas of Brindisi Sud (Irsina,

Castellaneta, Erchie, and Latiano), S. So�a (Ariano Irpino, Spinazzola, and Bisaccia), and Laino

(Marcedusa, Maida, and Carlopoli).

The additional reactive resource is about 1250 Mvar, according to the allowed power factor range:

0.95 under-excited/0.95 over-excited. The reactive power productions in Central-Southern Italy

in Case 4 are lower than in Case 1 (about -402 Mvar under AVR and -200 Mvar under SVR),

with main changes in Villanova area, while the voltage pro�le does not show signi�cant variations.

As given in Table 3.13, reactive power margins available in the most critical areas improve. In

particular, as regards Villanova area, whose reactive capability is the same of Case 1, its reactive

margin increases:

� under AVR: from 0.21 p.u. in Case 1 to 0.79 p.u. in Case 4;

� under SVR: from 0.24 p.u. in Case 1 to 0.75 p.u. in Case 4.

This reduction is due to the reactive power production by the wind farms' generators belonging

to Foggia control area, which produce about 280 Mvar under AVR operation and nearly 360 Mvar

when also SVR functions.



The bene�ts of WTG participation to voltage control are re�ected by decreasing nodal reactive

values with respect to Case 1:

� Case 1




� Case 4




Figure 3.38 displays the nodal reactive marginal costs in wind collector substations: it con�rms

the overall decrease in reactive power values in Central-Southern Italy thanks to the contribution

of the wind generators to reactive support.

The test case 5 is derived from Case 2 assuming that the wind farms' generators participate to

voltage regulation. Case 2, in which all network upgrades are not supposed in service, represents

a very stressed operating condition from the viewpoint of reactive power provision by the System

Operator, because the reactive resources in some grid areas are not enough to support voltage so

that in some nodes it drops under 370 kV. Also the simulation on Case 5 has the aim of assessing

the possible bene�ts that may derive from the participation of the wind farms to voltage control

and reactive power support. Table 3.14 summarizes some ORPF outcomes.

The comparison between Case 2 (Table 3.9) and Case 5 (Table 3.14) makes it clear that the

contribution of WTGs to voltage regulation can be very important to manage the system with

an adequate security level, particularly in stressed operation conditions. The availability of more

reactive resources in Southern Italy causes a substantial increase in voltage magnitudes in the most

critical areas (Villanova and S. So�a), which are now within the acceptable range (Figure 3.39).

The bene�ts already shown in the preceding test case are very crucial in Case 5. For instance,

as regards Villanova area, its reactive margin increases notably and in particular the new reactive


Figure 3.38: Reactive marginal values in wind collector substations - Case 1 and Case 4



Figure 3.39: Voltage pro�le of pilot nodes - Case 2 and Case 5

resources in the neighbouring area of Foggia allow the saturation of the reactive capability in

Villanova area to be avoided:

� under AVR: from 0.07 p.u. in Case 2 to 0.24 p.u. in Case 5;

� under SVR: from saturation in Case 2 to 0.13 p.u. in Case 5.

The highest nodal marginal values change as follows:

� Case 2




� Case 5




3.9.3.5 Real losses' variation

The importance of transmission system development, from both economic and security point of

view, is demonstrated also by real losses' variation in the various test cases, as shown in Table 3.15.

The most favourable scenario is Case 3, i. e. without wind power generation, while Cases 2 and

5 have the highest losses because of the absence of network reinforcements (about 100 MW addi-

tional losses, i. e. 20% of power losses in the grid model under study). Bene�ts can be quanti�ed

multiplying the reduction of real power losses by the price of real power determined by market


Table 3.15: Real losses and their variations with reference to Case 3

clearing. In the cases without grid reinforcements, WTG participation to voltage regulation (Case

5) allows a 25 MW decrease of real losses compared to Case 2. The security increase, already

remarked by the comparison of reactive margins Case 4 vs. Case 5, would also reduce the practical

need for constraining on expensive generators in South Italy.

3.10 Chapter conclusions

Liberalised electricity markets consider voltage regulation and reactive power support as an ancil-

lary service. Reactive power is required for transmission of real power, voltage and system control,

and normal operation of power systems. Therefore, reactive power service can be considered one

of the most important ancillary services in electricity market. However, the origin and the main

characteristics of reactive power, �rst of all its very local nature and its highly limited ability to

travel in the network, raise some di�culties in its management in a deregulated environment. The

acquisition and pricing of the reactive power and voltage support services is the major challenge.

In vertically integrated structures, one utility operated power generation units, on the one hand,

and transmission and distribution systems, on the other hand. It also handled the voltage control

issue, both in the short-term (day-to-day dispatch of units) and long-term (system planning). The

cost of this service was implicitly taken into account in the cost of the energy supply for end

consumers.

As a consequence of the restructuring of electric industry and the resulting deintegration of gen-

eration and transmission, the reactive power support and the voltage regulation are no longer an

integral part of the electricity supply. Further, the competition requires that the costs associated

with this ancillary service is made explicit by means of suitable methods. The provision mecha-

nism and above all the tari� structure for reactive power must thus consider the di�erent views of

buyers and sellers. The former, the TSO, tends to give a �societal� evaluation of available reactive

resources based on the expected bene�ts deriving from their utilization. The latter, producers, on

the contrary, aim at the economic compensation in order to recover costs that they incur, while

sometimes forgetting the concept that voltage regulation and reactive power support are essential

system services needed to deliver the real power which they supply to consumers. Main task of

the TSO is to determine the value of the reactive power support required to the generation buses

in order to �t its needs for a secure and e�cient system operation. Also a consistent reactive price

structure for �nancial compensation of reactive power providers needs to be de�ned: the basis for

its implementation can be the estimated values of the reactive support in grid nodes.

Besides the above aspects which derive from the peculiarities of reactive power service and the

restructuring process, among the recent developments that challenge the traditional approach to

voltage control, there is the increasing concern towards wind energy exploitation for generating


electricity. An increasing penetration of wind power, normally characterised by limited reactive

support and voltage control capabilities and displacing thermoelectric generation with greater

capabilities, causes a reduction of the reactive resources available in the power system. For this

reason, transmission operators and planners and wind project developers alike are facing increasing

challenges with regard to reactive power control. The economies of scale of larger and larger plants

and increasing development of sites far from load centers are contributing factors. Regulations and

standards in this area are in a state of �ux as a result of the rapid changes in market incentives and

in the wind turbine technology itself. Wind turbine and power system equipment manufacturers

are responding to these challenges by making technical solutions available to the project planner,

and regulations and standards with regard to wind reactive power capability are slowly catching

up with the market.

The analysis has investigated three main issues: the optimal reactive power provision that �ts the

needs of system operator, the de�nition of an economic compensation structure for reactive power

suppliers, and the impact of wind power on voltage control and reactive power support. The study

has focused on the Italian case with reference to the projection horizon of the year 2014 in peak

load conditions, and the simulations have been carried out by means of an Optimal Reactive Power

Flow (ORPF) procedure and by considering the voltage control structure designed for the Italian

EHV network.

The problem has been analysed mainly from the TSO perspective, though the adoption of a

hierarchical voltage regulation architecture and of a suitable reactive power optimization program

allow a possible remuneration scheme for reactive power providers to be de�ned. In particular,

in addition to the voltage and reactive reference values for the voltage regulators, resulting from

the optimization of the reactive power schedule problem, the ORPF procedure calculates a nodal

indicator (¿/Mvarh) which represents the marginal real losses' variation consequent to a nodal

reactive injection in a certain grid bus and thus gives a �measure� of reactive power value. These

indicators provide signi�cant price signals needed for the economic compensation for reactive power

supply so quantifying the reactive power cost in grid nodes and identifying the system areas where

this resource is particularly valuable.

The simulations on the Italian EHV continental system has demonstrated that the power sys-

tem operation bene�ts from the optimization of the reactive power schedule problem also under

Automatic Voltage Regulation (AVR) only, from both technical (voltage increase) and economic

(real losses' reduction) point of view. The adoption of a higher voltage control level (SVR) allows

system security to be further enhanced since, while minimizing real power losses, it aligns the

reactive power margins of the controlling generators in each SVR areas, so increasing the system

controllability.

Moreover, the determination of nodal marginal reactive values by the ORPF procedure can be used

to propose a reactive pricing structure suitable for deregulated electric market frameworks. The

tests described in the chapter have highlighted that the presence of an adequate HVC (Hierarchical

Volatge Control) scheme and above all an appropriate subdivision of the electrical system into SVR

control areas can be useful to de�ne a zonal structure for eventual locational di�erences in reactive

power valorisation.

Finally, the test cases, to which the ORPF program has been applied, have been de�ned with the

aim of assessing the expected impact of an increasing penetration of wind energy in the Italian

transmission system, on the one hand, and the bene�ts deriving from the realization of the major

network reinforcements planned by the TSO, on the other hand.


In order to quantify wind impact on voltage regulation and reactive support, both the economic

aspect, represented by the nodal marginal values, and the security one, based on the reactive power

margins available on controlling generating units and on their usability to cope with possible per-

turbations, have been investigated. The results could be taken into account when evaluating the

eventual update of the regulatory treatment of the voltage control ancillary service and of reactive

transits at the connection points across grids. Speci�c results have shown that the optimization

outcomes vary remarkably depending on the actual high or low level of wind production. Further,

the e�ect of WTGs' participation in voltage control and reactive power support has been analysed.

The simulations have shown that their participation to primary and also secondary voltage regu-

lation can be helpful to increase the reactive resources available in a certain grid area, which can

be indispensable especially in very stressed operating conditions.

Finally, the tests' outcomes have underlined the need to complete the grid development plan de�ned

by the TSO for the medium term for a better exploitation of reactive resources, also in view of the

expected growth of wind power.

Chapter 4

Conclusions

The research work presented in this thesis has focused on the consequences of the deintegration

of generation and transmission resulting from the restructuring and liberalisation of the electricity

industry. In the new environment these activities are no longer combined in vertically integrated

utilities as they used to be. The objectives of power producers and system operators are completely

di�erent and thus the new situation has introduced new challenges a�ecting both planning and

operation of power systems.

The �rst part of the research work has dealt with the relationship between generation expansion and

transmission development in presence of competition on the supply side. The objective has been

to demonstrate that a more coordination in the planning process of generation and transmission

systems can contribute to a more coherent development of the whole power system enhancing

its operational reliability and security and improving electricity market e�ciency. The need for a

well-coordinated planning activity is based on several considerations, particularly on the reciprocal

dependence between the development decisions of these two systems.

The methodology described in Chapter 2 is based on the concept that generation and transmis-

sion investments can be interchangeable and, if properly de�ned, they can favourably a�ect both

system operation security and market e�ciency. The implementation in the Matlab program-

ming language of the procedure for calculating and plotting Weighted Transmission Loading Relief

(WTLR) sensitivities and the tests on the CIGRE 63-bus network and then on the Italian EHV

electric system have highlighted the e�ectiveness of these nodal indices for the selection of invest-

ments in both generation and transmission. In particular, it has proved to be a useful tool for

transmission planner since it is able to provide very interesting information about the weakest grid

sections and the impact of generation expansion on network security, and to help the grid planner

to de�ne possible priority lists of planned reinforcements and to determine new network upgrades.

Further, it can be used to underline the bene�ts of the grid development plan and the importance

of its realization and to send generation owners clear indications about the most suitable grid areas

for installing new power plants in order to avoid possible limitations on power production due to

some network constraint.

Besides these application aspects, which have been demonstrated and shown by the simulations'

outcomes, an important phase of the research work has been to investigate the limits of the original

WTLR methodology and to propose possible solutions. The �rst objective has been the reduction

of the total computational time of the Matlab-coded procedure by introducing the Line Outage

Distribution Factors (LODFs) to calculate the real power �ows in post-contingency conditions, and

164

CHAPTER 4. CONCLUSIONS 165

by using the base ISDFs, that is, in intact system conditions, to compute the WTLRs. The second

objective has been to remove the WTLR dependence on the selection of the slack bus in the grid.

Therefore, the concept of distributed slack bus has been introduced in both load �ow calculations

and ISDF computation. Finally, the MVA rating approximation, that is the main limit of the

original methodology, has been removed by suitably modifying the original Matlab-coded program

to consider the actual power �ow limits in the calculation of branch overloads.

The second part of the research work has focused on the reactive power service in a liberalised

environment. The three main issues investigated in Chapter 3 have been: the optimal reactive

power provision that �ts the needs and requirements of system operator, the de�nition of a �nancial

compensation structure for reactive power suppliers, and the impact of wind power on voltage

control and reactive power support.

The analysis has been carried out considering the perspective of system operators, which are re-

sponsible for a secure and reliable system operation and for the acquisition of all services, including

reactive power support and voltage regulation, indispensable for maintaining adequate standards

of power quality. Therefore, they have the task of implementing a suitable structure for e�ciently

managing this ancillary service and of assessing which resources are required according to both

economic and technical (i. e. grid topology) criteria. The adoption of a HVC scheme and an Op-

timal Reactive Power Flow procedure to de�ne its reference values (voltage and reactive power)

has proved to be an interesting starting point for the implementation of an e�cient mechanism for

reactive power provision by the TSO. Furthermore, on the basis of the estimated values of reactive

power when Secondary Voltage Regulation operates, a consistent reactive pricing structure and an

e�ective economic compensation scheme for reactive power suppliers can be de�ned.

Besides the above general issues, the tests carried out on the Italian EHV network with reference

to the projection year 2014 have investigated other two aspects: on the one hand, the impact of the

wind farms expected for the medium term in Southern Italy, and, on the other hand, the bene�ts

of realizing the major network reinforcements planned by the Italian TSO. The forecasted increase

of wind power has in fact various implications in system design, planning, and operation. The

analysis has assessed the impact on voltage control, taking into account the current legislative,

regulatory, and technical framework with respect to voltage regulation and reactive requirements

for producers connected to the Italian national transmission grid. Further, WTGs participation in

voltage control has been considered and the outcomes have shown that it can be an e�ective way

to integrate wind power in electrical systems. Finally, some speci�c simulations have highlighted

the need for the completion of the transmission system development planned by the TSO, to better

exploite the available reactive resources and to support the increasing wind penetration. Therefore,

simulation results and conclusions that are derived from them might be useful in power system

planning and for regulatory purposes as well.

Appendix A

CIGRE-63 bus test system

The CIGRE 63-bus test system [18], shown in Figure A.1, has been used in this thesis to implement

and test the proposed Matlab-coded procedure for the calculation and graphical representation of

the Weighted Transmission Loading Relief (WTLR) sensitivities. Moreover, it has been used to

implement some modi�cations in the original WTLR methodology: the introduction of the Line

Outage Distribution Factors (LODFs) and the adoption of the distributed slack bus concept.

The system can be divided in �ve areas, named R, M, F, T, and V. The buses of each area

are labeled with an integer number with three �gures, the area code, and the voltage level. For

instance, the buses 11R3, 65T2, and 9V1 belong to area R, T, and V respectively, and are referred

to the voltage levels 15 kV, 150 kV, and 220 kV.

The system encompasses a total demand of 2080 MW and has 63 nodes, 112 branches (lines and

transformers), and 16 thermoelectric generators. Bus 41M3 is selected as the slack bus.

The generators' cost curves are quadratic functions of the production P :

C(P ) = C0 + C1P + C2P2 (A.1)

Area R represents an independent power producer, area M is the main grid at 220 kV, while areas

F, T, and V can represent three sub-transmission systems at 150 kV with embedded generation.

The prices of the generators in areas R and F are very low, while prices o�ered in area V are very

high.

Demand is supposed inelastic and so the aggregate consumer curve is represented by a vertical line

in the diagram quantity-price.

The data for generator buses is provided in Table A.1, including the generators' limits and the

three coe�cients of the cost curves. The demand at load buses are given in Table A.2. The data

for the transmission lines connecting system buses is given in Table A.3.

166

APPENDIX A. CIGRE-63 BUS TEST SYSTEM 167

Figure A.1: CIGRE 63-bus test system

Table A.1: Generator buses

APPENDIX A. CIGRE-63 BUS TEST SYSTEM 168

Table A.2: Load buses

Table A.3: Transmission lines

Appendix B

Power Distribution Factors

B.1 Basic distribution factors

We consider a system with N + 1 buses and L lines [13, 14]. We denote by N = {0, 1, 2, . . . , N}the set of buses, with the slack bus at bus 0, and by L = {l1, l2, . . . , lL} the set of transmission

lines and transformers that connect the buses in the set N . We denote each element l ∈ Lby the ordered pair l = (i, j) with the convention that the direction of the �ow on line l is

from node i to node j. The serial admittance of line l is gl − jbl, the real power �ow is fl and

f = [f1, f2, . . . , fL]T . The net real power injection at node n ∈ N is denoted by pn and we de�ne

p =[p1, p2, . . . , pN

]T. Transactions are represented by the set of power injection-withdrawal

(I −W ) node pairs, W = {w1, w2, . . . , wW }, with each element in this set denoted by the ordered

triplet w = {m, n, t} representing an I−W node pair with from node m, to node n, in the amount

t.

We study the response of the real line �ow to changes in nodal injections. Consider the nodal

injection vector p and the corresponding real line �ow vector f . Denote the system state by

s =[θT , V T

]T, where θ =

[θ1, θ2, . . . , θN

]T(V =

[V 1, V 2, . . . , V N

]T) is the voltage phase

angle (magnitude) vector. Denote the reference conditions by p(0), s(0) and f (0) that satisfy both

the equations:

g(s(0))− p(0) = 0 (B.1)

h(s(0))− f (0) = 0 (B.2)

where equation (B.1) represents a statement of the real power �ow equations and the component

l of h(·) is the expression for the real �ow on line l = (i, j), l ∈ L:

hl (s) = gl

[(V i)2 − V iV jcos (θi − θj)

]+ blV

iV jsin (θi − θj) (B.3)

For a small change ∆p that changes the value from p(0) to p(0) + ∆p, we denote by ∆s (∆f) the

corresponding change in the state s (real line �ows f). We assume the system stays in balance for

the change ∆p and neglect the changes in losses so that, for every MW increase in the injection at

node n 6= 0, there is a corresponding MW increase in the withdrawal at the slack node 0. In other

words, ∆p0 = −∑

n∈N , n 6=0

∆pn. We apply the �rst order Taylor's series expansion near the reference

169

APPENDIX B. POWER DISTRIBUTION FACTORS 170

point s(0):

g(s(0) + ∆s) = g(s(0)) +

(∂g

∂s

)s(0)

∆s+ h.o.t. (B.4)

h(s(0) + ∆s) = h(s(0)) +

(∂h

∂s

)s(0)

∆s+ h.o.t. (B.5)

For �small� ∆p, ∆s is small and so we neglect the higher order terms (h.o.t.). We furthermore

assume (∂h/∂s)s(0) to be non-singular and henceforth drop the bar in the notation so that:

∆s ≈[∂g

∂s

]−1∆p (B.6)

∆f ≈ ∂h

∂s∆s =

∂h

∂s

[∂g

∂s

]−1∆p (B.7)

The sensitivity matrix in equation (B.7) depends on s(0) and this dependence on the system

operating point makes it less than practical for power system applications.

To simplify the computation of the sensitivity matrix, we next introduce the assumptions used in

the derivation of DC power �ow models and make use of the reduced nodal susceptance matrix:

B = ATB′A (B.8)

whereB′ = diag [b1, b2, . . . , bL] is the diagonal branch susceptance matrix and A = [a1, a2, . . . , aL]T

is the branch-to-node incidence matrix with the row l of the matrix: al =

[0 . . . 0

i1 0 . . . 0

j

−1 0 . . . 0

]T.

We assume B to be non-singular. Under these assumptions, s reduces to θ and the expressions for

the partial derivatives become ∂g/∂θ≈ B and ∂hl/∂θ≈ blal. We furthermore de�ne A = B′A to

be the admittance weighted branch-node incidence matrix, then

∆f ≈ AB−1∆p = Ψ ∆p (B.9)

We henceforth replace the approximation by the equality:

∆f = Ψ ∆p (B.10)

The L × N matrix Ψ = AB−1 is an approximation of the sensitivity matrix and is called the

Injection Shift Distribution Factor (ISDF) matrix. Since A and B are solely determined by the

network topology and the line parameters, Ψ is independent of s(0). The ISDF of a line l ∈ L with

respect to a change in injection at node n ∈ N , n 6= 0 is the element ψnl in row l, column n of

Ψ. Note that ψnl is de�ned implicitly under the assumption that there is a corresponding change

∆p0 in the injection at the slack node 0 with ∆p0 = −∆pn. Therefore, the ISDF is dependent on

the slack bus. As the location of the slack bus changes, the values of the ISDFs may change. The

notion of the ISDF may be extended to include the slack bus 0. Since the injection and withdrawal

buses are identical in this case, ψnl ≡ 0 for any l ∈ L.

In many applications, the impacts of changes in the quantity of an I −W node pair on the real

line �ows are of interest. We may evaluate the change in the real �ow on a line l due to a change

∆t in the transfer quantity of an I −W node pair w = {m, n, t} ∈ W with ISDFs. This change is


represented by setting ∆pm = ∆t = −∆pn. The corresponding real �ow change on line l is

∆fl = ψml ∆pm + ψn

l ∆pn = (ψml − ψn

l ) ∆t (B.11)

The ISDF di�erence term is called the Power Transfer Distribution Factor (PTDF) of line l with

respect to the I −W node pair w ∈ W and is de�ned by

ϕ(w)l =

∆fl∆t

= ψml − ψn

l (B.12)

In this case, the compensation at the slack bus cancels out since ∆pm −∆pn =(∆pm −∆p0

)−(

∆pn −∆p0). As such, the PTDF is independent of the slack bus.

A line l = (i, j) is radial if either Hi = {l} or Hj = {l}, where Hi (Hj ) is the set of lines that

connect to node i (j). For the radial line l with Hi = {l}, i 6= 0,

ψnl =

{1

0

if n = i

otherwise(B.13)

since the only impact on line l comes from the injection at node i. For any other line l 6= l, the

injection change at the terminal nodes i and j has the same impact,

ψil

= ψj

l∀l 6= l (B.14)

B.2 Impact of changes in network topology and parameter

values

The ISDFs and PTDFs play a key role in congestion modeling used in the new competitive envi-

ronment. Clearly, these factors are evaluated for a given topology and parameter values and an

operating point that satis�es, to a greater or lesser extent, the assumptions cited in the previous

section. However, in many cases of interest, there are changes in the network topology, parameter

values and the operating point, while the ISDFs and PTDFs are held constant in the applications

in which they are used. Such usage, in e�ect, neglects the impacts of these changes. In this section,

we evaluate the e�ect of these changes.

We �rst consider the impacts of changes in network parameters. Let us denote by L′ = {l′1, l′2, . . . , l′L} ⊆L the subset of lines whose parameters are changed. For each line l′ ∈ L′, its line susceptance ischanged from bl′ to bl′+∆bl′ . Denote the analogues of the matricesB′ (L×L), A and Ψ (L×N) cor-

responding to the lines in L′ byB′L′ = diag[bl′1 , bl′2 , . . . , bl′L′

](L′×L′), AL′ =

[al′1

, al′2, . . . , al′

L′

]Tand ΨL′ =

[ψ

l′1, ψ

l′2, . . . , ψ

l′L′

]T(L′ × N) where ψT

l′is row l′ of Ψ , the ISDF matrix. Let

∆B′L′ = diag[∆bl′1 , ∆bl′2 , . . . , ∆bl′

L′

], ∆bl′ 6= 0, ∀l′ ∈ L′. The changes in L′ result in changing the

B matrix into B + AT

L′∆B′L′AL′ . This, in turn, changes each row of the ISDF matrix by:

∆ψT

l=

∆bl

blψT

l−bl + ∆bl

blψT

lA

T

L′

(B′L′∆B′−1L′ + ΨL′A

T

L′

)−1ΨL′

−ψT

lA

T

L′

(B′L′∆B′−1L′ + ΨL′A

T

L′

)−1ΨL′ per l /∈ L′

(B.15)


The derivation of equation (B.15) is straightforward using the Sherman-Morrison-Woodbury for-

mula.

For l /∈ L′, the L′-dimensional row vector φT

l,L′ = −ψT

lA

T

L′

(B′L′∆B′−1L′ + ΨL′A

T

L′

)−1establishes

the relation between the pre-change real �ows fL′ =[fl′1 , fl′2 , . . . , fl′L′

]Tand the change ∆fl in

the real �ows on line l /∈ L′ due to the parameter changes with ∆fl = φT

l,L′fL′ . Particularly,

φl,l′

= −ψi′

l − ψj′

l

bl′

∆bl′+(ψi′l′ − ψ

j′

l′

) (B.16)

is proportional to the quantity ψi′

l − ψj′

l , if L′ = {l′ = (i′, j′)}. Note that if both B and B +

AT

L′∆B′L′AL′ are non-singular, B′L′∆B′−1L′ + ΨL′AT

L′ is invertible.

B.2.1 Outage of a line

Network topology changes such as line outages and line additions may be considered as special

cases of parameter changes. For example, for the outage of a line l′ = (i′, j′), L′ = {l′}, AL′ = aTl′

and ∆bl′ = −bl′ , so that:

∆ψT

l=

−ψT

l′if l = l′

ψi′

l − ψj′

l

1−(ψi′l′ − ψ

j′

l′

)ψT

l′otherwise

where the factor

φl,l′ =ψi′

l − ψj′

l

1−(ψi′l′ − ψ

j′

l′

) (B.17)

is called Line Outage Distribution Factor (LODF) which establishes the relationship between the

pre-outage real �ow fl′ on line l′ and the change ∆fl on the real �ows on line l 6= l′ due to the

outage of line l′ with ∆fl = φl,l′fl′ . Note that ψi′

l′ − ψj′

l′ = 1 only when {l} is a cutset of the

network. In that case, the outage of line l breaks the system into two separate subnetworks and

the ISDFs needs to be rede�ned for each subnetwork.

B.2.2 Closure of a line

Another example is the addition of a line l′ = (i′, j′). Two possible situations of interest are:

1. l′ is a radial line with i′ /∈ N whose addition results in L = L ∪ l′ and N = N ∪ i′. We may

apply equations (B.13) and (B.14) to construct the augmented ISDF matrix

Ψ =

[Ψ ψi′

0T 1

](B.18)

where ψi′ = ψj′ , the column j′ of Ψ.


2. l′ is a new line with i′, j′ ∈ N whose addition results in L = L ∪ l′. We de�ne a new ISDF

row vector ψT

l′= aT

l′B = bl′ aTl′B and construct the augmented (L+ 1)×N ISDF matrix

Ψ =

[Ψ + ∆Ψ

ψT

l′+ ∆ψT

l′

](B.19)

where ∆ψT

l′and each row of ∆Ψ is determined by ∆ψT

l= −

ψi′

l − ψj′

l

1−(ψi′l′ − ψ

j′

l′

)ψT

l′.

Appendix C

Slack bus modeling in load �ow

solutions

Power �ow analysis is a basic tool for power system studies. In a traditional power �ow with a

single slack bus model, one generator bus is selected to be the voltage phase angle reference and

balances the power mismatch due to uncertain system loss. Without the angle reference bus, that

is, if all buses are included in the Newton-Raphson formulation, the Jacobian matrix will certainly

be singular: so the slack bus allows the solution of the non-linear set of power �ow equations to be

feasible. The loss-compensating characteristic of the slack bus means that total losses are assigned

to only one slack bus: in fact, since the power losses in the network are not known in advance, to

maintain the real power balance in the system one cannot specify the real power generated at all

generators.

However, in the actual operation of electric power systems there is no single slack bus, instead

there are many generators distributed geographically throughout the system which take on the

function of a slack bus. So the concept of slack bus, as the voltage phase angle reference, is a

mathematical necessity but its loss-compensating characteristic has no physical relationship to any

generator bus. Exception arises when a small system is linked to a much bigger system via a single

tie line (single bus). In this case, one can represent the large system with an equivalent generator,

which can hold the voltage constant and generate as much power as needed, i. e. the slack bus

features. For instance, in a distribution network fed by a substation, the transmission network

acts as a slack bus with respect to the distribution network.

In the light of these considerations, a distributed slack bus power �ow is a better tool, even if the

adoption of a single slack bus usually does not represent a problem in a well de�ned deterministic

load �ow problem.

C.1 Single slack bus power �ow

The load �ow real power equations in a single slack bus model are [114]:

∆Pi = P i − Ci − Pi(θ1, . . . , θn−1, Vm+1, . . . , Vn−1) i ∈ [1, n− 1]

∆Ps = P s − Cs − Ps(θ1, . . . , θn−1, Vm+1, . . . , Vn−1) + ∆Pimb

(C.1)

174

APPENDIX C. SLACK BUS MODELING IN LOAD FLOW SOLUTIONS 175

where:

� buses 1, . . . ,m are P-V buses, buses m + 1, . . . , n − 1 are P-Q buses, and bus n is the slack

bus;

� ∆Pi is the real power mismatch at bus i;

� P i and Ci are the real power generation and the real load at bus i respectively;

� Pi(θ1, . . . , θn−1, Vm+1, . . . , Vn−1) is the sum of the real power �ows on the branches connected

to bus i: it is a function of the voltage phase angles and magnitudes;

� ∆Pimb is the real power unbalance due to uncertain power losses.

Denote the vector of the real power unknowns by:

∆θ = [θ1, θ2, . . . , θm, θm+1, . . . , θn−1,∆Pimb]T (C.2)

By linearizing the system (C.1) around the equilibrium point:

∆Pi =∑n−1

j=1

∂Pi

∂θj∆θj + 0 ·∆Pimb i ∈ [1, n− 1]

∆Ps =∑n−1

j=1

∂Ps

∂θj∆θj + 1 ·∆Pimb

(C.3)

The load �ow real power equations, that can be solved by the Newton-Raphson method, can be

formulated as follows:

∆P1

∆P2

...

∆Pn−1

∆Ps

=

∂P1

∂θ1

∂P1

∂θ2· · ·

∂P1

∂θn−10

∂P2

∂θ1

∂P2

∂θ2· · ·

∂P1

∂θn−10

......

......

...

∂Pn−1

∂θ1

∂Pn−1

∂θ2· · ·

∂Pn−1

∂θn−10

∂Ps

∂θ1

∂Ps

∂θ2· · ·

∂Ps

∂θn−11

·

∆θ1

∆θ2...

∆θn−1

∆Pimb

(C.4)

Figure C.1 shows the �ow-chart of a single slack bus load �ow procedure. At each iteration the

load �ow Jacobian is updated and the new system state is determined. The voltage phase angles

θi, the voltage magnitudes Vi, and the slack bus injection As are updated, after calculating the

real and reactive state variables (∆θi and ∆Vi):

θ(k+1)i = θ

(k)i + ∆θ

(k)i i ∈ [1, n− 1]

V(k+1)i = V

(k)i + ∆V

(k)i i ∈ [m+ 1, n− 1]

A(k+1)s = A

(k)s + ∆P

(k)imb

(C.5)

The convergence is achieved when the real and reactive power mismatches are lower than the given

tolerances. At the end, the slack bus power generation has to be updated on the basis of the �nal


injection calculated by the procedure:

Ps = As + Cs (C.6)

where Ps, As, Cs are the real power generation, the real power injection, and the real load at the

slack bus respectively.

Usually, the largest generator is arbitrarily proposed as slack in absence of better criteria, which

is a good choice in case the total imbalance is relatively large [115]. Other suggested criteria for

single slack bus selection are [116]: a) have the largest short-circuit current, b) have a large number

of lines connected to it, c) have a voltage leading all other voltages of the system.

C.2 Distributed slack bus power �ow

The basic concept is that of de�ning a small set of generation units which function as the slack bus

to balance the real power mismatch due to uncertain system losses. In particular, it is distributed

to these generation units according to the so called participation factors ρi.

To introduce the distributed slack bus, the load �ow equations have to be properly modi�ed. So

the system (C.1) becomes:

∆Pi = P i − Ci − Pi(θ1, . . . , θn−1, Vm+1, . . . , Vn−1) + ρi∆Pimb i ∈ [1,m]

∆Pi = P i − Ci − Pi(θ1, . . . , θn−1, Vm+1, . . . , Vn−1) i ∈ [m+ 1, n− 1]

∆Ps = P s − Cs − Ps(θ1, . . . , θn−1, Vm+1, . . . , Vn−1) + ρs∆Pimb

(C.7)

By linearizing the system (C.7) around the equilibrium point:

∆Pi =∑n−1

j=1

∂Pi

∂θj∆θj + ρi∆Pimb i ∈ [1,m]

∆Pi =∑n−1

j=1

∂Pi

∂θj∆θj + 0 ·∆Pimb i ∈ [m+ 1, n− 1]

∆Ps =∑n−1

j=1

∂Pi

∂θj∆θj + ρs∆Pimb

(C.8)

Only the last column of the load �ow real power Jacobian has to be modi�ed introducing the

participation factors ρi of those P-V buses that act as the slack bus:

∆P1

...

∆Pm+1

...

∆Ps

=

∂P1

∂θ1· · ·

∂P1

∂θm+1· · · ρ1

......

......

...

∂Pm+1

∂θ1

...∂Pm+1

∂θm+1

... 0

......

......

...

∂Ps

∂θ1· · ·

∂Ps

∂θm+1· · · ρs

·

∆θ1...

∆θm+1

...

∆Pimb

(C.9)


Figure C.1: Flow-chart of a single slack bus load �ow


At each iteration the load �ow Jacobian, modi�ed according to matrix calculation (C.9), is updated

and the new system state is determined. After calculating the real and reactive state variables (∆θiand ∆Vi), not only the voltage phase angles θi and the voltage magnitudes Vi, but also the real

power injections at the buses that participate in redistributing the real power losses, are updated:

θ(k+1)i = θ

(k)i + ∆θ

(k)i i ∈ [1, n− 1]

V(k+1)i = V

(k)i + ∆V

(k)i i ∈ [m+ 1, n− 1]

A(k+1)i = A

(k)i + ρi∆P

(k)imb i ∈ [1,m]

A(k+1)s = A

(k)s + ρs∆P

(k)imb

(C.10)

When the convergence is achieved, the real power generations at the distributed slack buses have

to be updated on the basis of the �nal injections calculated by the procedure:

Pi = Ai + Ci i ∈ [1,m]

Ps = As + Cs

(C.11)

C.2.1 Participation factors

As explained in the previous paragraph, a distributed slack bus is modelled using scalar participa-

tion factors to assign the unknown system loss to the participating sources. In the distributed slack

bus model, the system real power losses are treated as an unknown and distributed to participating

sources according to their assigned participation factors. The sum of all participation factors is

one:

Ngen∑i=1

ρi = 1 (C.12)

where Ngen is the number of generation units that participate in balancing the power mismatch

due to uncertain system loss.

There are several methods to calculate the participation factors. The �rst one, which is also the

simplest, de�nes the participation factor ρi as follows:

ρi =Pmax i∑Ngen

i=1 Pmax i

(C.13)

where Pmax i is the maximum real power by generation unit i.

Another method considers the participation factors of each generator to the economic load dispatch

(ELD).

Appendix D

Devices for reactive power support

The devices that provide reactive power support can be divided into two categories, static and

dynamic. Static devices can only be switched on and o� manually if they are installed with

switching abilities. They deliver a �xed amount of reactive power when switched on and they are

only capable of limited switching operations. They are therefore not able to respond to reactive

power needs instantaneously. Dynamic devices are instead capable of regulating their reactive

output according to requirements for voltage levels in real-time. The dynamic nature of reactive

support devices is much more desirable and so more valuable than the output from static ones,

which are more applicable in dealing with seasonal �uctuations in reactive power demand or in

supplying basic, invariable load at speci�c points in the system [43].

D.1 Synchronous generators

Most generators connected to the electricity grid are synchronous generators. Generator settings

can be adjusted to produce combinations of real and reactive power. When the generator increases

its reactive power output, its real power capability may need to be reduced if the generator reaches

its limits.

A generator's output capabilities depend on the thermal limits of various parts of the generator

and on system stability limits. Thermal limits are physical limits of materials such as copper, iron

and insulation; if the generator overheats, insulation begins to degrade and over time this could

result in equipment damage. Increasing real power output of a generator heats up the armature.

Increasing reactive power output heats up the �eld windings and the armature. To supply reactive

power, the generator must increase the magnetic �eld to raise the voltage that it is supplying to

the power system; this means increasing the current in the �eld windings, which is limited by

the thermal properties of the metal and insulation. The �eld current is supplied by the generator

exciter, which is a DC power supply connected to the generator. The �eld current can be quickly

adjusted by automatic control or with a dial to change the reactive power supplied or consumed

by the generator. Stability limits are determined by the ability of the power system to accept

delivery of power from the connected generator under a de�ned set of system conditions including

recognized contingencies. All generators connected to a power system operate at the same electrical

frequency; if a generator loses synchronism with the rest of the system, it will trip o�-line to protect

itself.

Figure D.1 is an example of a generator capability set, or curve. Due to the shape of the boundary,

179

APPENDIX D. DEVICES FOR REACTIVE POWER SUPPORT 180

Figure D.1: An example of synchronous generator output capability curve [117]

it is referred to as a D-curve. It has three components, labeled �eld heating limit, armature heating

limit and core-end heating limit.

The armature current limit is a circle with a radius VtIa, centered at the origin, and expressed by

the following equation:

P 2G +Q2

G ≤ (VtIa)2 (D.1)

The �eld current limit, on the other hand, is a circle with radiusVtEf

Xsat

(0,−

V 2t

Xs

)and expressed

by the following equation:

P 2G +

(QG +

V 2t

Xs

)2

≤

(VtEf

Xs

)2

(D.2)

where:

� PG is the real power generation of the synchronous generator;

� QG is the reactive power generation of the synchronous generator;

� Vt is the terminal voltage of the synchronous generator at which its capability curves are

calculated;

� Ia is the rated armature current of the synchronous generator at which its capability curves

are calculated;

� Ef is the excitation voltage of the synchronous generator;

� Xs is the synchronous reactance of the synchronous generator.

The core-end heating limit constrains the generator's capabilities in under-excited mode.


Reactive power supply from generators requires a minimal additional amount of fuel or real power

from the network. The cost of a generator depends on the capacity, fuel type and voltage level.

Because the reactive power constraints in generators are thermal and equipment takes some time to

heat to the point of degradation, generators are designed to provide signi�cantly increased amounts

of reactive power output for short periods. A generator can increase or decrease reactive power

output smoothly and almost instantaneously within its designed capabilities. Generators have a

longer response time if the real power output needs to be adjusted or the generator is o�-line; the

generator ramp rate and start-up time will determine how quickly the generator can adjust its

reactive power output in these situations. Generators have high maintenance costs due to their

moving mechanical parts and cooling systems.

D.2 Distributed generators

Distributed generators are small power sources including microturbines, fuel cells and engine gen-

erators connected to lower-voltage electric distribution systems. They may be owned by utilities

or by customers, and are often owned by large industrial plants. Distributed generators have the

same reactive power characteristics as large generators, they produce dynamic reactive power and

the amount of reactive power does not necessarily decrease when voltage decreases. The reactive

power output can be quickly adjusted within the generator operating limits, but will require more

time if the generator needs to be started or its real power output needs to be adjusted. The major

advantage of distributed generators is that they provide reactive power capability locally, often at

the site of large loads, reducing reactive power losses in transmission lines [118].

D.3 Synchronous condensers

Synchronous condensers are another type of dynamic reactive support device. They are basically

unloaded synchronous generators, i. e. they run without a prime mover or a mechanical load. They

deliver reactive power at leading or lagging power factor as their static counterparts, but they

possess many advantages over static devices. The most important is their ability to continuously

handle �uctuating local demand for reactive power and their reactive output is not a�ected by

system voltage conditions. Power factor correction with synchronous condensers also provides

lower line losses and so helps the real power transmission. They are rotating machines with moving

parts and therefore need signi�cantly more maintenance than their static alternatives accompanied

by maintenance costs.

D.4 Supervar machines

Supervar machines are rotating machines, much like motors and generators, that use high tem-

perature superconductor technology. They serve as reactive power �shock absorbers� for the grid,

dynamically delivering or absorbing reactive power, depending on the voltage level of the trans-

mission system. They are speci�cally designed for continuous, steady-state dynamic var support

while having multiples of their rated output in reserve for transient problems.


D.5 Shunt capacitors

Capacitor batteries can be either switched or �xed to the power grid although the latter is not

very desirable unless a basic, invariable local reactive power demand is present at the bus or its

surroundings. Switched capacitor banks are nonetheless considered static devices due to their

reactive power output being unadjustable whilst switched on. In addition, their reactive output

is proportional to the square of the bus voltage. This causes the output of a capacitor to be low

during low voltage periods when extra reactive power is likelier to be needed more, rendering the

capacitor less useful. Their advantages are that they can be bundled up to match the static reactive

power demand and individually added, removed, and replaced as needed. They are also light, most

often free of any required cooling and are relatively inexpensive on their own.

D.6 Shunt reactors

Shunt reactors, like their capacitor counterparts, can be either switched or �xed to the grid.

Reactors have the opposite e�ect to that of capacitors: they absorb reactive power from the power

grid. They are mainly used to compensate for the line capacitance in long overhead transmission

lines and cable systems. Their purpose is to keep the voltage from rising during light load periods

by absorbing excess local reactive power.

D.7 Series capacitors

Series compensation is based on controlled insertion and removal of series capacitors in AC trans-

mission lines. Series capacitors provide reactive power to the power system according to the square

of the line current: the higher the line current, the more reactive power support. Due to charac-

teristics of the impedance of a series capacitor compared to that of the line impedance, a series

compensated transmission line is electrically reduced to a shorter distance, so increasing its transfer

capability.

D.8 Flexible AC Transmission Systems (FACTS)

FACTS are technologies that increase �exibility of transmission systems by allowing control of

power �ows and increasing stability limits of transmission lines. There are several varieties of

FACTS devices. Some of the FACTS devices for reactive power management are static var com-

pensators (SVC), static synchronous compensators (STATCOM), static synchronous series com-

pensator (SSSC), dynamic var (D-var), distributed superconducting magnetic energy storage (D-

SMES), uni�ed power �ow controller (UPFC), and interline power �ow controller (IPFC) [119].

D.8.1 Static Var Compensators

Static var compensators (SVCs) are basically shunt capacitors and reactors connected to the grid

through and controlled by thyristors. They therefore possess many of the same physical char-

acteristics as static capacitor banks. They are however regarded as dynamic control because of

the addition of the fast switching capabilities of the thyristors brings dynamic properties to the

compensators.


D.8.2 Static Synchronous Compensators

Static synchronous compensators (STATCOMs) are devices that use power electronic technology

to synthesize reactive output to the grid. They convert a DC voltage source to a 3-phased output

at system frequency with capabilities to control both amplitude and phase-angle of the output.

STATCOMs are made to both generate and absorb reactive power and because of the power

electronics utilization the output range is symmetric, i. e. equal generation and consumption capa-

bilities. The response time of the STATCOM is similar to that of the SVC, but the STATCOM's

reactive output is not as sensitive to voltage degradation as the SVC's since the output of the

STATCOM falls linearly with voltage instead of proportionally to the square of the voltage. In

addition, a STATCOM device is slightly less space consuming than an SVC, but the STATCOMs

are slightly more expensive.

D.8.3 Static Synchronous Series Compensators

The Static Synchronous Series Compensator (SSSC) is a series device of the Flexible AC Trans-

mission Systems (FACTS) family using power electronics to control power �ow and improve power

oscillation damping on power grids. The SSSC injects a voltage in series with the transmission line

where it is connected, 90º phase-shifted with the load current, operating as a controllable series

capacitor. The basic di�erence, as compared with series capacitor, is that the voltage injected by

an SSSC is not related to the line current and can be independently controlled.

D.8.4 D-var (Dynamic Var)

D-var voltage regulation systems dynamically regulate voltage levels on power transmission grids

and in industrial facilities; D-var is a type of STATCOM. D-var dynamic voltage regulation systems

detect and instantaneously compensate for voltage disturbances by injecting leading or lagging re-

active power to the part of the grid to which the D-var is connected. D-var systems provide dynamic

var support for transmission grids that experience voltage sags, which are typically caused by high

concentrations of inductive loads, usually in industrial manufacturing centers, or from weaker por-

tions of the transmission grid, typically in remote areas or at the end of radial transmission lines.

D-var systems also are suited to address the need for dynamic var support at wind farms.

D.8.5 Distributed SMES (D-SMES)

A superconducting magnetic energy storage (SMES) system is a device for storing and instanta-

neously discharging large quantities of power. A distributed-SMES (D-SMES) system is a new

application of proven SMES technology that enables utilities to improve system reliability and

transfer capacity. D-SMES is a shunt-connected Flexible AC Transmission (FACTS) device de-

signed to increase grid stability, improve power transfer and increase reliability. Unlike other

FACTS devices, D-SMES injects real power as well as dynamic reactive power to more quickly

compensate for disturbances on the utility grid.

D.8.6 Uni�ed Power Flow Controllers

A Uni�ed Power Flow Controller (UPFC) is an electrical device for providing fast-acting reactive

power compensation on high-voltage electricity transmission networks. The UPFC is a versatile


controller which can be used to control real and reactive power �ows in a transmission line. The

concept of UPFC makes it possible to handle practically all power �ow control and transmission line

compensation problems, using solid state controllers, which provide functional �exibility, generally

not attainable by conventional thyristor controlled systems. The UPFC is a combination of a

static synchronous compensator (STATCOM) and a static synchronous series compensator (SSSC)

coupled via a common DC voltage link. It is capable of controlling simultaneously or selectively,

all the parameters a�ecting the power �ow in a transmission line. The parameters usually are

voltage, impedance, and phase angle.

D.8.7 Interline Power Flow Controllers

An Interline Power Flow Controller (IPFC) consists of two series voltage sources converters (VSCs)

whose DC capacitors are coupled, allowing real power to circulate between di�erent power lines.

When operating below its rated capacity, the IPFC is in regulation mode, allowing the regulation

of the P and Q �ows on one line, and the P �ow on the other line. In addition, the net real power

generation by the two coupled VSCs is zero, neglecting power losses.

D.9 Wind generators

The intermittent nature of wind power generation is particularly challenging when it comes to power

system operations. The uncontrollable operations of windmill farms make it di�cult to assign any

de�nite reactive power supply to the generators, especially older windmills, which are commonly

equipped with asynchronous generators. Such generators do not contribute any reactive power to

the grid but rather deliver power at lagging power factor meaning that they draw reactive power

from the grid. Newer installations are equipped with �xed capacitor banks or power electronics

like SVCs at their grid connection point.

D.10 User plants

All user plants connected to the network may contribute to voltage regulation, absorbing power

with a power factor greater than a certain minimum value. This goal, technically attainable by

correcting the power factor, can be easily achieved by means of the same static devices used in the

transmission network, mainly capacitors.

D.11 Transmission lines

Electric transmission lines have both capacitive and inductive properties. The line capacitance

supplies reactive power, while the line inductance consumes reactive power. At a loading known

as Surge Impedance Loading (SIL), the reactive power supplied by the line capacitance equals

the reactive power consumed by the line inductance, meaning that the line provides exactly the

amount of Mvar needed to support its voltage. Lines loaded above SIL consume reactive power,

while lines loaded below SIL supply reactive power. The amount of reactive power consumed by a

line is related to the current �owing on the line or the voltage drop along the line; the amount of

reactive power supplied by a line is related to the line voltage.


When an overhead transmission line is lightly loaded, the capacitance of the line generates more

reactive power than is absorbed by the inductive component and the line generates reactive power.

If the line becomes heavily loaded, the inductive reactance starts to absorbs more reactive power

than the capacitive component generates. This results in the line overall consuming reactive power

and therefore reactive power has to be supplied to the line in order to maintain a decent voltage

pro�le.

The capacitances have greater e�ect at higher voltage levels. Because of the capacitive nature of

HV transmission cables the inductive component of the conductors generally never absorbs more

reactive power than the shunt capacitances manage to generate. Cables therefore generate reactive

power which often has to be compensated to maintain voltage levels.

D.11.1 High voltage DC transmission lines

High voltage DC transmission lines (HVDC) transmit power via DC (direct current). Because DC

transmission lines are transmitting power at zero hertz, the reactive power consumption on the

line is zero. The converters require reactive power for the conversion process typically in the range

of 40% of the power rating of each of the converter terminals. The reactive power is required to

compensate for the reactive power consumption in the converter transformers and to maintain an

acceptable AC voltage level on the AC side of the converter terminals. Much of this reactive power

requirement is provided by shunt capacitors and �lters. Therefore, a properly designed HVDC

system is essentially self-su�cient in reactive power.

D.12 Transformers

Transformers are electromagnetic devices that convert power from one voltage level to another;

they are inductive devices and therefore consume reactive power.

D.12.1 Transformer taps

Large power transformers are generally equipped with �voltage tap changers�, with tap settings

to control the voltages either on the primary or secondary sides of the transformer by changing

the amount and direction of reactive power �ow through the transformers1. Tap changers do not

consume or supply reactive power; taps force voltage on one side of the transformer up, at the

expense of lowering the voltage on the other side. Taps can be thought of as pumping reactive

power from one side of the transformer to the other to regulate voltage. The tap changers can

be controlled to automatically adjust to system conditions. Transformers can be categorized as

semi-dynamic reactive power support devices. They deliver continuous voltage control, however,

they are slow in doing so.

D.12.2 Phase Shifting Transformers

Phase Shifting Transformers (PSTs), also called Phase Angle Regulators (PARs), allow system

operators to control real power �ow. Phase shifting transformers have taps that control the phase

angle di�erence across the transformer. Increasing the phase angle di�erence across a transformer

has the e�ect of increasing the impedance of the line, which will reduce the amount of real power

1They are called OLTC transformers (On Load Tap Changing transformers).


on the line. Phase shifting transformers are usually installed to control real power �ow, especially

along parallel paths. Phase shifting transformers are also a useful tool for reactive power control.

Controlling the real power �ow along a line allows for control of the reactive power consumed or

produced by the line.

D.13 Di�erences among equipment types

Generators, synchronous condensers, SVCs, and STATCOMs all provide fast, continuously control-

lable reactive support and voltage control. OLTC transformers provide nearly continuous voltage

control but they are slow. Because the transformer moves reactive power from one bus to an-

other, the control gained at one bus is at the expense of the other. Capacitors and inductors

are not variable and o�er control only in large steps. An unfortunate characteristic of capacitors

and capacitor-based SVCs is that output drops dramatically when voltage is low and support is

needed most. The output of a capacitor, and the capacity of an SVC, is proportional to the square

of the terminal voltage. STATCOMs provide more support under low-voltage conditions than

do capacitors or SVCs because they are current-limited devices and their output drops linearly

with voltage. The output of rotating machinery (i. e. generators and synchronous condensers) rises

with dropping voltage unless the �eld current is actively reduced. Generators and synchronous

condensers generally have additional emergency capacity that can be used for a limited time.

Voltage-control characteristics favour the use of generators and synchronous condensers. Costs,

on the other hand, favour capacitors. Generators have extremely high capital costs because they

are designed to produce real power, not reactive power. Even the incremental cost of obtaining

reactive support from generators is high, although it is di�cult to unambiguously separate reactive-

power costs from real-power costs. Operating costs for generators are high as well because they

involve real-power losses. Finally, because generators have other uses, they experience opportunity

costs when called upon to simultaneously provide high levels of both reactive and real power.

Synchronous condensers have the same costs as generators; but, because they are built solely to

provide reactive support, their capital costs do not include the prime mover or the balance of plant

and they incur no opportunity costs. SVCs and STATCOMs are high-cost devices, as well, although

their operating costs are lower than those for synchronous condensers and generators [117].

Table D.1: Characteristics of voltage-control equipment [43]


Di�erences in e�ectiveness and costs of the di�erent devices dictate that reactive power generally is

provided by a mix of static and dynamic devices. The cost of reactive power service depends upon

the choice of equipment. The costs of satisfying static reactive power demands are much lower

than those of satisfying dynamic reactive power demands. While capital costs tend to dominate,

the costs of providing reactive power also include generator fuel costs, operating expenses and the

opportunity costs from not generating real power. The capital costs of static sources of reactive

power, such as capacitors, are orders of magnitude lower than the capital costs of dynamic sources,

such as generators, SVCs, and synchronous condensers.

Table D.1 shows the speed of response, voltage support and costs for the di�erent sources of reactive

powers and does not include transformer tap changers. The ability to support voltage means the

ability to produce reactive power when voltage is falling. The availability of voltage support

indicates how quickly a device can change its reactive power supply or consumption. Disruption is

low for devices that can smoothly change reactive power output and high for devices that cannot

change reactive power output smoothly [43].

Appendix E

Italian hierarchical voltage control

The hierarchical voltage control scheme, presented in Chapter 3 and shown in Figure E.1, provides

closed-loop real-time regulation of voltages at the main buses (pilot nodes) of the transmission

network, through coordinated control of the reactive power resources associated with each pilot

node (control area), mainly those of generators (control plants). The most signi�cant levels of this

hierarchical control realize the Secondary and Tertiary Voltage Regulations (SVR and TVR). SVR

is a decentralized control scheme which automatically maintains the pilot node voltage at its set-

point, through the adjustment of the reactive powers of local control generators and compensators:

this area level control has a dominant time constant of 50 s.With a slower dynamics, SVR [80, 99]

can also switch local shunt reactors/capacitor banks and control OLTCs and SVCs. Conversely,

TVR [96, 98] acts on the overall transmission network, with a dominant time constant of about

5 min, automatically updating all the pilot nodes voltage set-points. TVR aims at both minimizing

network losses and improving operation voltage security.

The hierarchical voltage control scheme is very simple in comparison with other theoretical and

unrealistic centralized schemes due to the small number of EHV controlled buses and telecommu-

nication requirements. Notwithstanding the pursued objective of system complexity minimization,

the e�ort to achieve an e�ective control system is still considerable, especially for large transmission

networks.

E.1 Secondary Voltage Regulation

E.1.1 SART apparatus

SART1 [120] regulates the units' reactive power or local EHV bus-bar voltage by controlling the

AVR set-points and sharing out total generated reactive power among power plant units in a

balanced way. In the �rst control mode, SART regulates the reactive powers of local generators,

according to the reactive level received from the Regional Voltage Regulator. In the second mode,

it regulates the local high-side bus-bar voltage on the basis of a suitable daily voltage trend or an

operator-de�ned set-point. In both these control modes, the reactive power of each generator is

controlled through a closed loop whose set-point is obtained by multiplying the reactive level signal

by the generator's reactive power limit. Over/under excitation unit reactive limits are computed,

in real-time, as a function of the actual values of real power and voltage, also taking into account

1In the past it was called REPORT.

188

APPENDIX E. ITALIAN HIERARCHICAL VOLTAGE CONTROL 189

Figure E.1: Hierarchical voltage control for the Italian EHV system


the actual operating conditions of the generator cooling system.

SART recognizes particular network contingencies (power plant islanding, local bus-bars isolation,

etc.) in real-time on the basis of local information and chooses the most suitable control mode

accordingly. It also adapts the regulation parameters according to the identi�ed equivalent external

reactance seen from the bus-bar (network side). Under steady-state operating conditions, the

reactive level signal is limited between minimum and maximum excitation. During transients

these limits can be exceeded, according to the generators' overloading capabilities, thus permitting

the highest network support in response to heavy perturbations. SART's dynamic behaviour is

characterized by dominant time constants of about 5 s and 50 s for unit reactive power and EHV

bus-bar voltage control respectively. The reactive power gradient is limited on the basis of generator

constraints in the case of major perturbations.

E.1.2 RVR apparatus

RVR [95] is installed at the regional control centers. It regulates at the same time, but with

independent and parallel operation, the voltages of its pilot nodes through real-time remote control

of the reactive power productions of those power plants with the greatest impact on pilot node

voltages. For this purpose, RVR de�nes and updates the value of its area reactive power levels

through a separate voltage regulator for each pilot node in the region, whose main characteristics

are:

� the regulation law is of the proportional-integral type, with an adaptive control algorithm

which keeps loop dynamics unchanged in real-time, taking into account the number and

actual capabilities of the plants participating in pilot node voltage regulation, as well as the

equivalent external reactance experienced by the pilot node;

� full dynamic de-coupling among di�erent pilot node voltage control loops within the same

region, to avoid oscillations of reactive power between neighboring areas: for this purpose

it is also possible to select a positive, null or negative static droop for pilot node voltage

regulation;

� each pilot node voltage regulator can be started without any preliminary manual alignment

of control generator voltages, and its set point value can be determined locally by either the

manual calibrator (manual local reference) or the stored pro�les (automatic local reference).

Otherwise it is received by remote from TVR. Tracking functions among pilot node voltage

calibrators and corresponding controlled magnitudes enable switching between the RVR's

di�erent operation modes at any time without causing noise for controlled variables.

For each area, one or two vicarious pilot nodes can be chosen to deal with possible tele-measurement

equipment failures at the main pilot node. The con�guration of the control system in the region can

be also modi�ed taking into account network changes and in response to requests coming from TVR.

The regulation areas can be con�gured on-line in terms of control plants (participating in pilot node

voltage control), peripheral plants (performing local high-side voltage control), stations reactive

reserves under SVR control, and control law parameters. In particular network con�gurations,

some control plants may gravitate to an area close to that they electrically belong to, due to their

geographic position. These boundary plants, considered peripheral ones in the initial con�guration,

can either participate in tele-control of their pilot nodes or of the neighboring ones, as the grid

con�guration varies. In the automatic operation mode, based on local reference, the set-point value


of each pilot node voltage is automatically updated on the basis of a voltage pro�le associated with

the current day and stored in the RVR. The voltage daily generic pro�le consists of 96 values

corresponding to the set-point values to put into operation every quarter of an hour. During such

an interval, the reference of the pilot node voltage is automatically updated every minute, on the

basis of a tracking ramp, from the current reference value to that foreseen for the start of the

subsequent quarter of an hour.

E.2 Tertiary Voltage Regulation

E.2.1 NVR apparatus

NVR [121] includes the real-time regulator TVR and the optimal forecasting controller LMC.

TVR has two main objectives: minimizing network losses and increasing load margins in the

transmission network in response to heavy operating conditions (critical from the voltage stability

viewpoint). These goals are basically achieved by proper coordination between the TVR and the

SVR: TVR establishes network voltages by updating the voltage set-points optimization of the

pilot nodes, at any cycle. The TVR uses the last available minimum losses ORPF as the voltages-

reactive powers reference and achieves minimum feasible losses by minimizing a real-time control

function OF (see equation (E.6)).

The load margin is maximized by the automatic and real-time coordinated control contemporarily

exercised by SVR on all reactive resources, according to the SVR control philosophy. In terms of

stability, TVR and RVRs operate to prevent units from reaching their over-excitation limits: in

the presence of the TVR, this condition is in fact related to the tap-changer reverse action which

normally anticipates the triggering of the voltage collapse mechanism. Whenever the reactive power

control margins made available to SVR are strongly reduced as a result of severe perturbations

or abnormal load patterns, the TVR attends the grid voltage reduction to the minimum allowed

by the operating conditions, progressively renouncing the not applicable optimal forecasted grid

voltage pro�le. The TVR will therefore avoid the risk of instability by allowing the power plants

under SVR to operate at their capability limits only when transmission network voltages are very

low even though all the network's reactive power resources are engaged for voltage support. In

this way there is a reduced risk of the triggering of a voltage collapse in response to intervention

of over-excitation limits, and the overall loadability of the transmission system is increased.

The second NVR main function is achieved by the LMC controller, which de�nes the optimal

forecast voltage plan required as input by the TVR. This very slow o�-line ORPF computing is

the main LMC activity, taking into account the estimation of system state and the constraints

determined by the hierarchical structure of the SVR and its control ties (pilot nodes and control

power plants). On the basis of a forecasted state estimation, LMC computes in advance (i. e. the

day before) the provisional optimal voltage and reactive power plan, which is stored and used by

the TVR. If the TVR recognizes signi�cant di�erences between expected and real system operating

conditions, it requires the LMC to compute the updated optimal forecasted voltage plan based on

the last system state estimation (which, in the best case, could refer to about �ve minutes before).

This delayed ORPF will be continuously computed by LMC every state estimation update and

sent to the TVR until the stored and new optimal forecasted voltage plans resemble each other. In

addition, the LMC shows and compares, for each area, on-progress daily traces of the pilot node

voltage and required set-point, the reactive power levels operating on the plants and the optimal


forecasted references used by the TVR.

E.3 Control system algorithms and dynamics design

In the hierarchical voltage control system, the inner loop is typically faster than the outer one,

in such a way as to achieve substantial dynamic de-coupling between overlapped levels. In other

words, the time-decomposition criterion requires that the dominant time constant of any external

control loop be higher than the dominant time constants of all its internal loops. Such a criterion

is applied to unit voltage regulation, unit reactive power control, EHV bus voltage regulation, pilot

node voltage regulation, and pilot nodes voltage set-point optimization:

� AVR closes the conventional unit voltage control loop, which is basically of the proportional-

integral type. It is characterized by closed-loop dynamics dominated by a time constant of

about 0.5 s.

� Unit reactive power control within SART de�nes, in closed-loop and real-time, the AVR

voltage set-point VREF in the range between minimum Vmin and maximum value Vmax,

which obtains the unit reactive power production QG corresponding to its reference value

QREF :

VREF = KIQ

[∫ t

0

(QREF −QG) dt

]Vmax

Vmin

(E.1)

where KIQ is the regulator integral gain, tuned in such a way that the closed loop has a

dominant time constant of 5 s. The fastest AVR dynamic responses, mainly required in

response to major local network perturbations, are then not signi�cantly a�ected by the

reactive power loop. The reference value QREF is obtained from the product of the reactive

power level qLEV by the unit capability limit QLIM , computed on-line according to the actual

operating conditions of the electrical generator and cooling system:

QREF = qLEVQLIM (E.2)

� The reactive power level qLEV may be provided by the local EHV bus-bar voltage regulator

(SART in high-side voltage control) or by the pilot node voltage regulator (RVR control).

Both of them de�ne, in closed-loop and real-time, the reactive level qLEV in the interval

between its minimum qmin = −100% and maximum value qmax = +100%, which achieves

the EHV bus-bar or pilot node voltage VP corresponding to its reference value VPREF :

qLEV =

[KPV (VPREF − VP ) +KIV

∫ t

0

(VPREF − VP ) dt

]qmax

qmin

(E.3)

where KPV and KIV are the regulator proportional and integral gains respectively, tuned

in such a way that the closed loop has minimum-phase and a dominant time constant of

50 s. The fastest contribution to the dynamic responses is properly given by proportional

correction.

� The pilot node voltage set-point VPREF may be provided by the local daily trend (RVR

automatic setting) or by the regional dispatcher operator (RVR manual setting) or voltage


set-point optimization (TVR output). The latter de�nes the most appropriate pilot node

voltage set-points VPREF for secure/e�cient operation, on the basis of an integral law of the

optimal variations ∆VPREF with respect to the present voltage values VP :

VPREF = KIT

[∫ t

0

(Q2 +R2S−2

)−1Q2(VP − V 0

P

)dt]VPmax

VPmin

+

+KIT

[∫ t

0

(Q2 +R2S−2

)−1R2S−1

(qLEV − q0LEV

)dt]VPmax

VPmin

(E.4)

where KIT is the regulator integral gain, tuned in such a way that the closed loop has a

dominant time constant of 5 min, and S is the sensitivity matrix between area reactive levels

∆qLEV and pilot node voltages ∆VPREF

∆VPREF = S∆qLEV (E.5)

Relation (E.4) integrates the result of the TVR objective function minimization, which is based on

the actual network state estimation and the forecasted optimal voltages and reactive powers plan:

OF =[VP + ∆VPREF − V 0

P

]TQ2[VP + ∆VPREF − V 0

P

]+

+[qLEV + S−1∆VPREF − q0LEV

]TR2[qLEV + S−1∆VPREF − q0LEV

] (E.6)

where [VP ] and [qLEV ] are the vectors of pilot node voltages and area reactive power levels;[V 0P

]and

[q0LEV

]are the vectors of the optimal forecasted pilot node voltages and area reactive power

levels; Q2 and R2 are weight matrices whose selection allows bestowing a privilege on pilot node

voltage di�erences, rather then on the e�ort of control area reactive power levels. The compromise

reached by TVR, when the available optimal forecasted plan does not �t the real situation, should

properly consist in the achievement of the highest voltage plan consistent with real operating

conditions, which minimize network losses as much as is feasible. To achieve this result it is

necessary to preserve system controllability, even if close to the limits, in such a way as to avoid

the disastrous consequences of open-loop operation. In this condition, in fact, the uncontrolled

voltages determine undesired heavy reactive power �ows, which increase system losses and worsen

the operation e�ciency. TVR is therefore the correct and necessary completion of the hierarchical

automatic real-time voltage control system.

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