1

Congestion management using demand response and FACTS devices 1

2 A. Yousefi 1*, T.T Nguyen 1, H.zareipour 2, MO.P Malik2 3

1-University of Western Australia, Perth, Australia 4 2-University of Calgary, Calgary, Canada 5

6

Abstract 7

An approach for transmission lines congestion management in a restructured market environment using a 8

combination of demand response (DR) and flexible alternating current transmission system (FACTS) devices 9

is proposed. To achieve this aim, a two step market clearing procedure is implemented. In the first step, 10

generation companies bid to the market for maximizing their profit and the ISO clears the market based on 11

social welfare maximization. In the second step, if there is congestion in the network, the ISO releases the 12

congestion using FACTS devices, DR and generation re-dispatch. IEEE 30-bus, system is used for 13

illustrating, testing, and discussing the proposed technique. 14

Keywords 15

Demand Response (DR) program, FACTS devices, congestion management. 16

Nomenclature 17

maxDikP Maximum size of the power block k that demands i is willing to buy at price Dik . 18

maxGjlP Maximum size of the power block l offered by generator j at price Gjl . 19

maxGjP Maximum power output of generator j . 20

minGjP Minimum power output of generator j . 21

min

downreDiP Minimum load reduction by responsive demand i . 22

max

downreDiP Maximum load reduction by responsive demand i . 23

minTCSCX

Minimum operational limit of TCSC. 24

* Corresponding author, Phone: +61-433786405, email address: a.yousefi@ieee.org.

Email addresses: tam@ee.uwa.edu.au (T.T Nguyen), a.yousefi@ieee.org (A. Yousefi),

zareipour@ucalgary.ca (H.Zareipour), maliko@ucalgary.ca (Om Malik).

2

maxTCSCX Maximum operational limit of TCSC. 1

minSVCB Minimum operational limit of SVC. 2

maxSVCB Maximum operational limit of SVC. 3

ju 0/1 Binary variable, equal to 1 if generator j is running and 0 otherwise. 4

( )E t Elasticity of the demand. 5

( )t Electricity price. 6

0 ( )L t Customer demand before demand response program. 7

( )L t Customer demand after demand response program. 8

DikP Power block k that demand i is willing to buy at price Dik up to a maximum of maxDikP . 9

GjlP Power block l that generator j is willing to sell at price Gjl up to a maximum of maxGjlP . 10

Dik Price offered by demand i to buy power block k . 11

Gjl Price offered by generator j to sell power block l . 12

AGjP Cleared active power for generator j as determined by the auction dispatch. 13

ADiP Cleared active power for demand j as determined by the auction dispatch. 14

upjr Price offered by generator j to increase its output schedule, for congestion-management. 15

downjr Price offered by generator j to decrease its pool power schedule. 16

downDir Price offered by responsible demand i to decrease its demand. 17

upGjP Increment in the schedule of generator j . 18

downGjP Decrement in the schedule of generator j . 19

downreDiP Decrement in the schedule of responsive demand i . 20

upGnP Total increments of active power generation. 21

3

downGnP Total decrements of active power generation. 1

downDnP Total load reduction by responsive demand. 2

DN Number of demands. 3

DiN Number of blocks requested by demand i . 4

GN Number of generators 5

reDN Number of responsible demands 6

GjN Number of blocks offered by generator j 7

1. Introduction 8

1.1 Motivation and technique 9

Restructuring in electric power industry has led to intensive usage of transmission grids. In a competitive 10

market environment, transmission companies usually maximize the utilization of transmission systems as 11

construction of new transmission lines is not as straightforward as in centrally planned systems. Thus, in high 12

demand periods, the system operates near its capacity limit with security margin being reduced [1]. Existence 13

of network constraints dictates the finite amount of power that can be transferred between two points on the 14

electric grid. In practice, it may not always be possible to deliver all bilateral and multilateral contracts in full 15

and to supply the entire market demand due to violation of operating constraints such as voltage and line 16

power flow limits. The presence of such network or transmission limitation is referred to as congestion. 17

Congestion or overload in one or more transmission lines may occur due to the lack of coordination between 18

generation and transmission companies or as a result of contingencies [2]. Congestion may be relieved, in 19

many cases by cost-free means such as network reconfiguration, operation of transformer taps and operation 20

of flexible alternating current transmission system (FACTS) devices [3-8]. In other case, however, it may not 21

be possible to remove or relieve congestion by cost-free means, and some non-cost-free control methods, such 22

as re-dispatch of generation and curtailment of loads, are required [9, 10]. Since there is a wide range of 23

events which can lead to transmission system congestion, a key function in system operation is to manage and 24

respond to operating conditions in which system voltages and/or power flow limits are violated [2]. A 25

congestion management method proposed in this paper based on a combination of FACTS devices and 26

4

demand response programs. In the present paper, Demand response is modeled considering incentives and 1

penalty factors. The incentive and penalty factor enables the system operator to have more control on 2

responsive demand contributions rather than just relying on changing the electricity price in the market and its 3

effects on response rate of elastic loads. The penalty factor can also improve the response rate of responsive 4

demands and also enhance the reliability level of these resources by decreasing the rate of response failure. In 5

addition , deploying demand response resources at appropriate locations would allow generation to operate at 6

a lower cost as the congestion is reduced and also transmission network investment can be postponed while 7

maintaining the existing level of security [11-13]. In fact, the responsive demand improves the operation of 8

electricity market and also would make electricity market more efficient and more competitive [12]. 9

1.2. Literature review and contribution 10

In general, three main forms of congestion management exist in competitive electricity markets[2]. The first 11

is based on centralized optimization with some form of optimal power flow program or depends on specific 12

control measures operated by the independent system operator (ISO). The second is based on tariff and use of 13

price signals derived from the market to release congestion by generator re-scheduling. Lastly, the third form 14

seeks to mitigate congestion by allowing or disallowing bilateral transmission agreements between a producer 15

and a consumer [1, 2]. 16

FACTS devices are considered to be one technology that can benefit transmission systems in many ways 17

including congestion management and enhancing the loadability of the transmission lines[6]. FACTS devices 18

and their associated benefits for efficient operation of electricity markets have been widely addressed in the 19

literature [2-4, 6, 7, 14]. 20

The efficient model for optimizing the location of FACTS devices for congestion management by 21

controlling the device parameters presented in [7]. In this approach, a two-step procedure is applied for 22

congestion management using FACTS devices. Two new methodologies for the placement of series FACTS 23

devices in deregulated electricity market to reduce congestion based on the use of local marginal price (LMP) 24

differences and congestion rent are presented in [3]. The optimal placement of parallel and series FACTS 25

devices is studied in [6]. In this study, the static synchronous compensator (STATCOM) is selected as a 26

parallel FACTS device and static synchronous series compensator (SSSC) as a series one. The optimization 27

5

problem is formulated in regard to restructured environment and a new objective function is defined so that its 1

minimization can alleviate the congestion and provide fairer conditions for power market participants. A 2

quantitative analysis of the effect of TCSC on congestion and spot price in deregulated electricity markets is 3

presented in [14]. In this approach, studies are carried out with and without TCSC at peak and low load 4

conditions to capture the influence and to see the effectiveness of TCSC at different loading conditions. The 5

paper further explores the effect of TCSC compensation level on the spot prices and the congestion under 6

varying pool and bilateral loading conditions. 7

Additionally, a significant volume of technical literature focuses on demand response [15, 16] and the 8

associated benefits for electricity network; examples are improving the operation of renewable generation 9

[17], providing ancillary services for the market [18, 19], enabling infrastructure for utilizing large amount of 10

renewable resources [20], network reliability enhancement [21], improving the loadability of the transmission 11

lines and congestion management in electricity networks [9]. 12

The role of demand elasticity in congestion management in a competitive electricity market is investigated 13

in [10], where elasticity of demand at different prices is known. The load at each bus ceases to be a fixed 14

quantity and becomes a decision variable in the ISO’s optimization problem. In this way, the ISO has 15

additional degrees of freedom in determining the necessary actions for congestion management. An Optimal 16

Power Flow based framework is proposed in [22] to determine the optimal incentive rates in an interruptible 17

tariff mechanism. It is shown that interruptible tariffs are able to aid system operation during peak load 18

periods by increasing the reliability margin, improving voltage profile and relieving network congestion. An 19

integrated technical market based framework for congestion management, that uses interruptible load services 20

as a tool for the ISO to provide transmission congestion relief is investigated in [9], where interruptible load 21

service procurement by the ISO is explored. Additionally, the technical literature includes a significant 22

number of references dealing with demand response modeling and its effects on improving the market 23

operation. The impact of incentive-based demand response (DR) programs on capacity markets is investigated 24

in [23]. The response of a nonlinear mathematical model is analyzed in [24] for the calculation of optimal 25

prices for electricity assuming typical customers under different scenarios using five different mathematical 26

6

functions. The electricity cost saving potential of real time pricing (RTP) through demand management is 1

presented in [25]. 2

The main contribution of this paper is providing a methodology that allows identifying the effectiveness of 3

combining incentive-based demand response programs and FACTS devices to help the system operator in 4

making appropriate strategies for congestion management. In addition, the incentive and penalty terms are 5

added to the existing mathematical model of demand response to enable the ISO to have two factors to control 6

the response rate of responsive demands and also increase the number of demand response participants at 7

specific load buses which are more important for the security of the system. 8

1.3. Paper Organization 9

The rest of this paper is organized as follows. The proposed method including the problem formulation and 10

demand response modeling is described in section 2. Results from a case study are provided and discussed in 11

Section 3 and some relevant conclusions are given in Section 4. 12

2. Problem description 13

In this paper, at the first step, certain numbers of demands are selected according to a sensitivity analysis 14

based on generation shift factor (GSF) [26]. Loads on these selected buses are considered for participation in 15

the demand response program. Later, a non-linear load economic model is extended by considering the 16

intensive and penalty factor to predict the price and the size of their bidding to the electricity market. Then, a 17

two step market clearing procedure is implemented. In the first step, generation companies bid to the market 18

for maximizing their profit and the ISO clears the market based on social welfare maximization without 19

considering the electricity network constrains. In the second step, if there is congestion in the network, the 20

ISO runs the congestion management procedure. In congestion management part, generators and responsive 21

demands bid to the market for re-dispatch and load reduction respectively. In addition, the market operator 22

controls the FACTS device referencing to minimize the congestion cost by combining different alternatives 23

for congestion management summary of the two step market clearing procedure is shown in Fig.1. 24

2.1. Demand response formulation 25

In order to evaluate the impact of DR programs on load profile characteristics, development of load 26

economic model is necessary. A load economic model based on elasticity to quantify the customers response 27

7

to spot electricity price is introduced in [27]. This mathematical model is developed in [24], assuming typical 1

customers under different scenarios and using five different mathematical functions for the consumer 2

response including linear, hyperbolic, potential, logarithmic and exponential. However, this model does not 3

consider any penalty and incentive terms. The mentioned model is then extended in [19], with considering the 4

incentive factor. 5

In the present paper, the nonlinear load economic model of [24] is extended by considering incentive and 6

penalty terms to enable the independent system operator to have two controlling terms to increase the number 7

of demand response participants in specific load buses which are important to system security enhancement 8

and also control the response rate of responsive demands based on incentive and penalty factors. To show the 9

effectiveness of the penalty factor, the customer response is modeled with and without the penalty term to 10

show the benefit of this factor. The detailed formulation of the load economic model is presented next. 11

2.1.1. Modeling of elastic demand 12

If the customer demand is changed from 0 ( )L t to ( )L t , based on the value which is determined for the 13

incentive and the penalty, the load change can be expressed as follows: 14

0( ) ( ) ( )L t L t L t (1) 15

If ( )CR t is paid as incentive to the customer in hour t for each unit of load reduction, the total incentive for 16

participating in DR program will be calculated based on equation (2). 17

0( ( )) ( ).[ ( ) ( )]P L t CR t L t L t (2) 18

If the customers participating in the DR program do not respond to the load reduction invoked, the 19

customers have to pay the penalty which is determined by utility or market operator. 20

If the reduction level for hour t and the penalty for the same period are assumed to be ( )LR t and ( )pen t , 21

respectively, then the total penalty ( ( ))PEN L t is calculated as follows: 22

0( ( )) ( ).{ ( ) [ ( ) ( )]}PEN L t pen t LR t L t L t (3) 23

If the customer revenue is considered as ( ( ))B L t for using ( )L t during hour t , the customer net benefit can 24

be calculated as follows: 25

( ( )) ( ) . ( ) ( ( )) ( ( ))S B L t L t t P L t PEN L t (4) 26

8

To maximize the customer’s net benefit, ( )

S

L t

in equation (5) must be equal to zero. 1

( ( )) ( ( )) ( ( ))

( ) 0( ) ( ) ( ) ( )

S B L t P L t PEN L tt

L t L t L t L t

(5) 2

from (5), 3

( ( ))( ) ( ) ( )

( )

B L tt CR t pen t

L t

(6) 4

In this paper the benefit function based on potential function is used for explaining the customer revenue, 5

different versions of this type are mentioned by diverse authors [27-30]: 6

1( )

00 1

0

( ) ( ) ( )( ( )) ( ) 1

( )1 ( )

E tt L t L t

B L t B tL tE t

(7) 7

Differentiating equation (7) yields: 8

1 1( ) ( ) 1

10 0

1 10 0 0

( ) ( ). ( )( ( )) ( ) 1 ( )1 ( ) .

( ) ( ) ( ) ( )1 ( ) 1 ( )

E t E tt t L tB L t L t L i

E tL t L t L t L iE t E t

(8) 9

Simplifying equation (8) and substituting into equation (6) yields equation (9). 10

1 1( ) ( )

1 1

0 0 0

( ) ( ) ( ) ( ) ( )(1 ( ) ). 1 ( ) .

( ) ( ) ( )

E t E tt CR t pen t L t L t

E t E tt L t L t

(9) 11

Rearranging equation (9) leads to: 12

1( )

10 0

( ) ( ) ( ) ( ) 1

( ) ( ) 1 ( )

E tt CR t pen t L t

t L t E t

(10) 13

The second term of equation (10) can be discarded for small amount of elasticity and finally the demand 14

response model can be achieved as follows: 15

( )

00

( ) ( ) ( )( ) ( ).

( )

E tt CR t pen t

L t L tt

(11) 16

2.1.2. Priority of Demand Response implementation 17

For successful implementation of demand response programs, a set of candidate load buses should be 18

selected. In this regard, loads with high impact on line overloads, and loads with high impact on network 19

9

restoration to normal situation are chosen. To achieve this goal, Generation Shift Factor (GSF) is used [26]. 1

In addition, this index could be either positive or negative and for the implementation of responsive demands 2

those buses with most negative values are selected. 3

2.2. FACTS device modeling 4

FACTS devices are able to change the power flow through transmission lines by changing the amplitude 5

and angle of bus voltages as well as the effective reactance of transmission lines. Hence, congestion can be 6

alleviated or removed by changing power flow in the transmission lines. However, selecting the optimal type 7

and placement of these devices has considerable effect on their performance. In this paper, thyristor controlled 8

series capacitor (TCSC) and static VAR compensator (SVC), two popular series and parallel FACTS devices, 9

are used to control the effective technical parameters on transmission lines to alleviate the congestion [6]. In 10

the present paper, the locations of TCSC and the SVC are selected based on the method presented in [31]. 11

Detailed explanation of static model of TCSC and SVC are presented in appendix A. 12

2.3. Market clearing formulation 13

A two step market clearing procedure is implemented in this paper. In the first step, generation companies bid 14

to the market for maximizing their profit and the ISO clears the market based on social welfare maximization 15

without considering the electricity network constrains. In the second step, if there is congestion in the 16

network, the ISO runs the congestion management procedure which is described in section 2.4. It is necessary 17

to mention that the considered electricity market-clearing procedure is similar to the one used by the Ontario 18

electricity market operator [32, 33]. 19

1 1 1 1

: ( ) ( )

GjDi GDNN NN

Dik Dik Gjl Gjl

i k j l

Max P P

(12) 20

subject to: 21

max0 1,..., , 1,...,Dik Dik D DiP P i N k N (13) 22

max0 , 1,...,Gjl Gjl GjP P j G l N (14) 23

min max

1

GjN

j Gj Gjl j Gj G

l

u P P u P j N

(15) 24

10

1 1 1 1

GjDi GDNN NN

Dik Gjl

i k j l

P P

(16) 1

0,1j Gu j N (17) 2

The objective function (12) presents the social welfare and it has two terms. The first term consists of the 3

sum of accepted demands times their corresponding bid prices and the second term is the sum of acceptable 4

production bids times their corresponding bid prices. The block of constraints (13) specifies the sizes of the 5

demand bids. The block of constraints (14) limits the sizes of the production bids, while (15) ensures that 6

every generator, if running, runs between its minimum and its maximum power output. Constraint (16) 7

ensures that the production should be equal to the demand and finally (17) is the binary variables declaration. 8

The solution of problem (12)–(17) provides the power produced by every generator and the power 9

consumed by every demand. 10

1

GjN

A AGj Gjl G

l

P P j N

(18) 11

1

1,...,DiN

A ADi Dik D

k

P P i N

(19) 12

In this study, the market-clearing price is defined as the price of the most expensive production bid that has 13

been accepted. 14

2.4. Congestion management formulation 15

In Section 2.3, the bids are considered without taking into account the electricity network limitations such as 16

thermal limit of transmission lines and voltage constraints. To manage the congestion due to such limits, the 17

following problem should be optimized [32]. 18

: ( )upup down down down down

j j Gj Di reDiGj

j G i reD

Min r P r P r P

(20) 19

Subject to: 20

0upA down A down

Gj Gn Di DnGnP P P P P (21) 21

min maxupA downj Gj Gj Gj j Gj GGju P P P P u P j N (22) 22

11

G

up upGn Gj

j N

P P

(23) 1

G

down downGn Gj

j N

P P

(24) 2

reD

down downDn reDi

i N

P P

(25) 3

0 ( ) ( )downreDiP L i L i (26) 4

min max

down down downi reDi reDi i reDi reDu P P u P i N (27) 5

min maxTCSC TCSC TCSCX X X (28) 6

min maxSVC SVC SVCB B B (29) 7

The objective function (20) has two parts. The first section is the sum of the amounts received by the 8

generators for changing their output as compared to the original auction schedule and the second term shows 9

the total payment received by demand response participants to reduce their load. The set of constraints (21) 10

enforces power balance at every bus. Set of constraints (22) guarantees that the rescheduled generators stay 11

within their respective maximum and minimum power outputs. Constraints (23) and (24) illustrate total power 12

increment and decrement for generators. Constraint (25) shows the total amount of load reduction by 13

responsive demand. Constraint (26) explains the responsive demand bids based on load economic model 14

formulation and (27) shows the responsive demand bids limitations. The set of constraints (28) and (29) 15

enforce the operational limits of the TCSC and the SVC respectively. 16

In addition to constraints (21-29) power flow constraints including equality constraints and inequality 17

constraints should be considered in optimization procedure. Equality constraints consist of power flow 18

equations applied for individual power network nodes, which can be written in a compact form as: 19

, , 0E V u (30) 20

In (30), V and are the vectors of system voltage magnitudes and phase angles, and u is the vector of 21

control variables such as generator excitation control. Additionally, the inequality constraints can be written 22

in the compact form as: 23

12

, , 0H V u (31) 1

In (31), H is in general a nonlinear function relating to operating conditions such as power – flow 2

constraints and generator reactive power limit. An example for inequality constraint is voltage magnitude 3

constraint: 4

max 0i iV V (32) 5

Solution of the problems (20)–(31) provides the modified generation levels after congestion management. 6

3.1. Numerical studies 7

3.1.1. Data 8

A case study based on the modified IEEE 30 bus system which is shown in Fig. 2 is presented in this 9

section. Topology, line, generator, and demand data can be found in [34]. In this study, it is assumed that 10

every generator bids at its marginal cost. This bidding criterion is used for simplicity and it does not affect the 11

comparison process. In this paper, three different scenarios, as presented in Table 1, are considered for the 12

demands. The demand scenarios are generated based on random numbers. Random numbers are generated for 13

determination of the loads in every load bus according to a typical Load Duration Curve (LDC) shown in Fig 14

3. In scenario 1, all demands are considered to be in their peak value. Demand values for each load bus in 15

different scenarios are shown in Table 1. In this study three load scenarios including peak load and two other 16

random generated demands are considered. Fig.4. shows a typical load curve to illustrate the effect of penalty 17

and incentive factor on changing the response rate of demand response participants based on load economic 18

model. The load profile is divided into three main sections; low-load period (00.00–9:00), off-peak period 19

(10:00–18:00), and peak period and the load curve is normalized to its standard value for each load bus [19]. 20

The load profile before and after implementation of demand response programs with penalty factor 21

and without penalty factor is shown to emphasis on advantages of having penalty factor in load 22

economic model formulation. As it is shown, the penalty factor increases the contribution of the 23

responsive demands and also enhances the reliability level of these resources as the market operator 24

has two control variables (incentive and penalty factor). In this paper, three values of incentives and 25

penalties are considered for DR programs. The incentives are assumed to be 40, 50 and 60 $/MWh and the 26

13

penalties are considered as 25, 30 and 35 $/MWh. As shown in Table 2, seven load buses are selected based 1

on their potential to reduce the transmission line overload according to generation shift factor which is 2

presented in section 2.1.2. The capacity of each FACTS device used in this study is presented in Table 3. 3

3.1.2. Results and Discussion 4

The Results of the proposed method described in section 2 is analyzed using the data provided in the 5

previous subsection. At first, the electricity market is cleared without considering the electricity network. The 6

generator schedules for demand scenario 1 after first step of electricity market clearing is shown in Table 4. In 7

order to show the benefits of the proposed approach, two alternatives are considered: 8

1. With demand response. The optimization problem is solved using the technique described in section 9

2.4. 10

2. Without demand response. In this case demand response is not considered for congestion 11

management. 12

Results of generation re-dispatch (generation increment and decrement) for congestion management is 13

shown in Table 5 which Column 2 refers to the generators participated in re-dispatch procedure while 14

columns 3 and 4 show the re-dispatch amount without DR and with combination of FACTS and DR, 15

respectively. As it is shown the total amount of re-dispatch for generators without using demand response is 16

52.6MW. However, this amount is noticeably, reduced to 37.19MW which shows almost 29.3% reduction in 17

re-dispatch amount by using demand response programs. This reduction is a consequence of using 18

combination of incentive-based demand response programs and FACTS devices. 19

20 The load reduction associated with each responsive demand is presented in Table 6. This Table shows the 21

demand response locations and the reduction level that is achieved based on optimization problem presented 22

in section 2.4. The total cost of market operation in three different scenarios and two considered alternatives is 23

shown in Fig. 5. Comparison of both alternatives (with and without demand response) shows that using the 24

combination of DR and FACTS devices can reduce the total market cost (including market clearing and 25

congestion cost) by 7.2% . In fact, total market cost is lower when the market operator deployed the 26

combination of FACTS and DR programs. 27

14

Evolution of the re-dispatch cost in three demand scenarios and two different alternatives is shown in Fig. 6. 1

The use of combination of demand response and FACTS devices allows achieving up to 28.6% reduction for 2

congestion management cost. 3

In addition, different contingencies are considered to show the effectiveness of the proposed method in 4

contingency condition. In this study, two severe contingencies are selected. The generator located at bus 22 5

and line 7 which connects bus 6 to bus 9 are selected as contingency cases. 6

Re-dispatch cost corresponding to different demand scenarios and two considered alternatives is shown in 7

Figs. 7 and 8 for generator and line contingency cases. Results obtained from this comparison show that in 8

contingency cases combining the alternatives for congestion management leads to noticeable improvement. 9

As shown in Figs. 7 and 8, the use of combination of demand response and FACTS devices decreases the re-10

dispatch cost by 38.9% and 36.2%, respectively. 11

The method presented in this paper by combining different alternatives for congestion management provides 12

better solution than using each of these methods individually. In fact, the incentive paid to the responsive 13

demand to encourage them to participate actively in the electricity market can result in a noticeable benefit by 14

decreasing the congestion cost, especially, if the market operator combines other congestion management 15

tools such as FACTS device controllers. 16

4. Conclusions 17

An approach for congestion management to be used by electricity market operator in deregulated 18

environment is proposed in this paper. This approach minimizes the congestion management cost and also 19

total cost of market. The combination of two alternatives is a key issue presented in this approach. A case 20

study demonstrates the usefulness of the proposed method to minimize the congestion management cost. 21

Appendix A. 22

Static Model of TCSC 23

In this paper, the static model of TCSC used is based on a model described in [35] and the maximum line 24

compensation by TCSC is limited to 50 percent. In the steady-state operation, the equivalent TCSC reactance 25

is presented as follows: 26

csc csct t refX X (33) 27

15

In (33) csctX and csct refX are the reactance and its reference value, respectively. On this basis, a TCSC is 1

represented as a controllable reactance as shown in Fig.9. 2

The nodal powers at nodes K and L in Fig.9 are described as follows: 3

*

csc

( ). .

.

K LK K K Ki i

ti L

V VP j Q V Y V

j X

(34) 4

*

csc

( ). . L K

L L L Li iti K

V VP j Q V Y V

jX

(35) 5

In (34) and (35), KiY and LiY are the elements (K,i) and (L,i) of the admittance matrix of the power system 6

excluding the TCSC; KV , LV and iV are nodal voltages at nodes K, L and i, respectively. 7

8 Static Model of SVC 9

SVC has capacitive and inductive characteristics, and is predominantly utilized to improve voltage profile, 10

reduce network active power loss, and enhance security margin. A typical SVC, connected to the network via 11

a coupling transformer, is shown in Fig. 10. The active and reactive-power constraint equations, (36) and (37), 12

are applicable to the high-voltage node: 13

HK HKsP P (36) 14

HK HKsQ Q (37) 15

Where HKP and HKQ are nodal active and reactive-power at the high-voltage node. 16

However, there is another constraint at the high-voltage node in Fig. 10 as its voltage magnitude is 17

controlled based on steady-state terminal voltage and current characteristic at the supply frequency as shown 18

in Fig. 11 [5]: 19

.Hk refk k TkV V a I (38) 20

In (38), HkV is the magnitude of the voltage at the high voltage node of SVC; refkV , ka and TkI are 21

reference voltage, slope reactance and current of SVC, respectively. 22

The linear control represented by (38) is valid only when the operating limits of SVC are not exceeded. For 23

SVC, the operating limits are specified in terms of susceptances: 24

16

Lsvck svck CsvckB B B (39) 1

where svckB , CsvckB and LsvckB are equivalent susceptance, limit of capacitive and inductive susceptance of 2

SVC, respectively. 3

4

References 5

[1] Christie RD, Wollenberg BF, Wangensteen I. Transmission management in the deregulated environment. 6 Proceedings of the IEEE. 2000;88(2):170-95. 7 [2] Kumar A, Srivastava SC, Singh SN. Congestion management in competitive power market: A 8 bibliographical survey. Electric Power Systems Research. 2005;76(1-3):153-64. 9 [3] Acharya N, Mithulananthan N. Locating series FACTS devices for congestion management in deregulated 10 electricity markets. Electric Power Systems Research. 2007;77(3-4):352-60. 11 [4] Besharat H, Taher SA. Congestion management by determining optimal location of TCSC in deregulated 12 power systems. International Journal of Electrical Power & Energy Systems. 2008;30(10):563-8. 13 [5] Nguyen TT, Nguyen VL. Application of wide-area network of phasor measurements for secondary 14 voltage control in power systems with FACTS controllers. Conference Application of wide-area network of 15 phasor measurements for secondary voltage control in power systems with FACTS controllers. p. 2927-34 16 Vol. 3. 17 [6] Rahimzadeh S, Tavakoli Bina M. Looking for optimal number and placement of FACTS devices to 18 manage the transmission congestion. Energy Conversion and Management. 2011;52(1):437-46. 19 [7] Singh SN, David AK. Optimal location of FACTS devices for congestion management. Electric Power 20 Systems Research. 2001;58(2):71-9. 21 [8] Ying X, Song YH, Chen-Ching L, Sun YZ. Available transfer capability enhancement using FACTS 22 devices. Power Systems, IEEE Transactions on. 2003;18(1):305-12. 23 [9] Tuan LA, Bhattacharya K, Daalder J. Transmission congestion management in bilateral markets: An 24 interruptible load auction solution. Electric Power Systems Research. 2005;74(3):379-89. 25 [10] Bompard E, Carpaneto E, Chicco G, Gross G. The role of load demand elasticity in congestion 26 management and pricing. Conference The role of load demand elasticity in congestion management and 27 pricing, vol. 4. p. 2229-34 vol. 4. 28 [11] Albadi MH, El-Saadany EF. Demand Response in Electricity Markets: An Overview. Conference 29 Demand Response in Electricity Markets: An Overview. p. 1-5. 30 [12] Kirschen DS. Demand-side view of electricity markets. Power Systems, IEEE Transactions on. 31 2003;18(2):520-7. 32 [13] Strbac G. Demand side management: Benefits and challenges. Energy Policy. 2008;36(12):4419-26. 33 [14] Acharya N, Mithulananthan N. Influence of TCSC on congestion and spot price in electricity market 34 with bilateral contract. Electric Power Systems Research. 2007;77(8):1010-8. 35 [15] Le Anh T, Bhattacharya K. Competitive framework for procurement of interruptible load services. Power 36 Systems, IEEE Transactions on. 2003;18(2):889-97. 37 [16] Fahrioglu M, Alvarado FL. Designing incentive compatible contracts for effective demand management. 38 Power Systems, IEEE Transactions on. 2000;15(4):1255-60. 39 [17] Sioshansi R, Short W. Evaluating the Impacts of Real-Time Pricing on the Usage of Wind Generation. 40 Power Systems, IEEE Transactions on. 2009;24(2):516-24. 41 [18] Parvania M, Fotuhi-Firuzabad M. Demand Response Scheduling by Stochastic SCUC. Smart Grid, IEEE 42 Transactions on. 2010;1(1):89-98. 43 [19] Shayesteh E, Yousefi A, Parsa Moghaddam M. A probabilistic risk-based approach for spinning reserve 44 provision using day-ahead demand response program. Energy. 2010;35(5):1908-15. 45 [20] Moura PS, de Almeida AT. Multi-objective optimization of a mixed renewable system with demand-side 46 management. Renewable and Sustainable Energy Reviews. 2010;14(5):1461-8. 47

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[21] Billinton R, Lakhanpal D. Impacts of demand-side management on reliability cost/reliability worth 1 analysis. Generation, Transmission and Distribution, IEE Proceedings-. 1996;143(3):225-31. 2 [22] Bhattacharya K, Bollen MHJ, Daalder JE. Real time optimal interruptible tariff mechanism incorporating 3 utility-customer interactions. Power Systems, IEEE Transactions on. 2000;15(2):700-6. 4 [23] Horowitz I, Woo CK. Designing Pareto-superior demand-response rate options. Energy.31(6-7):1040-51. 5 [24] Yusta JM, Khodr HM, Urdaneta AJ. Optimal pricing of default customers in electrical distribution 6 systems: Effect behavior performance of demand response models. Electric Power Systems Research. 7 2007;77(5-6):548-58. 8 [25] Roos JG, Lane IE. Industrial power demand response analysis for one-part real-time pricing. Power 9 Systems, IEEE Transactions on. 1998;13(1):159-64. 10 [26] Allen J. Wood BFW. Power Generation, Operation, and Control. 2 edition ed: Wiley-Interscience, Jan 11 1996. 12 [27] Fred C. Schweppe MCC, Richard D. Tabors and Roger E. Bohn. Spot pricing of electricity. Boston: 13 Kluwer Academic Publishers, 1989. 14 [28] Schweppe FC, Caramanis MC, Tabors RD. Evaluation of Spot Price Based Electricity Rates. Power 15 Apparatus and Systems, IEEE Transactions on. 1985;PAS-104(7):1644-55. 16 [29] Joon Young C, Seong-Hwang R, Jong-Keun P. Optimal real time pricing of real and reactive powers. 17 Power Systems, IEEE Transactions on. 1998;13(4):1226-31. 18 [30] Kim BH, Baughman ML. The economic efficiency impacts of alternatives for revenue reconciliation. 19 Power Systems, IEEE Transactions on. 1997;12(3):1129-35. 20 [31] Wibowo RS, Yorino N, Eghbal M, Zoka Y, Sasaki Y. FACTS Devices Allocation With Control 21 Coordination Considering Congestion Relief and Voltage Stability. Power Systems, IEEE Transactions on. 22 2011;PP(99):1-9. 23 [32] Conejo AJ, Galiana FD, Arroyo JM, Garcia-Bertrand R, Cheong Wei C, Huneault M. Economic 24 inefficiencies and cross-subsidies in an auction-based electricity pool. Power Systems, IEEE Transactions on. 25 2003;18(1):221-8. 26 [33] IESO. Independent Electricity System Operator 25/March/2011. 27 [34] Bompard E, Wene L, Napoli R. Network constraint impacts on the competitive electricity markets under 28 supply-side strategic bidding. Power Systems, IEEE Transactions on. 2006;21(1):160-70. 29 [35] Nguyen TT, Nguyen VL. Power System Security Restoration by Secondary Control. Power Engineering 30 Society General Meeting,. 2007:1-8. 31 32 33

Figure Captions: 34

Fig.1. Two step market clearing procedure. 35

Fig.2.IEEE 30-bus system. 36

Fig.3.Typical LDC used for determining load demand. 37

Fig.4.Load reduction of responsive demand in two scenarios. 38

Fig.5.Total cost of market operation in different scenarios and system states. 39

Fig.6.Total re-dispatch cost in different scenarios and system states. 40

Fig.7.Total re-dispatch cost of market operation in different scenarios and system states for generator 41

contingency. 42

18

Fig.8.Total re-dispatch cost of market operation in different scenarios and system states for line 1

contingency. 2

Fig.9.TCSC model. 3

Fig.10.The SVC connected to the grid via a transformer. 4

Fig.11.The operating limit of SVC. 5

6

Tables: 7

Table 1: Three scenarios of load demand. 8 Bus Number Scenario 1 Scenario 2 Scenario 3

1 0 0 0

2 21.7 20.21 20.12

3 2.4 1.67 1.55

4 7.6 3.38 6.84

5 0 0 0

6 0 0 0

7 22.8 14.31 13.75

8 30 21.48 25.17

9 0 0 0

10 5.8 4.49 4.02

11 0 0 0

12 11.2 11.02 7.15

13 0 0 0

14 6.2 4.71 4.4

15 8.2 3.68 5.87

16 3.5 2.27 2.003

17 9 5.007 8.25

18 3.2 2.45 2.87

19 9.5 6.81 7.93

20 2.2 1.24 1.69

21 17.5 7.81 9.77

22 0 0 0

23 3.2 1.68 3.06

24 8.7 5.12 6.59

25 0 0 0

26 3.5 1.73 2.31

27 0 0 0

28 0 0 0

29 2.4 1.517 1.91

30 10.6 8.072 7.62

9 10 11 12 13 14

19

1 2

Table 2: selected buses for Demand response implementation. 3 Responsible Demand

Number Bus Number Initial Demand

1 7 22.8

2 8 30

3 12 11.2

4 17 9

5 19 9.5

6 21 17.5

7 30 10.6

4 5 6 7 8

Table 3: capacities of the facts devices [31]. 9 Type of FACTS Capacity (MVAr)

SVC 13.270

TCSC 0.182

10 11 12

Table 4: The Auction Results for Generators participated in electricity market. 13 Generator Number Bus Number Production (MW)

1 1 35

2 2 33.37

3 22 36

4 27 36

5 23 18.39

6 13 32.24 14 15

Table 5: Generation increment and decrement for all generators due to congestion management (MW). 16

Generator number Bus Number

Without DR

With

FACTS

With

DR

With

FACTS

Generation increment

1 22 17.77 9.36

2 27 12.18 9.01

3 23 0.22 0

Generation decrement

Generator number Bus Number

Without DR

With

FACTS

With DR

With

FACTS

1 1 0.4 0.79

2 2 12.16 10.64

3 23 0 0.29

4 13 9.89 7.1

17

20

Table 6: demand response contribution for congestion management (MW). 1 Responsible demand number Bus Number Demand Response

contribution

1 7 1.61

2 8 2.16

3 12 0.79

4 17 0.64

5 19 0.67

6 21 1.24

7 30 0.75

2

3

Figures: 4 5

6

7

8

9

10

11

12

13

14

15

16 Fig. 1. Two step market clearing procedure. 17

18

ISO

Receives information

From market participants

Market clears without

Considering network constraints

ISO finalize the market

Violation?

No

Yes

ISO analyze network congestion

and voltage profile

Congestion management

Procedure using

Responsive demand

Generation re-dispatch

FACTS devices

21

1

Fig. 2. IEEE 30-bus system 2

3 4

Fig. 3. Typical LDC used for determining load demand. 5 6

SVC

TCSC

22

1

Fig. 4. Load reduction of responsive demand in two scenarios. 2 3 4

5 Fig. 5. Total cost of market operation in different scenarios and system states. 6

7

8

9

10 11

23

1

Fig. 6. Total re-dispatch cost in different scenarios and system states. 2 3

4 5

Fig. 7. Total re-dispatch cost of market operation in different scenarios and system states for generator 6 contingency. 7

8

24

1 2

Fig. 8. Total re-dispatch cost of market operation in different scenarios and system states for line contingency. 3 4

5 6

7

8

Fig. 9.TCSC model. 9 10

11

Fig. 10. The SVC connected to the grid via a transformer. 12 13

14

15

16

17

K L

Transmission line

jXtcsc

25

1

Fig. 11.The operating limit of SVC 2 3

4

5