Optimal multiobjective planning of dynamic series compensation devices for power quality improvement

C.S.Chang and S.W.Yang

Abstract: An optimisation algorithm using tabu search is presented for optimal planning of series compensation devices for power quality improvement in distribution systems. The proposed algorithm is posed for optimal placement of two types of devices, named the series voltage restorer and the fault current limiter. A multiobjective problem is formulated to optimise a composite set of fuzzy performance indices comprising the cost expenditure of installed series compensation devices, voltage boosts across sensitive loads and overall voltage improvement. To ensure robustness, distribution networks are reinforced for preselected internal fault, external fault and simultaneous disturbances. Five case studies are presented to demonstrate the properties of the proposed algorithm.

List of major symbols

F = composite performance index FI = fuzzy performance index for different fault model AI = probability of occurrence of each fault K = candidate installation placement N = total number of candidate SVRs M = total number of candidate FCLs VsvRi = magnitude of voltage across ith SVR Z,,,; = output reactance of FCLi V, = magnitude of ith node voltage ymax = maximum voltage at node i at which the load can

operate properly Vimin = minimum voltage at node i at which the load can

operate properly Cl = capacity of ith SVR N, = set of nodes with sensitive loads N,,, = number of nodes without sensitive loads V s E j = maximum voltage injected by the ith SVR into

w = bicriterion constant in the range of 0 and 1 dl = phase angle of voltage across ith SVR

the system

1 Introduction

Modern technological advances are sensitive to supply quality. Even a slight dip in voltage magnitude for a short duration can result in equipment malfunction [l]. In order to avoid uneconomic losses, industries have devoted considerable effort to developing compensation devices for mitigating voltage sags. The implementation of series compensation devices, which includes series voltage restor- ers (SVRS) and fault current limiters (FCLS), has been

0 IEE, 2001 IEE Proceedings online no. 20010364 DOL 10.1049/ip-gtd:20010364 Paper first received 25th April 2000 and in revised form 24th January 2001 The authors are with the Department of Electrical Engineering National University of Singapore, 119260, Republic of Singapore

proven, with the development of low-cost, fast-controlled, force-commutated power electronic switches, such as GTOs and IGCTs [2, 31.

Before installing SVRs and FCLs in distribution systems, proper placement (locations, parameters and rating) of these devices needs to be selected. In [4], it has been suggested that SVRs could be installed at critical feeders [4]. However, with large voltage depression occurring during nearby faults, it may not be suficient to employ only the SVRs. FCLs can be used to support SVRs to boost voltages on sensitive loads. They are traditionally installed at feeder ends [5, 61 in order to limit the fault current effectively. However, with external faults occurring outside distribution systems, FCLs are of limited use. In addition, other factors (such as capital costs, running and maintenance costs and site limitation) should be considered before installing SVRs and FCLs. Hence, optimisation should be performed as suggested in [7], which has proposed multiobjective planning to solve this problem. Note that the work in [7] considers only the criterion of voltage sag improvement for one selected internal fault and the paper considered that only SVRS should be installed. Robustness is not guaranteed, as both the overall and sensitive-load voltage profiles should be improved with least cost. Last, but not the least, all the foreseeable fault conditions should be considered.

In this paper, all these aforementioned design criteria are blended into one composite multiobjective optimisation. The objectives considered include the cost expenditure of devices, as well as voltage sag enhancement on sensitive loads and the overall system. Fuzzy models have been increasingly used for multiobjective decision-making. A method is proposed in 181 for multiobjective optimal reac- tive power planning against voltage collapse. All the violated load busbar voltages are fuzzified and their enforcements are maximised. Fuzzy logic is used to obtain a trade-off among all objectives being considered. To ensure robustness, the user preselects one internal fault, one external and one set of simultaneous disturbances for synthesising the optimal SVR and FCL placement. The algorithm is a three-step procedure to: (i) optimise the placement with the occurrence of one inter- nal fault.

IEE Proc-Getter. Transm. Distrib., Vol. 148, No. 4, July 2001 361

(ii) optimise the placement with the occurrence of one external fault, (iii) evaluate performance of the above design using one set of simultaneous external and internal disturbances. One of the most widely used approaches for solving this kind of problem is the 'benders decomposition' [9-111. Two main drawbacks of the approach are seen here. First, the nonconvexity of optimisation problem may pose certain problems against convergence. Secondly, the application to large-scale optimisation will face increasing computational requirements. These drawbacks have motivated research toward heuristic or combinatorial algorithms such as tabu search [12, 131, simulated annealing [I41 and genetic algo- rithms [15]. Various techniques have been proposed to overcome the drawbacks against the traditional approach, some of which are explored in this paper. Tabu search is proposed here for multiobjective optimal SVR and FCL placement. It is a highly efficient search paradigm for find- ing fast high-quality solutions to combinatorial optimisa- tion problem. It is characterised by gathering knowledge during the search, and subsequently profited from this knowledge. It has the added advantage of being relatively insensitive to problems arising from complex study systems.

2 Outline of series compensation planning design

Section 1 has outlined the design objectives of the proposed algorithm. A set of fuzzy performance indices is used to assess each candidate placement under the three preselected faults. According to the probabilities of occurrence of these faults, the three fuzzy performance indices are blended together by appropriately adjusting al. u2, and u3:

F = alF1 + azF2 + asF3

where F,, F2 and F3 are the fuzzy performance indices under external, internal and simultaneous disturbances, calculated by eqns. 11, 14 and 16. The sum of all ul is equal to 1.

Fig. 1 shows the recursive applications of tabu search among candidate placements of series compensation for maximising the composite fuzzy performance index F. The original problem is solved by three suboptimisations. In each suboptinisation, the SVRs and FCLS are placed by optimising a vector K for each fault.

(1)

where K j is a binary variable. 4. can be equal to 1 or 0, indicating that series compensation is installed or not installed at location 5. 3 model

Formulation of series compensation planning

In each suboptimisation, SVRS and FCLS parameters and locations are optimised for each preselected disturbance by (i) minimising the cost expenditure required, (ii) maximising the sensitive-load voltages and (iii) maximising the overall system voltage improvement. From the models in the Appendix, the SVR parameters are represented for each sag as a vector [VsvRl, VSvR2 .... VsvRn, 61, S, ... S,,]. AS described in the Appendix, the FCL model can be repre- sented by a reactance ZFcL. Hence, parameters to be opti- mised are organised into a vector:

Calculate Fcurrent without SVR and FCL installed. Set the maximum number of TS

and neighbourhood sampling number.

<:>=, Maximum number of

I

Choose a candidate scheme K from the neighbour of the current

scheme.

I Calculate F,

for an installation scheme K by TS. Output the

Calculate F2 with an installation scheme K and determined ratings of

SVRs by TS. Output the optimal reactance of FCLs and ratings of

SVRs.

Calculate F with determined ratings of SVds and reactance of

FCLs by TS

Calculate F for this installation scheme K by eqn. 1. Output F and the ratings of SVRs and reactance

of FCLs.

I

Choose the best trial installation scheme to update the best installation

scheme by the rules of TS.

I output the best installation scheme.

Fig. 1 Overalljlowchart of proposed algorithm

To simplify the calculation, fault models in the following subsections, 3.1-3.3, deal only with three-phase faults in the steady state. All distribution substations and loads are represented by equivalent voltage sources and fixed imped- ances. Faults can be external, internal or simultaneous. From the model in the Appendix, the FCL is seen to have no voltage improvement for external faults. Hence, param- eters for a given candidate placement K are synthesised in three suboptimisations as in Fig. 1.

IEE Proc.-Gener. Trcmsm. Disrrib., Vol. 148, No. 4, July 2001 362

3.1 Fault model for one external fault Each candidate SVR placement should be assessed by how much it contributes to voltage sag improvement when external fault occurs. It is necessary to ensure proper SVRs operation by maintaining the voltages at sensitive nodes within predetermined range as follows:

Sensitive load voltages arc normalised: y m a x > - v. 2 - > y i n (4)

VI,, I I, v, < l p n

V! = yn= > - v. 2 - > 1/Zmin ( 5 ) { l 1 - (Vi - y n = ) vi 2 ,inax

where 0 5 Vimin s; 1.0 and Kmin 5 Vimax. P is a constant between 0.0 and 1.0 and eqn. 5 penalises all sensitive load voltages outside the range of [I/r", Vimax]. If V i is set to 0, when Ti < 0.0. The first objective function to be maxim- ised is:

Trade-off must also be made against the cost expenditure. If the SVR cost is proportional to its capacity, the second objective function to be minimised is:

V, = min(y'); i E Ns (6)

n

c = c C,l (7) i=l

Supposing that the flow through the ith SVR is Zj, the rating of this SVR is:

cil = 3 ' l vSVRi l ' lfil ( 8 )

1 .o a

By adjusting parameters of SVRs, such as the turns ratio of the series transformer and so on, it is possible to improve the voltages at the other nodes. Generally, equipment can operate at typically 80% of the nominal voltage for several cycles. Voltages at the other nodes are thus normalised between 0 and 0.8:

The third objective function to be maximised is:

(9)

where V,, is the average normalised voltage on all nodes without sensitive loads.

To obtain a single objective function by combining eqns. 6, 7 and 10, V, and C, V,, are each quantified into a fuzzy membership function V,m. i = I , 2, 3. These membership functions are represented in Figs. 2 4 b and c whereh, i = 1,2, 3 represent v,, C and Vn.9. In Fig. 2c, conl is a constant, which regulates the importance of VIE) among the three objective functions. With a lower conl, V,, is emphasised. To best utilise the performance of a candi- date SVR placement, a fuzzy performance index needs to be maximised:

which is subjected to all other system constraints and I VsvRil s I VT$ii I. To have a practical set of values, each candidate SVR rating is rounded up to the nearest stand- ard rating. No loss of accuracy would incur as a result, as only standard SVR ratings are entered for performance evaluation.

3.2 Fault model for one internal fault The first and third objectives are the same as those in Section 3.1. However, as the ratings and locations of SVRs are determined in Section 3.1, the second objective function is modified. In principle, ZFCLj is varied to minimise the second objective function, while limiting the capacity of SVRs within predetermined ratings. The second objective function C in eqn. 12 is minimised:

where

where C,2 is capacity of the ith SVR calculated by eqn. 8. Member functions for the internal fault are shown in

Figs. 3 4 b and c where h, i = 1, 2, 3 represent V,, C and V,,. A fuzzy performance index is also used to describe the performance of a candidate SVR and FCL placement. This is to maximise:

Ns b *NS

1 .o C

Fig. 2 Membership function of&zzji petjGormance index for external f d t

which is subjected to all other system constraints and

For each of the faults considered, this suboptimisation is solved to obtain fuzzy index F2i Then F2 is the average of F2i of all the internal faults. From this optimisation, ratings of FCLs are determined. Rating of the ith SVR CsvRi is updated towards the maximum Ci, and C,2. The value obtained is rounded up to the next standard value.

I Vs,,l I VSY& I.

363 IEE Proc.-Gener Transm. Distrib., Vol 148. No. 4, July 2001

t

I .o

0.5

C

1 .o b

1 .o a

1 .o

a I .o

: Vns I c

1 .o c Fig.3 Membership fwciion of fuzzy p e r f m c e in&x for internalfiuli

3.3 Fault model for simultaneous internal and external disturbances With ratings of SVRs and reactances of FCLs determined, the second objective function is given by the following eauation:

where CbvRi is calculated using eqn. 13. The first and the third objective functions are the same as in Sections 3.1 and 3.2. Membership functions for eqns. 6, 10 and 15 are shown in Fig. 4. From Sections 3.1 to 3.3, the third objec- tive function is seen to play a less important role, hence the con values for the three sections should be set in the follow- ing order: con1 < con2 < con3. The aim of this optimisation is to maximise the fuzzy performance index:

subjected to all other system constraints and lVsvRl 5

IVf@I. wherefi: represents V,, C or V,.

4 Tabu search for series compensation planning

The method of tabu search is described here for seeking the best placement and parameters of SVRs and FCLs with the largest composite performance index F. Tabu search is a restricted neighbourhood search technique. The funda- mental idea of tabu search is the use of flexible memory of

364

b 1 .o

i Vns

C 1 .o Fig.4 disturbances

Mendership fwction of fuzzy perfrmance index for sh.iltaneour

search history and thus guides the search progress to surmount local optimal solutions. It is capable of optimis- ing, not only the integer variable, but also the continuous variable, by discretising technique. By discretising variables in eqn. 3, tabu search is also used to solve these suboptimi- sations with continuous variables. Basic steps of tabu search for SVR and FCL planning are described as follows: (U) Calculate the prefault flow and replace all the loads with impedances. (b) Set iteration counter m = 0 and randomly generate an initial (current) solution K". Set the best candidate place- ment vector Kbest = K". Calculate the composite perform- ance index F for K". (c) If m is equal to the prespecified maximum iteration Mmax, the program is terminated and the final output er, ratings of SVRs and reactances of FCLs give the desired solution. Otherwise, set m = m + 1, and go to the next step. (dj Select a trial solution from the neighbourhood of Z f by applying moves and compute the corresponding composite performance index. Repeat this process until the specified neighbourhood sampling number, S,,, has been reached.

IEE Proc-Gener. Transm. Distrib.. Vol. 148, No. 4, July 2001

(e) If Pest is not better than the best trial solution, which has the biggest objective function value, assign this best trial solution to pest Otherwise, go to next step. 0,) K* is updated to the best trial solution which has the biggest objective function value, as evaluated in step d, and the corresponding move is not in the tabu list or its aspira- tion level is attained. Then, put the move in the tabu list and go to step c. If the best trial solution corresponds to a tabu move and its aspiration level is not attained, check the next best trial solution and repeat this step. (g) Output Pest, optimal ratings of SVRs and reactances of FCLs.

21 22 23 24 25 20 I 1 I

Fig. 5 Distribution network configuration

5 Study system

The proposed algorithm has been implemented in MATLAB. The described method is applied to a 34-busbar system as shown in Fig. 5. The system is fed from a lOMVA transformer. Details of the feeders and load char- acteristics are given in Table 1. Nodes 20, 25 and 30 are connected to sensitive loads. There are 9 candidate SVR sites located at the feeder sections between: nodes 3 and 15, nodes 18 and 19, nodes 19 and 20, nodes 19 and 21, nodes 23 and 24, nodes 24 and 25, nodes 24 and 26, nodes 28 and 7 and nodes 29 and 30. There are five candidate sites for FCLs located between nodes 3 and 4, nodes 5 and 6, nodes 7 and 8, nodes 7 and 28, and nodes 6 and 7. Parameters used in the optimisation problem are listed below on a base of 100MVA and 1lkV:

U&" = 0.85 vz" = 0.90 vE" = 0.95 vYaX = 1.05 i = 20,25,30 vYFR = 0.5 P.U. V = 0.85 w = 0.8

0.75 04 = 0.20 a3 = 0.05 conl = 0.4 con2 = 0.6 con3 = 0.7

6 Study results and discussions

Five case studies are presented here to demonstrate the performance of the algorithm. The placement of SVR and FCL, in each case study, is optimised with one external fault causing a voltage depression of AVl at the source of supply (node 1) and one internal fault occurring at a selected node Location,. The performance of the optimal design is verified with a separate set of simultaneous distur- bances, which includes one internal fault at a selected node Locationb and a voltage depression of AV, at node 1. Based on the above fault specification, the five case studies are formed in Table 2:

IEE Proc-Gener. Transm. Distrib., Vol. 148, No. 4, July 2001

Table 1: Distribution system data

Line impedance Node Node Node Load

number P, kW Q, kVar r, Q x, Q

1 0.0 0.0 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

260.0

0.0

260.0

260.0

0.0

0.0 260.0

260.0

76.0

76.0

76.0

76.0

76.0

90.0

90.0

90.0

53.5

260.0

1087.0

260.0

260.0

260.0

137.0

824.5

95.0

95.0

95.0

260.0

1550.0

260.0

260.0

260.0

125.0

0.0

125.0

125.0

0.0 0.0

125.0

125.0

34.5

34.5

34.5

34.5

34.5

45.0

45.0

45.0

7.5

125.0

650.0

125.0

125.0

125.0

85.0

400.0

48.0

48.0

48.0

125.0

509.2

125.0

125.0

125.0

260.0 125.0

2

3

4

5

6

7

8

9

10

11

12

13

3

15

16

17

18

19

19

21

22

23

24

24

26

27

28

6

29

30

31

32

33

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

7

29

30

31

32

33

34

0.0024 0.018

0.0036 0.027

0.0046 0.022

0.0042 0.020

0.0033 0.016

0.0045 0.019

0.0040 0.016

0.0060 0.024 0.0040 0.016

0.0050 0.020

0.0040 0.016

0.0030 0.012

0.0020 0.008

0.0027 0.011

0.0036 0.015

0.0018 0.008

0,0009 0.004

0.0036 0.015

0.0023 0.009

0.0054 0.023

0.0036 0.015

0.0023 0.009

0.0018 0.008

0.0018 0.008

0.0054 0.023

0.0027 0.011

0.0027 0.011

0.0027 0.011

0.0050 0.024

0.0046 0.022

0.0047 0.021

0.0047 0.021

0.0043 0.019

0.0043 0.019

Cases 1, 2 and 4 include only the first and second objec- tive functions, by setting conl, con2 and con3 to 1. Table 3 shows the synthesised SVR and FCL locations, parameters and ratings for cases 1-3. Table 4 shows the voltage per- formance of the three synthesised placements under the specified faults. Fig. 6 presents a typical convergence plot of the proposed algorithm taken from case 3.

In case 1, only SVRs are installed with a total rating of 4MVA. As objective 3 is not included, nodes with sensitive loads (20, 25 and 30) receive far greater voltage improve- ment than most other nodes in the system. Nodes closer to the sensitive nodes also receive improvement. With the same combination of objective functions as in case 1, case 2 retains the same SVR locations for local voltage support. In addition, case 2 places one FCL between nodes 7 and 8, and reduces the SVR capacity at node 29 to 1 MVA. With objective 3 included, case 3 provides universal voltage support at all nodes by using a different set of SVR loca- tions from case 2 with the same overall SVR capacitv. In addition, case 3 uses the same FCL location but a higher FCL rating of 0.075p.u.

365

Table 2: Fault data specification and objectives included in case studies

8 1.0-

g 0.8 z 0.9 .- (FI

0.7 0.6

.- $2 0.5

E 0.3 8 0.2 n

P

go.4

2 0.1

c

Fault data specification Case number Location,, Locationb,

A ' 1 , % node node

1" 30 12 12 10 Yes Yes no 2 30 12 12 10 Yes Yes no

3 30 12 12 10 Yes Yes Yes

4 30 5 5 10 yes Yes no

5 30 5 5 10 Yes Yes Yes * FCL is not included in case 1

Objectives included in optimisation

AV2, % Objective 1 Objective 2 Objective 3

-

- - -

- - - - -

o a " " ' I * " " " "

Table 3: SVR and FCL placements for cases 1,2 and 3

External Internal Simultaneous fault fault disturbances Rating Output

svR,FcL Location (between node and node)

Case1 SVRI 19 20 1 MVA output voltage VS~R, p.u. 0.2 0.5 0.3

SVR2

SVRB

Case2 SVRI

SVR2

SVRB

FCL

Case3 SVRI

SVR2

SVR3

FCL

24 25

29 30

19 20

24 25

29 30

7 8 29 30

3 15

28 7

7 8

1 MVA

2 MVA

1 MVA

1 MVA

1 MVA

0.035p.u.

1 MVA

1 MVA

1 MVA

0.075p.u.

angle 6, rad

output voltage VS~R, p.u.

angle 6, rad

output voltage Vsv~, PA.

angle 6, rad

output voltage Vsv~, p.u.

angle S, rad

output voltage VSVR, p.u.

angle 6, rad

output voltage Vsv~, p.u.

angle 6, rad

output reactance, p.u.

output voltage VSVR, P.U.

angle 6, rad output voltage Vsv~, p.u.

angle 6, rad

output voltage Vsv~, p.u.

angle 6, rad

output reactance, p.u.

0.0

0.25

0.0 0.3

0.0

0.3

0.0 0.3 0.0

0.3

0.0 0.0

0.3

0.0

0.25 0.0

0.25

0.0

0.0

-1.0996

0.5

-0.9425 0.4

0.1571

0.2

0.0

0.245

0.0

0.32

0.0 0.035

0.295

0.0

0.05 0.0

0.305

-0.0471

0.075

0.0

0.375

0.0 0.45

0.0

0.2

0.0

0.31

0.0

0.375

0.0 0.035

0.36

0.0 0.14

0.0

0.365

-0.0314

0.075

ratings are more necessary in case 5 than case 4 due to the inclusion of objective 3.

In all the five cases studied, FCLs do not have any effect during external faults, which only lead to a voltage depres- sion at node 1. FCLs become effective during internal faults and play a different role according to the severity of the chosen fault location. In cases 2 and 3 where the inter- nal fault occurs at an outgoing feeder (node 12), the influ- ence of FCL is limited. The FCL is located at the sending end of the feeder and has a relative small rating. In cases 4 and 5 where the internal fault occurs at the central loop (node 5), two FCLs are placed at the loop to limit the fault currents in both directions. Higher FCL ratings are required for these two cases.

The structure of the study system has been carefully designed to illustrate essential features of the proposed algo- rithm. For dealing with wider variations of planning prob- lem and configuration, the proposed algorithm has a robust structure for immediate application or extension as follows: (a) This present study system is radially dominated and singly fed. Only one external fault location exists in the present system. For distribution networks highly meshed or with multiple infeeds, the number of external faults to be considered will increase. This will necessitate more subopti- misations as in Fig. 1. However the basic steps in each

IEE Proc-Gener Transm. Distrib., Vol. 148, No. 4, July 2001

Table 4 Voltage performance of cases 1,2 and 3

External fault Internal fault Simultaneous disturbances

Node No Case I Case 2 Case 3 FoipcnSation case I Case 2 Case 3 Foipensation Case I Case 2 Case 3

compensation

0.7 0.7 0.7 1.0 1.0 1.0 1.0 0.9 0.9 0.9 0.9 Voltages, 1 P.U. 2

3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

0.7 0.6995 0.6987 0.6984 0.6980 0.6978 0.6977 0.6975 0.6976 0.6975 0.6975 0.6975 0.6975 0.6975 0.6986 0.6983 0.6982 0.6982 0.6980 0.6979 0.6978 0.6977 0.6977 0.6977 0.6976 0.6977 0.6977 0.6977 0.6976 0.6974 0.6973 0.6972 0.6972 0.697 1

Voltage improvement, %*

0.6944 0.6985 0.6980 0.6976 0.6973 0.6972 0.6972 0.6971 0.6971 0.6970 0.6970 0.6970 0.6970 0.6983 0.6980 0.6979 0.6978 0.6976 0.8975 0.6974 0.6973 0.6972 0.6972 0.9471 0.6972 0.6972 0.6972 0.6970 0.9967 0.9966 0.9965 0.9964 0.9964 5.5

0.6994 0.6984 0.6980 0.6976 0.6973 0.6972 0.6971 0.6970 0.6970 0.6970 0.6970 0.6970 0.6970 0.6982 0.6979 0.6978 0.6978 0.6975 0.9974 0.6973 0.6972 0.6971 0.6971 0.9971 0.6971 0.6971 0.6971 0.6969 0.9966 0.9965 0.9964 0.9964 0.9963 9.0

0.6993 0.6983 0.6979 0.6975 0.6971 0.6970 0.6970 0.6969 0.6969 0.6969 0.6968 0.6968 0.6968 0.9481 0.9478 0.9477 0.9476 0.9474 0.9473 0.9471 0.9470 0.9470 0.9469 0.9469 0.9470 0.9470 0.9470 0.6968 0.9965 0.9964 0.9963 0.9962 0.9962 19.3

0.9061 0.7655 0.6869 0.6155 0.5584 0.4896 0.4045 0.2767 0.1916 0.0851 0.0 0.0

0.0 0.7464 0.7209 0.7081 0.7018 0.6763 0.6763 0.6382 0.6129 0.5971 0.5844 0.5844 0.5465 0.5275 0.5086 0.5582 0.5581 0.5580 0.5579 0.5579 0.5579

0.9060 0.7651 0.6865 0.6151 0.5579 0.4892 0.4041 0.2765 0.1914 0.0851 0.0 0.0

0.0 0.7459 0.7204 0.7076 0.7012 0.6757 1.0150 0.6376 0.6122 0.5964 0.5837 0.9741 0.5459 0.5270 0.5081 0.5576 0.9530 0.9529 0.9528 0.9527 0.9527 9.6

0.9224 0.8060 0.7412 0.6824 0.6353 0.5789 0.3327 0.2276 0.1576 0.0700 0.0 0.0 0.0 0.7902 0.7692 0.7587 0.7534 0.7324 0.9323 0.7010 0.6812 0.6671 0.6567 0.9017 0.6256 0.6100 0.5944 0.6350 0.9547 0.9546 0.9545 0.9544 0.9544 20.8

0.9405 0.8513 0.7789 0.7131 0.6606 0.5976 0.2541 0.1739 0.1204 0.0535 0.0 0.0 0.0 0.9012 0.901 1 0.901 1 0.901 1 0.9010 0.9009 0.901 1 0.9012 0.9013 0.9013 0.9013 0.9016 0.9018 0.9020 0.6602 0.9550 0.9548 0.9548 0.9547 0.9547 31.2

0.81 55 0.6887 0.6179 0.5536 0.5022 0.4403 0.3637 0.2489 0.1723 0.0766 0.0 0.0 0.0 0.6717 0.6488 0.6373 0.6316 0.6087 0.6086 0.5744 0.5516 0.5374 0.5260 0.5259 0.4918 0.4748 0.4577 0.5024 0.5022 0.5022 0.5021 0.5021 0.5021

0.81 54 0.6887 0.6179 0.5536 0.5022 0.4403 0.3637 0.2489 0.1723 0.0766 0.0 0.0 0.0 0.67 15 0.6485 0.6370 0.6313 0.6083 0.9081 0.5740 0.5512 0.5369 0.5255 0.9004 0.4914 0.4744 0.4574 0.5019 0.951 4 0.9513 0.9512 0.9512 0.951 1 12.1

0.8301 0.7253 0.6670 0.6141 0.5717 0.5209 0.2994 0.2048 0.1418 0.0630 0.0 0.0 0.0 0.71 1 1 0.6922 0.6827 0.6780 0.6591 0.8590 0.6309 0.6121 0.6003 0.5910 0.9009 0.5629 0.5489 0.5347 0.57 14 0.9461 0.9460 0.9459 0.9458 0.9458 24.4

0.8463 0.7658 0.7010 0.6421 0.5950 0.5386 0.2290 0.1567 0.1085 0.0482 0.0 0.0 0.0 0.9055 0.9051 0.9049 0.9048 0.9045 0.9044 0.9041 0.9039 0.9037 0.9037 0.9036 0.9035 0.9034 0.9034 0.5947 0.9544 0.9543 0.9542 0.9542 0.9541 41.4

suboptimisation are problem-independent, and the compu- tational requirement in each iteration of the algorithm will remain largely unchanged. This is because of the lion's share of computation taken up during simulation for evalu- ating the performance of each candidate scheme. The above characteristic is clearly advantageous over the bend- ers decomposition. There are, however, needs for tuning study parameters such as al - a3, as in eqn. 1 and the fuzzy performance parameters as in Fig. 4 for achieving best performance for different problems. (6) Observing the results obtained, placements of SVR are essentially decided by external faults and FCLs by internal faults. To limit the number of unnecessary suboptimisa- tions, it would be advantageous to develop statistical models for both internal and external fault distributions and line outages. Suboptimisations could then be applied to the most frequently occurred or the worst-case faults, on the discretion of the user.

IEE Proc -Gener Trunsm Dirtrib, Vol 148. No 4, July 2001

(c) Results from each suboptimisation also depend on factors such as the number of sensitive nodes and the number of FCL and SVR sites. The number of suboptimi- sations would, however, remain unchanged.

7 Conclusion

The paper proposes an algorithm for optimal SVR and FCL placement of the distribution system. The design procedure optimises the performance of each candidate placement by minimising three objectives, namely, capital cost expenditure, as well as voltage sag improvement on sensitive loads and other nodes. The optimisation problem is based on tabu search and fuzzy performance indices. The former is a search technique with high efficiency. The latter provides a trade-off among the three objectives. Five case studies have been presented and satisfactory results have been obtained.

367

Table 5 SVR and FCL placements for cases 4 and 5

SVR,FCL Location (between Rating node and node)

output External Internal fault fault

Case4 SVRI 19 20 1 MVA

SVR2 24 25 1 MVA

SVR3 29 30 1 MVA

FCL 3 4 0.215p.u.

FCL 5 6 0.37 p.u.

Case5 SVRI 29 30 1 MVA

SVR2 3 15 1 MVA

SVR3 28 7 1 MVA

FCL 3 4 0.84p.u.

FCL 5 6 1.525p.u.

output voltage VSVR, p.u.

angle 6, rad

output voltage VSVR, p.u.

angle 6, rad

output voltage V.VR, p.u.

angle 6, rad

output reactance, p.u.

output reactance, p.u. output voltage V.VR, p.u.

angle 6, rad

output voltage V.VR, p.u.

angle 6, rad output voltage VSVR, p.u.

angle 6, rad

output reactance, p.u.

output reactance, p.u.

0.2

0.0

0.25

0.0

0.3

0.0

0.0

0.0

0.3

0.0

0.25

0.0 0.25

0.0

0.0

0.0

0.2

0.0

0.225

0.0

0.37

0.0

0.215

0.37

0.105 0.0157

0.015

0.0 0.015

0.0

0.84

1.525

Simultaneous disturbances

0.4950

1.5551

0.4950

1.2881

0.390

0.0785

0.215

0.37

0.19 0.2356

0.015 0.1414

0.015

0.0

0.84

1.525

8 References

1 DOUGLAS, J.: ‘Custom power: optimising distribution Services’, EPRI J., May/June 1996, pp. 7-15

2 HEYDT, G.T., TAN, W., LAROSE, T., and NEGLEY, M.: ‘Simu- lation and analysis of series voltage boost technology for power qual- ity enhancement’, IEEE Trans. Power Deliv., 1998, 13, (4), pp. 1335- 1341

DARAM, A., and ADAPA, R.: ‘Transient behaviour model (TBM) for power converters’. IEEE Workshop on Computers in Power Elec- tronics, Piscataway, NJ, USA, 1996,96TH8288, pp. 18-24

4 KARA, A., DAHLER, P., AMHOF, D., and GRUNING, H.: ‘Power supply quality improvement with a Dynamic Voltage Restorer (DVR)’. Proceedings of IEEE Applied Power Electronics Conference and Exposition, APEC, Piscataway, NJ, USA, 1998, Vol. 2, pp. 986- 993 QUAIA, S., and TOSATO, F.: ‘Power supply quality improvement by short-circuit current limitation on distribution nets’, Int. J. Model.

6 SARMIENTO, H.G., TOVAR, C., and MOLERO, B.: ‘A feasibility study for a fault current l i t e r to reduce voltage sags at sensible loads’. Proceedings of IEEE 1995 Annual Meeting, 1995, pp. 99-103 CHANG, C.S., and YANG, S.W.: ‘Tabu search application for opti- mal multiobjective planning of series devices’. Procedings of IEEE

8 VENKATESH, B., SADASIVAM, G., and KHAN, M.A.: ‘Optimal reactive power planning against voltage collapse using the successive multiobjective fkzy LP technique’, IEE Proc. Gener., Transm. Distrib., 1999, 146, (4), pp. 343

9 GEOFFRION, A.M.: ‘Generalized benders decomposition’, J. Uptim. Theory Appl., 1972, 10,

10 ROMERO, R., and MONTICELLI, A.: ‘A hierarchical decomposi- tion approach for transmission network planning’, IEEE Trans. Power

11 ALGUACI, N., and CONEJO, A.J.: ‘Multiperiod optimal power flow using bender decomposition’, IEEE Trans. Power Syst., 2000,15, (l), pp. 196-201

12 GAN, D., QU, Z., and CAI, H.: ‘Large-scale var optimisation and planning by tabu search’, Electr. Power Syst. Res., 1996, 39, (3), pp. 195-204

13 CHANG, C.S., and WEN, F.S.: ‘Tabu search based approach to trouble call analysis’, ZEE Proc.. Gener., Transm. Distrib., 1998, 145,

14 ROMERO, R., GALLEGO, R.A., and MONTICELLI, A.: ‘Trans- mission system expansion planning by simulated annealing’. Proceed- ings of IEEE Trans. PAS, June 1995, pp. 278-283

15 YANG, H.T., YANG, P.C., and HUANG, C.L.: ‘A parallel genetic algorithm approach to solving the unit commitment problem: imple- mentation on the transputer network‘, IEEE Trans. Power Syst., 1997,

16 LAMOREE, J., MUELLER, D., VINETT, P., JONES, W., and SAMOTYJ, M.: ‘Voltage sag analysis case studies’, IEEE Trans. Ind

3 KAGALWALA, R., VENKATA, S.S., LAURITZEN, P.O., SUN-

5

SkUl., 1995, 15, (I), pp. 1-7

7

PES WM 2000, Vol. 4, pp. 2751-2756

Sy~t . , 1994, 9, (l), pp. 373-380

(6), pp. 731-738

12, (2), pp. 278-283

Appl., 1994,30, (4), pp. 1083-1089

368

9

9.1 Series voltage restorer (SVR) The SVR comprises major components, namely, capacitor bank, pulse-width-modulated (PWM) inverter fired by a suitable control system, AC harmonic filters, injection transformers and an optional energy storage system [4], as shown in Fig. 7. An energy storage system is necessary if the SVR is expected to provide active power compensation. The PWM inverter is used to generate series boost voltages of the desired magnitude and phase. It can be designed to produce any voltage magnitude V,, (within component and modulation limits) and any voltage phase angle 6 (by controlling the PWM carrier phase shift). During normal operating conditions, the SVR injects only a small voltage to compensate for the voltage drop of the injection trans- former and device losses. During voltage sag, the SVR control system calculates and synthesises the voltage

Appendix - description of SVR and FCL

“I I 4 busbar

transformer

load busbar

injection transformer

I I I I I rectifier

I

1 PWM T inverter rectifier

Tshifi

Fig.7 SVR layout

load current71L Fig .8 SVR phasor diagram

IEE Proc-Gener. Transm. Distrib., Vol. 148, No. 4, July 2001

Table 6 Voltage performarlce of cases 4 and 5

External fault Internal fault Simultaneous disturbances

compensation case 4 case 5 cNoqnpensation No Node No

Case 4 Case 5 compensation Case 4 Case 5

Voltages, 1 0.7 0.7 0.7 1 .o 1 .o 1 .o 0.9 0.9 0.9 p.u. 2

3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

0.6995 0.6987 0.6984 0.6980 0.6978 0.6977 0.6975 0.6976 0.6975 0.6975 0.6975 0.6975 0.6975 0.6986 0.6983 0.6982 0.6982 0.6980 0.6979 0.6978 0.6977 0.6977 0.6977 0.6976 0.6977 0.6977 0.6977 0.6976 0.6974 0.6973 0.6972 0.6972 0.6971

Voltage improvement, %*

0.6994 0.6985 0.6980 0.6976 0.6973 0.6972 0.6972 0.6971 0.6971 0.6970 0.6970 0.6970 0.6970 0.6983 0.6980 0.6979 0.6978 0.6976 0.8975 0.6974 0.6973 0.6972 0.6972 0.9471 0.6972 0.6972 0.6972 0.6970 0.9967 0.9966 0.9965 0.9964 0.9964 8.4

0.6993 0.6983 0.6979 0.6975 0.6971 0.6970 0.6970 0.6969 0.6969 0.6969 0.6968 0.6968 0.6968 0.9481 0.9478 0.9477 0.9476 0.9474 0.9473 0.9471 0.9470 0.9470 0.9469 0.9469 0.9470 0.9470 0.9470 0.6968 0.9965 0.9964 0.9963 0.9962 0.9962 21.6

0.7742 0.4359 0.2075 0.0343 0.0756 0.0756 0.0756 0.0756 0.0756 0.0756 0.0756 0.0756 0.41 10 0.3778 0.3612 0.3529 0.3197 0.3197 0.2701 0.2369 0.2162 0.1997 0.1997 0.1501 0.1252 0.1004 0.0343 0.0342 0.0342 0.0342 0.0342 0.0342 0.0342

0.9276 0.81 90 0.0547 0.0 0.5823 0.6063 0.6063 0.6062 0.6062 0.6062 0.6062 0.6062 0.6062 0.8042 0.7844 0.7746 0.7696 0.7499 0.9498 0.7205 0.7010 0.6887 0.6790 0.9038 0.6499 0.6353 0.6208 0.5819 0.951 1 0.9510 0.9509 0.9508 0.9508 289.7

0.9752 0.9379 0.0179 0.0 0.8491 0.8580 0.8579 0.8579 0.8578 0.8578 0.8578 0.8578 0.8578 0.9473 0.9398 0.9360 0.9441 0.9267 0.9266 0.9156 0.9083 0.9037 0.9000 0.9000 0.8892 0.8838 0.8784 0.8488 0.9535 0.9534 0.9533 0.9533 0.9532 375.2

0.6968 0.3923 0.1868 0.0 0.0308 0.0681 0.0680 0.0680 0.0680 0.0680 0.0680 0.0680 0.0680 0.3699 0.3400 0.3251 0.3176 0.2878 0.2878 0.2431 0.2132 0.1946 0.1797 0.1 797 0.1351 0.1 127 0.0904 0.0308 0.0308 0.0308 0.0308 0.0308 0.0308

0.8349 0.7374 0.0492 0.0 0.5246 0.5463 0.5463 0.5462 0.5462 0.5462 0.5462 0.5462 0.5462 0.7241 0.7065 0.6976 0.6932 0.6755 0.8539 0.6491 0.6316 0.6206 0.61 18 0.901 3 0.5856 0.5725 0.5594 0.5243 0.9141 0.91 40 0.9139 0.9138 0.9138 297.0

0.8776 0.8441 0.0161 0.0 0.7643 0.7723 0.7722 0.7721 0.7721 0.7721 0.7721 0.7721 0.7721 0.8541 0.8473 0.8439 0.8422 0.8355 0.8354 0.8255 0.8189 0.81 48 0.8115 0.81 15 0.8017 0.7969 0.7920 0.7640 0.9500 0.9499 0.9498 0.9497 0.9497 384.2

required to maintain the output voltage and injects this voltage in synchronous real time. The operating principle of the SVR can be illustrated vectorially in Fig. 8:

IVEjq = .\/IVL12 - 2 ~ v L ~ ~ v l m i n ~ cos(a) + Iyminl2

(17) where Vp+fi = maximum voltage injected by SVR into the system VL = voltage across the load Vlmin = mini" voltage of the supply VI = prefault voltage of the supply a = phase shift between VI and V,. The rating SsvR of the SVR is

S ~ V R = Vs$; * I L = J~vL12-2~vL~~vl""~ cos(a)+IV1""12 . - S L

VL

(18)

where ZL = load current S, The active power PsvR provided by SVR is given by

= apparent power of the load

where $ is the power factor angle.

9.2 Fault current limiter (FCL) The FCL as shown in Fig. 9 is used to limit the current when a fault occurs. The FCL limits fault current by insert- ing an inductor in series with the line. During normal system operation, the thyristors are not conducting. Volt- age drop across the FCL will be negligible as the series- connected inductor and capacitor are tuned to resonate at the supply frequency. When fault is detected, the thyristors are turned on. This effectively short-circuits the capacitor,

369 IEE Proc.-Gener. Transm. Distrib., Vol. 148, h'o. 4, July 2001

leaving the series inductor (impedance X = wL) to limit the fault current.

thyristor

,WPPiYVl ~~~ thyristor fault f

Fig.9 FCL layout

-L - Fig. 10 Simple radial distribution system

Besides limiting fault current, the FCL can be used to mitigate voltage sag. To illustrate the sag mitigation capa- bility of the FCL, consider the ‘simple voltage divider’ concept proposed in [16]. With a fault on feeder 1, as in Fig. 10, the voltage at the distribution busbar FBm (in P.u.) can be written as

distribution busbar voltage during normal sys- tem condition source impedance impedance between the distribution busbar and fault, including the FCL impedance

As the FCL introduces a very large series impedance dur- ing fault, 2, + Z2 - Z2 and hence VBus - Vprefau~p This implies that the during-fault condition does not dewate much from the prefault condition. Hence, there will be little significant voltage dip and shift in phase angle.

370 IEE Proc.-Gener. Trunsm. Distrib.. Vol. 148, No. 4, July 2001