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Volt/VAr control in distribution systems using a time-interval based approach Z. Hu, X. Wang, H. Chen and G. A. Taylor Abstract: A strategy for volt/VAr control in distribution systems is described. The aim is to determine optimum dispatch schedules for on-load tap changer (OLTC) settings at substations and all shunt capacitor switching based on the day-ahead load forecast. To reduce switching operations for OLTC at substations, a time-interval based control strategy is adopted that decomposes a daily load forecast into several sequential load levels. A genetic algorithm based procedure is used to determine both the load level partitioning and the dispatch scheduling. The proposed strategy minimises the power loss and improves the voltage profile for a whole day across the whole system, whilst ensuring that the number of switching operations is less than the maximum daily allowance. A comparison of numerical studies and their associated results illustrates both the feasibility and the effectiveness of the proposed strategy.

1

Introduction

At present, research in the field of volt/VAr control for distribution systems can be divided into two categories: offline setting control and real-time control. Research in offline setting control aims to find dispatch schedules for switching capacitors and OLTC setting at substations for the day ahead according to optimisation calculations based on load forecasts for the day ahead, while research real-time control aims to control the aforementioned devices based on real-time measurements and experiences. The second category of control requires a higher level of distribution system automation and more hardware and software support. Until recently the majority of distribution systems did not reach such standards. Furthermore, it is very difficult for real-time control to consider the overall load change as well as the constraints of maximum allowable switching operations for a number of volt/VAr control devices. In the off-line setting control category, dynamic programming is often applied [1–4], but because of the heavy computational burden such approaches are very timeconsuming even when simplifications are made. When dynamic programming is employed to determine the optimal dispatch of capacitors on a feeder of a distribution system [1] or optimal volt/VAr control in a distribution substation [2], the burden is acceptable because of the relatively small searching space. However, to find the optimal dispatch schedule for OLTC settings at a substation and all switching capacitors across the whole distribution system for the day ahead by dynamic programming [3] requires a very large search space that is computationally time-consuming. To reduce the computation burden, [4] r IEE, 2003 IEE Proceedings online no. 20030562 doi:10.1049/ip-gtd:20030562 Paper first received 19th December 2002 and in revised form 31st March 2003. Online publishing date: 24 June 2003 Z. Hu, X. Wang and H. Chen are with the Electrical Power Engineering Department, Xi’an Jiaotong University, Xi’an 710049, China G. A. Taylor is with the Brunel Institute of Power Systems, Brunel University, Uxbridge, UB8 3PH, UK

548

decomposes the problem into two subproblems, one at the substation level and the other at the feeder level. Dynamic programming and fuzzy logic control algorithms are utilised to solve the two subproblems, respectively. This paper presents a volt/VAr control strategy to solve the off-line setting control problem by co-ordinating all volt/VAr control devices in a distribution system. The aim of this paper is to find the optimal dispatch schedule for all such devices in a distribution system based on the forecasted hourly loads of each bus, so that the total energy loss can be minimised. The constraints taken into account include the maximum allowable number of switching operations in a day for OLTC setting and all capacitor switching, as well as the nodal voltage limits. To simplify the control of OLTC setting at substations, this paper proposes a time-interval control strategy that is based on load forecasts. The daily load at the secondary bus of substations is divided into several continuous load levels using a genetic algorithm. OLTC setting can occur between different load levels, but no OLTC setting can occur during a load level. The optimal dispatch of all volt/VAr control devices is a multi-phase decision-making problem. For each hour, it is a discrete and nonlinear problem. Therefore, using traditional mathematical methods can be very complex, while dynamic programming entails a heavy computational burden. In this paper a genetic algorithm is employed that uses a special encoding method to avoid such problems. 2

Problem formulation

With the development of a distribution management system (DMS), loads along each feeder bus and substation secondary bus can be obtained for the day ahead by employing short-term load forecasting techniques. Generally, voltages at the primary bus of a substation change slightly over a day and are therefore assumed to have a constant value in this paper. OLTC setting is based on the change of load. To more effectively minimise energy losses the voltage at the secondary bus of a substation can vary within its limits and is not kept close to a specified value, which differs from that [2–4]. All volt/VAr control IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003

100

percent of peak load

devices are constrained by a maximum number of switching operations that can be performed during a day. To avoid control engineer inconvenience, the maximum number of switching operations for a capacitor along a feeder is two, which is less than that of a capacitor at a substation secondary bus. The following objective function is used to minimise the energy loss for the day ahead: 24 X ðDPi þ DPiþ1 ÞDTi =2 ð1Þ J ¼ Min

80

P

60 Q 40 20 0 0:00

i¼1

8:00

16:00

where: DTi ¼ period between time i and i+1 (1 h in this paper) DPi, DPi+1 ¼ real power loss at times i and i+1, respectively (DPi+DPi+1) DTi/2 ¼ approximate energy loss in a period. The objective function is subject to the standard power balancing equality constraints as well as the following additional inequality constraints ð2Þ Vmin oVm;i oVmax 24 X

jTAPi  TAPi1 j  MKT

ð3Þ

jCm;i  Cm;i1 j  MKCm

ð4Þ

i¼1 24 X

Fig. 2

Typical daily load curve (2)

and is then kept fixed during each continuous load level. This method not only takes into account the overall daily load change, but also removes unnecessary movements. If the error of the load forecast is not too great, a dispatch schedule of load levels found in this way that last several hours can be put into the operation for the day ahead directly. The question now is how to recognize the location of each load level. Firstly, the number of load levels S in a day is assumed known, it can be based on the load forecast, MKT and control engineer experience. After that, the genetic algorithm (GA) is employed to determine the start and end times of each load level. The fitness function is:

i¼1

F ¼ Fmax  Min

where: Vm,i ¼ voltage of node m at time i Vmax, Vmin ¼ nodal voltage limits TAPi ¼ tap position at hour i MKT ¼ maximum switching operations for OLTC Cm,i ¼ status of capacitor m (on or off) at time i MKcm ¼ maximum switching operations for capacitor m. Load level division

It is difficult to specify the controlling parameters when applying automated techniques to control OLTC at a substation level. It should also be noted that, because of the probabilistic nature of load forecasting, it could be construed as inaccurate to determine a dispatch schedule of OLTC settings based only on load forecasting [2–4]. However, from inspection of two typical load curves [5] shown in Figs. 1 and 2, it can be seen that several apparent load levels exist during a day. Therefore, if the start and end time of each load level are found, the tap position may only move when the load transits from one load level to another

80

P

60

Q

½ðPij  PAi Þ2 þ ðQij  QAi Þ2 ð5Þ

i¼1 j¼1

subject to: s X

Ki ¼ 24

ð6Þ

i¼1

where, Fmax ¼ constant (converts fitness function to standard form) Pij, Qij ¼ active and reactive power of the jth load point of the ith load level PAi, QAi ¼ average active and reactive power of the ith load level Ki ¼ number of load points of the ith load level There are 24 forecasted load points representing each hour of the following day; each load level lasts 25–S hours at most and 1 h at least. The method for handling this problem is shown in Fig. 3. It should be noted that there are S variants and a duration of S load levels. The start time of the first load level is not always the start time of the forecasted load, usually 0:00. Dividing the 24 load points into S+1 parts, the (S+1)th part refers to the first load point. When the (S+1)th part lasts 0 h, the start time of the first load level is 0:00.

40 Hour: 0

1

2

20

23

24

...

0 0:00

22

Stage: 8:00

16:00

1

2

...

percent of peak load

100

Ki S X X

.......

3

24:00

time, h

S

S +1

24:00

time, h

Fig. 1

Typical daily load curve (1)

IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003

Fig. 3

Load level partition specification 549

4 Optimal dispatch of OLTC and capacitors using genetic algorithm A GA is suitable for solving a problem with discrete, nonlinear and multi-phase decision-making features. However, to choose a proper selection strategy, controlling parameters and evolutionary operators, an encoding method, state space and fitness function must be considered.

4.1

Encoding

4.1.1 Capacitors along feeder: They are allowed at most to switch on once and switch off once in a day. Therefore, each capacitor occupies two segments in the genome. The first segment represents the start time of the first switch operation; the second segment represents status duration after the first operation. For example, if the original status of a capacitor is off, the decimal value of the first binary segment can be 10 (such that the binary segment is ‘01010’) and the decimal value of the second segment can be 8. This means that the capacitor will be switched on at 10:00 and switched off at 18:00. Qualified segments are those for which the sum of these two values is not greater than 24.

4.1.2 Capacitors at secondary bus: Their switching numbers are unknowns, but they must be constrained by the maximum number of switches that are allowable each day. Each capacitor holds one segment in the genome. The length of the segment is 24 bits. If the value of the ith bit is 0, it denotes that the capacitor is off at time i. Qualified segments should satisfy the constraint of (4).

4.1.3 OLTC: The operational characteristic is that the tap position can be different at different load levels and remains constant during each load level. Hence, it occupies s segments in the genome. The length of each segment is equal and is dependent on the number of tap positions. The OLTC in the test system has 17 tap positions; the segment length can be 4 (assuming that the tap position difference between two neighbouring load levels is no greater than 15). Qualified segments should be subject to s X jTAPi  TAPi1 j  MKT ð7Þ

many states in the searching space violate the constraints of (3) and (4), and therefore load flow calculation is unnecessary for them. In this way the computational burden can be greatly reduced.

4.3

Fitness function

The evolutionary objective of the GA is the minimisation of energy loss while satisfying all of the constraints. If any states violate the constraints of (3) and (4), a small fitness function value will be returned, skipping the calculation of energy loss. So, considering the constraint of (2), the fitness function is " F ¼ Max Fmax 

w 1 JP þ w 2

24 X M X

!# DUm;n

ð9Þ

n¼1 m¼1

where JP is the percent energy loss, DUm,n is the value of voltage violation of node m at hour n, and w1, w2 are coefficients of energy loss and voltage violation, respectively.

4.4 Selection strategy and evolutionary operators A canonical GA has been adopted, which can be described as follows. During the evolutionary process the individuals with the best fitness function values enter directly into the next generation. A tournament selection model has been adopted to choose the parents for crossover. The children are generated by one-point crossover of their parents and the mutation probability is fixed with regard to the mutation operator.

4.5

Computational procedure

A schematic flowchart of the computational procedure is shown in Fig. 4. The input data includes network parameters, forecasted loads, a specified number of load levels S, parameters of volt/VAr control devices including original status and parameters for the GA. The GA and load flow calculation are two independent modules.

i¼1

Start

Here TAPi represents the tap position during the ith load level.

4.2

Analysis of computational burden

input data

According to the aforementioned encoding method, the genome length will be L ¼ LU1 S þ 2LU2 Cf þ 24Cs

ð8Þ

where LU1, LU2 are the segment length of each OLTC and capacitors along feeders, respectively, and Cf, Cs are the number of capacitors along feeders and at the secondary bus of the substation, respectively. If there are five and two capacitors along the feeders and at secondary bus of the substation, respectively, let LU1 ¼ 4, LU2 ¼ 5, S ¼ 4, then L ¼ 114. The size of the searching space is 2114. If dynamic programming is applied there will be 27  17 states at each load point. If N ¼ 24, the size of the searching space would be (27  17)24 – greater than 2264. Even if four tap positions are chosen at each stage, the size of the search space is still very large (2216). It should also be emphasised that to test each state of the genome using the method presented in this paper, a load flow must be calculated 24 times. However, it should also be noted that 550

GA module

load curve partition

encode load flow module find optimal schedule

decode, output result

End

Fig. 4

Flowchart of time-interval base volt/VAr control algorithm IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003

Volt/VAr control simulations

The distribution system in Fig. 5 is used to demonstrate the effectiveness of the proposed method. The study system has been developed from the distribution system in [6]. For research purposes, the branch between node 0 and 1 is changed from a line to a transformer branch equipped with OLTC. Two switched capacitors (C6 and C7) are added at node 1. The OLTC has 17 tap positions ([8, 7, y, 0, 1, y, 7, 8]). It can change the voltage from 5% to +5%. Table 1 presents the detailed data of the capacitors. The impedance of the transformer between nodes 0 and 1 is (0.0178+j0.3471) per unit and the base power is 52.9 MVA. The length of each branch line is set to 1 mile. Let MKT ¼ 30 and let MKC ¼ 2 and 6 for capacitors along feeders and at the secondary bus of a substation, respectively. The upper and lower limits of voltage for each bus are 1.05 per unit and 0.95 per unit, respectively. The voltage at the primary bus of a substation is 1.0 per unit. See [5] for the maximum reactive load of the bus. The load model has a great influence on the optimal result. All loads are linked via lines without transformers in the test system. Therefore, if a load model of constant power is adopted, the proposed method must lead to high voltage of the whole system under the objective function (1). In simulation tests, 50% of the load of each bus is constant power load and the other 50% is constant impedance load. We assume that all the loads change during a day according to the load profile shown in Fig. 2, but that they all vary randomly by 715% around the nominal level, both real and reactive parts. In this way, loads for all 24 hours are obtained. For the case of S ¼ 4, the load profiles at buses 1 and 4 are shown in Fig. 6, where the dash dot lines indicate the boundaries between load levels. Again, we assume that all load changes according to the load profile shown in Fig. 1. In the same way, 24-h loads of each load bus can be obtained. The results for the case S ¼ 6 are shown in Fig. 7. Table 2 shows one optimal dispatch result of OLTC and capacitors based on the loads and load levels shown in Fig. 6. The original position of tap is 0, and the original status of each capacitor is off (0). The number of switching

operations for OLTC in the whole day is 10. C1 and C2 switch six times in a day. Some of the capacitors along the feeder switch twice, and some switch only once. C4 is on for the whole day. The voltage at node 14 is the lowest in the test system. The voltage change is shown in Fig. 8. Before optimisation all the capacitors are off and the tap position is fixed at 0 for the whole day. After optimisation, the schedule of Table 2 is carried out to simulate the effects. The voltage profile at node 14 is greatly improved. The partial DP curve plotted in Fig. 8 illustrates the optimised solution that has been obtained using the partial dynamic programming method as described in [3]. The same objective function as used in [3] has also been adopted for this study. At each stage all the 27  17 possible states are calculated and 29 optimal paths are saved. In this system the voltage of node 14 relies heavily on capacitor C3 because the objective function aims to keep the secondary bus voltage close to a specified value (in this case 1.0 p.u.). With regard to the results obtained to plot the partial DP curve, capacitor C3 is ‘on’ from 05:00 to 23:00, which leads to higher voltage at the light load hours and lower voltage at

0.18 0.15

P Q

0.12 load, p.u.

5

0.09 0.06 0.03 0 0

Fig. 6

4

8

12 time, h

16

20

24

Four-load level partition results

0.18

C3

27 20

C5

25

12 11

19

24

C6

10

18

23 22

P Q

0.15

13

26

load, p.u.

C7

14

9

0.12

0.09

s substation

1

2

3

4

5

6

7

8

28 C1

C2

C4

0.06

15 29

21

0.03

16

0

17

4

8

30

Fig. 5

Fig. 7

One-line diagram of test distribution system

12 time, h

16

20

24

Six-load level partition results

Table 1: Capacitor data for distribution system Capacitor number Location (bus no.) Cap., kV Ar

C1

C2

C3

C4

C5

C6

C7

1

1

13

15

19

23

25

900

600

600

600

300

900

900

IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003

551

Table 2: Optimal dispatch schedule for day ahead (for capacitors: 0 ¼ off; 1 ¼ on) Hour

TAP

C1

C2

C3

C4

C5

C6

C7

0

1

1

1

0

1

0

0

0

1

1

1

1

0

1

0

0

0

2

1

1

1

0

1

0

0

0

3

1

1

1

0

1

0

0

0

4

1

1

0

0

1

0

0

0

5

1

0

0

0

1

0

0

1

6

1

0

1

0

1

0

0

1

7

1

1

0

1

1

0

1

1

8

+2

1

0

1

1

1

1

1

9

+4

1

1

1

1

1

1

1

10

+4

1

1

1

1

1

1

1

11

+4

1

1

1

1

1

1

1

12

+4

1

1

1

1

1

1

1

13

+4

1

0

1

1

1

1

1

14

+4

1

0

1

1

1

1

1

15

+4

1

0

1

1

1

1

1

16

+4

0

0

1

1

1

1

1

17

0

1

0

1

1

1

0

1

18

0

1

0

1

1

1

0

1

19

0

1

0

0

1

1

0

1

20

0

1

0

0

1

1

0

1

21

0

1

0

0

1

1

0

1

22

0

0

0

0

1

1

0

1

23

0

0

0

0

1

1

0

1

1.00

Table 3: Influence of maximum allowable switching operations for capacitors

0.98

u, p.u.

0.96 0.94 0.92

MKC

2

4

6

8

TAP1

0

0

1

0

0

TAP2

+2

+2

+2

+2

+2

TAP3

+5

+4

+4

+4

+4

TAP4

0.90

J, kWh propsed method partial DP before control

0.88

Umin

+7

+6

2526.5

2433.6

0.947

0.951

0 2428.1 0.952

0 2430.7 0.952

10

0 2430.8 0.953

0.86 0

Fig. 8

4

8

12 time, h

16

20

24

Voltage change of bus 14 over a day

the heavy load hours when compared against the proposed method. A real power loss comparison is shown in Fig. 9. During the peak load hours the real power loss is greatly decreased, which meets the volt/VAr control aim of this method. From Fig. 9 one can see that the proposed method is more effective than the partial DP method with regard to reducing real power losses. Now let us study the influence of the maximum number of allowable switching operations MKC for capacitors at the secondary bus of the substation. For the load profile shown in Fig. 2 and according to the 4 levels of load partitioning shown in Fig. 6, let MKC ¼ 2, 4, 6, 8 and 10, respectively. Table 3 lists the tap positions across the four load levels 552

(TAPi, i ¼ 1–4), the energy loss (J) and the minimum voltage for the day ahead (Umin) for different values of MKC. One can see that the minimum voltage is o0.95 when MKC ¼ 2; TAP44TAP3 whilst the load value of the fourth load level is less than that of the third load level when MKC ¼ 2 and 4. The OLTC schedule is almost identical when MKC ¼ 6, 8 and 10. Therefore, for the test system, MKC ¼ 6 is optimal as we need to find a balance between improvement of voltage profile, loss reduction, schedule complexity and capacitor depreciation cost. With regard to the load profile shown in Fig. 1, its change is more complicated than the one shown in Fig. 2. If we change S and keep the value of MKT and MKC constant, we can study the influence on the OLTC schedule. Letting S range from 2 to 7, the results are shown in Table 4. As the peak value of the load is so heavy the maximum tap position value is +8 for all S. As S increases, there are more and more tap positions during a whole day. At the same time it means that the complexity to schedule or control OLTC increases. Therefore, considering the IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003

0.08

10

8

0.06 propsed method before control partial DP

0.05

tap position

real power loss, 0.1 p.u.

0.07

0.04 0.03

proposed method partial DP

6

4

0.02 2 0.01 0

0 0

Fig. 9

4

8

12 time, h

16

20

24

Comparison of real power losses

Fig. 10

Table 4: OLTC schedule under different S S

2

Hour

Tap position

3

0

4

5

6

7

0

+1

+1

0

0

1

1

1

+1

+1

0

0

1

1

2

+1

+1

0

0

1

1

3

+1

+1

0

0

1

1

4

+1

+1

0

0

+1

+1

5

+1

+1

0

0

+1

+1

6

+1

+1

0

0

+1

+1

7

+1

+1

0

0

+1

+1

8

+1

+1

+8

+8

+1

+1

9

+8

+8

+8

+8

+8

+8

10

+8

+8

+7

+7

+7

+7

11

+8

+8

+7

+7

+7

+7

12

+8

+8

+7

+7

+7

+7

13

+8

+8

+7

+7

+6

+7

14

+8

+8

+7

+7

+6

+5

15

+8

+8

+7

+3

+6

+5

16

+8

+8

+7

+3

+6

+5

17

+8

+8

+7

+3

+6

+5

18

+8

+1

+1

+1

+1

+1

19

+8

+1

+1

+1

+1

+1

20

+8

+1

+1

+1

+1

+1

21

+8

+1

+1

+1

+1

+1

22

+1

+1

+1

+1

+1

0

23

+1

+1

+1

+1

+1

0

results shown in Table 4, S ¼ 5 should be appropriate for the load profile shown in Fig. 1. Based on the load level partition result shown in Table 4 for S ¼ 5, a dispatch schedule of OLTC is obtained. Fig. 10 illustrates the tap movements in a day for both the proposed and partial DP methods. It is important to note that tap positions at 0 indicate no movement and that the cumulative tap movement in a day is 16 for both methods. However, the OLTC schedule obtained from the proposed method is simpler and easier to implement in practice when compared against the schedule obtained from the partial DP method. The proposed method has been implemented using the C++ programming language. Population size and evoluIEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003

4

8

12 time, h

16

20

24

OLTC schedule of the next day under five load levels

tionary generation of the GA is 30 and 4500, respectively. The average computing time for the method is B3 min running on a P4 1.8 GHz/512 MB RAM, while the partial DP method requires B40 min computing time on the same processor. 6

Discussion and conclusions

A new volt/VAr control approach to distribution systems is proposed in this paper. It includes two steps: (i) dividing the forecasted load of the next day into several load levels; (ii) determining the optimal dispatch schedule of all volt/VAr control devices. A GA is employed in both steps and a specifically developed encoding method is used in step, (ii). OLTC settings remain unchanged in each load level. Simulations show that the control of OLTC settings via this method is both simple and effective. By using a valid encoding method, the searching space of this optimisation problem is reduced considerably, especially when compared to a dynamic programming approach. Test results indicate that the proposed method improves the voltage quality, whilst also reducing the energy loss significantly. However, the following conclusions should be noted: (i) Most load profiles have several apparent load levels during a day. For complicated load curves, a large number of load levels should be chosen. (ii) In the current method the number of load levels is obtained from the load forecast, system conditions and experience. Future research can develop mathematical methods to determine the optimum number of load levels. (iii) In this paper, 24 load points representing each hour are chosen. If 48 or 96 load points are necessary, the allowable time interval between two switching operations of volt/VAr control devices must be considered. Furthermore, a more effective encoding method would be needed for capacitors at the secondary bus of a substation. (iv) Voltage at the primary bus of a substation is a constant value in this paper, as it usually changes little during a day. If its change cannot be ignored, it must also be considered during the load level division. (v) The tap position may differ greatly from two neighbouring load levels. So when the load is altering from one level to another, the OLTC settings should be modified gradually. (vi) In the simulations, the number of switching operations for OLTC over the whole day is much less than the 553

maximum allowable number. This leaves a large margin with regard to operational changes of the day ahead. (vii) In this paper, the minimisation of energy loss is the single objective of volt/VAr optimisation. If additional objectives, such as keeping the voltage at the secondary bus of a substation close to a specified value or restraining the reactive power flowing into main transformer [3], are included the results may show different characteristics with regard to the optimum schedule. 7

Acknowledgments

The authors would like to acknowledge that this research project is sponsored by the Doctoral Foundation of the State Education Ministry of China (no. 1999069801) and the National Natural Science Foundation of China (no. 50207007).

554

8

References

1 Hsu, Y.-Y., and Kuo, H.-C.: ‘Dispatch of capacitors on distribution system using dynamic programming’, IEE Proc. C, Gener. Transm. Distrib., 1993, 140, (6), pp. 433–438 2 Lu, F.-C., and Hsu, Y.-Y.: ‘Reactive power/voltage control in a distribution substation using dynamic programming’, IEE Proc., Gener. Transm. Distrib., 1995, 142, (6), pp. 639–645 3 Liang, R.-H., and Cheng, C.-K.: ‘Dispatch of main transformer ULTC and capacitors in a distribution system’, IEEE Trans. Power Deliv., 2001, 16, (4), pp. 626–630 4 Liu, Y., and Qiu, X.: ‘Optimal reactive power and voltage control for radial distribution system’. Proc. IEEE Power Engineering Society Summer Meeting, Seattle, WA, July 2000, Vol. 1, pp. 85–90 5 Shenkman, A.L.: ‘Energy loss computation by using statistical techniques’, IEEE Trans. Power Deliv., 1990, 5, (1), pp. 254–258 6 Civanlar, S., and Grainger, J.J.: ‘Volt/VAr control on distribution systems with lateral branches using shunt capacitors and voltage regulatory. Part III: Numerical results’, IEEE Trans. Appar. Syst., 1985, 104, (11), pp. 3291–3297

IEE Proc.-Gener. Transm. Distrib., Vol. 150, No. 5, September 2003