Feeder Reconfiguration And Capacitor Setting For Loss Reduction Of Distribution Systems

Electric Power Systems Research 58 (2001) 97 – 102 www.elsevier.com/locate/epsr

Feeder reconfiguration and capacitor setting for loss reduction of distribution systems Ching-Tzong Su *, Chu-Sheng Lee Institute of Electrical Engineering, National Chung Cheng Uni6ersity, Chiayi 621, Taiwan Received 7 August 2000; received in revised form 11 December 2000; accepted 18 December 2000

Abstract The stress to elevate overall efficiency has forced utilities to look for greater efficiency in electric power distribution. This study presents an effective approach to feeder reconfiguration and capacitor settings for power-loss reduction and voltage profile enhancement in distribution systems. The optimization technique of simulated annealing (SA) can be relied on to solve the problem efficiently. The merit of the method is that it can provide a global or near-global optimum for feeder reconfiguration and capacitor settings. The objective of this study is to recognize beneficial load transfer, to take the objective function composed of power losses be minimized and voltage limits be satisfied. The proposed approach is demonstrated by employing an IEEE illustrative example. Computational results show that by taking into account feeder reconfiguration and capacitor settings simultaneously, one can minimize losses more efficiently than by considering them separately. © 2001 Elsevier Science B.V. All rights reserved. Keywords: Capacitor setting; Distribution system; Feeder reconfiguration; Power loss reduction; Simulated annealing; Switching operation

1. Introduction Feeder reconfiguration is the process of changing the topology of distribution network by altering the open/ closed status of switches. During normal operating conditions, a distribution system is connected with the others through tie lines, reducing the power interruption and increasing the system reliability. The configuration may be varied with manual or automatic switching operations to transfer loads among the feeders. Through the application of reactive power compensation, one can reduce power loss and improve the voltage profile. Capacitors have been very commonly employed to provide reactive power compensation in distribution systems. The benefits of compensation depend greatly on the size of the capacitors added. The size of the capacitors installed on feeders can be varied by using switched capacitors. The idea is to optimize the discrete setting of those capacitors in a radial * Corresponding author. Tel.: + 886-5-2428162; fax: +886-52720862. E-mail address: [email protected] (C.-T. Su).

distribution system. That is, finding the optimal setting of switched capacitors to minimize losses. The early work on feeder reconfiguration for loss reduction is presented by Civanlar et al. [1]. In Ref. [2], Baran et al. defined the problem for loss reduction and load balancing as an integer programming problem. Nara et al. [3] present an implementation using a genetic algorithm (GA) to look for the minimum loss configuration. Chiang et al. propose a solution procedure employed simulated annealing [4,5] to search for an acceptable non-inferior solution. The other approach to feeder reconfiguration considering the ability of system transformers and feeders, power loss, and voltage profiles had been respectively presented [6–10]. Optimal capacitor placement is a combinatorial optimization problem that is commonly solved by employing mathematical programming techniques. Grainger and Lee [11 –13] formulated the problem as a non-linear programming model that can be solved by simple iterative procedures based on gradient search. Bala et al. used the sensitivity factor [14] and distribution-analyzer-recorder (DAR) [15] to solve optimal capacitor placement problems. In Refs. [16,17], the authors used the genetic algorithm (GA) to select capacitors for

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radial distribution systems. Su et al. [18] applied fuzzyreasoning approach to optimum capacitor allocation. In Refs. [19,20], the authors used evolutionary programming to solve optimal reactive power planning problems. Most previous studies handled reconfiguration problems without considering the capacitor addition [1–10], or handled capacitor compensation problems without considering feeder reconfiguration [11– 20]. They dealt with the feeder reconfiguration and capacitor addition in a separate manner [1– 20], which may result in unnecessary losses and cannot yield the minimum loss configuration. However, only a few papers on loss minimization applying heuristic techniques for feeder reconfiguration and capacitor placement had been presented [21– 23]. In view of this, we try the simulated annealing method to determine the feeder reconfiguration and capacitor settings for optimal loss minimization of distribution systems. The proposed method can attain a global or near-global optimal feeder reconfiguration and capacitor setting.

2. Problem description In this study, we propose an approach for feeder reconfiguration and capacitor setting for distribution systems. We aim to minimize the power loss of the system, subject to load and operating constraints. For simplicity, the implementation issues of operation and maintenance cost and various timing loads are not taken into account. To illustrate the advantages of the two functions of feeder reconfiguration and capacitor placement, consider the distribution system displayed in Fig. 1 [23]. It is a single-phase system consisting of two feeders, four capacitors, and a single load. There are two switches (switches S1 and S2) placed for feeder reconfiguration and four switches (switches S3, S41, S42, and S43) for capacitor setting. The system load on the system will be supplied from either of the two feeders depending on the states of S1 and S2. Meanwhile, switch S3 controls capacitor C2, switches S41, S42, and S43 control capacitor bank C1. Suppose that the system is initially in the configuration displayed in Fig. 1. Switch S1 is closed, and other switches are open. The load is supplied from feeder 1. The initial real power losses are 15 kW. This is the case of A in Table 1. Now, considering feeder reconfiguration of the system, but without considering capacitor placement in the optimization problem, there are only two cases to be considered. One is the original case. The other case has switch S2 closed and switch S1 open; this is the case of B in Table 1. The real power losses of the system are 10 kW. Furthermore, capacitor placement, together with feeder reconfiguration, is considered. In the network, capacitor C1 is a capacitor bank, which can be set with various tap settings making the current through capacitor C1 be 0A,

j100A, j200A, or j300A, while capacitor C2 is a capacitor with an ‘on’ or ‘off’ setting. In Table 1, case C has the same feeder configuration as case B, but a different capacitor setting, and the losses are 4 kW. Similarly, case D, case E, and case F all have the same feeder configurations as case A, but each has different capacitor placement, and the losses are 6, 3, and 6 kW, respectively. In this example, the losses simultaneously taking into account system reconfiguration and capacitor placement (case E, with 3 kW losses) are lower than that considering a system feeder reconfiguration alone (case B, with 10 kW losses). Furthermore, by first performing feeder reconfiguration only, and then optimizing capacitor placement, it would still yield a sub-optimal solution (case C, with 4 kW losses). Considering feeder reconfiguration simultaneously with capacitor placement would yield the optimal solution (case E, with 3 kW losses) for this network. Adding capacitors blindly would yield too much of compensation to be an optimal solution (case F, with 6 kW losses). Mathematically, the objective function of the problem can be described as min f= min (PT,Loss)

(1)

where PT,Loss is the total real power loss of the system. The voltage magnitude at each bus must maintain within its margins. The current on each branch has to lie within its capacity limits. These constraints are expressed as follows Vmin 5 Vi 5 Vmax

(2)

Ii 5 Ii,max

(3)

where

Fig. 1. Example system as an illustration of combined feeder reconfiguration and capacitor setting.

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Table 1 Losses in the system of Fig. 1 Case

IC1(A)

IC2(A)

S1

S2

S3

S41

S42

S43

Losses (kW)

A B C D E F

0 0 0 j100 j200 j300

0 0 j100 0 0 0

C O O C C C

O C C O O O

O O C O O O

O O O C C C

O O O O C C

O O O O O C

15 10 4 6 3 6

O: open; C: closed.

Vi is the voltage magnitude of bus i; Vmin, Vmax are the bus minimum and maximum voltage limits; Ii , Ii,max are the current magnitude and maximum current limit of branch i. 3. Simplified power-flow formulation Power-flow study includes the calculation of bus voltages and line flows of a network. In this study, we employ a set of simplified power flow formulation to avoid the complex iteration process needed for power flow analysis. Associated with each bus, there are four quantities to be determined or specified, which are the real and reactive powers, the voltage magnitude and phase angle. Considering the one-line diagram displayed in Fig. 2, the system is assumed to be a balanced three-phase system. The following set of recursive equations is used for power-flow calculation [2] Pi = Pi + 1 +PLi + 1 + Ri,i + 1[(P 2i +Q 2i )/ Vi 2]

(4)

Qi = Qi + 1 + QLi + 1 +Xi,i + 1[(P 2i +Q 2i )/ Vi 2]

(5)

Vi + 1 2 = Vi 2 −2(Ri,i + 1Pi +Xi,i + 1Qi ) (P 2i +Q 2i ) Vi 2

+ (R 2i,i + 1 + X 2i,i + 1)

(6)

where the real and reactive powers flowing out of bus i are denoted by Pi and Qi, respectively. The real and reactive load powers at bus i are denoted by PLi and QLi, respectively. The resistance and reactance of the line section between buses i and i +1 are denoted by Ri,i + 1 and Xi,i + 1, respectively. The voltage magnitude at bus i is denoted as Vi . The power loss of the line section connecting buses i and i+ 1 may be computed as PLOSS(i,i + 1)= Ri,i + 1

P 2i +Q 2i . Vi 2

(7)

The total power loss of the feeder, PT,LOSS, may then be determined by summing up the losses of all line sections in the feeder, which is given by n−1

PT,LOSS = % PLOSS(i,i + 1). i=0

(8)

4. Simulated annealing In this study, an optimization technique based on simulated annealing (SA) for finding a global non-inferior point is employed. In thermodynamic systems, annealing is known as a thermal process for obtaining low energy states of a solid in a heat bath [4,5,10,21]. The procedures of algorithm of the SA may be summarized as follows. Step 1. Initial state. Initialize the iteration counter k=0, and select the beginning control parameter, T0, which can assure a high acceptance probability in the initial search. Step 2. Metropolis process. This is based on a Monte Carlo simulation and generates a series of states of the solid. Given the current state, i, of the solid with energy, Ei, then a subsequent state, j, with energy Ej is generated by applying a small perturbation. If the energy difference, Ej − Ei, is less than or equal to 0, state j is accepted; otherwise, it is accepted with a certain probability given as Pc = exp



Ei − Ej KBT



(9)

where T is the temperature of the heat bath, and KB is a physical constant known as the Boltzmann constant. The acceptance rule described above is generally known as the Metropolis criterion. Step 3. Equilibrium criterion. In general, the initial temperature should be chosen to be high enough so that the initial acceptance ratio is close to 1, then decreases monotonically. In this, we would perform Metropolis process many times, and check the acceptance ratio. If the acceptance ratio is below 0.1, then we say that the equilibrium state is reached at this temperature. If the state developed from step 2 reaches an equilibrium state, then go to step 4; otherwise, go back to step 2, where the acceptance ratio is defined as the number of accepted cases divided by the number of Metropolis processes. Step 4. Cooling schedule. Temperature, T, is gradually reduced as Ti + 1 = h(Ti )× Ti, i =1, 2, 3,…

(10)

100

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Fig. 2. One-line diagram of a main feeder.

where the cooling rate, h(Ti ), can be a constant or a function of Ti. Step 5. Convergence criterion. If the state reaches the minimal energy of the system, the algorithm is completed, and the solution is obtained; otherwise, let k =k +1 and go back to step 2. We assume an analogy between a physical annealing system and the studied combinatorial optimization problem based on the following equivalencies. 1. Solutions in the investigated problem are equivalent to states of a physical system. 2. The real power loss of a solution is equivalent to the energy of a state.

system displayed in Fig. 4 [1]. The system consists of three feeders, 13 sectionalizing switches, and three tie switches. The load of the system is assumed to be constant. Table 2 shows the data of the three-feeder

5. Computational procedures of the proposed method A technique employing feeder reconfiguration and setting of switched capacitor to reduce power loss for distribution systems is presented. Simulated annealing is employed as the optimization technique. The computational procedures of the proposed method are mainly composed of power-loss calculation, bus voltage determination, and simulated annealing application. The computational procedures find a series of configurations with different status of switches and addition of capacitors such that the objective function is successively reduced. During the solution process, the number of the switches will be fixed, regardless of the variation in the topology of the system. The fixed-type capacitors of distribution systems can be seen as straight reactive load that cannot be changed. Therefore, the parameters that decide the minimum loss configuration are the status of the switches and settings of the switched capacitors. A flow chart describing the main computational procedures is shown in Fig. 3.

6. Application example To demonstrate the application of the proposed method, we employ an IEEE three-feeder distribution

Fig. 3. Main computational procedures.

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Fig. 5. Modification of the three-feeder distribution system considering setting of switched capacitors.

Fig. 4. Three-feeder distribution system.

distribution system [1]. This system had been studied in Refs. [1] [10], in which only feeder reconfiguration is considered. In this study, both feeder reconfiguration and setting of switched capacitors are taken into account together. The data for SA application are selected as KB = 1, T0 =30, Tf =6.4, h =0.95, kmax = 300 and base power=100 Mva. Moreover, assume that buses 4, 8, and 13 are selected to set up switched capacitor banks for feeders 1, 2, and 3, respectively. Practical sizes available for the switched capacitor banks are 300, 600, 900, 1200, 1500, and 1800 Kvar. Fig. 4 is redrawn in Fig. 5 to further display the switched capacitor banks. For comparison, we had investigated four cases for this application example. These four cases are as follows. Case 1. Only feeder reconfiguration is considered. Case 2. Only capacitor addition is considered. Case 3. Both capacitor addition and feeder reconfiguration are considered. However, capacitor addition is carried out before feeder reconfiguration. Case 4. Both capacitor addition and feeder reconfigu-

ration are considered and are taken into account simultaneously. The computer program used in this paper has been written in MATLAB language implemented on the Pentium II 266 MHz compatible personal computer. Table 3 shows the final results. Where case 1 has the same result as that of Ref. [10]. The computational results show that case 4 can reduce power loss the most among these four cases. This method has been applied to a practical 11.4 Kv distribution system of Taiwan Power Company as well. The distribution network includes nine feeders, 41 sectionalizing switches, and nine tie switches. Numerical results show that the proposed method is efficient on power-loss reduction.

7. Conclusions An useful feeder reconfiguration and capacitor placement approach employing simulated annealing technique for loss reduction of distribution systems is

Table 2 Data of the three-feeder distribution system Bus to bus

Section resistance (P.U.)

Section reactance (P.U.)

End bus load (MW)

End bus load (MVAR)

1–4 4–5 4–6 6–7 2–8 8–9 8–10 9–11 9–12 3–13 13–14 13–15 15–16 5–11 10–14 7–16

0.075 0.08 0.09 0.04 0.11 0.08 0.11 0.11 0.08 0.11 0.09 0.11 0.04 0.04 0.04 0.12

0.1 0.11 0.18 0.04 0.11 0.11 0.11 0.11 0.11 0.11 0.12 0.11 0.04 0.04 0.04 0.12

2.0 3.0 2.0 1.5 4.0 5.0 1.0 0.6 4.5 1.0 1.0 1.0 2.1

1.6 1.5 0.8 1.2 2.7 3.0 0.9 0.1 2.0 0.9 0.7 0.9 1.0

End bus fixed capacitor (MVAR)

1.1 1.2

1.2 0.6 3.7 1.8 1.8

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Table 3 Final results for the four cases investigated Main items

Original configuration

Case 1

Switches status alternated Maximum bus voltage Minimum bus voltage

– 1 0.9693

(15,19), (21,17) 1 0.9716

Capacitors added (K6ar) Bus 4 Bus 8 Bus 13 Total power loss (MW) Power-loss reduction (%) CPU time (s)

Case 2

–

–

0.5111 – –

0.4660 8.82 7.5

proposed. From the studies, several important observations can be concluded as follows: 1. The power losses of distribution systems can be effectively reduced by proper feeder reconfiguration and capacitor addition. 2. Considering both feeder reconfiguration and setting of switched capacitor simultaneously can generate more losses reduction than considering them lonely or separately. 3. In addition to power-loss reduction, the voltage profile can be improved as well by the proposed method. This method is helpful either for operation of an existing system or for planning of a future system. Further research taking reliability enhancement and load balancing into account using the proposed method is suggested. References [1] S. Civanlar, J.J. Grainger, H. Yin, S.S.H. Lee, Distribution feeder reconfiguration for loss reduction, IEEE Trans. Power Deliv. 3 (1988) 1217 –1223. [2] M.E. Baran, F.F. Wu, Network reconfiguration in distribution systems for loss reduction and load balancing, IEEE Trans. Power Deliv. 4 (1989) 1401 –1407. [3] K. Nara, A. Shiose, M. Kitagawoa, T. Ishihara, Implementation of genetic algorithm for distribution systems loss minimum reconfiguration, IEEE Trans. Power Syst. 7 (1992) 1044 – 1051. [4] H.-D. Chiang, J.-J. Rene, Optimal network reconfiguration in distribution systems: part 1: a new formulation and a solution methodology, IEEE Trans. Power Deliv. 5 (1990) 1902 –1908. [5] H.-D. Chiang, J.-J. Rene, Optimal network reconfiguration in distribution systems: part 2: solution algorithms and numerical results, IEEE Trans. Power Deliv. 5 (1992) 1568 – 1574. [6] T.P. Wagner, A.Y. Chikhani, R. Hackam, Feeder reconfiguration for loss reduction: an application of distribution automation, IEEE Trans. Power Deliv. 6 (1991) 1922 – 1931. [7] R.P. Broadwater, A.H. Khan, H.E. Shaalan, R.E. Lee, Time varying load analysis to reduce distribution losses through reconfiguration, IEEE Trans. Power Deliv. 8 (1993) 294 –300. [8] S.K. Goswami, S.K. Basu, A new algorithm for the reconfiguration of distribution feeders for loss minimization, IEEE Trans. Power Deliv. 7 (1992) 1484 –1491.

– 1 0.9713 1800 1800 0 0.4938 3.38 7.7

Case 3

Case 4

(15,19), (21,17) 1 0.9736

(15,19), (21,17) 1 0.9736

1800 1800 0 0.4521 11.54 14.9

1800 1800 900 0.4513 11.70 12.4

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