Abstract-- This paper presents a novel approach that determines the optimal location and size of capacitors on radial distribution systems to improve voltage profile and reduce the active power loss. Capacitor placement & sizing are done by Loss Sensitivity Factors and Particle Swarm Optimization respectively. The concept of Loss sensitivity Factors and can be considered as the new contribution in the area of distribution systems. Loss Sensitivity Factors offer the important information about the sequence of potential nodes for capacitor placement. These factors are determined using single base case load flow study. Particle Swarm Optimization is well applied and found to be very effective in Radial Distribution Systems. The proposed method is tested on 10, 15, 34, 69 and 85 bus distribution systems.

Index Terms--Capacitor Placement, Radial Distribution Systems, Loss Sensitivity Factors and Particle Swarm Optimization.

.

I. INTRODUCTION S Distribution Systems are growing large and being stretched too far, leading to higher system losses and

poor voltage regulation, the need for an efficient and effective distribution system has therefore become more urgent and important. In this regard, Capacitor banks are added on Radial Distribution system for Power Factor Correction, Loss Reduction and Voltage profile improvement. With these various Objectives in mind, Optimal Capacitor Placement aims to determine Capacitor location and its size. Optimal Capacitor Placement has been investigated over decades. Early approaches were based on heuristic techniques. In the 80s, more rigorous approaches were suggested as illustrated by Grainger [1],[2] and Baran Wu [3],[4] formulated the Capacitor Placement as a mixed integer non-linear program. In the 90s combinatorial algorithms were introduced as a means of solving the Capacitor Placement Problem and neural network technique based papers [5] and [6] were investigated. Ng and Salama [7] have proposed a solution approach to the capacitor placement problem based on fuzzy sets theory. Using this approach, the authors attempted to account for uncertainty in the parameters the

K.Prakash, Research Scholar in National Institute of Technology, Deemed University, Warangal (A.P), 506004 India (e-mail: prakashkam@yahoo.co.in).

M.Sydulu is with the Department of Electrical Engineering, National Institute of Technology, Deemed University, Warangal (A.P), 506004 India (e-mail: msydulu@nitw.ernet.in).

problem. They model these parameters by possibility distribution functions. Chin [8] uses a fuzzy dynamic programming model to express real power loss, voltage deviation, and harmonic distortion in fuzzy set notation. Sundharajan and Pahwa [9] used genetic algorithm for capacitor placement. Particle Swarm Optimization (PSO) was developed by James Kennedy and Russell Eberhart [10]. It is based on metaphor of social interaction, searches a space by adjusting the trajectories of moving points in a multi dimensional space and used for optimization of continues non linear problems. The main advantages of the PSO are summarized as follows: simple concept, easy implementation robustness to control parameters and better computational efficiency when compared with other heuristic algorithms. Shi and Eberhart [11] uses an extra inertia weight term which is used to scale down the velocity of each particle and this term is typically decreased throughout a run. Shi and Eberhart [12] also described an empirical study of PSO. In this paper, Capacitor Placement and Sizing is done by Loss Sensitivity Factors and Particle Swarm Optimization (PSO) respectively. PSO is used for estimation of required level of shunt capacitive compensation to improve the voltage profile of the system. The proposed method is tested on 10, 15, and 34 bus radial distribution systems and results are very promising. In this paper, Vector based Distribution Load Flow method (VDLF) [13] with Sparsity Technique [14] is used. With the support of sparsity technique the VDLF found to be very effective.

II. SENSITIVITY ANALYSIS AND LOSS SENSITIVITY FACTORS A new methodology is used to determine the candidate

nodes for the placement of capacitors using Loss Sensitivity Factors. The estimation of these candidate nodes basically helps in reduction of the search space for the optimization procedure.

Consider a distribution line connected between p and q buses.

p R+jX q

kth line Peff + jQeff

Active power loss in the kth line is given by [Ik2]*R[k],

Particle Swarm Optimization Based Capacitor Placement on Radial Distribution Systems

K. Prakash, Member, IEEE, and M. Sydulu

A

1-4244-1298-6/07/$25.00 2007 IEEE.

which can be expressed as,

( )( )2

22

][][.][][][

qV

kRqQqPqP effefflineloss

+=

(1)

Similarly the reactive power loss in the kth line is given by

( )( )2

22

][][.][][][

qV

kXqQqPqQ effefflineloss

+=

(2)

Where, Peff[q] = Total effective active power supplied beyond the node q. Qeff [q] = Total effective reactive power supplied beyond the node q. Now, both the Loss Sensitivity Factors can be obtained as

shown below:

( )( )2][

][*][*2qV

kRqQQ

P effeff

lineloss=

(3)

( )( )2][

][*][*2qV

kXqQQ

Q effeff

lineloss=

(4)

Candidate Node Selection using Loss Sensitivity Factors: The Loss Sensitivity Factors (

efflineloss QP ) are calculated from the base case load flows and the values are arranged in descending order for all the lines of the given system. A vector bus position bpos [i] is used to store the respective end buses of the lines arranged in descending order of the values (

efflineloss QP ). The descending order of (

efflineloss QP ) elements of bpos[i] vector will decide the sequence in which the buses are to be considered for compensation. This sequence is purely governed by the (

efflineloss QP ) and hence the proposed Loss Sensitive Coefficient factors become very powerful and useful in capacitor allocation or Placement. At these buses of bpos[i] vector, normalized voltage magnitudes are calculated by considering the base case voltage magnitudes given by (norm[i]= V[i]/0.95). Now for the buses whose norm[i] value is less than 1.01 are considered as the candidate buses requiring the Capacitor Placement. These candidate buses are stored in rank bus vector. It is worth note that the Loss Sensitivity factors decide the sequence in which buses are to be considered for compensation placement and the norm[i]decides whether the buses needs Q-Compensation or not. If the voltage at a bus in the sequence list is healthy (i.e., norm[i]>1.01) such bus needs no compensation and that bus will not be listed in the rank bus vector. The rank bus vector offers the information about the possible potential or candidate buses for capacitor placement. Now sizing of Capacitors at buses listed in the rank bus vector is done by using Particle Swarm Optimization based algorithm. Table I shows the active power Line Loss Sensitivity Coefficients placed in descending order along with its bus identification and normalized voltage magnitudes of 15 bus radial

distribution system.

TABLE I LOSS SENSITIVITY COEFFICIENTS PLACED IN DESCENDING

ORDER OF A 15-BUS RADIAL DISTRIBUTION SYSTEM. efflineloss QP

(descending) Bus No.

Norm[i] V[i]/0.95

Base voltage

0.029661 2 1.0224 0.971283 0.016437 6 1.0086 0.958232 0.015485 3 1.0069 0.956669 0.008526 11 0.9990 0.949952 0.006182 4 1.0009 0.949952 0.005266 12 0.9955 0.945829 0.004134 9 1.0188 0.967971 0.003141 15 0.99835 0.94844 0.002966 14 0.9985 0.948608 0.002811 7 1.0063 0.956008 0.001678 13 0.9942 0.944517 0.001613 8 1.007263 0.956954 0.001342 10 1.01768 0.966897 0.001256 5 0.99985 0.949918

Rank bus vector of 15-bus Radial Distribution System contains set of sequence of buses given as {6,3,11,4,12,15,14,7,13,8,5}

III. PARTICLE SWARM OPTIMIZATION Particle Swarm Optimization (PSO) is a meta heuristic parallel search technique used for optimization of continues non linear problems. The method was discovered through simulation of a simplified social model. PSO has roots in two main component methodologies perhaps more obvious are ties to artificial life in general, and to bird flocking, fish schooling and swarming theory in particular. It is also related, how ever to evolutionary computation and has ties to both genetic algorithms and evolutionary programming. It requires only primitive mathematical operators, and is computationally inexpensive in terms of both memory requirements and speed. It conducts searches using a population of particles, corresponding to individuals. Each particle represents a Candidate solution to the capacitor sizing problem. In a PSO system, particles change their positions by flying around a multi dimensional search space until a relatively unchanged position has been encountered, or until computational limits are exceeded. In social science context, a PSO system combines a social and cognition models. The general elements of the PSO are briefly explained as follows: Particle X(t): It is a k-dimensional real valued vector which represents the candidate solution. For an ith particle at a time t, the particle is described as Xi(t)={Xi,1(t), Xi,2(t), Xi,k(t)}. Population: It is a set of n number of particles at a time t described as {X1(t), X2(t) Xn(t)}. Swarm: It is an apparently disorganized population of moving particles that tend to cluster together while each particle seems to be moving in random direction.

Particle Velocity V(t): It is the velocity of the moving particle represented by a k-dimensional real valued vector Vi(t)= {vi,1(t), vi,2(t) vi,k(t)}. Inertia weight W(t): It is a control parameter that is used to control the impact of the previous velocity on the current velocity. Particle Best (pbest): Conceptually pbest resembles autobiographical memory, as each particle remembers its own experience. When a particle moves through the search space, it compares its fitness value at the current position to the best value it has ever attained at any time up to the current time. The best position that is associated with the best fitness arrived so far is termed as individual best or Particle best. For each Particle in the swarm its pbest can be determined and updated during the search. Global Best (gbest): It is the best position among all the individual pbest of the particles achieved so far. Velocity Updation: Using the global best and individual best, the ith particle velocity in kth dimension is updated according to the following equation. V[i][j]=K*(w*v[i][j]+c1*rand1*(pbestX[i][j]- X[i][j])+c2*rand2*(gbestX[j]-X[i][j])). where, K constriction factor c1, c2 weight factors w Inertia weight parameter i particle number j control variable rand1, rand2 random numbers between 0 and 1 Stopping criteria: This is the condition to terminate the search process. It can be achieved either of the two following methods:

i. The number of the iterations since the last change of the best solution is greater than a pre-specified number.

ii. The number of iterations reaches a pre-specified maximum value.

IV. ALGORITHM FOR CAPACITOR PLACEMENT AND SIZING USING LOSS SENSITIVITY FACTORS AND

PARTICLE SWARM OPTIMIZATION Step1: Run the base case Distribution load flow and determine the active power loss. Step2: Identify the Candidate buses for placement of capacitors using Loss Sensitivity Factors. Step3: Generate randomly n number of particles, where each particle is represented as particle[i]={Qc 1,Qc 2,.,Qc j} Where j represents number of candidate buses. Step4: Generate the particle velocities (v[i]) between vmax and vmax. Where, vmax = (capmax-capmin)/N Capmax= maximum capacitor rating in kvar Capmin= minimum capacitor rating in kvar N= number of steps to move the particle from one position to the other. Step5: Set the Iteration count, iter=1.

Step6: Run the load flows by placing a particle i at the candidate bus for reactive power compensation and store the active power loss (pl). Step7: Evaluate the fitness value (base power loss-pl) of the particle i and compare with previous particle best (pbest) value. If the current fitness value is greater than its pbest value, then assign the pbest value to the current value. Step8: Determine the current global best(gbest) maximum value among the particles individual best (pbest) values. Step9: Compare the global position with the previous global position. If the current global position is greater than the previous, then set the global position to the current global position. Step10: Update the velocities by using v[i][j]=K*(w*v[i][j]+c1*rand1*(pbestparticle[i][j]- particle[i][j])+c2*rand2*(gbestparticle[j]-particle[i][j]). Where, particle[i] position of individual i pbestparticle[i] best position of individual i gbestparticle best position among the swarm v[i] velocity if individual i Step11: If the velocity v[i][j] violates its limits (-vmax, vmax), set it at its proper limits Step12: Update the position of the particle by adding the velocity (v[i][j]) to it. Step13: Now run the load flow and determine the active power loss (pl) with the updated particle. Step14: Repeat step 7 to step 9 Step15: Repeat the same procedure for each particle from steps from 6 to 13. Step16: Repeat steps from 6 to 13 until the termination criteria are achieved.

V. TEST RESULTS The proposed method for loss reduction by capacitor placement is tested on 10bus [15], 15bus [13], 34bus [16], 69 bus [3] and 85bus radial distribution systems. The various constants used in the proposed algorithm are capmin=200kvar, capmax=1200kvar, K=0.7259, c1=c2=2.05 and w=1.2.The test results are shown below in various tables. The 10 bus test system with the proposed method is compared with the paper [15] in which the total kvar placed is 5500 kvar with a loss reduction of 10.06% where as the proposed method for the identified locations the total kvar placed only 3186 kvar that too with a loss reduction of 11.17% as shown in Table II. When the proposed method is tested on 15 bus system and compared with the paper [18], nearly similar results are obtained as shown in Table III. The proposed method is also tested on 34 bus test system and compared with the heuristic method [16] and Fuzzy Expert Systems (FES) approach [20], results obtained are more promising. as shown in Table IV. In practice the capacitor size should be in discrete in value. With this in mind, for a 34 bus system, when buses 19, 22 and 20 are compensated by 800kvar, 800kvar and 450kvar instead of 781kvar, 803kvar and 479kvar respectively as shown in Table IV, the load flow results

indicate the active power loss of 168.87kw instead of 168.89kw can be achieved. Similarly the other systems can also be compensated by round off discrete capacitor values. Table V shows the test results of the proposed method on 69 bus system with a loss reduction of 32.23% and Table VI shows the test results of the 85bus radial distribution system with a loss reduction of 48.27%.This proposed PSO based capacitor placement with Loss sensitivity Factors method saves not only initial investment on the capacitors but also running cost as it places the capacitors in a minimum number of locations.

TABLE II COMPARISION OF PREVIOUS METHOD [15] AND PROPOSED

METHOD FOR OF 10BUS RADIAL DISTRIBUTION SYSTEM. BASE CASE ACTIVE POWER LOSS=783.77 KW

Fuzzy Reasoning based[15] Proposed PSO based Bus No Size (kvar) Bus No Size (kvar) 4 1050 6 1174 5 1050 5 1182 6 1950 9 264 10 900 10 566 Total kvar placed 4950 Total kvar placed 3186 Active power loss(kw) 704.88 Active power loss(kw) 696.21

TABLE III COMPARISION OF PREVIOUS METHOD [18] AND PROPOSED

METHOD FOR OF 15BUS RADIAL DISTRIBUTION SYSTEM. BASE CASE ACTIVE POWER LOSS=61.79 KW

Method proposed in[18] Proposed PSO based Bus No Size (kvar) Bus No Size (kvar) 3 805 3 871 6 388 6 321 Total kvar placed 1193 Total kvar placed 1192 Active power loss(kw) 32.6 Active power loss(kw) 32.7

TABLE IV COMPARISION OF PREVIOUS METHODS AND PROPOSED METHOD

FOR OF 34BUS RADIAL DISTRIBUTION SYSTEM. BASE CASE ACTIVE POWER LOSS=221.723 KW

Heuristic based [16] FES based[20] Proposed PSO based Bus No kvar Bus No kvar Bus No kvar 26 1400 24 1500 19 781 11 750 17 750 22 803 17 300 7 450 20 479 4 250 ---------- ---------- Total kvar 2700 Total kvar 2700 Total kvar 2063 Power loss(kw) 168.47 Power loss(kw) 168.98 Power loss(kw) 168.8

TABLE V PROPOSED PSO METHOD TESTED ON 69 BUS RADIAL DISTRIBUTION

SYSTEM. BASE CASE ACTIVE POWER LOSS=225 KW Bus No Kvar

46 241 47 365 50 1015

Total Kvar 1621 Active Power Loss (kw) 152.48

TABLE VI PROPOSED PSO METHOD TESTED ON 85 BUS RADIAL DISTRIBUTION

SYSTEM. BASE CASE ACTIVE POWER LOSS=315.714 KW

Bus No Kvar

8 796 58 453 7 314

27 901 Total Kvar 2464

Active Power Loss (kw) 163.32

VI. CONCLUSION In this paper, an algorithm that employs Particle Swarm Optimization, a meta heuristic parallel search technique for estimation of required level of shunt capacitive compensation to improve the voltage profile of the system and reduce active power loss. Loss Sensitivity Factors are used to determine the optimum locations required for compensation. The main advantage of this proposed method is that it systematically decides the locations and size of capacitors to realize the optimum sizable reduction in active power loss and significant improvement in voltage profile. Test results on 10, 15, 34, 69 and 85 bus systems are presented. The method places capacitors at less number of locations with optimum sizes and offers much saving in initial investment and regular maintenance.

VII. ACKNOWLEDGMENT The authors gratefully acknowledge the support and facilities extended by the Department of Electrical Engineering, National Institute of Technology, Warangal and Vaagdevi College of Engineering, Warangal (A.P) India.

VIII. REFERENCES [1] J.J. Grainger and S. Civanlar, Volt/var control on Distribution systems

with lateral branches using shunt capacitors as Voltage regulators-part I, II and III, IEEE Trans. Power Apparatus and systems, vol. PAS-104, no. 11, pp. 3278-3297, Nov. 1985.

[2] J.J .Grainger and S.H Lee, Capacitor release by shunt capacitor placement on Distribution Feeders: A new Voltage Dependent Model, IEEE Trans .PAS, pp 1236-1243 May 1982.

[3] M. E Baran and F. F. Wu, Optimal Sizing of Capacitors Placed on a Radial Distribution System, IEEE Trans. Power Delivery, vol. no.1, pp. 1105-1117, Jan. 1989.

[4] M. E. Baran and F. F. Wu, Optimal Capacitor Placement on radial distribution system, IEEE Trans. Power Delivery, vol. 4, no.1, pp. 725-734, Jan. 1989.

[5] N. I. Santoso, O. T. Tan, Neural- Net Based Real- Time Control of Capacitors Installed on Distribution Systems, IEEE Trans. Power Delivery, vol. PAS-5, no.1, pp. 266-272, Jan. 1990.

[6] P. K. Dash, S. Saha, and P. K. Nanda, Artificial Neural Net Approach for International forum on Applications of Neural Networks to Power Systems, pp. 247-250, 1991.

[7] H.N. Ng, M.M.A. Salama, Fuzzy Optimal Capacitor Sizing and Placement, Canadian Conference on Electrical and Computer Engineering, pp. 680-683, 1995.

[8] H.C.Chin, Optimal Shunt Capacitor Allocation by Fuzzy Dynamic Programming, Electric Power Systems Research, pp.133-139, Nov. 1995.

[9] Sundharajan and A. Pahwa, Optimal selection of capacitors for radial distribution systems using genetic algorithm, IEEE Trans. Power Systems, vol. 9 no.3, pp.1499-1507, Aug. 1994.

[10] J. Kennedy and R. Eberhart, Particle Swarm Optimization, proceedings of IEEE International Conference Neural Networks, vol.,IV, pp.1942-1948,1995.

[11] Y.Shi and Eberhart, A modified particle swarm optimization, pro. IEEE, Int. Conf. Evol. Comput. pp. 69-73, May 1998.

[12] Y.Shi and Eberhart, Empirical study of particle swarm optimization, pro. IEEE, Int. Conf. Evol. Comput., NJ, pp. 1945-1950, 1999

[13] D.Das, D. P. Kothari, and A. Kalam, Simple and efficient method for load flow solution of radial distribution networks, Electrical Power & Energy Systems, vol. 17. N0.5,pp 335-346, Elsevier Science Ltd 1995.

[14] M. Sydulu, An Effective Algorithm for Power System Topological Observability proceedings of IEEE TENCON 98, International Conference on Global Connectivity in Energy, Computer Communication and Control, 17-19 Dec. 1998.

[15] Ching-Tzong Su and Chih-Cheng Tsai, A New Fuzzy- Reasoning Approach to Optimum Capacitor Allocation for Primary distribution Systems, proceedings of IEEE International Conference on Industrial Technology, 1996.

[16] M.Chis, M. M. A. Salama and S. Jayaram, Capacitor Placement in distribution system using heuristic search strategies, IEE Proc-Gener, Transm, Distrib, vol, 144, No.3, pp. 225-230, May 1997.

[17] M. M. A. Salama and A.Y. Chikhani, An expert system for reactive power control of a distribution system, part1: System configuration. IEEE Trans. Power Delivery, vol. 7, no.2, pp. 940-945, Apr. 1992.

[18] M. H. Haque, Capacitor placement in radial distribution systems for loss reduction, IEE Proc-Gener, Transm, Distrib, vol, 146, No.5, Sep. 1999.

[19] J.R.Laframboise, G. Ferland, A.Y. Chikhani and M. M. A. Salama, An expert system for reactive power control of a distribution system, part2: System implementation, IEEE Trans. Power Systems, vol. 1, no.3, pp. 1433-1441, Aug. 1995.

[20] H.N.Ng, M.M.A. Salama and A.Y.Chikhani, Capacitor Allocation by Approximate Reasoning: Fuzzy Capacitor Placement, IEEE Trans. Power Delivery, vol. 15, no.1, pp. 393-398, Jan. 2000.

IX. BIOGRAPHIES

K.Prakash received his B.E (Electrical and Electronics Engineering, 1999) from University of Madras, M.Tech (Power Systems, 2003) from National Institute of Technology, Warangal. He is currently pursuing his PhD (Power Systems Engineering) in National Institute of Technology, Warangal, Andhra Pradesh, INDIA. His areas of interest include Distribution system studies, Meta Heuristic Techniques in Power Systems and Economic operation of Power Systems.

Maheswarapu Sydulu received his B.Tech (Electrical Engineering,1978), M.Tech (Power Systems,1980), PhD (Electrical Engineering Power Systems,1993), all degrees from Regional Engineering College, Warangal, Andhra Pradesh, INDIA. His areas of interest include Real Time power system operation and control, ANN, fuzzy logic and Genetic Algorithm applications in Power Systems, Distribution system studies, Economic operation, Reactive power planning and management. Presently he is working as Professor and Head of Electrical Engineering Department, National Institute of Technology, Warangal (formerly RECW).

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