Optimal capacitor placement using firefly algorithm for ...

IEEE - International Conference on Advances in Engineering and Technology-(ICAET 2014)

Optimal capacitor placement using firefly algorithm for power loss reduction in distribution system Dinakara Prasad Reddy P

M C V Suresh

Member of IEEE, Lecturer Department of EEE, S V University, Tirupati Email: [email protected]

Assistant Professor Department of EEE,S V CE, Tirupati Email: [email protected]

Abstract - This paper presents a new method that determines the optimal location and size of capacitors on radial distribution systems to improve voltage profile and to reduce the active power loss. Capacitor placement and sizing are done by Sensitivity Analysis and Firefly Algorithm. Sensitivity Analysis gives the sequence of capacitor locations in which optimal capacitor sizes are to be placed. In this paper Firefly Algorithm is used for finding the optimal capacitor sizes in Radial Distribution Systems. The proposed method is tested on IEEE 15, 34, 69 and 85 bus distribution systems. The results are promising when compared to other methods. The proposed method places capacitors at less number of locations when compared to other methods. This saves initial investment on capacitors and also running cost.

distribution system capacitor placement problem. Ng et al [11] proposedan approach to the capacitor placement problembased on fuzzy expert system. This system containing a set of heuristic rules used to determine the capacitor placement suitability index of each node in the distribution system. Capacitors are placed on the nodes with the highest suitability index.

Keywords: Capacitor Placement, Radial Distribution systems, Loss Sensitivity Analysis, Firefly Algorithm

The Firefly Algorithm (FFA) is a meta heuristic nature inspired population based optimization algorithm, introduced in 2010 by X. S. Yang [16]. FFA is used forestimation of optimal capacitor sizes to improve the voltage profile and to reduce active power loss of the system.

I. INTRODUCTION In the past few decades the distribution systems were facing several persistent problems. Presently many electric companies in a number of countries experiencing very high losses. Studies shows that 13% of total power generated is wasted in the form of losses at the distribution level [1]. To reduce these losses, shunt capacitor banks are installed on radial distribution feeders.With active power loss reduction and voltage profile improvement as objectives, the optimal capacitor placement problem aims to determine the optimal capacitor location and capacitor sizes in radial distribution systems. Efficient methods are required to determine the best location and sizes. The early approaches were based on heuristic optimization algorithms. In previous methods the problem formulated as a nonlinear programming model and considered both location and capacitor sizes as continuous variables [2-6]. Sundharajan and Pahwa [7] proposed the genetic algorithm approach to determine the optimal placement of capacitors. A simple heuristic numerical algorithm that is based on the method of local variation is proposed in [8]. In this paper genetic algorithm is proposed to determine the optimal selection of capacitors. Das [9] proposed the genetic algorithm approachfor reactive power compensation in distribution systems to reduce the energy loss under varying load conditions. Prakash and Sydulu [10] proposed the Particle swarm optimization method to size the capacitors in

Papers [13-15] presented a two stage methodology using Practical swarm optimization method, real coded genetic algorithm and differential evolution algorithm with combination of Fuzzy approach for optimal capacitor sizing and location respectively.

II. PROBLEM FORMULATION Capacitor placement in the distribution system is to minimize active power loss of the system, subjected to voltage constraints. The three phase system is considered here as balanced and loads are assumed as time invariant. Mathematically, the objective function of the problem is described as Minimizef = min (PT,Loss) Subjected to Vmin ≤│Vi │≤ Vmax Where PT,Loss is the total real power loss of the system,|Vi| voltage magnitude of bus i,Vmin and Vmaxare bus minimum and maximum voltage limits. III. SENSITIVITY ANALYSIS Capacitor locations in distribution system can be identified using sensitivity analysis [10]. The sensitivity factors gives the buses which will have the biggest loss reduction when a capacitor is placed. Therefore, these buses can be used as candidate buses for the capacitor placement. The estimation of these best buses basically helps in reduction of the search space for the optimization problem. From this method less number of

ISBN No.: 978-1-4799-4949-6 @ 2014 IEEE


capacitors are used for placement so that the initial investment on capacitors can be reduced. Consider a distribution line with an impedance R + jX and a load of Peff + jQeff connected between ‘i’ and ‘j’ buses as given below in Figure 3.

Figure 1. A distribution line with an impedance and a load. Real power loss in the line of the above Figure 1 is given by [Ik2] * [Rk], which can also be expressed as,

2 2 (Peff [j] + Q eff [j])R[k] Ploss [j] = 2 (V[j])

(1)

Similarly the reactive power loss in the kth line is given by 2 2 (Peff [j] + Q eff [j])X[k] Q loss [j] = 2 (V[j])

(2)

Where Peff [j] = Total effective active power supplied beyond the bus ‘j’ Qeff[j] = Total effective reactive power supplied beyond the bus ‘j’ Now, the Loss Sensitivity Factors can be calculated as ∂Ploss (2 * Q eff [j]) * R[k]) (3) = 2 ∂Q eff (V[j]) ∂Q loss ∂Q eff

=

(2 * Q eff [j]) * X[k]) 2 (V[j])

(4)

A. Bus Selection Using Sensitivity Analysis

The Sensitivity Factor ( ∂Ploss

/ ∂ Q eff ) as given in (3)

has been calculated from the base case load flows. The values of sensitivity factors have been arranged in descending order and correspondingly the bus numbers are stored in bus position bpos [i] vector. The descending order of( ∂Ploss / ∂Qeff )elements of bpos [i] vector will give the sequence in which the buses are considered for compensation. At these buses of bpos [i] vector, normalized voltage magnitudes are calculated by considering the base case voltage magnitudes given as below Norm[i] = |V[i]|/0.95

(5)

Where V[i] is the base voltages of the corresponding IEEE bus. The Norm[i] decides whether the buses need reactive

compensation or not. The buses whose Norm[i] value is less than 1.01 can be selected as the best buses for capacitor placement. The buses are stored in bus vector. Sensitivity Factors decide the sequence in which buses are to be considered for capacitor placement and Norm[i] decides whether the buses needs reactive compensation or not. If Norm[i] is greater than 1.01 such bus needs no compensation and that bus will not be listed in bus vector. The following steps are to be performed to find out the potential buses for capacitor placement Calculate the Sensitivity Factor at the buses of distribution system using (3). 2. Arrange the value of Sensitivity Factor in descending order. Also store the respective buses into bus position vector bpos[i]. 3. Calculate the normalized voltage magnitude Norm[i] of the buses of using (5). 4. The buses whose Norm[i] is less than 1.01 are selected as best buses for capacitor placement. The bus vector of 15, 34, 69 and 85 bus Radial Distribution System contains set of sequence of buses given as {6,3},{19,22,20},{57, 58, 61} and {8,58,7,27} respectively. 1.

IV. FIREFLY ALGORITHM Over the last 20 years new meta heuristic algorithm has been introduced almost every year. The nature-inspired ones have become very interesting and distinguished. The Firefly Algorithm (FFA) is a meta-heuristic natureinspired population-based optimization algorithm, introduced in 2010 by X. S. Yang [16]. It is based on the firefly bugs behavior, including the light emission, light absorption and the mutual attraction, which was developed to solve the continuous optimization problems. In comparison with the other evolutionary algorithms, FFA has many major advantages in solving complex nonlinear optimization problems. Some of these advantages are simple concepts, usage of real random numbers, easy implementation, higher stability mechanism, depends on the global communication among the swarming particles and less execution efforts. The development of firefly inspired algorithm was based on three idealized rules 1. Artificial fireflies are unisex so that sex is not an issue for attraction. 2. Attractiveness is proportional to their flashing brightness which decreases as the distance from the other firefly increases due to the fact that the air absorbs light. Since the most attractive firefly is the brightest one, to which it convinces neighbors moving toward. In case of no brighter one, it freely moves any direction. 3. The brightness of the flashing light can be considered as objective function to be optimized. For maximization problems, the light intensity is proportional to the value of the objective function.

ISBN No.: 978-1-4799-4949-6 @ 2014 IEEE


Attractiveness Suppose it is a night with absolute darkness, where the only visible light is the light produced by fireflies. The light intensity of each firefly is proportional to the quality of the solution, it is currently located at. In order to improve own solution, the firefly needs to advance towards the fireflies that have brighter light emission than is his own. Each firefly observes decreased light intensity than the one firefly actually emit, due to the air absorption over the distance. There are two important issues in the firefly algorithm, variation of light intensity and formulation of the attractiveness. For simplicity, we can always assume that the attractiveness of a firefly is determined by its brightness. Attractiveness of a firefly abides the law β exp γr With n≥1 (6) β r Where, r is the distance between any two fireflies, β0 is the initial attractiveness at r =0, and γ is an absorption coefficient which controls the decrease of the light intensity. Distance The distance r between firefly i and j at positions xi and xj respectively and is defined as Cartesian distance (7) Movement The movement itself consists of two elements: approaching the better local solutions and the random step. Moreover, the movement of firefly i which is attracted by a more attractive or brighter firefly j is given by i.e., brighter firefly j is given by

(8) Where the first term is the current position of a firefly, the second term is used for considering a firefly’s attractiveness to light intensity seen by adjacent fireflies and the third term is used for the random movement of a firefly in case there are no brighter ones. The coefficient α is a randomization parameter determined by the problem of interest, rand is a random number generator uniformly distributed in the space [0, 1]. The parameter γ characterizes the variation of the attractiveness and its value is important to determine the speed of the convergence and how the FA behaves. For the most cases of implementations, β0 = 1. V. ALGORITHM FOR CAPACITOR SIZING USING FFA ALGORITHM The steps involved for solving this optimization problem for selecting the proper size of the capacitor in the distributed networks are shown clearly in the following section. 1. Initialize all the parameters and constants of Firefly Algorithm. They are capmin, capmax, noff, noc, α, β0, βmin, γ and itermax (maximum number of iterations).

2. Run the load flow program and find the total active power loss TPL (fitness value i.e FV) of the original system (before capacitor placement) 3. Generate noff * nocnumber of fireflies randomly between the limits capmin and capmax. noff is the number of fireflies and noc is the number of capacitors. 4. Set the iteration count to 1. 5. By placing all the noc number of capacitor of each firefly at the respective optimal capacitor locations, and run the load flow program to find fitness value. 6. Obtain the best fitness value gbestF by comparing all the fitness values and also obtain the best firefly values gbestFV corresponding to the best fitness value gbestF. 7. Determine new alpha (α) value of the current iteration α using the equation delta = 1-(0.005/0.9)^(1/current generation) alpha= (1-delta)*alpha 8. Determine rij values of each firefly using the following equation ,

,

rij is obtained by finding the difference between the best fitness value gbestFV (gbestFV is the best fitness value i.e., jth firefly) and fitness value FV of the ith firefly. 9. New xi values are calculated for all the fireflies using the following equation 1 2 Where β0 is the initial attractiveness , γ is the absorption coefficient , rij is the difference between the best fitness value gbestFV and fitness value FV of the ith firefly, αis the randomization parameter, rand is the random number between 0 and 1, Xinew is the capnew. 10. Increase the iteration count. Go to step 5, if iteration count is not reached maximum. 11. gbestFV gives the optimal capacitor sizes in optimal locations and, gbestF gives best fitness and the results are printed.

V. RESULTS Optimal capacitor placement problem is performed using proposed algorithm on IEEE test systems. The proposed method for loss reduction by capacitor placement is tested on IEEE 15 bus, 34 bus, 69 bus and 85 bus radial distribution systems. The algorithm has been implemented in Matlab 2012. The various constants used in the proposed algorithm are capmin=100 kvar, capmax=1500 kvar, noff=40, α=0.5, β0=1, βmin=0.2, γ=1, Itmax =1000. The test results are shown below in various tables and compared with various previous algorithms. The proposed FFA algorithm based capacitor placement with Loss sensitivity Analysis method gives better results when compared to previous methods. The proposed method places the capacitor at less number of

ISBN No.: 978-1-4799-4949-6 @ 2014 IEEE


locations compared to other methods. This will reduce the initial investment as well as running cost. TABLE I. COMPARISON OF RESULTS FOR 15 BUS SYSTEM. BASE CASE ACTIVE POWER LOSS=61.79 kW Method proposed in[17]

PSO based [10]

Proposed FFA based

Bus No

Size (kvar)

Bus No

Size (kvar)

Bus No

Size (kvar)

3 6

805 388

3 6

871 321

3 6

828 396

Total kvar placed

1193

Total kvar placed

1192

Total kvar placed

1224

Active Power loss(kW)

32.6


32.7


32.5

TABLE II.

COMPARISON OF RESULTS FOR 34 BUS SYSTEM. BASE CASE ACTIVE POWER LOSS=221.723 kW

Heuristic based [8]

FES based [11]

PSO based [10]

Proposed FFA based

Bus No

Size(kvar)

Bus No

Size(kvar)

Bus No

Size(kvar)

Bus No

Size(kvar)

26 11 17

1400 750 300

24 17 7

1500 750 450

19 22 20

781 803 479

19 22 20

957 861 229

4 Total kvar Placed

250 2700

---------Total kvar Placed

-------2700

----------Total kvar Placed


168.5


168.98


--------2063 168.8

---------Total kvar Placed

------2047


168.8

TABLE III. COMPARISON OF RESULTS FOR 69 BUS SYSTEM. BASE CASE ACTIVE POWER LOSS=225 kW PSO based [10 ]

Proposed FFA Based

BusNo

Kvar

BusNo

46

241

57

226

Kvar

47

365

58

67

50

1015

61

1143

Total kvar Placed

1621

Totalkvar Placed

1436

Active PowerLoss (kW)

152.48


151.37

TABLE IV. COMPARISON OF RESULTS FOR 85 BUS SYSTEM. BASE CASE ACTIVE POWER LOSS=315.7 kW PSO based [10]

Proposed FFA Based

BusNo

Kvar

BusNo

Kvar

8

796

8

1430

58

453

58

737

7

314

27 Totalkvar Placed

901 2464


163.32

7

316

----Totalkvar Placed

----2483


173.9

VI. CONCLUSIONS In this paper, optimal capacitor placement problem is solved using loss sensitivity analysis with Firefly algorithmto achieve minimum power lossin distribution system. Firefly Algorithm, a heuristic search technique is used to find the optimal capacitor sizes. Loss sensitivity

analysis is used to determine the optimum locations required for compensation. The proposed method is tested on IEEE 15, 34, 69 and 85 bus radial distribution systems. The proposed method places capacitors at less number of locations with optimal capacitor sizes which will decrease the initial investment as well as running cost.

ISBN No.: 978-1-4799-4949-6 @ 2014 IEEE


ACKNOWLEDGMENTS The authors gratefully acknowledge the support and facilities extended by the Department of Electrical & Electronics Engineering, Sri Venkatewara University and Sri Venkateswara College of Engineering,Tirupati, Andhra Pradesh, India. References [1] [2]

[3] [4]

[5] [6] [7]

[8]

[9] [10] [11]

[12] [13]

[14]

[15]

[16]

[17]

H. N. Ng, M. M. A. Salama, and A.Y. Chikhani “Classification of capacitor allocation techniques” IEEE Trans. Power Delivery, vol.15, pp387-392, Jan.2000. Duran H., “Optimum number, location and size of shunt capacitors in radial distribution feeders: A dynamic programming approach”, IEEE Transactions on Power Apparatus and Systems, vol. - 87, no. 9, pp. 1769-1774, September 1968. Bae Y.G., “Analytical method of capacitor allocation on distribution primary feeders”, IEEE Transactions on Power Apparatus and Systems, vol. PAS- 97, no. 4, pp. 1232-1238, July 1978. Grainger J.J and S.H. Lee, “Optimum size and location of shunt capacitors for reduction losses on distribution feeders” IEEE Transactions on Power Apparatus and Systems, vol. PAS- 100, no. 3, pp. 1105-1118, March 1981. Baran M.E. and Wu F.F., “Optimal capacitor placement on radial distribution systems”,IEEE Transactions on Power Delivery, vol.4,no-1, pp. 725-734, January 1989. Baran M.E. and Wu F.F., “Optimal sizing of capacitors placed on a radial distribution system”, IEEE Transactions on Power Delivery, vol.4, no-1, pp. 735-743, January 1989. Sundhararajan S. and Pahwa A., “Optimal selection of capacitors for radial distribution systems using a genetic algorithm”, IEEETransactions on Power Systems, vo1.9, no.3, pp.1499-1507, August 1994. Chis M., Salama M.M.A. and Jayaram “Capacitor placement in distribution systems using heuristic search strategies”, IEE proceedings on Generation, Transmission and Distribution, vol. 144, no.3, pp. 225-230, May 1997. D. Das, “Reactive power compensation for radial distribution networks using geneticalgorithms,” Electric Power and Energy Systems, Vol. 24, 2002, pp.573-581. Prakash K. and Sydulu M., “Particle swarm optimization based capacitor placement on radial distribution systems”, IEEE Power Engineering Society general meeting 2007, pp. 1-5, June 2007. Ng H.N., Salama M.M.A. and Chikhani .Y., “Capacitor allocation by approximate reasoning: fuzzy capacitor placement”, IEEE Transactions on Power Delivery, vol. 15, no.1, pp 393 – 398, January 2000. Das D., Kothari D.P. and Kalam A., “Simple and efficient method for load flow solution of radial distribution networks”, Electrical Power & Energy Systems, vol. 17, no. 5, pp.335-346, 1995. Damodar Reddy M. and Veera Reddy V.C., “optimal capacitor placement using fuzzy and real coded genetic algorithm for maximum savings” Journal of Theoretical and Applied Information Technology,Vol-4, No-3, p.p 219- 226, March – 2008. Damodar Reddy M. and Veera Reddy V.C.,“ Capacitor placement using fuzzy and practical swarm optimization method for maximum annual Savings ARPN Journal of engineering and applied sciences,Vol-3, No-3, June– 2008. V. Usha Reddy, Dr .T. GowriManohar, P.Dinakara Prasad Reddy, “Capacitor Placement for loss reduction in radial distribution networks: A two stage approach”, Journal of electrical engineering, 2012. X.-S. Yang, “Firefly Algorithm, Levy Flights and Global Optimization”, Research and Development in Intelligent Systems XXVI (Eds M. Bramer, R. Ellis, Petridis), Springer London, 2010, pp. 209-21. M. H. Haque, “Capacitor placement in radial distribution systems for loss reduction,” IEE Proc-Gener, Transm, Distrib, vol, 146, No.5, Sep. 1999.

ISBN No.: 978-1-4799-4949-6 @ 2014 IEEE