genetic algo. for radial distribution system to reduce losses

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A SEMINAR ON

Reduction of Losses in Radial Distribution System using Genetic Algorithm

By:- ABHISHEK JANGIDB-Tech. EE-final yearRoll No.:12EAXEE702

SWAMI KESHWANAND INSTITUTE OF ENGINEERING & TECHNOLOGY

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Introduction Problem Formulation GA and LSF Technique Solution algorithm for capacitor placement Result Analysis Conclusion References

OUTLINES

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The increase in power demand and high load density in the urban areas makes the operation of power systems complicated and increases the line losses.

To reduce these system losses, many papers have been published and many research works have done in recent years referring to optimal distribution planning.

Various methods have been used to reduce power losses economically. Optimal selection of capacitors, optimal selection of conductors, and feeder reconfiguration are among different ways of decreasing losses.

One of the most important methods to reduce losses in the radial distribution systems is the utilization of the shunt capacitors.

INTRODUCTION

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Power factor correction Feeder-Loss Reduction Release of System capacity Voltage- Stabilization/Regulation Efficient Power Utilization Power Quality Enhancement

MERITS OF CAPACITOR PLACEMENT

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1. The capacitor placement in distribution network is an optimization problem. Various approaches are identified by researchers. All approaches differ from each other by way of their problem formulation and problem solution methods employed.

2. The objective of this work is to reduce the energy losses in the system and maintain the voltage magnitudes of the system with in prescribed limit. Power flow evaluation in the system Includes the calculation of bus voltages and line flows of a network.

PROBLEM FORMULATION

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Cont…..

The power loss in each branch is given by:

total power loss of the system is given by:

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• Genetic Algorithm (GA) is a global search and optimization technique which is based on the mechanism of natural selection and genetics. The development of GA is mostly attributed to the work of Goldberg and Holland.

• GA is initiated with random criterion of initial population which represents possible solution of the optimization problem. The fitness of each individual is evaluated by the value of the objective function which is called as fitness function. The new population is formed by selecting the more fit individuals using Genetic operators(selection, crossover and mutation) until the assigned maximum number of generations are reached or some form of convergence criterion has been met. Finally the population stabilizes and most of the individuals in the population are found to be almost identical.

Genetic Algorithm

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[Start] Generate random population of n chromosomes (suitable solutions for the problem)

[Fitness] Evaluate the fitness f(x) of each chromosome x in the population.

If function is satisfied after step 2 then stop and return to the best solution otherwise go to the next step.

[New population] Create a new population by repeating following steps until the new population is complete

• [Selection] Select two parent chromosomes from a population according to their fitness (the better fitness, the bigger chance to be selected)

Steps for Genetic Algorithm

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◦ [Crossover] With a crossover probability cross over the parents to form a new offspring (children). If no crossover was performed, offspring is an exact copy of parents.

◦ [Mutation] With a mutation probability mutate new offspring at each locus (position in chromosome).

◦ [Accepting] Place new offspring in a new population [Replace] Use new generated population for a further run of

algorithm [Test] If the end condition is satisfied, stop, and return the best

solution in current population [Loop] Go to step 2

Cont…..

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Steps used for the placement of shunt capacitors through Genetic algorithm

Step1- Read system data (Bus data and line data). Step2- Calculate Y bus and perform load flow analysis to find

out the voltage magnitude and power flow in branches. Step3- Perform optimization process by GA and find optimal

location and size of capacitors thathas to be placed.

Step4- Place the capacitor at appropriate location as directed by GA.

ALGORITHM

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Flow chart of Genetic AlgorithmSTART

Input parameters

GEN=1

Randomly generate initial solution

Find the score of each individual in the current population

Check for convergence

Is Gen=Max. Generation

STOP

STOP

Select parents based on their score

Produce children by application of Genetic Operators

GEN=GEN+1

Replace the current population with children to form next Generation

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In order to determine the bus location for placing the capacitor at that particular node in the radial distribution system, sensitivity analysis method is employed. The evaluation of these locations helps in reducing the search space during optimization process as it has to optimize the size of capacitor not location. The sensitivity analysis is a method to select location that reduces the system real power losses when we place the capacitor at those locations. The loss sensitivity factor is calculated (LSF) at all the buses using the equation given as

After the calculation of LSF at all the buses, all the values of arrange in descending order so as to find out the most sensitive node where capacitor has to be placed.

Loss Sensitivity Factor

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Steps used for the placement of shunt capacitors through LSF –GA Step1- Read system data (Bus data and line data). Step2- Calculate Y bus and perform load flow analysis to find out the

voltage magnitude and power flow in branches. Step3- Determine Node location through LSF and then perform GA

to find optimal size of capacitor that has to be placed on that particular node.

Step4- Place the capacitor at appropriate location which determine in previous.

ALGORITHM

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Location and sizing of capacitor determined through GA

Location and sizing of capacitor determined through combined approach of LSF-GA

For 14 kV bus system

7 10 14 135 37.3 12.8 10.745.534.2

4 9 13 5 2 41.4 29.1 12.5 47.4 29.2

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4 22 2 324 43.1 14.7 31.615.141.3

25 17 4 3 2 26.8 25.8 44.7 39.3 42.1

16




10 13 30 1129 48.2 46.4 40.139.149.3

15 14 31 10 13 47.4 47.4 48.4 49.2 47.8

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RESULTS for 14 Bus System (Base Load)No. of

CapacitorLocation Size (kVAr) Losses (kW) Voltage

before capacitor

Voltage after capacitor

Elapsed time (CPU time) in

sec

1 9 30.546 13.374 1.049 1.066 148.7913852 5 25.349 13.315 1.033 1.038 170.202313

9 22.978 1.049 1.0613 5 24.625 13.274 1.033 1.036 210.280912

9 23.582 1.049 1.06113 10.192 1.037 1.060

4 9 27.601 13.268 1.049 1.062 214.97034013 11.644 1.037 1.0613 19.707 1.030 1.0345 22.231 1.033 1.035

5 5 20.843 13.259 1.033 1.035 239.52864710 11.185 1.059 1.0659 16.006 1.049 1.0603 20.480 1.030 1.03613 10.717 1.037 1.062

1. Effect of capacitor placement on the system losses is observed by incrementing the number of capacitors in the system.

2. It is clearly observed that when a single capacitor is placed on bus 9, losses of the system are 13.374 kW however a small reduction in losses is observed when we increase the number of capacitor to 5.

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RESULTS for 14 Bus System (Light Load)No. of

CapacitorCapacitor Location Size (kVAr) Losses

(kW)Capacitor Location

Size (kVAr)

Losses (kW)

1 9 24.916 10.533 9 28.065 10.5352 9 20.476 10.476 9 39.033 10.503

5 19.462 6 17.673 3 9 24.565 10.452 9 35.271 10.476

13 12.165 6 10.792 5 14.227 13 17.377

4 13 10.021 10.418 9 41.600 10.4283 15.623 6 13.291 9 19.722 13 11.517 5 21.064 3 18.693

5 10 14.753 10.341 9 37.313 10.3745 18.630 6 22.345 9 12.362 13 22.819 3 15.420 3 17.575

13 10.461 7 16.902 1. Light loading conditions, when the number of capacitors is

two, then the location provided by GA is on bus no. 9 and 5 it is bus 9 and bus 6 from LSF calculation and losses under this operating condition are 10.476 and 10.503 from GA and LSF approach.

2. With higher number of capacitors, results obtained through GA are more realistic.

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RESULTS for 14 Bus System (Medium Load)No. of


(kW)Capacitor Location Size (kVAr) Losses

(kW)1 9 34.064 16.231 9 35.583 16.2382 9 25.447 16.145 9 38.692 16.190

5 22.911 14 15.727 3 13 10.994 16.100 9 45.483 16.114

5 33.737 14 15.385 9 24.359 6 26.424

4 6 13.497 16.056 9 42.078 16.07813 13.398 14 14.509 10 24.979 6 40.984 9 39.687 13 15.167

5 6 10.095 15.982 9 46.808 15.9869 44.625 14 15.007 5 28.838 6 48.714

13 11.585 13 14.696 2 33.659 2 49.538

1. It is clearly observed that at base case with no capacitor in the system the losses are 16.329 kW.

2. After placement of five capacitors it reduces to 15.982 kW for first approach and it is 15.986 kW by LSF method. This suggests that location identification through GA is a better choice.

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No. of Capacitor

Capacitor Location Size (kVAr) Losses


(kW)1 5 48.506 23.990 4 49.781 23.9922 5 35.156 23.661 4 45.024 23.791

9 35.898 9 42.684 3 2 37.641 23.569 4 44.152 23.717

5 40.609 9 35.520 9 34.040 13 41.805

4 2 39.546 23.500 4 43.790 23.5315 41.199 9 37.217 9 31.320 13 12.907

13 10.341 5 43.572 5 7 37.325 23.389 4 41.448 23.428

10 12.896 9 29.185 14 34.292 13 12.549 5 45.589 5 47.403

13 10.709 2 29.278

RESULTS for 14 Bus System (Heavy load)

1. It is clearly observed from table that at base case with no capacitor in the system the losses are 24.00 kW. After placement of five capacitors it reduces to 23.389kW for first approach and it is 23.428 kW by LSF method.

2. The locations for various capacitors at bus 7, 10, 14,5,13 by GA and 4, 9, 13, 5 and 2 by using LSF. This suggests that location identification through GA is a better choice.

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RESULTS for 14 Bus System

1. Above table shows the calculation of Loss Sensitivity factor for IEEE 14 bus system under different loading conditions.

2. The amount of LSF is the indication of the suitable candidate for the placement of shunt capacitors.

14 Bus

Loading Condition 10% Redu. 10% Inc. 30% Inc.

Loss Sensitivity

Factorweak Bus Loss Sensitivity

Factor weak Bus Loss Sensitivity Factor weak Bus

1.00 9 1.00 9 0.66 40.50 6 0.89 14 0.40 90.45 13 0.65 6 0.37 130.40 3 0.50 13 0.30 50.33 7 0.41 2 0.25 20.29 5 0.33 7 0.22 7

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1 2 3 45

0

8

16

24

32

Losses (kW)

Base Case

Light Load

Medium Load (10%)

Medium Load (20%)

Heavy Load (30%)

Heavy Load (40%)

No.of Capacitor

Loss

esLoss Calculation through GA for 14 Bus

System

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1 2 3 45

0

5

10

15

20

25

30

Losses (kW)

Base Case

Light Load

Medium Load (10%)

Medium Load (20%)

Heavy Load (30%)

Heavy Load (40%)

No. of Capacitor

loss

es

Loss Calculation through LSF-GA 14 Bus System

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0 50 100 150 20013.25

13.3

13.35

13.4

13.45Optimal Capacitor Placement By Genetic Algorithm

Number of Generation

Loss

es M

inim

um(k

w)

Convergence characteristics of Base case for 14 Bus System

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RESULTS for 30 Bus System (Base Load)

1. It is clearly observed from the table that when a single capacitor is placed on bus 4, losses of the system were 17.639 kW however a small reduction in losses is observed when we increase the number of capacitor to 5.

No. of Capacitor


(kW)

Voltage before

capacitor

Voltage after

capacitor

Elapsed time (CPU time) in sec

1 4 41.909 17.639 1.003 1.030 223.2739132 4 37.689 17.479 1.003 1.026 240.145030

24 13.335 0.991 1.0303 4 36.127 17.315 1.003 1.024 254.594486

24 13.425 0.991 1.04610 33.050 1.014 1.058

4 3 21.665 17.214 1.014 1.038 260.00696010 38.038 1.014 1.06224 11.319 0.991 1.0488 35.953 0.993 1.024

5 24 13.097 17.026 0.991 1.038 294.89633526 40.204 0.977 1.05912 22.699 1.046 1.06310 42.959 1.014 1.0493 15.308 1.014 1.038

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RESULTS for 30 Bus System (Light Load)

1. Light loading conditions, when a single shunt capacitor is placed on bus 21, loss is reduced from 14.02 to 13.869 whereas using LSF is found to be maximum for bus 20 and the loss is reduced to 13.961.

2. When the number of capacitors is two, the losses under this operating condition are 13.790 and 13.867 from GA and LSF approach.

No. of Capacitor



(kW)1 21 14.539 13.869 20 18.154 13.9612 4 28.674 13.790 20 24.533 13.867

21 12.819 24 18.9683 24 16.425 13.751 20 20.169 13.787

4 24.830 24 17.2748 21.276 3 26.675

4 8 22.331 13.722 20 24.606 13.74621 14.338 24 18.2094 28.043 3 28.571

19 10.185 21 17.8915 4 22.922 13.032 20 17.348 13.523

7 13.196 24 15.45523 10.395 3 28.3778 21.690 21 17.100

21 14.047 7 16.423

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RESULTS for 30 Bus System (Medium Load)

1. It is observed that with no capacitor in the system the losses are 22.697kW.After placement of five capacitors it reduces to 21.345 kW for first approach and 21.425 kW by LSF method.

2. The location of shunt capacitors are 21, 7, 8, 4 and 24 determined through GA while 3, 4, 24, 21, and 27 through LSF approach.

No. of Capacitor



(kW)1 4 42.836 21.961 3 44.823 22.1002 22 20.626 21.776 3 36.833 21.872

4 41.949 4 46.134 3 3 19.850 21.660 3 34.811 21.675

24 14.208 4 46.487 4 42.150 24 16.322

4 24 10.838 21.556 3 37.764 21.5639 30.173 4 46.292

21 13.076 24 11.455 4 45.893 21 25.102

5 21 18.263 21.345 3 34.938 21.4257 13.200 4 44.168 8 26.290 24 17.039 4 37.437 21 24.780

24 14.789 27 12.002

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RESULTS for 30 Bus System (Heavy load)

1. It is observed that with no capacitor in the system the losses are 33.98 kW. After placement of five capacitors it reduces to 31.333 kW for first approach and it is 31.415 kW by LSF method.

2. As number of capacitors increased results obtained through GA are more realistic as size as well as losses calculated by the GA is less than LSF approach.

No. of Capacitor



(kW)1 21 34.159 33.029 25 39.474 33.4882 4 42.259 32.261 25 42.556 33.011

21 28.360 17 34.292 3 24 23.639 31.908 25 33.332 32.294

3 42.977 17 28.724 7 35.319 4 47.193

4 10 43.915 31.538 25 28.242 31.6237 32.390 17 26.935 3 44.961 4 48.442

24 17.766 3 47.557 5 4 43.152 31.333 25 26.813 31.415

22 14.724 17 25.863 2 41.356 4 44.740

24 15.118 3 39.399 3 31.628 2 42.150

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30 Bus


Loss Sensitivity

Factor

weak BusLoss Sensitivity

Factor

weak BusLoss Sensitivity

Factor

weak Bus

4.30 20 4.00 3 12.0 253.00 24 3.70 4 10.8 172.60 3 2.80 24 6.00 42.20 21 2.00 21 3.00 31.50 7 1.60 27 2.46 21.30 10 1.50 26 1.59 29

30

1 2 3 45

0

8

16

24

32

40

Losses (kW)

Base Case

Light Load

Medium Load (10%)

Medium Load (20%)

Heavy Load (30%)

Heavy Load (40%)

No.of capacitor

Los

ses

Loss Calculation through GA for 30 Bus System

31

1 2 3 45

0

8

16

24

32

40

48

Losses (kW)

Base Case

Light Load

Medium Load (10%)

Medium Load (20%)

Heavy Load (30%)

Heavy Load (40%)

No. of Capacitor

loss

esLoss Calculation through LSF-GA for 30

Bus System

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0 50 100 150 20017.00

17.026

17.6

17.7

17.8

17.92Optimal Capacitor Placement By Genetic Algorithm


Loss

es M

inim

um(k

W)


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RESULTS for 33 Bus System (Base Load)No. of


(kW)

Voltage before

capacitor

Voltage after

capacitor

Elapsed time (CPU

time) in sec1 12 49.027 173.249 0.958 0.987 219.0356262 12 47.045 167.914 0.958 0.989 227.778733

14 42.895 0.934 0.9703 10 38.422 163.304 0.961 0.991 239.630848

11 43.340 0.959 0.98029 43.240 0.969 0.994

4 29 48.276 160.733 0.969 0.991 248.59439411 47.118 0.959 0.97722 47.288 0.964 0.99213 49.650 0.952 0.975

5 21 46.158 156.805 0.965 0.989 260.23689312 48.171 0.958 0.97625 43.545 0.963 0.98222 48.068 0.964 0.98410 38.806 0.961 0.977

1. It is clearly observed that when a single capacitor is placed on bus 12, losses of the system were 173.249 kW from 178.735.

2. A significant reduction in losses is observed when the number of shunt capacitors is increased up to 5. Location of shunt capacitor is determined by GA.

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RESULTS for 33 Bus System (Light Load)

1. Under light loading conditions placement of single capacitor on bus 13 (GA) and bus 15 (LSF) results in reduction of from 141.698 to 136.951 and 137.943.

2. When the number of capacitors is two, then the location is on bus no. 12 and 29 (GA) however it is bus 15 and bus 10 (LSF) with losses under this condition are 133.420 and 134.853

No. of Capacitor



(kW)1 13 48.867 136.951 15 49.532 137.9432 12 48.187 133.420 15 48.688 134.853

29 44.590 10 46.1163 29 38.138 129.460 15 45.936 131.124

12 46.195 10 49.80613 49.038 14 49.959

4 25 45.269 121.304 15 45.366 128.16214 46.866 10 49.53122 49.215 14 48.95129 45.018 30 46.980

5 13 46.164 120.416 15 49.453 125.98014 42.324 10 48.71710 44.166 14 46.23829 45.949 30 48.78425 48.024 13 48.957

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RESULTS for 33 Bus System (Medium Load)

1. It is observed that at base case with no capacitor in the system the losses are 221.196 kW. After placement of five capacitors it reduces to becomes 192.045 kW for first approach and it is 195.651 kW by LSF method.

2. With increase in number of capacitors a significant reduction in losses are evaluated.

No. of Capacitor



(kW)1 12 49.145 214.623 15 49.233 215.9692 12 46.534 209.470 15 48.663 210.157

13 46.756 13 49.2193 12 48.823 205.538 15 47.503 206.146

14 47.539 13 48.87525 41.359 10 44.218

4 22 48.983 193.973 15 48.173 200.72011 46.989 13 49.72713 47.657 10 47.66325 48.332 29 47.995

5 29 47.508 192.045 15 46.353 195.65112 48.555 13 49.75030 45.873 10 48.21714 47.668 29 47.96011 46.620 12 49.807

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RESULTS for 33 Bus System (Heavy Load)

1. It is observed that at base case with no capacitor in the system the losses are 324.383 kW. After placement of five capacitors it becomes 284.038 kW (GA) and it is 289.386 kW (LSF).

2. The locations for various capacitors at bus 10, 13, 30, 29 and 11 by GA while 15, 14, 31, 10 and 13 through LSF.

No. of Capacitor



(kW)1 12 48.307 315.607 15 49.845 317.1432 13 49.387 308.030 15 49.400 310.042

11 44.357 14 48.5423 9 47.540 300.098 15 49.493 307.247

13 48.822 14 49.73512 45.008 31 47.482

4 11 48.579 294.642 15 47.723 298.39025 44.020 14 47.40913 47.357 31 49.93910 48.423 10 49.599

5 10 48.215 284.038 15 47.475 289.38613 46.481 14 47.46030 49.337 31 48.48629 39.158 10 49.21911 40.112 13 47.847

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33 Bus


Loss Sensitivity

Factorweak Bus Loss Sensitivity

Factor weak Bus Loss Sensitivity Factor weak Bus

11.0 15 19.0 15 17.7 156.75 10 5.45 13 15.5 142.75 14 2.92 10 3.35 312.06 30 1.90 29 2.53 100.49 13 0.55 12 0.62 130.39 32 0.46 32 0.47 30

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1 2 3 45

0

75

150

225

300

375

Losses (kW)

Base Case

Light Load

Medium Load (10%)

Medium Load (20%)

Heavy Load (30%)

Heavy Load (40%)

No. of Capacitor

Los

ses

Loss Calculation through GA for 33 Bus System

39

1 2 3 45

0

75

150

225

300

375

450

Losses (kW)

Base Case

Light Load

Medium Load (10%)

Medium Load (20%)

Heavy Load (30%)

Heavy Load (40%)

No. of Capacitor

loss

es

Loss Calculation through LSF-GA for 33 Bus System

40

0 50 100 150 200

154156158

160162

164

Optimal Capacitor Placement By Genetic Algorithm


Loss

es M

inim

um(k

W)


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Thus we conclude that with the placement of shunt capacitor in radial distribution system results in 1. Results are calculated for both approaches and compared for

different loading conditions. 2. GA optimization technique is effective in deciding the

position where different size capacitors to be placed, for different number of candidate buses.

3. GA Search optimization technique generate more superior results than LSF with GA optimization in terms of power loss reduction.

4. Optimal placement and sizing of capacitors give improved voltage profile and higher power loss reduction.

CONCLUSION

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Cont…..

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Cont…..

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Cont…..

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Cont…..

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[30] Y. Mohamed Shuaib, C.ChristoberAsirRajan, “Capacitor Sizing and Placement on Radial Distribution System Using Queen Bee Assisted Genetic Algorithm”,Process Automation, Control and Computing (PACC), 2011 International Conference, Vol. 1, No. 8, pages 20-22, July 2011.

[31] S.Neelima, Dr. P.S.Subramanyam, “Optimal capacitor placement in distribution system using Genetic Algorithm: A Dimension Reducing Approach”, Journal of Theoretical and Applied Information Technology, Vol.30, No.1, August 2011.

[32] Majid Davoodi, Mohsen Davoudi, IrajGanjkhany, Ali Aref, “Optimal Capacitor placement in Distribution Networks Using Genetic Algorithm”, Vol. 5 ,July 2012.

[33] Deepti Sharma, AmitaMahor, “Optimal Placement of Capacitor in Radial Distribution System Using Real Coded Genetic Algorithm”, International Journal of Electrical Engineering, August2013.[34] Attia A. El-Fergany, “Involvement of cost savings and voltage stability indices in optimal capacitor allocation in radial distribution networks using artificial bee colony algorithm”, International Journal of Electrical Power & Energy Systems, Vol. 62, Pages 608-616, November 2014.

[35] www.mathworks.com

Cont…..

http://www.indjst.org/index.php/indjst/search/authors/view?firstName=Ali&middleName=&lastName=Aref&affiliation=Department%20of%20Electrical%20Engineering,%20Takestan%20Branch,%20Islamic%20Azad%20University,%20Takestan&country=IR



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