Genetic Algo. for Radial Distribution System to reduce Losses

A SEMINAR
ON
Reduction of Losses in Radial Distribution
System using Genetic Algorithm
By:-
ABHISHEK JANGID
B-Tech. EE-final year
Roll No.:12EAXEE702
1

 Introduction
 Problem Formulation
 GA and LSF Technique
 Solution algorithm for capacitor placement
 Result Analysis
 Conclusion
 References
2

 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.
3

 Power factor correction
 Feeder-Loss Reduction
 Release of System capacity
 Voltage- Stabilization/Regulation
 Efficient Power Utilization
 Power Quality Enhancement
4

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.
5

6
The power loss in each branch is given by:
total power loss of the system is given by:

• 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.
7

 [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)
8

◦ [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
9

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 that
has to be placed.
 Step4- Place the capacitor at appropriate location as directed by
GA.
10

11
START
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

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. 12

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.
13

Location and sizing of capacitor determined through GA
Location and sizing of capacitor determined through combined
approach of LSF-GA
14
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

approach of LSF-GA
15
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

approach of LSF-GA
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

17
No. of
Capacitor
Location Size (kVAr) Losses (kW) Voltage before
capacitor
Voltage after
capacitor
Elapsed time
(CPU time) in sec
1 9 30.546 13.374 1.049 1.066 148.791385
2 5 25.349 13.315 1.033 1.038 170.202313
9 22.978 1.049 1.061
3 5 24.625 13.274 1.033 1.036 210.280912
9 23.582 1.049 1.061
13 10.192 1.037 1.060
4 9 27.601 13.268 1.049 1.062 214.970340
13 11.644 1.037 1.061
3 19.707 1.030 1.034
5 22.231 1.033 1.035
5 5 20.843 13.259 1.033 1.035 239.528647
10 11.185 1.059 1.065
9 16.006 1.049 1.060
3 20.480 1.030 1.036
13 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.

18
No. of
Capacitor
Capacitor
Location
Size (kVAr) Losses (kW)
Capacitor
Location
Size (kVAr)
Losses
(kW)
1 9 24.916 10.533 9 28.065 10.535
2 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 10.428
3 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 10.374
5 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.

19
No. of
Capacitor
Capacitor
Location
Capacitor
Location
1 9 34.064 16.231 9 35.583 16.238
2 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 16.078
13 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 15.986
9 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.

No. of
Capacitor
Capacitor
Location
Capacitor
Location
1 5 48.506 23.990 4 49.781 23.992
2 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 23.531
5 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
20
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.

21
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
Factor
weak Bus
Loss Sensitivity
Factor
weak Bus Loss Sensitivity Factor weak Bus
1.00 9 1.00 9 0.66 4
0.50 6 0.89 14 0.40 9
0.45 13 0.65 6 0.37 13
0.40 3 0.50 13 0.30 5
0.33 7 0.41 2 0.25 2
0.29 5 0.33 7 0.22 7

0
8
16
24
32
1 2
3
4
5
Losses
No.of Capacitor
Losses (kW)
Base Case
Light Load
Medium Load (10%)
Medium Load (20%)
Heavy Load (30%)
Heavy Load (40%)
22

0
10
20
30
1 2
3
4
5
losses
No. of Capacitor
Losses (kW)
Base Case
Light Load
Medium Load (10%)
Medium Load (20%)
Heavy Load (30%)
Heavy Load (40%)
23

0 50 100 150 200
13.25
13.3
13.35
13.4
13.45
Optimal Capacitor Placement By Genetic Algorithm
Number of Generation
LossesMinimum(kw)
24

25
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
Capacitor
Location
Voltage
before
capacitor
Voltage after
capacitor
Elapsed time (CPU
time) in sec
1 4 41.909 17.639 1.003 1.030 223.273913
2 4 37.689 17.479 1.003 1.026 240.145030
24 13.335 0.991 1.030
3 4 36.127 17.315 1.003 1.024 254.594486
24 13.425 0.991 1.046
10 33.050 1.014 1.058
4 3 21.665 17.214 1.014 1.038 260.006960
10 38.038 1.014 1.062
24 11.319 0.991 1.048
8 35.953 0.993 1.024
5 24 13.097 17.026 0.991 1.038 294.896335
26 40.204 0.977 1.059
12 22.699 1.046 1.063
10 42.959 1.014 1.049
3 15.308 1.014 1.038

26
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
Capacitor
Location
Capacitor
Location
1 21 14.539 13.869 20 18.154 13.961
2 4 28.674 13.790 20 24.533 13.867
21 12.819 24 18.968
3 24 16.425 13.751 20 20.169 13.787
4 24.830 24 17.274
8 21.276 3 26.675
4 8 22.331 13.722 20 24.606 13.746
21 14.338 24 18.209
4 28.043 3 28.571
19 10.185 21 17.891
5 4 22.922 13.032 20 17.348 13.523
7 13.196 24 15.455
23 10.395 3 28.377
8 21.690 21 17.100
21 14.047 7 16.423

27
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
Capacitor
Location
Capacitor
Location
1 4 42.836 21.961 3 44.823 22.100
2 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 21.563
9 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 21.425
7 13.200 4 44.168
8 26.290 24 17.039
4 37.437 21 24.780
24 14.789 27 12.002

28
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
Capacitor
Location
Capacitor
Location
1 21 34.159 33.029 25 39.474 33.488
2 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 31.623
7 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

29
2. The amount of LSF is the indication of the suitable candidate
for the placement of shunt capacitors.
30 Bus
Loading
Condition 10% Redu. 10% Inc. 30% Inc.
Loss Sensitivity
Factor
weak Bus
Loss Sensitivity
Factor
weak Bus
Loss Sensitivity
Factor
weak Bus
4.30 20 4.00 3 12.0 25
3.00 24 3.70 4 10.8 17
2.60 3 2.80 24 6.00 4
2.20 21 2.00 21 3.00 3
1.50 7 1.60 27 2.46 2
1.30 10 1.50 26 1.59 29

0
8
16
24
32
40
1 2
3
4
5
Losses
No.of capacitor
Losses (kW)
Base Case
Light Load
Medium Load (10%)
Medium Load (20%)
Heavy Load (30%)
Heavy Load (40%)
30

0
8
16
24
32
40
48
1 2
3
4
5
losses
No. of Capacitor
Losses (kW)
Base Case
Light Load
Medium Load (10%)
Medium Load (20%)
Heavy Load (30%)
Heavy Load (40%)
31

0 50 100 150 200
17.00
17.026
17.6
17.7
17.8
17.92
LossesMinimum(kW)
32

33
No. of
Capacitor
Capacitor
Location
Voltage
before
capacitor
Voltage after
capacitor
Elapsed time
(CPU time) in
sec
1 12 49.027 173.249 0.958 0.987 219.035626
2 12 47.045 167.914 0.958 0.989 227.778733
14 42.895 0.934 0.970
3 10 38.422 163.304 0.961 0.991 239.630848
11 43.340 0.959 0.980
29 43.240 0.969 0.994
4 29 48.276 160.733 0.969 0.991 248.594394
11 47.118 0.959 0.977
22 47.288 0.964 0.992
13 49.650 0.952 0.975
5 21 46.158 156.805 0.965 0.989 260.236893
12 48.171 0.958 0.976
25 43.545 0.963 0.982
22 48.068 0.964 0.984
10 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.

34
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
Capacitor
Location
Capacitor
Location
1 13 48.867 136.951 15 49.532 137.943
2 12 48.187 133.420 15 48.688 134.853
29 44.590 10 46.116
3 29 38.138 129.460 15 45.936 131.124
12 46.195 10 49.806
13 49.038 14 49.959
4 25 45.269 121.304 15 45.366 128.162
14 46.866 10 49.531
22 49.215 14 48.951
29 45.018 30 46.980
5 13 46.164 120.416 15 49.453 125.980
14 42.324 10 48.717
10 44.166 14 46.238
29 45.949 30 48.784
25 48.024 13 48.957

35
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
Capacitor
Location
Capacitor
Location
1 12 49.145 214.623 15 49.233 215.969
2 12 46.534 209.470 15 48.663 210.157
13 46.756 13 49.219
3 12 48.823 205.538 15 47.503 206.146
14 47.539 13 48.875
25 41.359 10 44.218
4 22 48.983 193.973 15 48.173 200.720
11 46.989 13 49.727
13 47.657 10 47.663
25 48.332 29 47.995
5 29 47.508 192.045 15 46.353 195.651
12 48.555 13 49.750
30 45.873 10 48.217
14 47.668 29 47.960
11 46.620 12 49.807

36
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
Capacitor
Location
Capacitor
Location
1 12 48.307 315.607 15 49.845 317.143
2 13 49.387 308.030 15 49.400 310.042
11 44.357 14 48.542
3 9 47.540 300.098 15 49.493 307.247
13 48.822 14 49.735
12 45.008 31 47.482
4 11 48.579 294.642 15 47.723 298.390
25 44.020 14 47.409
13 47.357 31 49.939
10 48.423 10 49.599
5 10 48.215 284.038 15 47.475 289.386
13 46.481 14 47.460
30 49.337 31 48.486
29 39.158 10 49.219
11 40.112 13 47.847

37
2. The amount of LSF is the indication of the suitable candidate
for the placement of shunt capacitors.
33 Bus
Loading
Condition
10% Redu. 10% Inc. 30% Inc.
Loss Sensitivity
Factor
weak Bus
Loss Sensitivity
Factor
weak Bus
Loss Sensitivity
Factor
weak Bus
11.0 15 19.0 15 17.7 15
6.75 10 5.45 13 15.5 14
2.75 14 2.92 10 3.35 31
2.06 30 1.90 29 2.53 10
0.49 13 0.55 12 0.62 13
0.39 32 0.46 32 0.47 30

0
75
150
225
300
375
1 2
3
4
5
Losses
No. of Capacitor
Losses (kW)
Base Case
Light Load
Medium Load (10%)
Medium Load (20%)
Heavy Load (30%)
Heavy Load (40%)
38

0
75
150
225
300
375
450
1 2
3
4
5
losses
No. of Capacitor
Losses (kW)
Base Case
Light Load
Medium Load (10%)
Medium Load (20%)
Heavy Load (30%)
Heavy Load (40%)
39

0 50 100 150 200
154
156
158
160
162
164
LossesMinimum(kW)
40

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.
41

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Genetic Algo. for Radial Distribution System to reduce Losses

Genetic Algo. for Radial Distribution System to reduce Losses

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