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Distribution System Operation Optimization through Capacitor Size Allocation by Genetic Algorithm for

69-bus System

ByYifang Ni (Electrical Engineering)

Faculty Advisor:Dr. Robert O’Connell, PhD, PE (Electrical and Computer Engineering)

ECE 4995 Undergraduate Honor Research Project Report

Department of Electrical and Computer Engineering

University of Missouri - Columbia

Columbia, Missouri

November 22, 2014

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Abstract

This paper shows use of MATLAB to solve a research project. In my research

project, I worked on capacitor optimization by analyzing the data on minimum power

loss, minimum voltage, number of switching operations and system load balancing

index, mainly focus on minimum power loss for light load, average load and heavy

load. In this paper, a detailed discussion of capacitor optimization will be included.

Results are provided by using the genetic algorithm.

Introduction

There are three main advantages to using capacitors in power loads: first,

capacitors reduce power loss in the load; second, they can raise voltages; and third,

they can be used for power factor correction. Therefore, capacitors play an important

role in power distribution systems. My research project is distribution system

operation optimization through capacitor size allocation by genetic algorithm using

MATLAB for a 69-bus test system (figure 1).

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Figure 1, 69-bus test system [8]

Genetic Algorithm and Code

Genetic Algorithm

My research project is based on the Genetic Algorithm method. The Genetic

Algorithm method can be divided into two categories: single function and multi-

objective functions.  The single function “is formulated as a single objective

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regardless of the number of objects and constraints” [1]. Multi-objective functions

generate a set of solutions based on non-dominated sorting. The steps of using the

genetic algorithm always includes codification of individuals (chromosomes),

population generation, evaluation (fitness) and crossover, mutation, and selection. [1]

Code

The following is the code I wrote to change the capacitor value at bus 65 in figure 1

from 0 to 1 mega-volt-amps reactive (MVAR) in steps of 0.1 MVAR, then got 11

solutions and compare the 11 minimum power loss values and output the minimum

power loss value form the 11 solutions and its corresponding capacitor size. All the

code belongs to file NDSGA2t.m in [2].

[NDSGA2t.m.]

The following code is used to change the average load to light lode and heavy load.

The code belongs to file Data_69_2.m.

[Data_69_2.m]

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Results and Discussion

Capacitor size = 0 MVAR analysis

1st run

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Figure 2, capacitor size = 0 MVAR solutions

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Figure 3, capacitor size = 0 MVAR analysis

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For my research project, I used MATLAB to run the program and analyze the data.

The program gives random solutions (sets of possible selections) for each run but

there are always 33 to 35 of them. The above figures are the data when capacitor size

is equal to 0 MVAR for one run. Figure 2 is the output solutions of tie switches,

power loss, minimum voltage, number of switching operations, and system load

balancing index.

The first row in figure 3 shows the maximum values of power loss, maximum

minimum voltage, maximum number of switching operations and maximum system

load balancing index. The second row are the minimum values for power loss,

minimum voltage, number of switching operations, system load balancing index. The

third line to last line values are calculated by using the actual value minus minimum

value divide by maximum value minus minimum value. The equation is:

(Xactual – Xminimum) / (Xmaximum – Xminimum)

For example, in the third row the first value 0 is calculated by (0.09959-0.09959) /

(0.22493-0.09959) = 0. The last column in figure 3 is the sum value of the values on

the first four columns. For example, 0 + 0.000596 + 0.6 + 0.514465 = 1.115062. If we

care about all four objects, the smaller the sum value is, the better the solution is.

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2nd run

Figure 4 and figure 5 are analysis of 0 MVAR, same process as first run.

Figure 4, capacitor size = 0 MVAR solutions

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Figure 5, capacitor size = 0 MVAR analysis

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Power loads

Results vary with the size of the load. In this section, average, light and heavy loads

are compared.

Average load

The following data is the mode results for each capacitor value after running

MATLAB ten times.

average load modesize min power lossloss (MW)

0 0.099590.1 0.096730.2 0.094780.3 0.093730.4 0.093560.5 0.094260.6 0.095790.7 0.09206 middle0.8 0.094370.9 0.09436

1 0.0951

Table 1, mode results for each capacitor value

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.088

0.09

0.092

0.094

0.096

0.098

0.1

0.102

Series1

Figure 6, plot of the data in table 1

In order to get a smooth curve, I ran the program five more times. The minimum

power loss mode value for the 0.7 MVAR is then 0.09513 MW.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.09

0.092

0.094

0.096

0.098

0.1

0.102

Figure 7, plot of the data in table 1 with new value at 0.7 MVAR

In this case, when capacitor size is equal to 0.4 MVAR, it gives the minimum power

loss of 0.09356 MW. Its mode corresponding tie switches are 69, 70, 14, 56 and 61.

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Light load (0.5 average)

The following data is the mode result for each capacitor value after running

MATLAB ten times.

light load modesize min power lossloss (MW)

0 0.023710.1 0.022570.2 0.022290.3 0.022850.4 0.022430.5 0.022660.6 0.023580.7 0.025180.8 0.2527 middle0.9 0.02733 middle

1 0.3398 middle

Table 2, mode results for each capacitor value

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Figure 8, plot of the data in table 2

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If we ignore the values at 0.8 MVAR, 0.9 MVAR and 1.0 MVAR, we get figure 7.

From figure 7, when capacitor size is equal to 0.2 MVAR, it gives the minimum

power loss of 0.02229 MW. Its mode corresponding tie switches are 69, 70, 14, 56

and 61.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70.0205

0.021

0.0215

0.022

0.0225

0.023

0.0235

0.024

0.0245

0.025

0.0255

Figure 9 plot of the data in table 1 except the last three values

Heavy load (1.6 average)

The following data is the mode results for each capacitor size after running MATLAB

ten times.

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heavy load modesize min power lossloss (MW)

0 0.272310.1 0.266850.2 0.262650.3 0.259430.4 0.257160.5 0.255820.6 0.255410.7 0.255890.8 0.257250.9 0.25947

1 0.26252

Table 3, mode results for each capacitor value

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.245

0.25

0.255

0.26

0.265

0.27

0.275

Series1

Figure 10, plot of the data in table 3

From the data, we can get a conclusion that when capacitor size is equal to 0.6

MVAR, it gives the minimum power loss 0.25541 MW for heavy load (1.6). Its mode

corresponding tie switches are 69, 70, 12, 57 and 73.

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Summary and Conclusion

This report discusses and analyzes the data for distribution system operation

optimization through capacitor size allocation by genetic algorithm for the 69-bus test

System. I analyzed the 69-bus system for three different load: light load (0.5), average

load (1.0) and heavy load (1.6). For light load, when capacitor size is equal to 0.2

MVAR, it gives the minimum power loss 0.02229 MW. Its mode corresponding tie

switches are 69, 70, 14, 56 and 61. For average load, when capacitor size is equal to

0.4 MVAR, it gives the minimum power loss 0.09356 MW with following mode tie

switches: 69, 70, 14, 56 and 61. For heavy load, when capacitor size is equal to 0.6

MVAR, it gives the minimum power loss 0.25541 MW. Its mode corresponding tie

switches are 69, 70, 12, 57 and 73. Thus, the optimization capacitor size and tie

switches depends on the type of the load.

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References

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