application of genetic algorithm for the reactive loss

First International Power and Energy Coference PECon 2006November 28-29, 2006, Putrajaya, Malaysia

Application of Genetic Algorithm for theReduction of Reactive Power Losses in Radial

Distribution SystemPerumal Nallagownden, Lo Thin Thin, Ng Chin Guan, Che Mat Hadzer Mahmud

Abstract- Power losses in distribution system havebecome the most concerned issue in power losses analysisin any power system. In the effort of reducing power losseswithin distribution system, reactive power compensationhas become increasingly important as it affects theoperational, economical and quality of service for electricpower systems. This paper presents the application ofgenetic algorithm approach for reactive power lossreduction in radial distribution system. IEEE 34-busStandard Test System is used together with the ERACSand MATLAB as powerful tools for the analysis andsimulation work. ERACS is used to perform load flowanalysis while MATLAB is used for the identifilcation ofcapacitor current via GAtool, and algorithm for thecalculation of loss savings, its particular capacitor size andlocation. The result is then compared with the heuristicsearch strategies to evaluate the performance of geneticalgorithm.

Index Terms- Capacitor Placement, Genetic Algorithm,kW/kVAR Ratio, Load Flow Analysis, Reactive Power,Voltage profile

I. INTRODUCTION

onsumer loads impose active and reactive power demand,C depending on their characteristics. Active power is

converted into useful energy whereas reactive power mustbe compensated. This is to guarantee efficient delivery ofactive power to loads, thus releasing system capacity, reducingsystem losses and improving system power factor and busvoltage profile. The achievement of these aims depends on thesizing and allocation of capacitors. [1] Malaysia has relativelyhigh power losses as compared to other developed countries.Hence, in this paper, Genetic algorithm has been considered asan approach to tackle the problem of optimal capacitorplacement in radial distribution systems. In this optimalcapacitor placement algorithm, two considerations namelyminimizing capacitor installation cost and minimizing systemlosses need to be taken into account in order to achieve theobjective.

II. LITERATURE REVIEW

A. Overview ofGenetic AlgorithmGenetic algorithm is a search algorithm based on themechanics of natural selection and natural genetics [3],provides a global optimal solution for non-linear problems [4].It considers a population of chromosomes as potential solutionto a given problem. In genetic algorithm model, chromosomesare composed of genes for various characteristics to beoptimized and can be binary strings of fixed length. Eachchromosome represents a point in the search space and offersconvenient way of handling constraints.

B. Concept ofGenetic AlgorithmThe genetic algorithm is a method for solving optimizationproblems that is based on natural selection, the process thatdrives biological evolution. The genetic repeatedly modifies a

population of individual solutions. At each step, the geneticalgorithm selects individuals at random from the currentpopulation to be parents and uses them to produce the childrenfor the next generation. Over successive generations, thepopulation "evolves" toward an optimal solution. You can

apply genetic algorithm to solve a variety of optimizationproblems that are not well suited for standard optimizationalgorithms, including problems in which the objective functionis discontinuous, non-differentiable, stochastic, or highly non-

linear [4].Genetic Operators

1) Selection: Select two parent chromosomes from a

population according to their fitness. Chance for the betterfitness individual will be selected is higher to produce the nextgeneration with the higher fitness value. [6]2) Crossover: The crossover operator involves the exchangeof genetic material between chromosomes (parents), in orderto create new chromosomes (offspring). Various forms of thisoperator have been developed. The simplest form, single pointcrossover, is shown as Fig 1. This operator selects twoparents, chooses random position in the genetic coding, andexchanges genetic information to the right of this point, thuscreating two new offspring. [6]

Perumal, Lo Thin Thin and Ng Chin Guan are from Universiti TeknologiPetronas.(e-mail:perumal petronas.com.my)C.M.Hadzer is a lecturer at USM(e-mail:cmhadzerAeng.usm.my)

0lo1olI11001

IO11001 1

Fig. 1. Single point crossover

1-4244-0273-5/06/$20.00 ©2006 IEEE

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Authorized licensed use limited to: QASSIM UNIVERSITY. Downloaded on July 11,2010 at 14:06:49 UTC from IEEE Xplore. Restrictions apply.

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2) Mutation: The mutation operator, in its simplest form,makes small, random, changes to a chromosome. For a binaryencoding, this involves swapping gene 1 for gene 0 with smallprobability for each bit in the chromosome, as illustrated inFig 2.

01010110 - * 01' 10110

Fig. 2. Binary mutation operators

III. ALGORITHMS

Genetic algorithm is a very powerful in performing varioussimulation works due to its distinctive characteristics asdiscussed. This project focuses greatly in the development ofgenetic algorithm for the reduction of reactive power losses.The strategy behind the idea of reduction of reactive power isto capitalize the superior features of genetic algorithm inperforming the mathematical simulation of a radial distributionnetwork. The fundamental mathematical expressions ofreactive power become the input to the genetic algorithm toolin this project. The mathematical expressions [2] involved inthis project will be discussed in detail in the following sectionof the report.The total power losses of a distribution system having

n number of branches can be expressed as:

current I,. For a radial distribution system, the insertion ofcapacitor will only affect the reactive component of current of

branch set o. Hence, the new reactive current Inew of the ith

branch is expressed as:

I new =ri+_DII (4)Where

Di=l

D 0, otherwiseThe compensated reactive power is represented as the

following:n

QL = (Iri+DI)Xii=l

Computing the overall saving as expressed.S =QL -QL

n n

= Y J2iXi-I + D IC)2xii=l i=l

n

i=l

(5)

(6)

n22

Ir2Xi- E (Iri + 2IriD IC + DiIC )Xii=l

n

PLTOTAL = ii=l

n

(1) =-E(2,riDiIc + Dic )xii=l

This power loss can be further associated into twocomponents by separating the current, I into two namely theactive branch, Ia and I, reactive branch. The individual powerlosses namely the active power loss and reactive power lossare given by (2a) and (2b).

n

PL=2

EI Ri (2a)i=ln

QL =1k1Xi (2b)i=l

The active and reactive components of branch currents arecomputed as:

Ia = IcosO (3a)Ir =I sin 0 (3b)

WhereI= magnitude of current0 = angle of current

Assume that a single source radial distribution system withn branches. A capacitor is to be placed at bus m with a is theset of branches connected between the source and capacitorbus.Assume that a capacitor is inserted at bus 21, the set of a

will then consists of braches 1, 2, 3, 4, 5, 16, 17, 18, 19, 20and 21. The capacitor that is inserted draws a reactive

(7)

From expression (6), further simplification on the expressionarrives at (7).

The typical method of locating the optimum value of capacitorcurrent I, is achieved by performing a differentiation onto

(7). The next step will be working on the differentiation of (7)to obtain an expression of the maximum saving per capacitorcurrent.as n

,i =-2y (DiIri + DiiC )Xi = 0 (8)

In order to obtain the individual capacitor current at each ofthe branches on IEEE- 34 bus, it is necessary to equate themaximum saving per capacitor current to zero

n

-2Z(DiIri +DJIC)Xi= 0i=1

n

Z DiICXii=l

n

-E Di Iri Xii=l

(9)

The following steps bring capacitor current I, to one side in

order to compute the new capacitor current new reactivecurrent Inew of the ith branch as in 4.4.


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n

E, Di Iri Xi Y Iri Xi

IC = ii_ _a= _ (10)cn

EDiXi ExiHowever by capitalizing the powerful features of MIATLABGATool, finding the optimum values of capacitor current

ICcan be performed by using (7). MATLAB GATool isinitially designed to locate the minimum value of anymathematical expression. In the case of interest, in order tolocate the individual capacitor current IC value at whichmaximum savings is achieved, the entire expression (7) needto be negated. This allows the computation of capacitor current

IC within the multidimensional expression of the total reactive

power saving. The computed set of capacitor currents IC are

optimized to obtain the maximum saving of reactive power.The capacitor current IC which produces the highest saving isthen used to compute the optimal capacitor size. This capacitoris then inserted to the respective branch in IEEE 34 bus wherethe capacitor current Ic is calculated to produces the highestsaving. The optimal capacitor size is computed using (11).

QC = VmIC (1 1)

1) Crossover rate [71

Crossover rate should be high generally, about 80%-95%.(However some results show that for some problemscrossover rate about 60% is the best.)

2) Mutation rate

On the other side, mutation rate should be very low. Bestrates seem to be about 0.5%-l%. [7]

3) Population size

It may be surprising that very big population size usuallydoes not improve performance of GA (in the sense ofspeed of finding solution). Good population size is about20-30 [7]

4) Selections

Basic roulette wheel selection is used.

5) Encoding

Encoding depends on the problem and also on the size ofinstance of the problem. [7]

6) Crossover and mutation type

IV. SYSTEM FUNCTIONALITYOperators depend on the chosen encoding and on theproblem. [7]

A. STOPPING CRITERIAThe genetic algorithm uses five criteria to decide when to

stop the algorithm automatically. By setting the stoppingcriteria, the algorithm will stop if any one of the conditions ismet. [5]1) Generations - The algorithm reaches the specified numberof generations.2) Time - The algorithm runs for the specified amount of timein seconds.3) Fitness limit - The best fitness value in the currentgeneration is less than or equal to the specified value.4) Stall generations - The algorithm computes the specifiednumber of generations with no improvement in the fitnessfunction.5) Stall time limit - The algorithm runs for the specifiedamount of time in seconds with no improvement in the fitnessfunction.

V. RESULTS AND DISCUSSION

A. Load Flow AnalysisUtilizing the ERACS software, the load flow analysis is

conducted. The results are produced giving the values of totalactive and reactive power losses. Besides, the value interestedfrom the load flow analysis is the bus voltage profile forfurther calculation and simulation of loss savings and capacitorsizing using the MATLAB.The IEEE- 34 bus system network constructed for

simulation of voltage profile is as shown in Fig. 3. It is noticedthat the active power losses is 0.222MW and the reactivepower losses is 0.065MVAR and its voltage profile is withinthe acceptable value.

B. Parameters ofGenetic AlgorithmThere are some basic recommendations in deciding to

implement genetic algorithm. There is no general theoryavailable that helps to tune Genetic Algorithms parameters forany specific problems. Recommendations are often results ofempiric studies of genetic algorithms that were oftenperformed on binary encoding only. [7]


79

Capacitor Size, kVar vs Bus Number

LoadfIoviPLO O22MQLO a05M

6000-

5000-

4000-

3000-

. 2000

0100

-1 000

-2000

-3000

-4000

Fig. 3. IEEE 34-Bus Test System Simulation Setup

B. GA ToolGAtool is utilized to obtain the capacitor current, Ic needed

for the further simulation of the loss saving. Hence, thefunction is written in the M-file format to obtain the simulationresult utilizing population of 20.

C. MATLAB

The source code of the MATLAB programming for thecalculation of loss saving at each branch and its capacitorsizing is written. The generated output of the program showsthat the maximum loss saving is 14.92 kW when a shuntcapacitor with a size of 914.34kVAR is placed at bus 21.

Fig. 4 and Fig. 5 summarize the loss saving in kW at everybus and its corresponding capacitor size for insertion.

Loss Saving, kW vs Bus Number

Bus Number

Fig. 5 Capacitor Size, kVar vs Bus Number

D. SINGLE CAPACITOR PLACEMENTFor, single capacitor insertion, insert 1 capacitor, then the

load flow is run again from the modified system to obtain thesecond bus where the second capacitor need to be inserted. a914.34kVAR capacitor is inserted at bus 21 in the original 34-bus system network. Then, run the load flow again to obtainnew real and reactive power losses. TABLE 1 summarized theresult of real and reactive power losses before and aftercompensation.

TABLE 1POWER LOSSES BEFORE AND AFTER COMPENSATION FOR 1

CAPACITOR INSERTION

From TABLE 1, it is noticed that the total real power issaved by 37kW and the reactive power is saved by 1 lkVar.The above method is repeated until the power losses cannot

be saved. Hence, only 2 capacitors are to be inserted in thesystem.From TABLE 2, the total loss savings after the insertion of 2

capacitors is 50kW.

BFg N4ib u m

Fig. 4 Loss Saving, kW vs Bus Number


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TABLE 2LOSS SAVING AFTER 2 SINGLE CAPACITOR INSERTIONS

Total Total TotalBs Cap Real Recie Loss Total

No Loc Size Power Power Savvng,kVar Losses, Losses, W k

kW kV ar

0 - - 222 65 - -

1 21 914.34 185 54 37 372 20 940.17 172 50 13 50

TABLE 4COMPARISON OF SINGLE AND MULTIPLE CAPACITOR INSERTIONS

The extra advantage of utilizing shunt capacitor insertion isthat it helps to improve the voltage profile of the entire system.This is due to the current flowing in the line is decreased dueto flow of less reactive component branch current, the voltagedrop will decrease which in turn improve the voltage profile.

E. MULTIPLE CAPACITOR PLACEMENT

For multiple capacitor insertion, the capacitors are insertedsimultaneously to reduce the reactive power losses. For thissimulation, 2 capacitors are inserted simultaneously to thesystem, which are bus location 21 and 20 with the capacitorsize of 914.34kVar and 1351.1kVar respectively. The totalreal and reactive power loss saved is 48kW and 15kVarrespectively. TABLE 3 summarized the result after themultiple capacitor insertion.

TABLE 3LOSS SAVING AFTER MULTIPLE CAPACITOR INSERTIONS

F. COMPARISONS

The total loss saving contribute from both single andmultiple capacitor insertions is 22.52% and 22.07%respectively. With that, the result is further compared todetermine the cost effectiveness of each method utilizing thekilo-watt per kilo-volt-amps-reactive ratio (kW/kVAR).Utilizing the same method, the Genetic Algorithm will also becompared with the existing method namely, Heuristic SearchStrategies. The higher the ratio, the more efficient the methodwould be. The higher the ratio, more saving is obtained byusing the same capacitor size.

2) Genetic Algorithm (GA) and Heuristic Search Strategies(HSS)TABLE 5 and TABLE 6 show the comparison result for

both Genetic Algorithm and Heuristic Search Strategies withsingle and multiple capacitor insertions respectively. AlthoughHeuristic Search Strategies is found to have total loss saving of24.18% and 23.82% respectively for single and multiplecapacitor insertions as compare to 22.52% and 22.07%respectively that of Genetic Algorithm. However, GeneticAlgorithm is identified to be more cost effective. It is becausethe kW/kVAR ratio is higher for which 2.696 as compared to2.163 for single and multiple capacitor insertion respectivelyfor Genetic Algorithm as compare to 1.9885 and 2.158 ofHeuristic Search Strategies. Hence, that shows that GeneticAlgorithm is more cost effective in both single and multiplecapacitor insertions.

TABLE 5COMPARISON OF SINGLE CAPACITOR INSERTION FOR GA AND HSS

No Bus Loss Savings Capacitor 100(kW) Size (kW/lVAR)

(kVAR)

GA HSS GA HSS GA HSS1 21 37 41.07 914.34 14002 20 13 10.64 940.17 7503 1.17 3004 0.81 250

TABLE 6COMPARISON OF MULTIPLE CAPACITOR INSERTION FOR GA & HSS

No Bus Loss Savings Capacitor 100(kW) Size (kW/lVAR)

(kVAR)

T |GA HSS GA HSS GA HSS1 21 - - 914.34 1400 - -

2 20 - - 1351.1 750 - -

3 - 300 - -

Tal 49 52.88 2265.1 2450 3 8

1) Single and Multiple Capacitor InsertionsTABLE 4 shows the comparison result for both single and

multiple capacitor insertions. Single capacitor placement isidentified to be more cost effective. It is because thekW/kVAR ratio is higher for single capacitor insertion whichis 2.696 as compared to 2.163 that of the multiple capacitorinsertions. Hence, it indicates that less capacitor size, thesystem is able to contribute to the same amount of loss saving.

Bus Loss Savings Capacitor 100(kW/kVAR)Loc (kW) Size

Single Multiple Single Multiple Single Multiple

21 37 - 914.34 914.34 - -

20 13 49 940.17 1351.1 - -

Total 50 49 1854.5 2265.1 2.696 2.163

Total Total TotalBs Cap Real Recie Loss Total

No Lc Size Power Power Saving, Saving,kVar Losses, Losses, W k

kW kV ar

0 222 651 21 914.34 - - - -

2 20 1351.1 173 50 49 49


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VI. CONCLUSION

As a conclusion, the total loss saving for both single andmultiple capacitor placements is 22.52% and 22.07%respectively. Single capacitor insertion is more cost effectiveas compare to multiple capacitor insertion because it havehigher kW/kVAR ratio which is 2.696 and 2.163 respectively.

Heuristic Search Strategies has total loss saving of 24.18%and 23.82% respectively for single and multiple capacitorinsertions while GA has 22.52% and 22.07%. However,Genetic Algorithm is identified to be more cost effectivebecause it has higher kW/kVAR ratio which is 2.696 and2.163 for single and multiple capacitor insertion respectivelyfor while 1.9885 and 2.158 for Heuristic Search Strategies

ACKNOWLEDGMENT

Lo Thin Thin would like to express the greatest gratitude toMr Tan Khong Hon for his time in sharing his previous work.

REFERENCES

[1] Carlos Henggerler Antunes, Carlos Barrico, Alvaro Gomes, DulceFernao, Antonio Gomes Martines, "An Evolutionary Algorithm forReactive Power Compensation in Radial Distribution Networks"

[2] Than Khong Hom "An Integrated Approach to the Reduction ofReactive Power Losses in Radial Distribution Network"

[3] Goldberg, David E. (David Edward), "Genetic Algorithms in Search,Optimization and Machine Learning", 1989 Addision WesleyLongman, Inc

[4] K.S.Rama Rao, Chew Hong Thye (2005), "Genetic Algorithm forDesign Optimization ofa Permanent Magnet DC Micrometer "

[5] Mark A. Abramson "Genetic Algorithm and Direct Search Toolbox",The MathWorks, Inc

[6] P.J. Fleming, R.C. Purshouse (May 2001), "Genetic Algorithms inControl System Engineering"

[7] Marek Obitko, 1998, " Introduction to Genetic Algorithm", Avaiable:

[8] Jayaraman, C, "What is reactive power", Kochi Refineries Ltd[9] V.C. Veera Reddy and Jamilah Karim, June 2004, "Multiple Shunt

Capacitor Placement to Minimize Losses in Distribution System", M.sc.Thesis, Universiti Sains Malaysia (USM), Malaysia, pg 10-12,52-57

[10] Taylor, CW, June 1999, "Explaining Reactive Power", IEEE Spectrum,Volume 36 Number 6

[11] V.C. Veera Reddy and Padmalalitha, "Loss Reduction in DistributionNetwork by Capacitor Placement"

[12] Haque M.H., September 1999, " Capacitor Placement in RadialDistribution System for Loss Reduction", IEE Proceedings -

Generation, Transmission and Distribution, vol. 146, pg 501-505[13] Chis. M., Salama M.M.A, Jayaram. S., May 1997, " Capacitor

Placement in Distribution Systems Using Heuristic Search Strategies",IEE Proceedings - Generation, Transmission and Distribution, vol. 144,No.3

Perumal Nallagownden obtained his B.E(Hons) in Electrical & ElectronicsEngineering from Portmouth Polytechnic, U.K and M.Sc from University ofWales, U.K. He is a Senior Lecturer attached to the Electrical & ElectronicsEngineering Programme of Universiti Teknologi PETRONAS. Hisemployment experience were at Polytechnic Ungku Omar and Conso LightSdn.Bhd. His special area of interest is electrical power system. Ir. N.Perumal is a member of the Institution of Engineers Malaysia and is aProfessional Engineer registered with the Board of Engineers Malaysia.

Lo Thin Thin was born in Kuching, Sarawak,Malaysia in 1982. She is currently a final year studentof Universiti Teknologi PETRONAS, Perak, pursuingB.E(Hons) in Electrical & Electronics Engineering.She is majoring in Power System Engineering and hermain interest is power systems. She has 8 months ofindustrial experience in PETRONAS LNG Complexdduring her internship in 2005.

Ng Chin Guan was born in Johor, Malaysia in 1982.He obtained his B.E(Hons) in Electrical & ElectronicsEngineering from Universiti Teknologi PETRONAS,Perak. His specialization is in Instrumentation &Control and his main interests are solution delivery,power systems, power electronics, plant process

_ l control, instrumentation engineering, semiconductor,microcontroller and knowledge management. He wasworking as a design and development engineer in

package innovation and design centre of a semiconductor company. He iscurrently working at PETRONAS LNG Complex as an instrument projectengineer.

Che Mat Hadzer Mahmud received his B.sc and Ir degrees in electronicengineering from Institute Technology Bandung Indonesia in 1976. After twoyears of working experience with Radio and TV Malaysia, he joined USm asfellow Academic Staff Training Scheme in 1978. He then started hisgraduate studies in Salford University for M.Sc degree and moved to UMISTin 1979 for his Ph.D degree in electronic control engineering and controlengineering respectively. He is a Associate Professor at the School ofElectrical & Electronic Engineering at the Engineering Campus, NibongTebal. Che Mat Hadzer is the Program Chairman of Electronic Engineering.His research interest includes Electronic Control Engineering, Power Qualityand Renewable Energy.


application of genetic algorithm for the reactive loss

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