Research ArticleOptimal Battery Sizing in Photovoltaic Based DistributedGeneration Using Enhanced Opposition-Based Firefly Algorithmfor Voltage Rise Mitigation

Ling Ai Wong Hussain Shareef Azah Mohamed and Ahmad Asrul Ibrahim

Faculty of Electrical Engineering and Built Environment Universiti Kebangsaan Malaysia 43600 Bangi Malaysia

Correspondence should be addressed to Ling Ai Wong ling ai89hotmailcom

Received 25 February 2014 Revised 7 May 2014 Accepted 29 May 2014 Published 19 June 2014

Academic Editor Zhihua Cui

Copyright copy 2014 Ling Ai Wong et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents the application of enhanced opposition-based firefly algorithm in obtaining the optimal battery energy storagesystems (BESS) sizing in photovoltaic generation integrated radial distribution network in order tomitigate the voltage rise problemInitially the performance of the original firefly algorithm is enhanced by utilizing the opposition-based learning and introducinginertiaweight After evaluating the performance of the enhanced opposition-based firefly algorithm (EOFA)with fifteen benchmarkfunctions it is then adopted to determine the optimal size for BESS Two optimization processes are conducted where the firstoptimization aims to obtain the optimal battery output power on hourly basis and the second optimization aims to obtain theoptimal BESS capacity by considering the state of charge constraint of BESS The effectiveness of the proposed method is validatedby applying the algorithm to the 69-bus distribution system and by comparing the performance of EOFA with conventionalfirefly algorithm and gravitational search algorithm Results show that EOFA has the best performance comparatively in termsof mitigating the voltage rise problem

1 Introduction

Recently distributed generation (DG) with green energysources such as photovoltaic (PV) generation has drawn alot of attention worldwide since they are clean environment-friendly and reliable However there are some issues to beresolved before the installation of PV-based DG (PVDG)in the distribution networks due to the intermittent poweroutput from PV systems The PVDG is usually uncontrolledand it depends greatly on solar radiation The amount ofpower generation increases or decreases irrespective of theload demand at a particular time instead it is depending uponthe availability of solar energy Therefore voltage fluctuationproblem occurs when the load demand is not in line withthe amount of power generated from PVDG Sudden voltagerise or voltage drop in the network can create undesireddamages which can be costly to the users Therefore somesolutions have been proposed in the literature to alleviatevoltage fluctuation problem A method using load control toregulate voltage on DG embedded network is proposed by

Scott et al [1] Besides voltage regulation of PV generatorcan also be controlled by introducing a series reactor in theservice line [2] Meanwhile battery energy storage system(BESS) can be one of the good options in mitigating thevoltage rise problem [3 4] Nevertheless high installationcost is required for BESS installation at every bus in thenetwork Thus it is crucial to obtain the optimal location forBESS in the system

Obtaining the optimal size for BESS is also importantsince the bigger the capacity of the BESS the more itcosts Optimal sizing of BESS helps to obtain a suitableBESS size for the system to maintain voltage regulation Inthe literature different approaches have been developed indetermining optimal size for BESS Shen [5] obtained theoptimal combined size for PV and BESS for standalone PVsystem by calculating the loss of power supply probability fordifferent size combinations of PV and BESS Meanwhile thechance constrained programming approach and the conceptof design space were used by Arun et al [6] Here a sizingcurve that relates both PV rating and the corresponding

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 752096 11 pageshttpdxdoiorg1011552014752096

2 The Scientific World Journal

minimum BESS capacities was plotted Brekken et al [7]proposed sizing and control methodologies for zinc-bromineBESS Khatib et al [8] utilized theMATLAB curve fitting toolto fit the sizing curve obtained from a standalone PV systemenergy flow and then derived a formula for optimal sizing ofPV andBESS Furthermore Ru et al [9] determined the BESSsize for grid-connected PV system by optimizing the BESScost and the net power purchase from the grid

In recent years heuristic optimization techniques havegained a lot of attention from researchers due to theirbetter performance compared to mathematical optimizationtechniques in coping with large and complex optimizationproblems There are different types of heuristic optimizationtechniquesOne of the early techniqueswas genetic algorithm(GA) [10] followed by other techniques such as ant colonyoptimization (ACO) [11] particle swarm optimization (PSO)[12] artificial bee colony algorithm (ABC) [13] gravitationalsearch algorithm (GSA) [14] firefly algorithm (FA) [15]artificial plant optimization algorithm (APOA) [16 17] arti-ficial physics optimization (APO) [18] shuffled frog leapingalgorithm (SFLA) [19] and membrane computing [20]Vrettos and Papathanassiou [21] applied GA in optimizingthe size of the hybrid system consisting of wind turbinesPV and BESS system The multiple-objective function inthis work minimizes the generation cost and maximizes therenewable energy source penetration Chen et al [22] alsoapplied GA to calculate the optimal energy storage size byoptimizing the investment cost model which is a nonlinearobjective function Apart from GA the ABC algorithm wasused to obtain the optimal BESS capacity in order to mitigatethe voltage rise problem in the PV embedded distributionnetwork [23]

However metaheuristic optimization algorithms havethe problem of being trapped in local optimum and slowconvergence rates due to their random searching processThis leads to the development of hybrid algorithms thatcan overcome these issues effectively FA is chosen for theoptimization process in this current study since it is relativelysimple and easy to implement However like most of themetaheuristic optimization algorithms FA also has its owndisadvantages In order to further improve the performanceof original FA in terms of convergence rate the opposition-based learning [24] is integrated into FA while the idea ofinertia weight FA [25] is also incorporated at the same timeto improve the ability of FA to escape from local optimumIn this paper enhanced opposition-based firefly algorithm(EOFA) is proposed to determine the optimal size of BESS ina PVDG integrated radial distribution network formitigatingthe voltage rise problem

2 Formulation of Optimization Problem

Asmentioned earlier the root cause of voltage rise in a PVGDintegrated system is the intermittent nature of power orcurrent injections at PVDG bus This problem can be solvedby using BESS as it has the ability to act as a power sourceor sink with the help of its bidirectional power converterThe BESS will operate in charging mode and as a current

sink if there is excess output power from PVDG while it willdischarge and act as a current source if more power is neededto maintain the voltage profile of the system The BESS isset to be charged when the PVDG is active while at nightwhen PVDG is idle the BESSwill discharge to a certain presetstate of charge In this study PVDG is modeled as a currentsource while BESS is modeled as a current source or sinkEOFA is first used to obtain the optimal average hourly BESSactive output power for the PVDG integrated system In thisoptimization the solution set (searching agent) is the BESSpower while the purpose of the optimization is to minimizethe voltage deviation of the PVDG bus by using the optimalBESS power value in order to maintain the voltage within095 pu to 105 pu rangeTherefore the objective function119891

1

can be expressed as

1198911= min

1003816100381610038161003816119881119894 (119905) minus 1051003816100381610038161003816 if 119881

119894(119905) gt 105

1003816100381610038161003816119881119894 (119905) minus 0951003816100381610038161003816 if 119881

119894(119905) lt 095

(1)

where 119881119894(119905) is the per unit (pu) value for voltage at bus 119894

at hour 119905 In this study it is assumed that the voltages areconstant at a particular hour of the day However it can beextended for shorter intervals for more accurate results

After the optimal BESS power values for each hour areobtained the state of charge (SOC) of the BESS for each hourcan be calculated as [26]

SOC = 100(1 minusint 119868bs119889119905

119876) (2)

where 119868bs is the current for the BESS 119905 is the time in hourand 119876 is the BESS capacity in Ampere hour (Ah) When theSOC reaches its maximum limit (SOCmax) or minimum limit(SOCmin) the BESS will be turned off temporarily until itcharges or discharges again Considering the SOC optimalsize or capacity of the BESS can be decided again by using theoptimization algorithm The performance of BESS increaseswhen the number of BESS inactive hours due to the SOCconstraint is minimized In this optimization the solutionset is the possible solution for BESS capacity The optimalBESS capacity should give the minimum number of off-time or inactive hours Considering this criterion the secondobjective function 119891

2 to obtain the size of the BESS can be

defined as

1198912= min (119873bs

idle) (3)

where 119873bsidle is the total number of time BESS is turned off

when SOC reaches either SOCmax or SOCmin

3 Enhanced Opposition-Based FireflyAlgorithm (EOFA)

31 Overview of Original FA FA is a heuristic optimizationalgorithm based on the flashing characteristics of fireflies[15] The main functions of the flashes are to attract themating partners as well as to attract the potential prey FA isillustrated based on three rules where firstly all fireflies are

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of the same sex and thus the attraction between fireflies isindependent regardless of their sex Secondly the attraction isproportional to the brightness of the fireflies and it decreaseswhen the distance between the fireflies increases In otherwords the brighter fireflies will attract the less bright onesThe fireflies will move randomly if all of them have the samebrightnessThirdly the brightness of the fireflies is decided bythe landscape of the objective function

Two main parts in FA are the variation of light intensityand the attractiveness between the firefliesThe attractivenessof the fireflies is affected by the light intensity (brightness)which then is related to the objective functionThe attractive-ness 120573(119903) of a firefly can be defined as [15]

120573 (119903) = 120573119900119890minus1205741199032

(4)

where120573119900is the attractiveness at 119903 = 0 120574 is the light absorption

coefficient and 119903 is the Cartesian distance between twofireflies as shown in [15]

119903119894119895=10038171003817100381710038171003817119909119894 minus 119909

119895

10038171003817100381710038171003817 =radic119889

sum119896=1

(119909119894119896

minus 119909119895119896)2

(5)

where 119894 and 119895 represent two different fireflies at 119909119894and 119909

119895

while 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of 119894th firefly Meanwhile the movement of the firefly 119894 whichis attracted by the brighter firefly 119895 is defined in [15]

119909119894= 119909119894+ 120573119900119890minus1205741199032

(119909119895minus 119909119894) + alpha(rand minus

1

2) (6)

where the second term is due to the attraction and the thirdterm is due to the randomization In the third term alphais the randomization parameter while rand is the randomnumber generator uniformly distributed between zero andone In each following iteration alpha decreases with adecreasing factor delta as shown in (7)The flowchart for FAis shown in Figure 1

alpha (119905 + 1) = alpha (119905) times delta 0 lt delta lt 1 (7)

FA can perform better if it is compared to other algo-rithms as particle swarm optimization (PSO) and geneticalgorithm (GA) in terms of efficiency and successful rate [27]However the performance of FA can become less satisfiedwhen the dimension of search space increases ThereforeEOFA is introduced to further improve the performance ofFA where FA is integrated together with the inertia weightfunction [25] and opposition-based learning [24]

32 Techniques for Improving Original FA

321 Opposition-Based Learning Opposition-based learningwas suggested by Tizhoosh [24] and it has been employedin several heuristic optimization algorithms such as geneticalgorithm [24] differential evolution algorithm [28] antcolony optimization [29] and gravitational search algorithm[30] in order to enhance the performance of these algorithmsBasically optimization process such as FA always starts with

Start

Generate initial population offireflies

Evaluate fitness of all firefliesfrom the objective function

Update the light intensity(fitness value) of fireflies

Rank the fireflies and update theposition

Reach maximumiteration

No

Yes

Optimalresult

Figure 1 Flowchart for FA

an initial population (solutions) which is created randomlydue to the absence of a priori information about the solutionsThen the algorithm will try to search for the best solutionsHowever there can be a possibility that the initial guessfor the solutions is far away from the actual solutions Theconvergence rate can be improved when the initial guess iscloser to the actual solutions The chance to start with thesolutions closer to the optimal value can be increased byobtaining the opposite set of solutions simultaneouslyThe setof population that is closer to the optimal value will be chosenas initial population The similar method can be adopted aswell for each solution in the current population The conceptof opposite number is demonstrated below

Let 119909 isin 119877 be a real number within a defined intervalwhere 119909 isin [119886 119887] The opposite number 119909

119900can be defined as

shown in

119909119900= 119886 + 119887 minus 119909 (8)

4 The Scientific World Journal

Generate the initial population

Calculate the opposite

Evaluate fitness of all fireflies fromthe objective function as shown in (1)

and Po

Rank the fireflies and update theposition using (11)

Reach maximumiteration

Optimalresult

No

YesEvaluate fitness of all fireflies fromthe objective function as shown in (1)

with a random number within 0

to 1

Calculate the opposite population

using (9)

No Yes

Update the light intensity (fitnessvalue) of fireflies

Choose n fittest individuals from P

Jr gt rand()

of fireflies P randomly

population Po using (9)

Compare the jumping rate Jr

Po from the current population P

Figure 2 Flowchart for EOFA

Similarly this concept can be extended to the case withhigher dimensions Let 119875(119909

1 1199092 119909

119898) be a set of points

in 119898 dimensional search space where 119909119894

isin [119886119894 119887119894] and

1199091 1199092 119909

119898isin 119877 Then the points in the opposition set

119875119900(1199091199001 1199091199002 119909

119900119898) can be defined as shown in

119909119900119894= 119886119894+ 119887119894minus 119909119894 119894 = 1 2 119898 (9)

By using the definition for opposite number the oppo-sition-based optimization can be developed as followsLet 119875(119909

1 1199092 119909

119898) be the set of points in 119898 dimen-

sions search space which is the candidate solution foran optimization problem According to opposition theo-rem 119875

119900(1199091199001 1199091199002 119909

119900119898) will be the opposition set for

119875(1199091 1199092 119909119898) Suppose that 119891(119909) is the function used to

measure the performance of candidate solution thus if 119891(119875)is greater than or equal to 119891(119875

119900) then a set of points in 119875 can

be replaced by 119875119900or else 119875 is maintained

322 Inertia Weight Inertia weight-based FA was proposedby Tian et al [25] where an inertia weight function as shownin (10) is applied to (6)

120596 (119905) = 120596max minus (120596max minus 120596min) lowast (119905

Maxgeneration) (10)

where 120596(119905) is the inertia weight at time 119905 120596max and 120596min arethe initial and final values of the inertia weight respectivelythroughout the iteration process 119905 is the current iterationand Maxgeneration is the maximum number of iterationsas defined in the initialization process of FA The inertiaweight function decreases linearly with respect to timewhereat the beginning stages large inertia weight increases theglobal exploration ability and thus prevents the algorithmfrom being trapped in local optima At the end of the stagesthe reduced inertia weight enhances the local exploration ofthe solutions

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The movement of the firefly to update its position usinginertia weight-based FA can be illustrated as shown in

119909119894(119905) = 120596 (119905) 119909

119894(119905) + 120573

119900119890minus1205741199032

119894119895 (119909119895(119905) minus 119909

119894(119905))

+ alpha(rand minus1

2)

(11)

The incorporation of opposition-based learning andinertia weight-based function in FA is to avoid prematureconvergence as well as to enhance the searching ability of thealgorithm where the global exploration at the beginning ofthe optimization process and the local exploration at the endof the optimization process are improved

33 EOFA Opposition-based population initialization andopposition-based steps for EOFA with the population sizeof 119899 and dimension of 119898 are shown in Figure 2 Forthe initialization the initial population of fireflies 119875 isgenerated randomly and then the opposite population 119875

119900

is calculated using (9) The 119899 fittest fireflies are chosen from119875 and 119875

119900to become the first population in opposition-based

optimization processIn EOFA each firefly updates the light intensity (fitness

value) after the evaluation of the fitness from the objectivefunction Then the fireflies rank and update their positionsusing (11) In EOFA a jumping rate Jr is used to decide if theopposite population is generated or not according to (12) IfJr is greater than the generated random number the oppositepopulation is generated and the next population containsthe 119899 fittest individuals chosen from currents 119875 and 119875

119900or

else the next population remains as the current populationand 119875 is generated from the update of fireflyrsquos position Theoptimization process repeats until the criteria given are metwhere in this case it is the maximum number of iterations

generation of opposite population=yes if Jr gt rand ()no otherwise

(12)

The opposition-based optimization enables the algorithmto search for the global optimum points in a faster way Thesuperior performance of EOFA in escaping from the localoptimum points as well as the higher convergence rate isshown in the results section The steps and implementationof EOFA in mitigating voltage rise problem are discussed inthe following section

4 Implementation of EOFA in MitigatingVoltage Rise Problem

In order to mitigate the voltage rise problem a BESS thathelps to control the suitable amount of power available in thegrid is needed At the same time the optimal size of the BESScan be determined by EOFA using the following steps

(i) Generate the initial population 119875 randomly with apopulation size 119899 Each firefly consists of the informa-tion of the BESS active power output value for eachhour

0 100 200 300 400 500 600 700 800 900 10000

2

4

6

8

10

12

14

16

18

20

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 3 Comparison of performance of FA GSA and EOFA forbenchmark function F1 with dimension size 30

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

400

450

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 4 Comparison of performance of FA GSA and EOFA forbenchmark function F10 with dimension size 30

(ii) Calculate the opposite population 119875119900using (9) and

choose only 119899 fittest firefly individuals from 119875 and 119875119900

(iii) Run the load flow program for the systemunder studywith a PVDG and BESS The 119899 fittest individuals areevaluated in the load flow according to the objectivefunction as shown in (1) for charging and dischargingrespectively

(iv) Update the light intensity (fitness value) of the fireflyand then rank and update the position of the fireflyusing (11)

(v) Check the stopping criteria where in this case it isthe maximum number of iterations If the maximum

6 The Scientific World Journal

18 2331 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 24 25 26 2722

51 52 68 69

4947 48 50

36 38 39 40 43 44 45 464137 42

66 67

53 55 56 57 61 62 6358 6459 65605428 30 32 33 35343129

Bus with PVDG and BESS

Figure 5 Single-line diagram of the 69-bus distribution system

number of iterations is not achieved yet compare thejumping rate (Jr) based on the criteria given by (12)If the opposite generation is generated again only 119899fittest current firefly individuals from 119875 and 119875

119900are

chosen for next iteration(vi) Repeat step (iii) until stopping criteria are achieved

The BESS output values for each hour are obtained(vii) Then EOFA is used again to determine the optimal

BESS size by considering the SOC constraints usingthe objective function as shown in (3)

5 Results and Discussion

51 Performance Assessment of the Proposed EOFA Fifteenbenchmark test functions for unconstrained global optimiza-tion [31] are chosen in order to evaluate the performance ofEOFA The name dimension size and the global minima ofeach test function are presented in Table 1 Besides a compar-ative study is conducted with gravitational search algorithm(GSA) [14] in order to show the superior performanceof EOFA in solving most of the benchmark optimizationproblems In addition FA [15] is included in the comparisonas well showing the improvement of conventional method byusing EOFA The setting of parameters including populationsize the number of maximum iterations and some param-eters from the optimization algorithms is decided throughtrial and error procedure and experimentation depends onthe system size the complexity of the objective functions andconvergence characteristics of the optimization algorithmsas well as the time consumed to complete the optimizationprocess In this work the population size 119899 is set to be 50and the number of maximum iterations is taken as 1000 forall algorithms used in the comparison For FA and EOFA thevalues for 120573

119900 initial alpha delta and gamma are defined as

1 02 097 and 1 respectively For EOFA the jumping rate isJr = 03 while the inertia weights 120596max and 120596min are 14 and

Table 1 Test functions for unconstrained global optimization

Function Name of the function Dimension size Global minimaF1 Ackley function 30 0F2 Beale function 2 0F3 Bohachevsky function 1 2 0F4 Bohachevsky function 3 2 0F5 Griewank function 30 0F6 Matya function 2 0F7 Michalewicz function 10 minus966F8 Perm function 30 0F9 Powell function 30 0F10 Rastrigin function 30 0F11 Rosenbrock function 30 0F12 Schwefel function 30 0F13 Sphere function 30 0F14 Sum square function 30 0F15 Zakharov function 30 0

05 respectively For GSA the initial gravity constant 119866119900 is

set to be 100 while the best applying force Kbest decreasesmonotonically from 100 to 25 The parameter 120591 is set tobe 8 of the total number of dimensions

After 50 runs on each test function the performances(fitness value) of each algorithm are reported in Table 2 wherethe values with ldquolowastrdquo indicate the best performance and thevalues with ldquolowastlowastrdquo indicate the worst performance It can beseen from Table 2 that the performances for FA are the worstmost of the time compared to GSA and EOFA This can becaused by premature convergence after trapping in a localoptimum On the other hand it can be observed that EOFAhas the best performance formost of the test functions exceptfor F2 F7 and F11 where GSA outperforms EOFA It is knownfrom the reviews that different algorithmsmayperformbetter

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Table 2 Comparison of performances for GSA FA and EOFA

Function

Optimization algorithmGSA FA EOFA

Optimized fitness valueBest Average Worst Best Average Worst Best Average Worst

F1 00096 0015 0024 1852 1960 1997lowastlowast 888119864 minus 16lowast 38119864 minus 15 799119864 minus 15

F2 207119864 minus 07lowast 609119864 minus 06 684119864 minus 05 360119864 minus 06 0069 091lowastlowast 546119864 minus 06 399119864 minus 04 00014F3 109119864 minus 06 206119864 minus 05 105119864 minus 04 000021 055 335lowastlowast 0lowast 488119864 minus 17 222119864 minus 16

F4 187119864 minus 07 987119864 minus 06 398119864 minus 05 611119864 minus 05 030 208lowastlowast 0lowast 178119864 minus 17 555119864 minus 17

F5 698119864 minus 06 00014 0030 44674 59246 68612lowastlowast 0lowast 226119864 minus 16 278119864 minus 15

F6 473119864 minus 09 135119864 minus 07 911119864 minus 07 130119864 minus 05 0043 058lowastlowast 159119864 minus 40lowast 145119864 minus 36 806119864 minus 36

F7 minus946lowast minus881 minus773 minus634 minus411 minus255lowastlowast minus933 minus890 minus785F8 141119864 + 82 162119864 + 85 889119864 + 85lowastlowast 422119864 + 81 224119864 + 84 252119864 + 85 515119864 + 77lowast 742119864 + 80 119119864 + 82

F9 00014 00052 0012 365818 585100 979440lowastlowast 969119864 minus 35lowast 614119864 minus 32 794119864 minus 31

F10 1599 3450 5379 35345 39446 42940lowastlowast 0lowast 099 319F11 2575lowast 2753 2947 71054620 1211549 1629028lowastlowast 2800 2873 2894F12 838922 971990 1027885 898136 1025749 1111171lowastlowast 6566lowast 1094737 162444F13 180119864 minus 4 326119864 minus 4 604119864 minus 4 11190 13960 15675lowastlowast 231119864 minus 35lowast 106119864 minus 32 513119864 minus 32

F14 00019 00048 0011 622804 878732 1027992lowastlowast 352119864 minus 34lowast 146119864 minus 31 656119864 minus 31

F15 2416 5179 7396 70822 547119864 + 08 392119864 + 09lowastlowast 584119864 minus 35lowast 192119864 minus 30 160119864 minus 29

0 20 40 60 80 100 120 140 160

02

025

03

035

04

Time (hour)

Load

pro

file (

pu

)

Figure 6 Hourly individual load profile for one week

than others for different problems [32 33] Performancesin terms of convergence between FA GSA and EOFA forrandomly chosen functions are illustrated in Figures 3 and4 It can be seen from the figures that FA always convergesprematurely and exhibits an unsatisfied result Meanwhileboth GSA and EOFA are able to escape from local minimaand provide better results However EOFA has the higherconvergence rate and gives better results compared to GSA

52 Performance of EOFA in Voltage Rise Mitigation In thiswork the 69-radial-bus system as shown in Figure 5 is usedwhere a 366MW PVDG is installed at Bus 61 The systemdata can be obtained from [34]The pattern for PVDGoutputpower values is obtained from the output of a lower scalegrid connected PVDG system installed at the Faculty ofEngineering and Built Environment Universiti KebangsaanMalaysia In this study the hourly PVDG output power from9 am to 6 pm collected for three months (91 days) is used

0 20 40 60 80 100 120 140 160096

098

1

102

104

106

Time (hour)

Volta

ge p

rofil

e (p

u)

With PV onlyWith PV and BESS

Without PV and BESSUpper limit

Figure 7 Effect of PV and BESS on PVDG bus voltage profiles

Besides BESS is assumed to be installed at the PVDG busAccording to the PVDG bus voltage at a particular hour ifthe voltage exceeds the maximum limit (105 pu) or is lowerthan the minimum limit (095 pu) the BESS will be activatedand the BESS power for that particular hour is decided bythe optimization process either to inject (discharge) or tostore (charging) power from the systemThe upper and lowerlimits for the SOC of the BESS are set to be 100 and 20respectivelyWeekly each load bus profile used in this study isshown in Figure 6 The BESS is turned off temporarily whenit achieves either upper or lower limits In this work sincethe voltage profiles at all times are above the minimum limitof 095 pu the BESS does not discharge when the PVDG isactive Therefore the BESS is set to discharge at 7 pm rightafter the PVDG is inactive at the night time in order toprovide a capacity for the BESS to continue charging on thefollowing day

8 The Scientific World Journal

0 1000 2000 3000 4000 5000 6000

0

5

10

Time (hour)

BESS

out

put p

ower

(W)

minus5

times105

(a)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(b)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(c)

Figure 8 Hourly BESS output power for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(a)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(b)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(c)

Figure 9 SOC for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

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Submit your manuscripts athttpwwwhindawicom

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

2 The Scientific World Journal

minimum BESS capacities was plotted Brekken et al [7]proposed sizing and control methodologies for zinc-bromineBESS Khatib et al [8] utilized theMATLAB curve fitting toolto fit the sizing curve obtained from a standalone PV systemenergy flow and then derived a formula for optimal sizing ofPV andBESS Furthermore Ru et al [9] determined the BESSsize for grid-connected PV system by optimizing the BESScost and the net power purchase from the grid

In recent years heuristic optimization techniques havegained a lot of attention from researchers due to theirbetter performance compared to mathematical optimizationtechniques in coping with large and complex optimizationproblems There are different types of heuristic optimizationtechniquesOne of the early techniqueswas genetic algorithm(GA) [10] followed by other techniques such as ant colonyoptimization (ACO) [11] particle swarm optimization (PSO)[12] artificial bee colony algorithm (ABC) [13] gravitationalsearch algorithm (GSA) [14] firefly algorithm (FA) [15]artificial plant optimization algorithm (APOA) [16 17] arti-ficial physics optimization (APO) [18] shuffled frog leapingalgorithm (SFLA) [19] and membrane computing [20]Vrettos and Papathanassiou [21] applied GA in optimizingthe size of the hybrid system consisting of wind turbinesPV and BESS system The multiple-objective function inthis work minimizes the generation cost and maximizes therenewable energy source penetration Chen et al [22] alsoapplied GA to calculate the optimal energy storage size byoptimizing the investment cost model which is a nonlinearobjective function Apart from GA the ABC algorithm wasused to obtain the optimal BESS capacity in order to mitigatethe voltage rise problem in the PV embedded distributionnetwork [23]

However metaheuristic optimization algorithms havethe problem of being trapped in local optimum and slowconvergence rates due to their random searching processThis leads to the development of hybrid algorithms thatcan overcome these issues effectively FA is chosen for theoptimization process in this current study since it is relativelysimple and easy to implement However like most of themetaheuristic optimization algorithms FA also has its owndisadvantages In order to further improve the performanceof original FA in terms of convergence rate the opposition-based learning [24] is integrated into FA while the idea ofinertia weight FA [25] is also incorporated at the same timeto improve the ability of FA to escape from local optimumIn this paper enhanced opposition-based firefly algorithm(EOFA) is proposed to determine the optimal size of BESS ina PVDG integrated radial distribution network formitigatingthe voltage rise problem

2 Formulation of Optimization Problem

Asmentioned earlier the root cause of voltage rise in a PVGDintegrated system is the intermittent nature of power orcurrent injections at PVDG bus This problem can be solvedby using BESS as it has the ability to act as a power sourceor sink with the help of its bidirectional power converterThe BESS will operate in charging mode and as a current

sink if there is excess output power from PVDG while it willdischarge and act as a current source if more power is neededto maintain the voltage profile of the system The BESS isset to be charged when the PVDG is active while at nightwhen PVDG is idle the BESSwill discharge to a certain presetstate of charge In this study PVDG is modeled as a currentsource while BESS is modeled as a current source or sinkEOFA is first used to obtain the optimal average hourly BESSactive output power for the PVDG integrated system In thisoptimization the solution set (searching agent) is the BESSpower while the purpose of the optimization is to minimizethe voltage deviation of the PVDG bus by using the optimalBESS power value in order to maintain the voltage within095 pu to 105 pu rangeTherefore the objective function119891

1

can be expressed as

1198911= min

1003816100381610038161003816119881119894 (119905) minus 1051003816100381610038161003816 if 119881

119894(119905) gt 105

1003816100381610038161003816119881119894 (119905) minus 0951003816100381610038161003816 if 119881

119894(119905) lt 095

(1)

where 119881119894(119905) is the per unit (pu) value for voltage at bus 119894

at hour 119905 In this study it is assumed that the voltages areconstant at a particular hour of the day However it can beextended for shorter intervals for more accurate results

After the optimal BESS power values for each hour areobtained the state of charge (SOC) of the BESS for each hourcan be calculated as [26]

SOC = 100(1 minusint 119868bs119889119905

119876) (2)

where 119868bs is the current for the BESS 119905 is the time in hourand 119876 is the BESS capacity in Ampere hour (Ah) When theSOC reaches its maximum limit (SOCmax) or minimum limit(SOCmin) the BESS will be turned off temporarily until itcharges or discharges again Considering the SOC optimalsize or capacity of the BESS can be decided again by using theoptimization algorithm The performance of BESS increaseswhen the number of BESS inactive hours due to the SOCconstraint is minimized In this optimization the solutionset is the possible solution for BESS capacity The optimalBESS capacity should give the minimum number of off-time or inactive hours Considering this criterion the secondobjective function 119891

2 to obtain the size of the BESS can be

defined as

1198912= min (119873bs

idle) (3)

where 119873bsidle is the total number of time BESS is turned off

when SOC reaches either SOCmax or SOCmin

3 Enhanced Opposition-Based FireflyAlgorithm (EOFA)

31 Overview of Original FA FA is a heuristic optimizationalgorithm based on the flashing characteristics of fireflies[15] The main functions of the flashes are to attract themating partners as well as to attract the potential prey FA isillustrated based on three rules where firstly all fireflies are

The Scientific World Journal 3

of the same sex and thus the attraction between fireflies isindependent regardless of their sex Secondly the attraction isproportional to the brightness of the fireflies and it decreaseswhen the distance between the fireflies increases In otherwords the brighter fireflies will attract the less bright onesThe fireflies will move randomly if all of them have the samebrightnessThirdly the brightness of the fireflies is decided bythe landscape of the objective function

Two main parts in FA are the variation of light intensityand the attractiveness between the firefliesThe attractivenessof the fireflies is affected by the light intensity (brightness)which then is related to the objective functionThe attractive-ness 120573(119903) of a firefly can be defined as [15]

120573 (119903) = 120573119900119890minus1205741199032

(4)

where120573119900is the attractiveness at 119903 = 0 120574 is the light absorption

coefficient and 119903 is the Cartesian distance between twofireflies as shown in [15]

119903119894119895=10038171003817100381710038171003817119909119894 minus 119909

119895

10038171003817100381710038171003817 =radic119889

sum119896=1

(119909119894119896

minus 119909119895119896)2

(5)

where 119894 and 119895 represent two different fireflies at 119909119894and 119909

119895

while 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of 119894th firefly Meanwhile the movement of the firefly 119894 whichis attracted by the brighter firefly 119895 is defined in [15]

119909119894= 119909119894+ 120573119900119890minus1205741199032

(119909119895minus 119909119894) + alpha(rand minus

1

2) (6)

where the second term is due to the attraction and the thirdterm is due to the randomization In the third term alphais the randomization parameter while rand is the randomnumber generator uniformly distributed between zero andone In each following iteration alpha decreases with adecreasing factor delta as shown in (7)The flowchart for FAis shown in Figure 1

alpha (119905 + 1) = alpha (119905) times delta 0 lt delta lt 1 (7)

FA can perform better if it is compared to other algo-rithms as particle swarm optimization (PSO) and geneticalgorithm (GA) in terms of efficiency and successful rate [27]However the performance of FA can become less satisfiedwhen the dimension of search space increases ThereforeEOFA is introduced to further improve the performance ofFA where FA is integrated together with the inertia weightfunction [25] and opposition-based learning [24]

32 Techniques for Improving Original FA

321 Opposition-Based Learning Opposition-based learningwas suggested by Tizhoosh [24] and it has been employedin several heuristic optimization algorithms such as geneticalgorithm [24] differential evolution algorithm [28] antcolony optimization [29] and gravitational search algorithm[30] in order to enhance the performance of these algorithmsBasically optimization process such as FA always starts with

Start

Generate initial population offireflies

Evaluate fitness of all firefliesfrom the objective function

Update the light intensity(fitness value) of fireflies

Rank the fireflies and update theposition

Reach maximumiteration

No

Yes

Optimalresult

Figure 1 Flowchart for FA

an initial population (solutions) which is created randomlydue to the absence of a priori information about the solutionsThen the algorithm will try to search for the best solutionsHowever there can be a possibility that the initial guessfor the solutions is far away from the actual solutions Theconvergence rate can be improved when the initial guess iscloser to the actual solutions The chance to start with thesolutions closer to the optimal value can be increased byobtaining the opposite set of solutions simultaneouslyThe setof population that is closer to the optimal value will be chosenas initial population The similar method can be adopted aswell for each solution in the current population The conceptof opposite number is demonstrated below

Let 119909 isin 119877 be a real number within a defined intervalwhere 119909 isin [119886 119887] The opposite number 119909

119900can be defined as

shown in

119909119900= 119886 + 119887 minus 119909 (8)

4 The Scientific World Journal

Generate the initial population

Calculate the opposite

Evaluate fitness of all fireflies fromthe objective function as shown in (1)

and Po

Rank the fireflies and update theposition using (11)

Reach maximumiteration

Optimalresult

No

YesEvaluate fitness of all fireflies fromthe objective function as shown in (1)

with a random number within 0

to 1

Calculate the opposite population

using (9)

No Yes

Update the light intensity (fitnessvalue) of fireflies

Choose n fittest individuals from P

Jr gt rand()

of fireflies P randomly

population Po using (9)

Compare the jumping rate Jr

Po from the current population P

Figure 2 Flowchart for EOFA

Similarly this concept can be extended to the case withhigher dimensions Let 119875(119909

1 1199092 119909

119898) be a set of points

in 119898 dimensional search space where 119909119894

isin [119886119894 119887119894] and

1199091 1199092 119909

119898isin 119877 Then the points in the opposition set

119875119900(1199091199001 1199091199002 119909

119900119898) can be defined as shown in

119909119900119894= 119886119894+ 119887119894minus 119909119894 119894 = 1 2 119898 (9)

By using the definition for opposite number the oppo-sition-based optimization can be developed as followsLet 119875(119909

1 1199092 119909

119898) be the set of points in 119898 dimen-

sions search space which is the candidate solution foran optimization problem According to opposition theo-rem 119875

119900(1199091199001 1199091199002 119909

119900119898) will be the opposition set for

119875(1199091 1199092 119909119898) Suppose that 119891(119909) is the function used to

measure the performance of candidate solution thus if 119891(119875)is greater than or equal to 119891(119875

119900) then a set of points in 119875 can

be replaced by 119875119900or else 119875 is maintained

322 Inertia Weight Inertia weight-based FA was proposedby Tian et al [25] where an inertia weight function as shownin (10) is applied to (6)

120596 (119905) = 120596max minus (120596max minus 120596min) lowast (119905

Maxgeneration) (10)

where 120596(119905) is the inertia weight at time 119905 120596max and 120596min arethe initial and final values of the inertia weight respectivelythroughout the iteration process 119905 is the current iterationand Maxgeneration is the maximum number of iterationsas defined in the initialization process of FA The inertiaweight function decreases linearly with respect to timewhereat the beginning stages large inertia weight increases theglobal exploration ability and thus prevents the algorithmfrom being trapped in local optima At the end of the stagesthe reduced inertia weight enhances the local exploration ofthe solutions

The Scientific World Journal 5

The movement of the firefly to update its position usinginertia weight-based FA can be illustrated as shown in

119909119894(119905) = 120596 (119905) 119909

119894(119905) + 120573

119900119890minus1205741199032

119894119895 (119909119895(119905) minus 119909

119894(119905))

+ alpha(rand minus1

2)

(11)

The incorporation of opposition-based learning andinertia weight-based function in FA is to avoid prematureconvergence as well as to enhance the searching ability of thealgorithm where the global exploration at the beginning ofthe optimization process and the local exploration at the endof the optimization process are improved

33 EOFA Opposition-based population initialization andopposition-based steps for EOFA with the population sizeof 119899 and dimension of 119898 are shown in Figure 2 Forthe initialization the initial population of fireflies 119875 isgenerated randomly and then the opposite population 119875

119900

is calculated using (9) The 119899 fittest fireflies are chosen from119875 and 119875

119900to become the first population in opposition-based

optimization processIn EOFA each firefly updates the light intensity (fitness

value) after the evaluation of the fitness from the objectivefunction Then the fireflies rank and update their positionsusing (11) In EOFA a jumping rate Jr is used to decide if theopposite population is generated or not according to (12) IfJr is greater than the generated random number the oppositepopulation is generated and the next population containsthe 119899 fittest individuals chosen from currents 119875 and 119875

119900or

else the next population remains as the current populationand 119875 is generated from the update of fireflyrsquos position Theoptimization process repeats until the criteria given are metwhere in this case it is the maximum number of iterations

generation of opposite population=yes if Jr gt rand ()no otherwise

(12)

The opposition-based optimization enables the algorithmto search for the global optimum points in a faster way Thesuperior performance of EOFA in escaping from the localoptimum points as well as the higher convergence rate isshown in the results section The steps and implementationof EOFA in mitigating voltage rise problem are discussed inthe following section

4 Implementation of EOFA in MitigatingVoltage Rise Problem

In order to mitigate the voltage rise problem a BESS thathelps to control the suitable amount of power available in thegrid is needed At the same time the optimal size of the BESScan be determined by EOFA using the following steps

(i) Generate the initial population 119875 randomly with apopulation size 119899 Each firefly consists of the informa-tion of the BESS active power output value for eachhour

0 100 200 300 400 500 600 700 800 900 10000

2

4

6

8

10

12

14

16

18

20

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 3 Comparison of performance of FA GSA and EOFA forbenchmark function F1 with dimension size 30

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

400

450

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 4 Comparison of performance of FA GSA and EOFA forbenchmark function F10 with dimension size 30

(ii) Calculate the opposite population 119875119900using (9) and

choose only 119899 fittest firefly individuals from 119875 and 119875119900

(iii) Run the load flow program for the systemunder studywith a PVDG and BESS The 119899 fittest individuals areevaluated in the load flow according to the objectivefunction as shown in (1) for charging and dischargingrespectively

(iv) Update the light intensity (fitness value) of the fireflyand then rank and update the position of the fireflyusing (11)

(v) Check the stopping criteria where in this case it isthe maximum number of iterations If the maximum

6 The Scientific World Journal

18 2331 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 24 25 26 2722

51 52 68 69

4947 48 50

36 38 39 40 43 44 45 464137 42

66 67

53 55 56 57 61 62 6358 6459 65605428 30 32 33 35343129

Bus with PVDG and BESS

Figure 5 Single-line diagram of the 69-bus distribution system

number of iterations is not achieved yet compare thejumping rate (Jr) based on the criteria given by (12)If the opposite generation is generated again only 119899fittest current firefly individuals from 119875 and 119875

119900are

chosen for next iteration(vi) Repeat step (iii) until stopping criteria are achieved

The BESS output values for each hour are obtained(vii) Then EOFA is used again to determine the optimal

BESS size by considering the SOC constraints usingthe objective function as shown in (3)

5 Results and Discussion

51 Performance Assessment of the Proposed EOFA Fifteenbenchmark test functions for unconstrained global optimiza-tion [31] are chosen in order to evaluate the performance ofEOFA The name dimension size and the global minima ofeach test function are presented in Table 1 Besides a compar-ative study is conducted with gravitational search algorithm(GSA) [14] in order to show the superior performanceof EOFA in solving most of the benchmark optimizationproblems In addition FA [15] is included in the comparisonas well showing the improvement of conventional method byusing EOFA The setting of parameters including populationsize the number of maximum iterations and some param-eters from the optimization algorithms is decided throughtrial and error procedure and experimentation depends onthe system size the complexity of the objective functions andconvergence characteristics of the optimization algorithmsas well as the time consumed to complete the optimizationprocess In this work the population size 119899 is set to be 50and the number of maximum iterations is taken as 1000 forall algorithms used in the comparison For FA and EOFA thevalues for 120573

119900 initial alpha delta and gamma are defined as

1 02 097 and 1 respectively For EOFA the jumping rate isJr = 03 while the inertia weights 120596max and 120596min are 14 and

Table 1 Test functions for unconstrained global optimization

Function Name of the function Dimension size Global minimaF1 Ackley function 30 0F2 Beale function 2 0F3 Bohachevsky function 1 2 0F4 Bohachevsky function 3 2 0F5 Griewank function 30 0F6 Matya function 2 0F7 Michalewicz function 10 minus966F8 Perm function 30 0F9 Powell function 30 0F10 Rastrigin function 30 0F11 Rosenbrock function 30 0F12 Schwefel function 30 0F13 Sphere function 30 0F14 Sum square function 30 0F15 Zakharov function 30 0

05 respectively For GSA the initial gravity constant 119866119900 is

set to be 100 while the best applying force Kbest decreasesmonotonically from 100 to 25 The parameter 120591 is set tobe 8 of the total number of dimensions

After 50 runs on each test function the performances(fitness value) of each algorithm are reported in Table 2 wherethe values with ldquolowastrdquo indicate the best performance and thevalues with ldquolowastlowastrdquo indicate the worst performance It can beseen from Table 2 that the performances for FA are the worstmost of the time compared to GSA and EOFA This can becaused by premature convergence after trapping in a localoptimum On the other hand it can be observed that EOFAhas the best performance formost of the test functions exceptfor F2 F7 and F11 where GSA outperforms EOFA It is knownfrom the reviews that different algorithmsmayperformbetter

The Scientific World Journal 7

Table 2 Comparison of performances for GSA FA and EOFA

Function

Optimization algorithmGSA FA EOFA

Optimized fitness valueBest Average Worst Best Average Worst Best Average Worst

F1 00096 0015 0024 1852 1960 1997lowastlowast 888119864 minus 16lowast 38119864 minus 15 799119864 minus 15

F2 207119864 minus 07lowast 609119864 minus 06 684119864 minus 05 360119864 minus 06 0069 091lowastlowast 546119864 minus 06 399119864 minus 04 00014F3 109119864 minus 06 206119864 minus 05 105119864 minus 04 000021 055 335lowastlowast 0lowast 488119864 minus 17 222119864 minus 16

F4 187119864 minus 07 987119864 minus 06 398119864 minus 05 611119864 minus 05 030 208lowastlowast 0lowast 178119864 minus 17 555119864 minus 17

F5 698119864 minus 06 00014 0030 44674 59246 68612lowastlowast 0lowast 226119864 minus 16 278119864 minus 15

F6 473119864 minus 09 135119864 minus 07 911119864 minus 07 130119864 minus 05 0043 058lowastlowast 159119864 minus 40lowast 145119864 minus 36 806119864 minus 36

F7 minus946lowast minus881 minus773 minus634 minus411 minus255lowastlowast minus933 minus890 minus785F8 141119864 + 82 162119864 + 85 889119864 + 85lowastlowast 422119864 + 81 224119864 + 84 252119864 + 85 515119864 + 77lowast 742119864 + 80 119119864 + 82

F9 00014 00052 0012 365818 585100 979440lowastlowast 969119864 minus 35lowast 614119864 minus 32 794119864 minus 31

F10 1599 3450 5379 35345 39446 42940lowastlowast 0lowast 099 319F11 2575lowast 2753 2947 71054620 1211549 1629028lowastlowast 2800 2873 2894F12 838922 971990 1027885 898136 1025749 1111171lowastlowast 6566lowast 1094737 162444F13 180119864 minus 4 326119864 minus 4 604119864 minus 4 11190 13960 15675lowastlowast 231119864 minus 35lowast 106119864 minus 32 513119864 minus 32

F14 00019 00048 0011 622804 878732 1027992lowastlowast 352119864 minus 34lowast 146119864 minus 31 656119864 minus 31

F15 2416 5179 7396 70822 547119864 + 08 392119864 + 09lowastlowast 584119864 minus 35lowast 192119864 minus 30 160119864 minus 29

0 20 40 60 80 100 120 140 160

02

025

03

035

04

Time (hour)

Load

pro

file (

pu

)

Figure 6 Hourly individual load profile for one week

than others for different problems [32 33] Performancesin terms of convergence between FA GSA and EOFA forrandomly chosen functions are illustrated in Figures 3 and4 It can be seen from the figures that FA always convergesprematurely and exhibits an unsatisfied result Meanwhileboth GSA and EOFA are able to escape from local minimaand provide better results However EOFA has the higherconvergence rate and gives better results compared to GSA

52 Performance of EOFA in Voltage Rise Mitigation In thiswork the 69-radial-bus system as shown in Figure 5 is usedwhere a 366MW PVDG is installed at Bus 61 The systemdata can be obtained from [34]The pattern for PVDGoutputpower values is obtained from the output of a lower scalegrid connected PVDG system installed at the Faculty ofEngineering and Built Environment Universiti KebangsaanMalaysia In this study the hourly PVDG output power from9 am to 6 pm collected for three months (91 days) is used

0 20 40 60 80 100 120 140 160096

098

1

102

104

106

Time (hour)

Volta

ge p

rofil

e (p

u)

With PV onlyWith PV and BESS

Without PV and BESSUpper limit

Figure 7 Effect of PV and BESS on PVDG bus voltage profiles

Besides BESS is assumed to be installed at the PVDG busAccording to the PVDG bus voltage at a particular hour ifthe voltage exceeds the maximum limit (105 pu) or is lowerthan the minimum limit (095 pu) the BESS will be activatedand the BESS power for that particular hour is decided bythe optimization process either to inject (discharge) or tostore (charging) power from the systemThe upper and lowerlimits for the SOC of the BESS are set to be 100 and 20respectivelyWeekly each load bus profile used in this study isshown in Figure 6 The BESS is turned off temporarily whenit achieves either upper or lower limits In this work sincethe voltage profiles at all times are above the minimum limitof 095 pu the BESS does not discharge when the PVDG isactive Therefore the BESS is set to discharge at 7 pm rightafter the PVDG is inactive at the night time in order toprovide a capacity for the BESS to continue charging on thefollowing day

8 The Scientific World Journal

0 1000 2000 3000 4000 5000 6000

0

5

10

Time (hour)

BESS

out

put p

ower

(W)

minus5

times105

(a)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(b)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(c)

Figure 8 Hourly BESS output power for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(a)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(b)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(c)

Figure 9 SOC for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

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Solar EnergyJournal of

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Nuclear EnergyInternational Journal of

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 3

of the same sex and thus the attraction between fireflies isindependent regardless of their sex Secondly the attraction isproportional to the brightness of the fireflies and it decreaseswhen the distance between the fireflies increases In otherwords the brighter fireflies will attract the less bright onesThe fireflies will move randomly if all of them have the samebrightnessThirdly the brightness of the fireflies is decided bythe landscape of the objective function

Two main parts in FA are the variation of light intensityand the attractiveness between the firefliesThe attractivenessof the fireflies is affected by the light intensity (brightness)which then is related to the objective functionThe attractive-ness 120573(119903) of a firefly can be defined as [15]

120573 (119903) = 120573119900119890minus1205741199032

(4)

where120573119900is the attractiveness at 119903 = 0 120574 is the light absorption

coefficient and 119903 is the Cartesian distance between twofireflies as shown in [15]

119903119894119895=10038171003817100381710038171003817119909119894 minus 119909

119895

10038171003817100381710038171003817 =radic119889

sum119896=1

(119909119894119896

minus 119909119895119896)2

(5)

where 119894 and 119895 represent two different fireflies at 119909119894and 119909

119895

while 119909119894119896

is the 119896th component of the spatial coordinate 119909119894

of 119894th firefly Meanwhile the movement of the firefly 119894 whichis attracted by the brighter firefly 119895 is defined in [15]

119909119894= 119909119894+ 120573119900119890minus1205741199032

(119909119895minus 119909119894) + alpha(rand minus

1

2) (6)

where the second term is due to the attraction and the thirdterm is due to the randomization In the third term alphais the randomization parameter while rand is the randomnumber generator uniformly distributed between zero andone In each following iteration alpha decreases with adecreasing factor delta as shown in (7)The flowchart for FAis shown in Figure 1

alpha (119905 + 1) = alpha (119905) times delta 0 lt delta lt 1 (7)

FA can perform better if it is compared to other algo-rithms as particle swarm optimization (PSO) and geneticalgorithm (GA) in terms of efficiency and successful rate [27]However the performance of FA can become less satisfiedwhen the dimension of search space increases ThereforeEOFA is introduced to further improve the performance ofFA where FA is integrated together with the inertia weightfunction [25] and opposition-based learning [24]

32 Techniques for Improving Original FA

321 Opposition-Based Learning Opposition-based learningwas suggested by Tizhoosh [24] and it has been employedin several heuristic optimization algorithms such as geneticalgorithm [24] differential evolution algorithm [28] antcolony optimization [29] and gravitational search algorithm[30] in order to enhance the performance of these algorithmsBasically optimization process such as FA always starts with

Start

Generate initial population offireflies

Evaluate fitness of all firefliesfrom the objective function

Update the light intensity(fitness value) of fireflies

Rank the fireflies and update theposition

Reach maximumiteration

No

Yes

Optimalresult

Figure 1 Flowchart for FA

an initial population (solutions) which is created randomlydue to the absence of a priori information about the solutionsThen the algorithm will try to search for the best solutionsHowever there can be a possibility that the initial guessfor the solutions is far away from the actual solutions Theconvergence rate can be improved when the initial guess iscloser to the actual solutions The chance to start with thesolutions closer to the optimal value can be increased byobtaining the opposite set of solutions simultaneouslyThe setof population that is closer to the optimal value will be chosenas initial population The similar method can be adopted aswell for each solution in the current population The conceptof opposite number is demonstrated below

Let 119909 isin 119877 be a real number within a defined intervalwhere 119909 isin [119886 119887] The opposite number 119909

119900can be defined as

shown in

119909119900= 119886 + 119887 minus 119909 (8)

4 The Scientific World Journal

Generate the initial population

Calculate the opposite

Evaluate fitness of all fireflies fromthe objective function as shown in (1)

and Po

Rank the fireflies and update theposition using (11)

Reach maximumiteration

Optimalresult

No

YesEvaluate fitness of all fireflies fromthe objective function as shown in (1)

with a random number within 0

to 1

Calculate the opposite population

using (9)

No Yes

Update the light intensity (fitnessvalue) of fireflies

Choose n fittest individuals from P

Jr gt rand()

of fireflies P randomly

population Po using (9)

Compare the jumping rate Jr

Po from the current population P

Figure 2 Flowchart for EOFA

Similarly this concept can be extended to the case withhigher dimensions Let 119875(119909

1 1199092 119909

119898) be a set of points

in 119898 dimensional search space where 119909119894

isin [119886119894 119887119894] and

1199091 1199092 119909

119898isin 119877 Then the points in the opposition set

119875119900(1199091199001 1199091199002 119909

119900119898) can be defined as shown in

119909119900119894= 119886119894+ 119887119894minus 119909119894 119894 = 1 2 119898 (9)

By using the definition for opposite number the oppo-sition-based optimization can be developed as followsLet 119875(119909

1 1199092 119909

119898) be the set of points in 119898 dimen-

sions search space which is the candidate solution foran optimization problem According to opposition theo-rem 119875

119900(1199091199001 1199091199002 119909

119900119898) will be the opposition set for

119875(1199091 1199092 119909119898) Suppose that 119891(119909) is the function used to

measure the performance of candidate solution thus if 119891(119875)is greater than or equal to 119891(119875

119900) then a set of points in 119875 can

be replaced by 119875119900or else 119875 is maintained

322 Inertia Weight Inertia weight-based FA was proposedby Tian et al [25] where an inertia weight function as shownin (10) is applied to (6)

120596 (119905) = 120596max minus (120596max minus 120596min) lowast (119905

Maxgeneration) (10)

where 120596(119905) is the inertia weight at time 119905 120596max and 120596min arethe initial and final values of the inertia weight respectivelythroughout the iteration process 119905 is the current iterationand Maxgeneration is the maximum number of iterationsas defined in the initialization process of FA The inertiaweight function decreases linearly with respect to timewhereat the beginning stages large inertia weight increases theglobal exploration ability and thus prevents the algorithmfrom being trapped in local optima At the end of the stagesthe reduced inertia weight enhances the local exploration ofthe solutions

The Scientific World Journal 5

The movement of the firefly to update its position usinginertia weight-based FA can be illustrated as shown in

119909119894(119905) = 120596 (119905) 119909

119894(119905) + 120573

119900119890minus1205741199032

119894119895 (119909119895(119905) minus 119909

119894(119905))

+ alpha(rand minus1

2)

(11)

The incorporation of opposition-based learning andinertia weight-based function in FA is to avoid prematureconvergence as well as to enhance the searching ability of thealgorithm where the global exploration at the beginning ofthe optimization process and the local exploration at the endof the optimization process are improved

33 EOFA Opposition-based population initialization andopposition-based steps for EOFA with the population sizeof 119899 and dimension of 119898 are shown in Figure 2 Forthe initialization the initial population of fireflies 119875 isgenerated randomly and then the opposite population 119875

119900

is calculated using (9) The 119899 fittest fireflies are chosen from119875 and 119875

119900to become the first population in opposition-based

optimization processIn EOFA each firefly updates the light intensity (fitness

value) after the evaluation of the fitness from the objectivefunction Then the fireflies rank and update their positionsusing (11) In EOFA a jumping rate Jr is used to decide if theopposite population is generated or not according to (12) IfJr is greater than the generated random number the oppositepopulation is generated and the next population containsthe 119899 fittest individuals chosen from currents 119875 and 119875

119900or

else the next population remains as the current populationand 119875 is generated from the update of fireflyrsquos position Theoptimization process repeats until the criteria given are metwhere in this case it is the maximum number of iterations

generation of opposite population=yes if Jr gt rand ()no otherwise

(12)

The opposition-based optimization enables the algorithmto search for the global optimum points in a faster way Thesuperior performance of EOFA in escaping from the localoptimum points as well as the higher convergence rate isshown in the results section The steps and implementationof EOFA in mitigating voltage rise problem are discussed inthe following section

4 Implementation of EOFA in MitigatingVoltage Rise Problem

In order to mitigate the voltage rise problem a BESS thathelps to control the suitable amount of power available in thegrid is needed At the same time the optimal size of the BESScan be determined by EOFA using the following steps

(i) Generate the initial population 119875 randomly with apopulation size 119899 Each firefly consists of the informa-tion of the BESS active power output value for eachhour

0 100 200 300 400 500 600 700 800 900 10000

2

4

6

8

10

12

14

16

18

20

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 3 Comparison of performance of FA GSA and EOFA forbenchmark function F1 with dimension size 30

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

400

450

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 4 Comparison of performance of FA GSA and EOFA forbenchmark function F10 with dimension size 30

(ii) Calculate the opposite population 119875119900using (9) and

choose only 119899 fittest firefly individuals from 119875 and 119875119900

(iii) Run the load flow program for the systemunder studywith a PVDG and BESS The 119899 fittest individuals areevaluated in the load flow according to the objectivefunction as shown in (1) for charging and dischargingrespectively

(iv) Update the light intensity (fitness value) of the fireflyand then rank and update the position of the fireflyusing (11)

(v) Check the stopping criteria where in this case it isthe maximum number of iterations If the maximum

6 The Scientific World Journal

18 2331 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 24 25 26 2722

51 52 68 69

4947 48 50

36 38 39 40 43 44 45 464137 42

66 67

53 55 56 57 61 62 6358 6459 65605428 30 32 33 35343129

Bus with PVDG and BESS

Figure 5 Single-line diagram of the 69-bus distribution system

number of iterations is not achieved yet compare thejumping rate (Jr) based on the criteria given by (12)If the opposite generation is generated again only 119899fittest current firefly individuals from 119875 and 119875

119900are

chosen for next iteration(vi) Repeat step (iii) until stopping criteria are achieved

The BESS output values for each hour are obtained(vii) Then EOFA is used again to determine the optimal

BESS size by considering the SOC constraints usingthe objective function as shown in (3)

5 Results and Discussion

51 Performance Assessment of the Proposed EOFA Fifteenbenchmark test functions for unconstrained global optimiza-tion [31] are chosen in order to evaluate the performance ofEOFA The name dimension size and the global minima ofeach test function are presented in Table 1 Besides a compar-ative study is conducted with gravitational search algorithm(GSA) [14] in order to show the superior performanceof EOFA in solving most of the benchmark optimizationproblems In addition FA [15] is included in the comparisonas well showing the improvement of conventional method byusing EOFA The setting of parameters including populationsize the number of maximum iterations and some param-eters from the optimization algorithms is decided throughtrial and error procedure and experimentation depends onthe system size the complexity of the objective functions andconvergence characteristics of the optimization algorithmsas well as the time consumed to complete the optimizationprocess In this work the population size 119899 is set to be 50and the number of maximum iterations is taken as 1000 forall algorithms used in the comparison For FA and EOFA thevalues for 120573

119900 initial alpha delta and gamma are defined as

1 02 097 and 1 respectively For EOFA the jumping rate isJr = 03 while the inertia weights 120596max and 120596min are 14 and

Table 1 Test functions for unconstrained global optimization

Function Name of the function Dimension size Global minimaF1 Ackley function 30 0F2 Beale function 2 0F3 Bohachevsky function 1 2 0F4 Bohachevsky function 3 2 0F5 Griewank function 30 0F6 Matya function 2 0F7 Michalewicz function 10 minus966F8 Perm function 30 0F9 Powell function 30 0F10 Rastrigin function 30 0F11 Rosenbrock function 30 0F12 Schwefel function 30 0F13 Sphere function 30 0F14 Sum square function 30 0F15 Zakharov function 30 0

05 respectively For GSA the initial gravity constant 119866119900 is

set to be 100 while the best applying force Kbest decreasesmonotonically from 100 to 25 The parameter 120591 is set tobe 8 of the total number of dimensions

After 50 runs on each test function the performances(fitness value) of each algorithm are reported in Table 2 wherethe values with ldquolowastrdquo indicate the best performance and thevalues with ldquolowastlowastrdquo indicate the worst performance It can beseen from Table 2 that the performances for FA are the worstmost of the time compared to GSA and EOFA This can becaused by premature convergence after trapping in a localoptimum On the other hand it can be observed that EOFAhas the best performance formost of the test functions exceptfor F2 F7 and F11 where GSA outperforms EOFA It is knownfrom the reviews that different algorithmsmayperformbetter

The Scientific World Journal 7

Table 2 Comparison of performances for GSA FA and EOFA

Function

Optimization algorithmGSA FA EOFA

Optimized fitness valueBest Average Worst Best Average Worst Best Average Worst

F1 00096 0015 0024 1852 1960 1997lowastlowast 888119864 minus 16lowast 38119864 minus 15 799119864 minus 15

F2 207119864 minus 07lowast 609119864 minus 06 684119864 minus 05 360119864 minus 06 0069 091lowastlowast 546119864 minus 06 399119864 minus 04 00014F3 109119864 minus 06 206119864 minus 05 105119864 minus 04 000021 055 335lowastlowast 0lowast 488119864 minus 17 222119864 minus 16

F4 187119864 minus 07 987119864 minus 06 398119864 minus 05 611119864 minus 05 030 208lowastlowast 0lowast 178119864 minus 17 555119864 minus 17

F5 698119864 minus 06 00014 0030 44674 59246 68612lowastlowast 0lowast 226119864 minus 16 278119864 minus 15

F6 473119864 minus 09 135119864 minus 07 911119864 minus 07 130119864 minus 05 0043 058lowastlowast 159119864 minus 40lowast 145119864 minus 36 806119864 minus 36

F7 minus946lowast minus881 minus773 minus634 minus411 minus255lowastlowast minus933 minus890 minus785F8 141119864 + 82 162119864 + 85 889119864 + 85lowastlowast 422119864 + 81 224119864 + 84 252119864 + 85 515119864 + 77lowast 742119864 + 80 119119864 + 82

F9 00014 00052 0012 365818 585100 979440lowastlowast 969119864 minus 35lowast 614119864 minus 32 794119864 minus 31

F10 1599 3450 5379 35345 39446 42940lowastlowast 0lowast 099 319F11 2575lowast 2753 2947 71054620 1211549 1629028lowastlowast 2800 2873 2894F12 838922 971990 1027885 898136 1025749 1111171lowastlowast 6566lowast 1094737 162444F13 180119864 minus 4 326119864 minus 4 604119864 minus 4 11190 13960 15675lowastlowast 231119864 minus 35lowast 106119864 minus 32 513119864 minus 32

F14 00019 00048 0011 622804 878732 1027992lowastlowast 352119864 minus 34lowast 146119864 minus 31 656119864 minus 31

F15 2416 5179 7396 70822 547119864 + 08 392119864 + 09lowastlowast 584119864 minus 35lowast 192119864 minus 30 160119864 minus 29

0 20 40 60 80 100 120 140 160

02

025

03

035

04

Time (hour)

Load

pro

file (

pu

)

Figure 6 Hourly individual load profile for one week

than others for different problems [32 33] Performancesin terms of convergence between FA GSA and EOFA forrandomly chosen functions are illustrated in Figures 3 and4 It can be seen from the figures that FA always convergesprematurely and exhibits an unsatisfied result Meanwhileboth GSA and EOFA are able to escape from local minimaand provide better results However EOFA has the higherconvergence rate and gives better results compared to GSA

52 Performance of EOFA in Voltage Rise Mitigation In thiswork the 69-radial-bus system as shown in Figure 5 is usedwhere a 366MW PVDG is installed at Bus 61 The systemdata can be obtained from [34]The pattern for PVDGoutputpower values is obtained from the output of a lower scalegrid connected PVDG system installed at the Faculty ofEngineering and Built Environment Universiti KebangsaanMalaysia In this study the hourly PVDG output power from9 am to 6 pm collected for three months (91 days) is used

0 20 40 60 80 100 120 140 160096

098

1

102

104

106

Time (hour)

Volta

ge p

rofil

e (p

u)

With PV onlyWith PV and BESS

Without PV and BESSUpper limit

Figure 7 Effect of PV and BESS on PVDG bus voltage profiles

Besides BESS is assumed to be installed at the PVDG busAccording to the PVDG bus voltage at a particular hour ifthe voltage exceeds the maximum limit (105 pu) or is lowerthan the minimum limit (095 pu) the BESS will be activatedand the BESS power for that particular hour is decided bythe optimization process either to inject (discharge) or tostore (charging) power from the systemThe upper and lowerlimits for the SOC of the BESS are set to be 100 and 20respectivelyWeekly each load bus profile used in this study isshown in Figure 6 The BESS is turned off temporarily whenit achieves either upper or lower limits In this work sincethe voltage profiles at all times are above the minimum limitof 095 pu the BESS does not discharge when the PVDG isactive Therefore the BESS is set to discharge at 7 pm rightafter the PVDG is inactive at the night time in order toprovide a capacity for the BESS to continue charging on thefollowing day

8 The Scientific World Journal

0 1000 2000 3000 4000 5000 6000

0

5

10

Time (hour)

BESS

out

put p

ower

(W)

minus5

times105

(a)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(b)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(c)

Figure 8 Hourly BESS output power for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(a)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(b)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(c)

Figure 9 SOC for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Renewable Energy

Submit your manuscripts athttpwwwhindawicom

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

4 The Scientific World Journal

Generate the initial population

Calculate the opposite

Evaluate fitness of all fireflies fromthe objective function as shown in (1)

and Po

Rank the fireflies and update theposition using (11)

Reach maximumiteration

Optimalresult

No

YesEvaluate fitness of all fireflies fromthe objective function as shown in (1)

with a random number within 0

to 1

Calculate the opposite population

using (9)

No Yes

Update the light intensity (fitnessvalue) of fireflies

Choose n fittest individuals from P

Jr gt rand()

of fireflies P randomly

population Po using (9)

Compare the jumping rate Jr

Po from the current population P

Figure 2 Flowchart for EOFA

Similarly this concept can be extended to the case withhigher dimensions Let 119875(119909

1 1199092 119909

119898) be a set of points

in 119898 dimensional search space where 119909119894

isin [119886119894 119887119894] and

1199091 1199092 119909

119898isin 119877 Then the points in the opposition set

119875119900(1199091199001 1199091199002 119909

119900119898) can be defined as shown in

119909119900119894= 119886119894+ 119887119894minus 119909119894 119894 = 1 2 119898 (9)

By using the definition for opposite number the oppo-sition-based optimization can be developed as followsLet 119875(119909

1 1199092 119909

119898) be the set of points in 119898 dimen-

sions search space which is the candidate solution foran optimization problem According to opposition theo-rem 119875

119900(1199091199001 1199091199002 119909

119900119898) will be the opposition set for

119875(1199091 1199092 119909119898) Suppose that 119891(119909) is the function used to

measure the performance of candidate solution thus if 119891(119875)is greater than or equal to 119891(119875

119900) then a set of points in 119875 can

be replaced by 119875119900or else 119875 is maintained

322 Inertia Weight Inertia weight-based FA was proposedby Tian et al [25] where an inertia weight function as shownin (10) is applied to (6)

120596 (119905) = 120596max minus (120596max minus 120596min) lowast (119905

Maxgeneration) (10)

where 120596(119905) is the inertia weight at time 119905 120596max and 120596min arethe initial and final values of the inertia weight respectivelythroughout the iteration process 119905 is the current iterationand Maxgeneration is the maximum number of iterationsas defined in the initialization process of FA The inertiaweight function decreases linearly with respect to timewhereat the beginning stages large inertia weight increases theglobal exploration ability and thus prevents the algorithmfrom being trapped in local optima At the end of the stagesthe reduced inertia weight enhances the local exploration ofthe solutions

The Scientific World Journal 5

The movement of the firefly to update its position usinginertia weight-based FA can be illustrated as shown in

119909119894(119905) = 120596 (119905) 119909

119894(119905) + 120573

119900119890minus1205741199032

119894119895 (119909119895(119905) minus 119909

119894(119905))

+ alpha(rand minus1

2)

(11)

The incorporation of opposition-based learning andinertia weight-based function in FA is to avoid prematureconvergence as well as to enhance the searching ability of thealgorithm where the global exploration at the beginning ofthe optimization process and the local exploration at the endof the optimization process are improved

33 EOFA Opposition-based population initialization andopposition-based steps for EOFA with the population sizeof 119899 and dimension of 119898 are shown in Figure 2 Forthe initialization the initial population of fireflies 119875 isgenerated randomly and then the opposite population 119875

119900

is calculated using (9) The 119899 fittest fireflies are chosen from119875 and 119875

119900to become the first population in opposition-based

optimization processIn EOFA each firefly updates the light intensity (fitness

value) after the evaluation of the fitness from the objectivefunction Then the fireflies rank and update their positionsusing (11) In EOFA a jumping rate Jr is used to decide if theopposite population is generated or not according to (12) IfJr is greater than the generated random number the oppositepopulation is generated and the next population containsthe 119899 fittest individuals chosen from currents 119875 and 119875

119900or

else the next population remains as the current populationand 119875 is generated from the update of fireflyrsquos position Theoptimization process repeats until the criteria given are metwhere in this case it is the maximum number of iterations

generation of opposite population=yes if Jr gt rand ()no otherwise

(12)

The opposition-based optimization enables the algorithmto search for the global optimum points in a faster way Thesuperior performance of EOFA in escaping from the localoptimum points as well as the higher convergence rate isshown in the results section The steps and implementationof EOFA in mitigating voltage rise problem are discussed inthe following section

4 Implementation of EOFA in MitigatingVoltage Rise Problem

In order to mitigate the voltage rise problem a BESS thathelps to control the suitable amount of power available in thegrid is needed At the same time the optimal size of the BESScan be determined by EOFA using the following steps

(i) Generate the initial population 119875 randomly with apopulation size 119899 Each firefly consists of the informa-tion of the BESS active power output value for eachhour

0 100 200 300 400 500 600 700 800 900 10000

2

4

6

8

10

12

14

16

18

20

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 3 Comparison of performance of FA GSA and EOFA forbenchmark function F1 with dimension size 30

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

400

450

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 4 Comparison of performance of FA GSA and EOFA forbenchmark function F10 with dimension size 30

(ii) Calculate the opposite population 119875119900using (9) and

choose only 119899 fittest firefly individuals from 119875 and 119875119900

(iii) Run the load flow program for the systemunder studywith a PVDG and BESS The 119899 fittest individuals areevaluated in the load flow according to the objectivefunction as shown in (1) for charging and dischargingrespectively

(iv) Update the light intensity (fitness value) of the fireflyand then rank and update the position of the fireflyusing (11)

(v) Check the stopping criteria where in this case it isthe maximum number of iterations If the maximum

6 The Scientific World Journal

18 2331 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 24 25 26 2722

51 52 68 69

4947 48 50

36 38 39 40 43 44 45 464137 42

66 67

53 55 56 57 61 62 6358 6459 65605428 30 32 33 35343129

Bus with PVDG and BESS

Figure 5 Single-line diagram of the 69-bus distribution system

number of iterations is not achieved yet compare thejumping rate (Jr) based on the criteria given by (12)If the opposite generation is generated again only 119899fittest current firefly individuals from 119875 and 119875

119900are

chosen for next iteration(vi) Repeat step (iii) until stopping criteria are achieved

The BESS output values for each hour are obtained(vii) Then EOFA is used again to determine the optimal

BESS size by considering the SOC constraints usingthe objective function as shown in (3)

5 Results and Discussion

51 Performance Assessment of the Proposed EOFA Fifteenbenchmark test functions for unconstrained global optimiza-tion [31] are chosen in order to evaluate the performance ofEOFA The name dimension size and the global minima ofeach test function are presented in Table 1 Besides a compar-ative study is conducted with gravitational search algorithm(GSA) [14] in order to show the superior performanceof EOFA in solving most of the benchmark optimizationproblems In addition FA [15] is included in the comparisonas well showing the improvement of conventional method byusing EOFA The setting of parameters including populationsize the number of maximum iterations and some param-eters from the optimization algorithms is decided throughtrial and error procedure and experimentation depends onthe system size the complexity of the objective functions andconvergence characteristics of the optimization algorithmsas well as the time consumed to complete the optimizationprocess In this work the population size 119899 is set to be 50and the number of maximum iterations is taken as 1000 forall algorithms used in the comparison For FA and EOFA thevalues for 120573

119900 initial alpha delta and gamma are defined as

1 02 097 and 1 respectively For EOFA the jumping rate isJr = 03 while the inertia weights 120596max and 120596min are 14 and

Table 1 Test functions for unconstrained global optimization

Function Name of the function Dimension size Global minimaF1 Ackley function 30 0F2 Beale function 2 0F3 Bohachevsky function 1 2 0F4 Bohachevsky function 3 2 0F5 Griewank function 30 0F6 Matya function 2 0F7 Michalewicz function 10 minus966F8 Perm function 30 0F9 Powell function 30 0F10 Rastrigin function 30 0F11 Rosenbrock function 30 0F12 Schwefel function 30 0F13 Sphere function 30 0F14 Sum square function 30 0F15 Zakharov function 30 0

05 respectively For GSA the initial gravity constant 119866119900 is

set to be 100 while the best applying force Kbest decreasesmonotonically from 100 to 25 The parameter 120591 is set tobe 8 of the total number of dimensions

After 50 runs on each test function the performances(fitness value) of each algorithm are reported in Table 2 wherethe values with ldquolowastrdquo indicate the best performance and thevalues with ldquolowastlowastrdquo indicate the worst performance It can beseen from Table 2 that the performances for FA are the worstmost of the time compared to GSA and EOFA This can becaused by premature convergence after trapping in a localoptimum On the other hand it can be observed that EOFAhas the best performance formost of the test functions exceptfor F2 F7 and F11 where GSA outperforms EOFA It is knownfrom the reviews that different algorithmsmayperformbetter

The Scientific World Journal 7

Table 2 Comparison of performances for GSA FA and EOFA

Function

Optimization algorithmGSA FA EOFA

Optimized fitness valueBest Average Worst Best Average Worst Best Average Worst

F1 00096 0015 0024 1852 1960 1997lowastlowast 888119864 minus 16lowast 38119864 minus 15 799119864 minus 15

F2 207119864 minus 07lowast 609119864 minus 06 684119864 minus 05 360119864 minus 06 0069 091lowastlowast 546119864 minus 06 399119864 minus 04 00014F3 109119864 minus 06 206119864 minus 05 105119864 minus 04 000021 055 335lowastlowast 0lowast 488119864 minus 17 222119864 minus 16

F4 187119864 minus 07 987119864 minus 06 398119864 minus 05 611119864 minus 05 030 208lowastlowast 0lowast 178119864 minus 17 555119864 minus 17

F5 698119864 minus 06 00014 0030 44674 59246 68612lowastlowast 0lowast 226119864 minus 16 278119864 minus 15

F6 473119864 minus 09 135119864 minus 07 911119864 minus 07 130119864 minus 05 0043 058lowastlowast 159119864 minus 40lowast 145119864 minus 36 806119864 minus 36

F7 minus946lowast minus881 minus773 minus634 minus411 minus255lowastlowast minus933 minus890 minus785F8 141119864 + 82 162119864 + 85 889119864 + 85lowastlowast 422119864 + 81 224119864 + 84 252119864 + 85 515119864 + 77lowast 742119864 + 80 119119864 + 82

F9 00014 00052 0012 365818 585100 979440lowastlowast 969119864 minus 35lowast 614119864 minus 32 794119864 minus 31

F10 1599 3450 5379 35345 39446 42940lowastlowast 0lowast 099 319F11 2575lowast 2753 2947 71054620 1211549 1629028lowastlowast 2800 2873 2894F12 838922 971990 1027885 898136 1025749 1111171lowastlowast 6566lowast 1094737 162444F13 180119864 minus 4 326119864 minus 4 604119864 minus 4 11190 13960 15675lowastlowast 231119864 minus 35lowast 106119864 minus 32 513119864 minus 32

F14 00019 00048 0011 622804 878732 1027992lowastlowast 352119864 minus 34lowast 146119864 minus 31 656119864 minus 31

F15 2416 5179 7396 70822 547119864 + 08 392119864 + 09lowastlowast 584119864 minus 35lowast 192119864 minus 30 160119864 minus 29

0 20 40 60 80 100 120 140 160

02

025

03

035

04

Time (hour)

Load

pro

file (

pu

)

Figure 6 Hourly individual load profile for one week

than others for different problems [32 33] Performancesin terms of convergence between FA GSA and EOFA forrandomly chosen functions are illustrated in Figures 3 and4 It can be seen from the figures that FA always convergesprematurely and exhibits an unsatisfied result Meanwhileboth GSA and EOFA are able to escape from local minimaand provide better results However EOFA has the higherconvergence rate and gives better results compared to GSA

52 Performance of EOFA in Voltage Rise Mitigation In thiswork the 69-radial-bus system as shown in Figure 5 is usedwhere a 366MW PVDG is installed at Bus 61 The systemdata can be obtained from [34]The pattern for PVDGoutputpower values is obtained from the output of a lower scalegrid connected PVDG system installed at the Faculty ofEngineering and Built Environment Universiti KebangsaanMalaysia In this study the hourly PVDG output power from9 am to 6 pm collected for three months (91 days) is used

0 20 40 60 80 100 120 140 160096

098

1

102

104

106

Time (hour)

Volta

ge p

rofil

e (p

u)

With PV onlyWith PV and BESS

Without PV and BESSUpper limit

Figure 7 Effect of PV and BESS on PVDG bus voltage profiles

Besides BESS is assumed to be installed at the PVDG busAccording to the PVDG bus voltage at a particular hour ifthe voltage exceeds the maximum limit (105 pu) or is lowerthan the minimum limit (095 pu) the BESS will be activatedand the BESS power for that particular hour is decided bythe optimization process either to inject (discharge) or tostore (charging) power from the systemThe upper and lowerlimits for the SOC of the BESS are set to be 100 and 20respectivelyWeekly each load bus profile used in this study isshown in Figure 6 The BESS is turned off temporarily whenit achieves either upper or lower limits In this work sincethe voltage profiles at all times are above the minimum limitof 095 pu the BESS does not discharge when the PVDG isactive Therefore the BESS is set to discharge at 7 pm rightafter the PVDG is inactive at the night time in order toprovide a capacity for the BESS to continue charging on thefollowing day

8 The Scientific World Journal

0 1000 2000 3000 4000 5000 6000

0

5

10

Time (hour)

BESS

out

put p

ower

(W)

minus5

times105

(a)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(b)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(c)

Figure 8 Hourly BESS output power for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(a)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(b)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(c)

Figure 9 SOC for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

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Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Renewable Energy

Submit your manuscripts athttpwwwhindawicom

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 5

The movement of the firefly to update its position usinginertia weight-based FA can be illustrated as shown in

119909119894(119905) = 120596 (119905) 119909

119894(119905) + 120573

119900119890minus1205741199032

119894119895 (119909119895(119905) minus 119909

119894(119905))

+ alpha(rand minus1

2)

(11)

The incorporation of opposition-based learning andinertia weight-based function in FA is to avoid prematureconvergence as well as to enhance the searching ability of thealgorithm where the global exploration at the beginning ofthe optimization process and the local exploration at the endof the optimization process are improved

33 EOFA Opposition-based population initialization andopposition-based steps for EOFA with the population sizeof 119899 and dimension of 119898 are shown in Figure 2 Forthe initialization the initial population of fireflies 119875 isgenerated randomly and then the opposite population 119875

119900

is calculated using (9) The 119899 fittest fireflies are chosen from119875 and 119875

119900to become the first population in opposition-based

optimization processIn EOFA each firefly updates the light intensity (fitness

value) after the evaluation of the fitness from the objectivefunction Then the fireflies rank and update their positionsusing (11) In EOFA a jumping rate Jr is used to decide if theopposite population is generated or not according to (12) IfJr is greater than the generated random number the oppositepopulation is generated and the next population containsthe 119899 fittest individuals chosen from currents 119875 and 119875

119900or

else the next population remains as the current populationand 119875 is generated from the update of fireflyrsquos position Theoptimization process repeats until the criteria given are metwhere in this case it is the maximum number of iterations

generation of opposite population=yes if Jr gt rand ()no otherwise

(12)

The opposition-based optimization enables the algorithmto search for the global optimum points in a faster way Thesuperior performance of EOFA in escaping from the localoptimum points as well as the higher convergence rate isshown in the results section The steps and implementationof EOFA in mitigating voltage rise problem are discussed inthe following section

4 Implementation of EOFA in MitigatingVoltage Rise Problem

In order to mitigate the voltage rise problem a BESS thathelps to control the suitable amount of power available in thegrid is needed At the same time the optimal size of the BESScan be determined by EOFA using the following steps

(i) Generate the initial population 119875 randomly with apopulation size 119899 Each firefly consists of the informa-tion of the BESS active power output value for eachhour

0 100 200 300 400 500 600 700 800 900 10000

2

4

6

8

10

12

14

16

18

20

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 3 Comparison of performance of FA GSA and EOFA forbenchmark function F1 with dimension size 30

0 100 200 300 400 500 600 700 800 900 10000

50

100

150

200

250

300

350

400

450

Iteration

Fitn

ess v

alue

FAGSAEOFA

Figure 4 Comparison of performance of FA GSA and EOFA forbenchmark function F10 with dimension size 30

(ii) Calculate the opposite population 119875119900using (9) and

choose only 119899 fittest firefly individuals from 119875 and 119875119900

(iii) Run the load flow program for the systemunder studywith a PVDG and BESS The 119899 fittest individuals areevaluated in the load flow according to the objectivefunction as shown in (1) for charging and dischargingrespectively

(iv) Update the light intensity (fitness value) of the fireflyand then rank and update the position of the fireflyusing (11)

(v) Check the stopping criteria where in this case it isthe maximum number of iterations If the maximum

6 The Scientific World Journal

18 2331 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 24 25 26 2722

51 52 68 69

4947 48 50

36 38 39 40 43 44 45 464137 42

66 67

53 55 56 57 61 62 6358 6459 65605428 30 32 33 35343129

Bus with PVDG and BESS

Figure 5 Single-line diagram of the 69-bus distribution system

number of iterations is not achieved yet compare thejumping rate (Jr) based on the criteria given by (12)If the opposite generation is generated again only 119899fittest current firefly individuals from 119875 and 119875

119900are

chosen for next iteration(vi) Repeat step (iii) until stopping criteria are achieved

The BESS output values for each hour are obtained(vii) Then EOFA is used again to determine the optimal

BESS size by considering the SOC constraints usingthe objective function as shown in (3)

5 Results and Discussion

51 Performance Assessment of the Proposed EOFA Fifteenbenchmark test functions for unconstrained global optimiza-tion [31] are chosen in order to evaluate the performance ofEOFA The name dimension size and the global minima ofeach test function are presented in Table 1 Besides a compar-ative study is conducted with gravitational search algorithm(GSA) [14] in order to show the superior performanceof EOFA in solving most of the benchmark optimizationproblems In addition FA [15] is included in the comparisonas well showing the improvement of conventional method byusing EOFA The setting of parameters including populationsize the number of maximum iterations and some param-eters from the optimization algorithms is decided throughtrial and error procedure and experimentation depends onthe system size the complexity of the objective functions andconvergence characteristics of the optimization algorithmsas well as the time consumed to complete the optimizationprocess In this work the population size 119899 is set to be 50and the number of maximum iterations is taken as 1000 forall algorithms used in the comparison For FA and EOFA thevalues for 120573

119900 initial alpha delta and gamma are defined as

1 02 097 and 1 respectively For EOFA the jumping rate isJr = 03 while the inertia weights 120596max and 120596min are 14 and

Table 1 Test functions for unconstrained global optimization

Function Name of the function Dimension size Global minimaF1 Ackley function 30 0F2 Beale function 2 0F3 Bohachevsky function 1 2 0F4 Bohachevsky function 3 2 0F5 Griewank function 30 0F6 Matya function 2 0F7 Michalewicz function 10 minus966F8 Perm function 30 0F9 Powell function 30 0F10 Rastrigin function 30 0F11 Rosenbrock function 30 0F12 Schwefel function 30 0F13 Sphere function 30 0F14 Sum square function 30 0F15 Zakharov function 30 0

05 respectively For GSA the initial gravity constant 119866119900 is

set to be 100 while the best applying force Kbest decreasesmonotonically from 100 to 25 The parameter 120591 is set tobe 8 of the total number of dimensions

After 50 runs on each test function the performances(fitness value) of each algorithm are reported in Table 2 wherethe values with ldquolowastrdquo indicate the best performance and thevalues with ldquolowastlowastrdquo indicate the worst performance It can beseen from Table 2 that the performances for FA are the worstmost of the time compared to GSA and EOFA This can becaused by premature convergence after trapping in a localoptimum On the other hand it can be observed that EOFAhas the best performance formost of the test functions exceptfor F2 F7 and F11 where GSA outperforms EOFA It is knownfrom the reviews that different algorithmsmayperformbetter

The Scientific World Journal 7

Table 2 Comparison of performances for GSA FA and EOFA

Function

Optimization algorithmGSA FA EOFA

Optimized fitness valueBest Average Worst Best Average Worst Best Average Worst

F1 00096 0015 0024 1852 1960 1997lowastlowast 888119864 minus 16lowast 38119864 minus 15 799119864 minus 15

F2 207119864 minus 07lowast 609119864 minus 06 684119864 minus 05 360119864 minus 06 0069 091lowastlowast 546119864 minus 06 399119864 minus 04 00014F3 109119864 minus 06 206119864 minus 05 105119864 minus 04 000021 055 335lowastlowast 0lowast 488119864 minus 17 222119864 minus 16

F4 187119864 minus 07 987119864 minus 06 398119864 minus 05 611119864 minus 05 030 208lowastlowast 0lowast 178119864 minus 17 555119864 minus 17

F5 698119864 minus 06 00014 0030 44674 59246 68612lowastlowast 0lowast 226119864 minus 16 278119864 minus 15

F6 473119864 minus 09 135119864 minus 07 911119864 minus 07 130119864 minus 05 0043 058lowastlowast 159119864 minus 40lowast 145119864 minus 36 806119864 minus 36

F7 minus946lowast minus881 minus773 minus634 minus411 minus255lowastlowast minus933 minus890 minus785F8 141119864 + 82 162119864 + 85 889119864 + 85lowastlowast 422119864 + 81 224119864 + 84 252119864 + 85 515119864 + 77lowast 742119864 + 80 119119864 + 82

F9 00014 00052 0012 365818 585100 979440lowastlowast 969119864 minus 35lowast 614119864 minus 32 794119864 minus 31

F10 1599 3450 5379 35345 39446 42940lowastlowast 0lowast 099 319F11 2575lowast 2753 2947 71054620 1211549 1629028lowastlowast 2800 2873 2894F12 838922 971990 1027885 898136 1025749 1111171lowastlowast 6566lowast 1094737 162444F13 180119864 minus 4 326119864 minus 4 604119864 minus 4 11190 13960 15675lowastlowast 231119864 minus 35lowast 106119864 minus 32 513119864 minus 32

F14 00019 00048 0011 622804 878732 1027992lowastlowast 352119864 minus 34lowast 146119864 minus 31 656119864 minus 31

F15 2416 5179 7396 70822 547119864 + 08 392119864 + 09lowastlowast 584119864 minus 35lowast 192119864 minus 30 160119864 minus 29

0 20 40 60 80 100 120 140 160

02

025

03

035

04

Time (hour)

Load

pro

file (

pu

)

Figure 6 Hourly individual load profile for one week

than others for different problems [32 33] Performancesin terms of convergence between FA GSA and EOFA forrandomly chosen functions are illustrated in Figures 3 and4 It can be seen from the figures that FA always convergesprematurely and exhibits an unsatisfied result Meanwhileboth GSA and EOFA are able to escape from local minimaand provide better results However EOFA has the higherconvergence rate and gives better results compared to GSA

52 Performance of EOFA in Voltage Rise Mitigation In thiswork the 69-radial-bus system as shown in Figure 5 is usedwhere a 366MW PVDG is installed at Bus 61 The systemdata can be obtained from [34]The pattern for PVDGoutputpower values is obtained from the output of a lower scalegrid connected PVDG system installed at the Faculty ofEngineering and Built Environment Universiti KebangsaanMalaysia In this study the hourly PVDG output power from9 am to 6 pm collected for three months (91 days) is used

0 20 40 60 80 100 120 140 160096

098

1

102

104

106

Time (hour)

Volta

ge p

rofil

e (p

u)

With PV onlyWith PV and BESS

Without PV and BESSUpper limit

Figure 7 Effect of PV and BESS on PVDG bus voltage profiles

Besides BESS is assumed to be installed at the PVDG busAccording to the PVDG bus voltage at a particular hour ifthe voltage exceeds the maximum limit (105 pu) or is lowerthan the minimum limit (095 pu) the BESS will be activatedand the BESS power for that particular hour is decided bythe optimization process either to inject (discharge) or tostore (charging) power from the systemThe upper and lowerlimits for the SOC of the BESS are set to be 100 and 20respectivelyWeekly each load bus profile used in this study isshown in Figure 6 The BESS is turned off temporarily whenit achieves either upper or lower limits In this work sincethe voltage profiles at all times are above the minimum limitof 095 pu the BESS does not discharge when the PVDG isactive Therefore the BESS is set to discharge at 7 pm rightafter the PVDG is inactive at the night time in order toprovide a capacity for the BESS to continue charging on thefollowing day

8 The Scientific World Journal

0 1000 2000 3000 4000 5000 6000

0

5

10

Time (hour)

BESS

out

put p

ower

(W)

minus5

times105

(a)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(b)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(c)

Figure 8 Hourly BESS output power for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(a)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(b)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(c)

Figure 9 SOC for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

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International Journal of

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FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

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StructuresJournal of

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

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International Journal ofPhotoenergy

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Nuclear InstallationsScience and Technology of

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Solar EnergyJournal of

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Wind EnergyJournal of

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Nuclear EnergyInternational Journal of

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High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

6 The Scientific World Journal

18 2331 2 4 5 6 7 8 9 10 11 12 13 14 15 16 17 19 20 21 24 25 26 2722

51 52 68 69

4947 48 50

36 38 39 40 43 44 45 464137 42

66 67

53 55 56 57 61 62 6358 6459 65605428 30 32 33 35343129

Bus with PVDG and BESS

Figure 5 Single-line diagram of the 69-bus distribution system

number of iterations is not achieved yet compare thejumping rate (Jr) based on the criteria given by (12)If the opposite generation is generated again only 119899fittest current firefly individuals from 119875 and 119875

119900are

chosen for next iteration(vi) Repeat step (iii) until stopping criteria are achieved

The BESS output values for each hour are obtained(vii) Then EOFA is used again to determine the optimal

BESS size by considering the SOC constraints usingthe objective function as shown in (3)

5 Results and Discussion

51 Performance Assessment of the Proposed EOFA Fifteenbenchmark test functions for unconstrained global optimiza-tion [31] are chosen in order to evaluate the performance ofEOFA The name dimension size and the global minima ofeach test function are presented in Table 1 Besides a compar-ative study is conducted with gravitational search algorithm(GSA) [14] in order to show the superior performanceof EOFA in solving most of the benchmark optimizationproblems In addition FA [15] is included in the comparisonas well showing the improvement of conventional method byusing EOFA The setting of parameters including populationsize the number of maximum iterations and some param-eters from the optimization algorithms is decided throughtrial and error procedure and experimentation depends onthe system size the complexity of the objective functions andconvergence characteristics of the optimization algorithmsas well as the time consumed to complete the optimizationprocess In this work the population size 119899 is set to be 50and the number of maximum iterations is taken as 1000 forall algorithms used in the comparison For FA and EOFA thevalues for 120573

119900 initial alpha delta and gamma are defined as

1 02 097 and 1 respectively For EOFA the jumping rate isJr = 03 while the inertia weights 120596max and 120596min are 14 and

Table 1 Test functions for unconstrained global optimization

Function Name of the function Dimension size Global minimaF1 Ackley function 30 0F2 Beale function 2 0F3 Bohachevsky function 1 2 0F4 Bohachevsky function 3 2 0F5 Griewank function 30 0F6 Matya function 2 0F7 Michalewicz function 10 minus966F8 Perm function 30 0F9 Powell function 30 0F10 Rastrigin function 30 0F11 Rosenbrock function 30 0F12 Schwefel function 30 0F13 Sphere function 30 0F14 Sum square function 30 0F15 Zakharov function 30 0

05 respectively For GSA the initial gravity constant 119866119900 is

set to be 100 while the best applying force Kbest decreasesmonotonically from 100 to 25 The parameter 120591 is set tobe 8 of the total number of dimensions

After 50 runs on each test function the performances(fitness value) of each algorithm are reported in Table 2 wherethe values with ldquolowastrdquo indicate the best performance and thevalues with ldquolowastlowastrdquo indicate the worst performance It can beseen from Table 2 that the performances for FA are the worstmost of the time compared to GSA and EOFA This can becaused by premature convergence after trapping in a localoptimum On the other hand it can be observed that EOFAhas the best performance formost of the test functions exceptfor F2 F7 and F11 where GSA outperforms EOFA It is knownfrom the reviews that different algorithmsmayperformbetter

The Scientific World Journal 7

Table 2 Comparison of performances for GSA FA and EOFA

Function

Optimization algorithmGSA FA EOFA

Optimized fitness valueBest Average Worst Best Average Worst Best Average Worst

F1 00096 0015 0024 1852 1960 1997lowastlowast 888119864 minus 16lowast 38119864 minus 15 799119864 minus 15

F2 207119864 minus 07lowast 609119864 minus 06 684119864 minus 05 360119864 minus 06 0069 091lowastlowast 546119864 minus 06 399119864 minus 04 00014F3 109119864 minus 06 206119864 minus 05 105119864 minus 04 000021 055 335lowastlowast 0lowast 488119864 minus 17 222119864 minus 16

F4 187119864 minus 07 987119864 minus 06 398119864 minus 05 611119864 minus 05 030 208lowastlowast 0lowast 178119864 minus 17 555119864 minus 17

F5 698119864 minus 06 00014 0030 44674 59246 68612lowastlowast 0lowast 226119864 minus 16 278119864 minus 15

F6 473119864 minus 09 135119864 minus 07 911119864 minus 07 130119864 minus 05 0043 058lowastlowast 159119864 minus 40lowast 145119864 minus 36 806119864 minus 36

F7 minus946lowast minus881 minus773 minus634 minus411 minus255lowastlowast minus933 minus890 minus785F8 141119864 + 82 162119864 + 85 889119864 + 85lowastlowast 422119864 + 81 224119864 + 84 252119864 + 85 515119864 + 77lowast 742119864 + 80 119119864 + 82

F9 00014 00052 0012 365818 585100 979440lowastlowast 969119864 minus 35lowast 614119864 minus 32 794119864 minus 31

F10 1599 3450 5379 35345 39446 42940lowastlowast 0lowast 099 319F11 2575lowast 2753 2947 71054620 1211549 1629028lowastlowast 2800 2873 2894F12 838922 971990 1027885 898136 1025749 1111171lowastlowast 6566lowast 1094737 162444F13 180119864 minus 4 326119864 minus 4 604119864 minus 4 11190 13960 15675lowastlowast 231119864 minus 35lowast 106119864 minus 32 513119864 minus 32

F14 00019 00048 0011 622804 878732 1027992lowastlowast 352119864 minus 34lowast 146119864 minus 31 656119864 minus 31

F15 2416 5179 7396 70822 547119864 + 08 392119864 + 09lowastlowast 584119864 minus 35lowast 192119864 minus 30 160119864 minus 29

0 20 40 60 80 100 120 140 160

02

025

03

035

04

Time (hour)

Load

pro

file (

pu

)

Figure 6 Hourly individual load profile for one week

than others for different problems [32 33] Performancesin terms of convergence between FA GSA and EOFA forrandomly chosen functions are illustrated in Figures 3 and4 It can be seen from the figures that FA always convergesprematurely and exhibits an unsatisfied result Meanwhileboth GSA and EOFA are able to escape from local minimaand provide better results However EOFA has the higherconvergence rate and gives better results compared to GSA

52 Performance of EOFA in Voltage Rise Mitigation In thiswork the 69-radial-bus system as shown in Figure 5 is usedwhere a 366MW PVDG is installed at Bus 61 The systemdata can be obtained from [34]The pattern for PVDGoutputpower values is obtained from the output of a lower scalegrid connected PVDG system installed at the Faculty ofEngineering and Built Environment Universiti KebangsaanMalaysia In this study the hourly PVDG output power from9 am to 6 pm collected for three months (91 days) is used

0 20 40 60 80 100 120 140 160096

098

1

102

104

106

Time (hour)

Volta

ge p

rofil

e (p

u)

With PV onlyWith PV and BESS

Without PV and BESSUpper limit

Figure 7 Effect of PV and BESS on PVDG bus voltage profiles

Besides BESS is assumed to be installed at the PVDG busAccording to the PVDG bus voltage at a particular hour ifthe voltage exceeds the maximum limit (105 pu) or is lowerthan the minimum limit (095 pu) the BESS will be activatedand the BESS power for that particular hour is decided bythe optimization process either to inject (discharge) or tostore (charging) power from the systemThe upper and lowerlimits for the SOC of the BESS are set to be 100 and 20respectivelyWeekly each load bus profile used in this study isshown in Figure 6 The BESS is turned off temporarily whenit achieves either upper or lower limits In this work sincethe voltage profiles at all times are above the minimum limitof 095 pu the BESS does not discharge when the PVDG isactive Therefore the BESS is set to discharge at 7 pm rightafter the PVDG is inactive at the night time in order toprovide a capacity for the BESS to continue charging on thefollowing day

8 The Scientific World Journal

0 1000 2000 3000 4000 5000 6000

0

5

10

Time (hour)

BESS

out

put p

ower

(W)

minus5

times105

(a)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(b)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(c)

Figure 8 Hourly BESS output power for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(a)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(b)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(c)

Figure 9 SOC for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 7

Table 2 Comparison of performances for GSA FA and EOFA

Function

Optimization algorithmGSA FA EOFA

Optimized fitness valueBest Average Worst Best Average Worst Best Average Worst

F1 00096 0015 0024 1852 1960 1997lowastlowast 888119864 minus 16lowast 38119864 minus 15 799119864 minus 15

F2 207119864 minus 07lowast 609119864 minus 06 684119864 minus 05 360119864 minus 06 0069 091lowastlowast 546119864 minus 06 399119864 minus 04 00014F3 109119864 minus 06 206119864 minus 05 105119864 minus 04 000021 055 335lowastlowast 0lowast 488119864 minus 17 222119864 minus 16

F4 187119864 minus 07 987119864 minus 06 398119864 minus 05 611119864 minus 05 030 208lowastlowast 0lowast 178119864 minus 17 555119864 minus 17

F5 698119864 minus 06 00014 0030 44674 59246 68612lowastlowast 0lowast 226119864 minus 16 278119864 minus 15

F6 473119864 minus 09 135119864 minus 07 911119864 minus 07 130119864 minus 05 0043 058lowastlowast 159119864 minus 40lowast 145119864 minus 36 806119864 minus 36

F7 minus946lowast minus881 minus773 minus634 minus411 minus255lowastlowast minus933 minus890 minus785F8 141119864 + 82 162119864 + 85 889119864 + 85lowastlowast 422119864 + 81 224119864 + 84 252119864 + 85 515119864 + 77lowast 742119864 + 80 119119864 + 82

F9 00014 00052 0012 365818 585100 979440lowastlowast 969119864 minus 35lowast 614119864 minus 32 794119864 minus 31

F10 1599 3450 5379 35345 39446 42940lowastlowast 0lowast 099 319F11 2575lowast 2753 2947 71054620 1211549 1629028lowastlowast 2800 2873 2894F12 838922 971990 1027885 898136 1025749 1111171lowastlowast 6566lowast 1094737 162444F13 180119864 minus 4 326119864 minus 4 604119864 minus 4 11190 13960 15675lowastlowast 231119864 minus 35lowast 106119864 minus 32 513119864 minus 32

F14 00019 00048 0011 622804 878732 1027992lowastlowast 352119864 minus 34lowast 146119864 minus 31 656119864 minus 31

F15 2416 5179 7396 70822 547119864 + 08 392119864 + 09lowastlowast 584119864 minus 35lowast 192119864 minus 30 160119864 minus 29

0 20 40 60 80 100 120 140 160

02

025

03

035

04

Time (hour)

Load

pro

file (

pu

)

Figure 6 Hourly individual load profile for one week

than others for different problems [32 33] Performancesin terms of convergence between FA GSA and EOFA forrandomly chosen functions are illustrated in Figures 3 and4 It can be seen from the figures that FA always convergesprematurely and exhibits an unsatisfied result Meanwhileboth GSA and EOFA are able to escape from local minimaand provide better results However EOFA has the higherconvergence rate and gives better results compared to GSA

52 Performance of EOFA in Voltage Rise Mitigation In thiswork the 69-radial-bus system as shown in Figure 5 is usedwhere a 366MW PVDG is installed at Bus 61 The systemdata can be obtained from [34]The pattern for PVDGoutputpower values is obtained from the output of a lower scalegrid connected PVDG system installed at the Faculty ofEngineering and Built Environment Universiti KebangsaanMalaysia In this study the hourly PVDG output power from9 am to 6 pm collected for three months (91 days) is used

0 20 40 60 80 100 120 140 160096

098

1

102

104

106

Time (hour)

Volta

ge p

rofil

e (p

u)

With PV onlyWith PV and BESS

Without PV and BESSUpper limit

Figure 7 Effect of PV and BESS on PVDG bus voltage profiles

Besides BESS is assumed to be installed at the PVDG busAccording to the PVDG bus voltage at a particular hour ifthe voltage exceeds the maximum limit (105 pu) or is lowerthan the minimum limit (095 pu) the BESS will be activatedand the BESS power for that particular hour is decided bythe optimization process either to inject (discharge) or tostore (charging) power from the systemThe upper and lowerlimits for the SOC of the BESS are set to be 100 and 20respectivelyWeekly each load bus profile used in this study isshown in Figure 6 The BESS is turned off temporarily whenit achieves either upper or lower limits In this work sincethe voltage profiles at all times are above the minimum limitof 095 pu the BESS does not discharge when the PVDG isactive Therefore the BESS is set to discharge at 7 pm rightafter the PVDG is inactive at the night time in order toprovide a capacity for the BESS to continue charging on thefollowing day

8 The Scientific World Journal

0 1000 2000 3000 4000 5000 6000

0

5

10

Time (hour)

BESS

out

put p

ower

(W)

minus5

times105

(a)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(b)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(c)

Figure 8 Hourly BESS output power for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(a)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(b)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(c)

Figure 9 SOC for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

8 The Scientific World Journal

0 1000 2000 3000 4000 5000 6000

0

5

10

Time (hour)

BESS

out

put p

ower

(W)

minus5

times105

(a)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(b)

0 1000 2000 3000 4000 5000 6000Time (hour)

0

5

10

BESS

out

put p

ower

(W)

minus5

times105

(c)

Figure 8 Hourly BESS output power for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(a)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(b)

0 1000 2000 3000 4000 5000 60002030405060708090

100

Time (hour)

SOC

()

(c)

Figure 9 SOC for optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 9

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(a)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(b)

0 1000 2000 3000 4000 5000 6000095

1

105

11

Time (hour)

Volta

ge p

rofil

e (p

u)

Without BESSWith BESSUpper limit

(c)

Figure 10 Comparison of voltage profile with and without optimal BESS size obtained with (a) EOFA (b) FA and (c) GSA

Figure 7 shows the comparison of voltage profiles ofPVDG bus for one week where 3 cases are included namelythe system without PVDG and BESS system with PVDGonly and system with PVDG and EOFA optimized BESSFrom Figure 7 it can be seen that the voltage rises greatlyafter the PVDG is installed into the system and exceeds thelimit of 105 pu However the voltage magnitude after theinstallation of BESS is limited within the maximum limit of105 pu All system modeling and simulations in this studyare done using MATLAB software and distribution load flowprogram adopted from [35 36]

Besides BESS optimized with GSA and FA is included inthis work to validate the effectiveness of EOFA in BESS sizingFor the first optimization process in getting the optimal BESSoutput power for each hour the maximum iteration numberand the population size 119899 in all algorithms are set to be50 and 10 respectively while for the second optimizationprocess in obtaining the optimal BESS size those parametersare set to be 100 and 50 respectively for three algorithmsnamely EOFA GSA and FA

Theperformances of EOFA FA andGSA in obtaining theoptimal BESS size are discussed as follows Figure 8 showsthe hourly BESS output power that is to be injected (negative

value) or sink (positive value) at Bus 61 in the 69-bus systemaccording to the SOC of optimal BESS size obtained fromall three algorithms The SOC for EOFA FA and GSA areillustrated in Figure 9 For EOFA the BESS was turned offdue to the SOC constraint for a total of 385 hours with theoptimal BESS capacity of 231MWh Meanwhile for FA andGSA the BESS was turned off due to the SOC constraint fora total of 336 hours and 287 hours with the optimal BESScapacity of 242MWh and 239MWh respectively From theresult it can be seen that by using EOFA the BESS size isthe smallest even though the number of total off-time for theBESS is relatively large Smaller BESS size is better in termsof saving the installation cost However the total number ofBESS off-time can be decreased by increasing the BESS sizeas suggested by GSA and FA algorithm

Figure 10 shows the comparison of the voltage profileat the PVDG bus with and without BESS for the whole 91days (6552 hours) In this study the voltage range is aimedat being between 105 pu and 095 pu where before the BESSwas installed the range falls between 108 pu and 096 puThis means that the only voltage rise problem existed inthis case After installing BESS with optimal size obtainedwith various algorithms the voltage rises are found to be

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

10 The Scientific World Journal

Table 3 Comparison of performance for GSA FA and EOFA in battery sizing

Optimizationalgorithm

PV size(MWp)

Maximum load(MW)

Minimum load(MW)

BESS capacity(MWh)

BESS off-time (hour)

Total number of hoursthe voltage exceeding 105 puWith BESS(hour)

Without BESS(hour)

GSA366 152 061

239 287 168 297FA 242 336 196 297EOFA 231 385 78 297

reduced to the targeted range in most of the time EOFAkeeps most of the voltage values within the range where thevoltage values exceed 105 pu for a total of 78 hours out of6552 hours (119) On the other hand the total number ofhours for the voltage values exceeding 105 pu for FA andGSA optimized BESS size is 196 hours (299) and 168 hours(256) respectively It can be seen that EOFA has the bestperformance comparatively in solving voltage rise problemin the PVDG integrated 69-bus system Table 3 shows thesummary and comparative results obtained from GSA FAand EOFA

6 Conclusion

A new optimization technique named EOFA is presentedfor determining optimal BESS sizing in order to solve theproblemof voltage rise due to the PVDG installation in powerdistribution systems The performance and effectiveness ofEOFA were extensively tested on 15 unconstrained globaloptimization functions and the results were compared withother existing optimization techniques namely FA and GSAIt can be concluded that the EOFA is more effective thanthe aforementioned optimization techniques in obtaining theglobal optimumvalue for the test functionsThe optimizationproblem formulation aims to reduce the voltage deviationof the system with optimal BESS size This method wasextensively tested on the 69-bus system and the results werecompared with FA and GSA Based on the results it can beconcluded that EOFA is more effective than the FA and GSAin obtaining optimal size for the BESS where EOFA gives theminimum BESS size of 239MWh and minimum number ofhours for the voltage values exceeding 105 pu which is 78hours

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

The authors are grateful to the Universiti KebangsaanMalaysia (UKM) for supporting this study under GrantsGUP-2013-001 and ERGS12013TK02UKM031

References

[1] N C Scott D J Atkinson and J EMorrell ldquoUse of load controlto regulate voltage on distribution networks with embeddedgenerationrdquo IEEE Transactions on Power Systems vol 17 no 2pp 510ndash515 2002

[2] N Kakimoto Q-Y Piao and H Ito ldquoVoltage control ofphotovoltaic generator in combination with series reactorrdquoIEEE Transactions on Sustainable Energy vol 2 no 4 pp 374ndash382 2011

[3] J Cappelle J Vanalme S Vispoel et al ldquoIntroducing smallstorage capacity at residential PV installations to preventovervoltagesrdquo in Proceedings of the International Conference onSmart Grid Communications (SmartGridComm 11) pp 534ndash539 Brussels Belgium October 2011

[4] H Kihara A Yokoyama K M Liyanage and H SakumaldquoOptimal placement and control of BESS for a distributionsystem integrated with PV systemsrdquo Journal of InternationalCouncil on Electrical Engineering vol 1 no 3 pp 298ndash303 2011

[5] W X Shen ldquoOptimally sizing of solar array and battery in astandalone photovoltaic system inMalaysiardquoRenewable Energyvol 34 no 1 pp 348ndash352 2009

[6] P Arun R Banerjee and S Bandyopadhyay ldquoOptimum siz-ing of photovoltaic battery systems incorporating uncertaintythrough design space approachrdquo Solar Energy vol 83 no 7 pp1013ndash1025 2009

[7] T K A Brekken A Yokochi A Von Jouanne Z Z Yen HM Hapke and D A Halamay ldquoOptimal energy storage sizingand control for wind power applicationsrdquo IEEE Transactions onSustainable Energy vol 2 no 1 pp 69ndash77 2011

[8] T Khatib A Mohamed K Sopian and M Mahmoud ldquoAnew approach for optimal sizing of standalone photovoltaicsystemsrdquo International Journal of Photoenergy vol 2012 ArticleID 391213 7 pages 2012

[9] Y Ru J Kleissl and S Martinez ldquoStorage size determinationfor grid-connected photovoltaic systemsrdquo IEEE Transactions onSustainable Energy vol 4 no 1 pp 68ndash81 2013

[10] D Goldberg and J Holland ldquoGenetic algorithms and machinelearningrdquoMachine Learning vol 3 no 2-3 pp 95ndash99 1988

[11] MDorigo VManiezzo andA Colorni ldquoAnt system optimiza-tion by a colony of cooperating agentsrdquo IEEE Transactions onSystems Man and Cybernetics B Cybernetics vol 26 no 1 pp29ndash41 1996

[12] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 Perth Australia December1995

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World Journal 11

[13] D Karaboga ldquoAn idea based on honey bee swarm for numer-ical optimizationrdquo Tech Rep TR06 Erciyes University PressMelikgazi Turkey 2005

[14] E Rashedi H Nezamabadi-pour and S Saryazdi ldquoGSA agravitational search algorithmrdquo Information Sciences vol 179no 13 pp 2232ndash2248 2009

[15] X Yang Nature-Inspired Metaheuristic Algorithms LuniverPress 2008

[16] Z Cui S Fan J Zeng and Z Shi ldquoArtificial plant optimisa-tion algorithmwith three-period photosynthesisrdquo InternationalJournal of Bio-Inspired Computation vol 5 no 2 pp 133ndash1392013

[17] B Yu Z Cui and G Zhang ldquoArtificial plant optimizationalgorithm with correlation branchesrdquo Journal of Bioinformaticsand Intelligent Control vol 2 no 2 pp 146ndash155 2013

[18] L Xie J Zeng and R A Formato ldquoSelection strategies forgravitational constant G in artificial physics optimisation basedon analysis of convergence propertiesrdquo International Journal ofBio-Inspired Computation vol 4 no 6 pp 380ndash391 2012

[19] A S Reddy and K Vaisakh ldquoEnvironmental constrained eco-nomic dispatch by modified shuffled frog leaping algorithmrdquoJournal of Bioinformatics and Intelligent Control vol 2 no 3pp 216ndash222 2013

[20] K Jiang B Song X Shi and T Song ldquoAn overview ofmembrane computingrdquo Journal of Bioinformatics and IntelligentControl vol 1 no 1 pp 17ndash26 2012

[21] E I Vrettos and S A Papathanassiou ldquoOperating policy andoptimal sizing of a high penetration RES-BESS system for smallisolated gridsrdquo IEEE Transactions on Energy Conversion vol 26no 3 pp 744ndash756 2011

[22] W Z Chen Q B Li L Shi et al ldquoEnergy storage sizing fordispatchability of wind farmrdquo in Proceedings of the 11th Inter-national Conference on Environment and Electrical Engineering(EEEIC 12) pp 382ndash387 Venice Italy May 2012

[23] T Chaiyatham and I Ngamroo ldquoBee colony optimization ofbattery capacity and placement for mitigation of voltage riseby PV in radial distribution networkrdquo in Proceedings of theInternational Power and Energy Conference (IPEC 12) pp 13ndash18 Ho Chi Minh City Vietnam December 2012

[24] H R Tizhoosh ldquoOpposition-based learning a new schemefor machine intelligencerdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation (CIMCA 05) and International Conferenceon Intelligent Agents Web Technologies and Internet Commerce(IAWTIC 05) pp 695ndash701 Vienna Austria November 2005

[25] Y Tian W Gao and S Yan ldquoAn improved inertia weightfirefly optimization algorithm and applicationrdquo in Proceedingsof the International Conference on Control Engineering andCommunication Technology (ICCECT 12) pp 64ndash68 LiaoningChina December 2012

[26] M Z Daud A Mohamed and M A Hannan ldquoAn improvedcontrol method of battery energy storage system for hourlydispatch of photovoltaic power sourcesrdquo Energy Conversion andManagement vol 73 pp 256ndash270 2013

[27] X S Yang ldquoFirefly algorithms for multimodal optimizationrdquo inStochastic Algorithms Foundations andApplications vol 5792 ofLecture Notes in Computer Science pp 169ndash178 Springer BerlinGermany 2009

[28] S Rahnamayan H R Tizhoosh and M M A SalamaldquoOpposition-based differential evolution algorithmsrdquo in Pro-ceedings of the IEEE Congress on Evolutionary Computation(CEC 06) pp 2010ndash2017 Vancouver Canada July 2006

[29] A R Malisia and H R Tizhoosh ldquoApplying opposition-basedideas to the Ant Colony Systemrdquo in Proceedings of the IEEESwarm Intelligence Symposium (SIS 07) pp 182ndash189 HonoluluHawaii USA April 2007

[30] B Shaw V Mukherjee and S P Ghoshal ldquoA novel opposition-based gravitational search algorithm for combined economicand emission dispatch problems of power systemsrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 35no 1 pp 21ndash33 2012

[31] A Hedar ldquoTest functions for unconstrained global opti-mizationrdquo 2013 httpwww-optimaampikyoto-uacjpmem-berstudenthedarHedar filesTestGO filesPage364htm

[32] E Elbeltagi T Hegazy and D Grierson ldquoComparison amongfive evolutionary-based optimization algorithmsrdquo AdvancedEngineering Informatics vol 19 no 1 pp 43ndash53 2005

[33] E Rashedi H Nezamabadi-Pour and S Saryazdi ldquoBGSAbinary gravitational search algorithmrdquo Natural Computing vol9 no 3 pp 727ndash745 2010

[34] N Rugthaicharoencheep and S Sirisumrannukul ldquoFeederreconfiguration with dispatchable distributed generators indistribution system by tabu searchrdquo in Proceedings of the 44thInternational Universities Power Engineering Conference (UPEC09) pp 1ndash5 Glasgow UK September 2009

[35] J-H Teng ldquoA network-topology-based three-phase load flowfor distribution systemsrdquo Proceedings of the National ScienceCouncil Republic of China A vol 24 no 4 pp 259ndash264 2000

[36] J-H Teng and C-Y Chang ldquoBackwardforward sweep-basedharmonic analysis method for distribution systemsrdquo IEEETransactions on Power Delivery vol 22 no 3 pp 1665ndash16722007

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

TribologyAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

FuelsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofPetroleum Engineering

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Power ElectronicsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Advances in

CombustionJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Renewable Energy

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

StructuresJournal of

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear InstallationsScience and Technology of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Solar EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Wind EnergyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nuclear EnergyInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

High Energy PhysicsAdvances in

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014