electrical power and energy systems · optimal sizing of battery energy storage for micro-grid...

Electrical Power and Energy Systems 56 (2014) 42–54

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Optimal sizing of battery energy storage for micro-grid operationmanagement using a new improved bat algorithm

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.10.019

⇑ Corresponding author. Address: Department of Electrical Engineering, Marv-dasht Branch, Islamic Azad University, P.O. 73711-13119, Marvdasht, Iran. Tel.: +98917 7154688; fax: +98 728 3311172.

E-mail address: [email protected] (B. Bahmani-Firouzi).

Bahman Bahmani-Firouzi ⇑, Rasoul Azizipanah-AbarghooeeDepartment of Electrical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran

a r t i c l e i n f o

Article history:Received 5 March 2013Received in revised form 11 September2013Accepted 12 October 2013

Keywords:Battery energy storage sizingDistributed generationImproved bat algorithmMicro-gridOperation managementRenewable energy sources

a b s t r a c t

In recent years, due to large integration of Renewable Energy Sources (RESs) like wind turbine and pho-tovoltaic unit into the Micro-Grid (MG), the necessity of Battery Energy Storage (BES) has increased dra-matically. The BES has several benefits and advantages in the MG-based applications such as short termpower supply, power quality improvement, facilitating integration of RES, ancillary service and arbitrage.This paper presents the cost-based formulation to determine the optimal size of the BES in the operationmanagement of MG. Also, some restrictions, i.e. power capacity of Distributed Generators (DGs), powerand energy capacity of BES, charge/discharge efficiency of BES, operating reserve and load demand satis-faction should be considered as well. The suggested problem is a complicated optimization problem, thecomplexity of which is increased by considering the above constraints. Therefore, a robust and strongoptimization algorithm is required to solve it. Herein, this paper proposes a new evolutionary techniquenamed improved bat algorithm that is used for developing corrective strategies and to perform least costdispatches. The performance of the approach is evaluated by one grid-connected low voltage MG wherethe optimal size of BES is determined professionally.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Micro-Grid (MG) is the corner stone and indispensable infra-structure of smart grid [1]. Nowadays, with increasing concernsand challenges about the fluctuation and intermittency of WindTurbine (WT) and Photo-Voltaic (PV) units as Renewable EnergySources (RESs) in the MG system, the Micro-Grid Central Controller(MGCC) needs to implement Battery Energy Storage (BES). Combi-nation of the BES can buffer the power output of RESs by storing ex-cess energy throughout times of high availability and inject it to theMG during a power shortage. So, in recent years, the studies ofresearchers have been compulsorily gravitated to determine theappropriate capacity or size of BES for an optimized Operation Man-agement of MG (OMMG). Lee and Chen [2] introduced the first BESsizing formulation for two industrial customers in Taiwan PowerCompany System. Mitra proposed a suitable technique of selectingthe size of a BES in such a manner as to satisfy a reliability index [3].Le and Nguyen presented the BES sizing approach for wind turbinesystems to guarantee the peak load demand [4]. Kaldellis et al. of-fered a selection method of the most cost-efficient BES in order tomatch an inconstant solar-based energy system in [5]. Chen et al.focused on determining the size of BES for a MG system in Singa-

pore using a modeling language for mathematical programming[6]. Mohammadi et al. [7] investigated an optimized design of MGcontaining PV array, Fuel Cell (FC) and BES in the presence of otherDistributed Generators (DGs) under pool and hybrid electricitymarket model. Ekren and Ekren Banu [8] investigated the size opti-mization of a PV/WT hybrid energy conversion system with BESusing Simulated Annealing (SA) algorithm. Aghamohammadi andAbdolahinia [9] presented a new method for determining optimalsize of a BES for primary frequency control of a MG consisting of Mi-cro-Turbine (MT), diesel generator, FC and PV system. Jia et al. [10]proposed a statistical model based on Monte Carlo to determine thecapacity of BES-super capacitor hybrid energy storage system in anautonomous MG.

Consequently, the study about BES sizing and its role in MG sys-tem has become a topic of interest in many literature. According tothe previous sentences, the OMMG is implemented to MG by theMGCC for obtaining optimum generation cost while at the sametime the BES with optimal and appropriate size can decrease gen-eration cost and that is why the study of OMMG in the presence ofBES sizing has become a common topic subject of discussion. Inthis regard, an appropriate method on the basis of cost model ofBES is proposed in this study in order to determine optimal sizeof BES for the OMMG problem.

The OMMG problem is one of the backbone optimization toolsfor smart energy manager or MGCC in which the optimal powerset points of BES and DGs are determined while all of the quality,

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Nomenclature

Indicesa velocity updating strategy indexiPV, iWT photo-voltaic (PV) and wind turbine (WT) indi-

ces, respectivelyiter iteration index of the proposed Improve Bat

Algorithm (IBA)BES, grid Battery Energy Storage (BES) and grid indices,

respectivelyFC, MT Fuel Cell (FC) and Micro-Turbine (MT) indices,

respectivelym bat indext time index

ConstantsBidgrid,t, BidBES,t, BidMT,t,BidFC,t, BidiPV ;t ;BidiWT ;t Bid of utility, BES, MT, FC, PV, WT at time t,

respectively (€ct/kW h)FCBES, MCBES fixed and maintenance cost for BES, respectively

(€ct/kW h)f maxm ; f min

m maximum and minimum pulse frequency for batm, respectively

IR interest rate for financing the installed BESIter_max maximum number of iteration for the proposed IBALT lifetime of the installed BES (year)NPOP number of bats in the population of IBANiter

1 ;Niter2 ;Niter

3 ;Niter4 number of bats which select the velocityupdating strategy 1, 2, 3, and 4, respectively

NT operation time horizon (h)nv number of variables of each batORt minutes operating reserve requirements (kW)OMDG fixed operation and maintenance cost of

Distributed Generators (DGs) (€ct)OMFC ;OMMT ;

OMiPV;OMiWT

fixed operation and maintenance cost of FC, MT, PVand WT, respectively (€ct/kW h)

Pgrid,max, Pgrid,min maximum/minimum limits of power produc-tion for the utility, respectively (kW)

PDemand,t electrical load demand at time t (kW)PBES,max, PBES,min maximum/minimum producible power of BES,

respectively (kW)PFC,max, PFC,min maximum/minimum producible power of FC,

respectively (kW)PMT,max, PMT,min maximum/minimum producible power of MT,

respectively (kW)rand(.) random function generators in the range [0,1]randm(1,nv) random vector with the dimension of 1 � nv relating

to the mth batShutFC, ShutMT shut-down cost coefficient for FC and MT, respec-

tively (€ct)StartFC, StartMT start-up cost coefficient for FC and MT, respec-

tively (€ct)tax tax rate of utility power gridXmin, Xmax minimum and maximum boundary vectors of the con-

trol variable X, respectivelyaBA, cBA constants parameters for the Bat Algorithm (BA)Dt time interval durationgdischarge, gcharge discharge and charge efficiency of BES, respectivelye random function generators in the range [�1,1]h learning rate to control the learning speed in

VariablesAiter

mean mean of the pulse loudness for all bats in itera-tion iter

ACUMa accumulator parameter for velocity updatingstrategy a

CBES,min, CBES,max minimum and maximum size of BESCBES,t energy stored in the BESCostgrid,t cost of trade with the up-stream grid at time t

(€ct)CostDG,t, CostBES,t cost of fuel and operating power of DGs and BES

at time t, respectively (€ct)f iterm ;Aiter

m ; riterm pulse frequency, loudness and emission rate for bat

m in iteration iter, respectivelyGbestiter, Worstiter best and worst position among all bats in iter-

ation iterF total costs (€ct)Meaniter mean population vector in iteration iterPgrid,t, PBES,t, PMT,t, PFC,t, PiPV ;t and PiWT ;t power of utility, BES, MT, FC,

PV and WT, respectively (kW)PBES;t ; PBES;t maximum discharge and charge rates of BES at time t,

respectively (kW)Pbestiter

m personal best position of bat m in iteration iterproba probability of velocity updating strategy aSDCFC,t,SDCMT,t shut-down cost for FC and MT at time t, respec-

tively (€ct)SUCFC,t, SUCMT,t start-up cost for FC and MT at time t, respectively

(€ct)TCPDBES total cost per day of BES (€ct)Xiter

m ;Viterm position and velocity of bat m in iteration iter,

respectivelyuBES,t, uMT,t, uFC,t status (On or Off) of BES, MT and FC at time t,

respectivelyWFm weighting factor for the mth bat

Subscriptt tth time step (h)

AbbreviationsABC Artificial Bee ColonyBA Bat AlgorithmBES Battery Energy StorageDG Distributed GeneratorFC Fixed CostFC Fuel CellFSAPSO Fuzzy Self Adaptive Particle Swarm OptimizationGA Genetic AlgorithmGENCO Generating CompanyIBA Improved Bat AlgorithmIR Interest RateLT LifetimeMC Maintenance CostMG Micro-GridMGCC Micro-Grid Central ControllerMT Micro-TurbineOMMG Operation Management of Micro-GridOR Operating ReservePSO Particle Swarm OptimizationPV Photo-VoltaicRES Renewable Energy SourceRWM Roulette Wheel MechanismSA Simulated AnnealingSMES Superconducting Magnetic Energy StorageSP Successful PerformanceStd Standard deviationTLBO Teaching–Learning-Based OptimizationTCPD Total Cost Per DayWT Wind Turbine

B. Bahmani-Firouzi, R. Azizipanah-Abarghooee / Electrical Power and Energy Systems 56 (2014) 42–54 43

44 B. Bahmani-Firouzi, R. Azizipanah-Abarghooee / Electrical Power and Energy Systems 56 (2014) 42–54

inequality and dynamic constraints should be satisfied. The MGCChas the main responsibility for optimizing the MG operation. Fromthe point of view of MGCC, the objective of this complex optimiza-tion tool is to minimize operation cost. The research works in thisarea can be categorized in two major groups: (i) articles which eval-uated the presence performance of BESs and its optimum size onOMMG problem [2–10] and (ii) papers that did not consider the im-pact of BES optimal sizing on OMMG problem, e.g. [11–21].Although there is a vast body of research on the OMMG problemwithout taking into consideration the impacts of BES optimal sizing,little attention has been paid to the influence of BES sizing onOMMG problem. Chen et al. [11] proposed a new smart energymanagement system on the basis of the matrix real-coded geneticalgorithm to optimize OMMG. Chedid and Raiman utilized a linearprogramming technique to optimize the average production cost ofpower in a hybrid solar-wind MG [12]. Chakraborty et al. used a lin-ear programming method to minimize operation cost of MG and tooptimize the charge states of BES [13]. Sortomme and El-Sharkawiapplied Particle Swarm Optimization (PSO) algorithm to the OMMGproblem in [14]. Moghaddam et al. [15] proposed an expert multi-objective adaptive modified PSO algorithm for solving OMMG withRESs as well as a Micro-Turbine (MT), FC and BES over 24 h timehorizon. Moreover, an attempt was made to find an optimal sche-dule for multi-operation of a MG implementing a Fuzzy Self Adap-tive Particle Swarm Optimization (FSAPSO) algorithm in [16].Mohamed and Koivo presented a generalized formulation to deter-mine the optimal operating strategy with cost objective function fora MG in [17]. Niknam et al. proposed a new modified honey beemating optimization algorithm for optimal operation managementof a MG, including FC/WT/PV neglecting the BES technology in [18].Alvarez et al. developed a fast response optimization algorithm foractive-power dispatch to DGs in a distributed generation MG in[19]. Liao proposed a new chaotic quantum genetic algorithm tosolve environmental economic dispatch of smart MG containingDGs system in [20]. Al-Saedi et al. presented an optimal power flowcontroller for a utility connected MG on the basis of real-time self-tuning and used a PSO algorithm to solve it in [21].

Since the traditional optimization methods have some con-straints including continuity and derivability of the objective func-tion, most of the algorithms in the literature are established uponmeta-heuristic search techniques [22,23]. These techniques can beconsidered suitable choices for solving power system optimizationproblems because they have global search power, their ownconstraint handling capacity, are derivative-free, and have norestrictions on the shape of the objective function. Like the math-ematical methods the evolutionary algorithms have some disad-vantages too such as trapping in local optima and convergence tothe global optima over a long period of time. Therefore, selectinga robust and strong evolutionary algorithm in order to solve thecomplex problem has an important role. One of the new evolution-ary algorithms which has great potential is Bat Algorithm (BA).This algorithm has been presented by Yang in 2010 [24]. BA is apopulation-based iterative method that is simple, easy to imple-ment and robust. Besides the significant privileges of BA, it hassome drawbacks too, such as the possibility of being trapped in lo-cal optima in some cases. In this regard, the new version of BA isproposed and utilized in this study in order to enhance the searchability of this algorithm. In this improved version of BA (IBA), anew self-adaptive learning approach is suggested to probabilisti-cally conduct four BA updating strategies of velocity parallel tooptimizing the non-linear and complex OMMG problem. The mainobjective of these four strategies is to achieve an appropriate veloc-ity by distributing the swarm in the problem search space in such away that the exploration and exploitation procedures are balanced.

Finally, to verify the suitability of the presented algorithm it isapplied to a typical low voltage MG system. Simulation results

prove the ability of the proposed algorithm in finding the near glo-bal optima in the optimization problem. The main contributions ofthis paper can be summarized as: (1) Proposing the novel IBA algo-rithm and (2) considering the effects of optimal sizing of BES onOMMG problem.

2. Problem formulation

The mathematical formulation of the OMMG problem compris-ing objective function and constraints can be described as follows:

Minimize total costs [6,25]

MinFðXÞ ¼XNT

t¼1

ft þ OMDG þ TCPDBES ð1Þ

where

ft¼Costgrid;tþCostDG;tþCostBES;tþSUCFC;tþSUCMT;tþSDCFC;tþSDCMT;t

ð2Þ

Costgrid;t ¼Bidgrid;tPgrid;t if Pgrid;t > 0ð1� taxÞBidgrid;tPgrid;t if Pgrid;t < 00 if Pgrid;t ¼ 0

8><>: ð3Þ

CostDG;t¼BidMT;tPMT;tuMT;tþBidFC;tPFC;tuFC;tþPiPV ;tBidiPV ;tþPiWT ;tBidiWT ;t

ð4ÞSUCFC;t ¼ StartFC �maxð0;uFC;t � uFC;t�1Þ ð5Þ

SUCMT;t ¼ StartMT �maxð0;uMT;t � uMT;t�1Þ ð6Þ

SDCFC;t ¼ ShutFC �maxð0;uFC;t�1 � uFC;tÞ ð7Þ

SDCMT;t ¼ ShutMT �maxð0;uMT;t�1 � uMT;tÞ ð8Þ

OMDG ¼ ðOMFC þ OMMT þ OMiWT þ OMiPV Þ � NT ð9Þ

The total energy and operating cost of the MG includes theoperation cost of utility and BES, fuel costs of DGs, operation andmaintenance cost of DGs, start-up/shut-down costs of FC and MTas well as Total Cost Per Day of BES (TCPDBES). The cost of BES con-tains the one-time Fixed Cost (FC) and the annual MaintenanceCost (MC). The first term of this presented cost arises from the pur-chase of small battery blocks to make up BES. The second term is avariable cost proportional to the size of BES. So, the total cost ofbattery is (FCBES + MCBES) � CBES,max. CBES,max is the size of BES. Thetime horizon which is selected in this study is one day and theoperation cost is calculated over 24 h. Hence, modeling the TCPDBES

in €ct/day is needed. If the interest rate for financing the installedBES and its lifetime are considered as IR and LT, then the TCPDBES

installed in €ct/day can be obtained as follows [6]:

TCPDBES ¼CBES;max

365IRð1þ IRÞLT

ð1þ IRÞLT � 1FCBES þMCBES

!ð10Þ

The proposed operation problem is subjected to the followingconstraints:

(1) Electrical load demand balance [15]For a given electrical load demand PDemand,t at time t, thesummation of total generated power of FC, MT, PV, andWT and total absorbed or injected power to BES and utilityshould be the same as the total load demand. Thus, the elec-trical load demand balance operation can be modeled asfollows:

PFC;tuFC;t þ PMT;tuMT;t þ PiPV ;t þ PiWT ;t þ PBES;tuBES;t þ Pgrid;t

¼ PDemand;t t ¼ 1; . . . ;NT ð11Þ


(2) Dispatchable DGs constraints [16]The operating output of each dispatchable DGs, that is, FCand MT should be within its minimum and maximum limits.The generating capacity constraints are written in (12) and(13):

PFC;min 6 PFC;t 6 PFC;max t ¼ 1; . . . ;NT ð12Þ

PMT;min 6 PMT;t 6 PMT;max t ¼ 1; . . . ;NT ð13Þ

(3) BES constraints [6]Discharging mode:

CBES;tþ1¼maxfðCBES;t�DtPBES;t=gdischargeÞ;CBES;ming t¼1; .. . ;NT ð14ÞPBES;t 6 PBES;t 6 PBES;t t ¼ 1; . . . ;NT ð15Þ

Charging mode:

CBES;tþ1 ¼minfðCBES;t�DtPBES;tgchargeÞ;CBES;maxg t¼1; . . . ;NT ð16ÞPBES;t 6 PBES;t 6 PBES;t t ¼ 1; . . . ;NT ð17Þ

where

PBES;t ¼minfPBES;max;ðCBES;t�CBES;minÞgdischarge=Dtg t¼1; . . . ;NT ð18Þ

PBES;t ¼maxfPBES;min;ðCBES;t�CBES;maxÞ=gchargeDtg t¼1; . . . ;NT ð19Þ

In recent years, several important energy storage technologiesavailable for MG so far have been studied intensively. They com-prise BESs, flywheel energy storage, super-capacitor and Supercon-ducting Magnetic Energy Storage (SMES) [1]. In this study theLithium ion (Li-ion) BES is selected and used in the MG. The Li-ion BES is one of the most popular and is used in different powerprojects around the world. It has several advantages and benefitssuch as no memory effect, the highest energy density among othertypes of the BESs and a slow loss of charge when not in use [6]. Fur-thermore, it is necessary to note that it is considered globally as themajor energy storage device for defense, automotive, and aerospaceapplications in terms of high energy density [26].The proposed BES should fulfill the constraints from (14)–(19). Con-straints (14) and (15) are the limitations of released energy from theBES and power discharged by the BES, respectively. Also, the restric-tions on the stored energy in the BES and power charged by the gridto the BES are expressed as (16) and (17), respectively. As a result,the maximum and minimum charging/discharging rates are deter-mined as (18) and (19), respectively.

(4) Grid constraint

Pgrid;min 6 Pgrid;t 6 Pgrid;max t ¼ 1; . . . ;NT ð20Þ

(5) Operating reserve constraintIn most MG systems, MG reliability is maintained throughprocuring the energy storage, e.g. BES in this study and oper-ating reserves from DGs and BES. Operating Reserve (OR) isthe sum of reserved electrical power generation capacity ofturned on BES, FC, MT and utility in each time step. It canbe injected to the MG in less than 10 min and formulatedas follows:

PFC;maxuFC;t þ PMT;maxuMT;t þ Pgrid;max þ PBES;tuBES;t

P ORt þ PDemand;t t ¼ 1; . . . ;NT ð21Þ

where, ORt is the 10-min OR requirement at time t.

3. Improved Bat Algorithm (IBA)

3.1. Overview of original BA

BA is the most recent nature inspired optimization methoddeveloped by Xin-She Yang in 2010 [24] and is used for solvingthe different optimization problems. For example, it has been usedfor classifications in [27] and engineering design in [28,29]. A fuzzy

bat clustering method has been developed to solve ergonomicworkplace problems in [30]. A new enhanced bat-inspiredalgorithm has been proposed in [31] for finding linear supply func-tion equilibrium of Generating Companies (GENCOs) in the compet-itive electricity market. In the BA, each micro-bat in the initialpopulation uses a homologous pattern by implementingecholocation process for updating its position. Bat echolocation isa perceptual system in which a series of considerably loud ultra-sound waves are emitted to the environment to produce echoes.These waves that return to the two ears arrive with temporal delaysand different sound levels which enable bats to detect a specific ob-ject or prey. In order to develop the structure of BA and idealize theecholocation characteristics of bats, some assumptions are consid-ered in [24]: (i) Echolocation system is utilized by each bat; withthis characteristic the difference between prey and obstacle is dis-tinguished. (ii) Each bat m in the population of BA flies randomlyand emits a pulse with frequency f iter

m and loudness Aiterm . (iii) Fre-

quency adjustment and pulse rate setting riterm are done automati-

cally by all bats. During the searching process of each bat to findprey, frequency, loudness and pulse emission rate are changed.So, (iv) during the algorithm, the loudness Aiter

m will be varied froma large value to a minimum constant value. It is assumed that con-trol variables in section two are used as a position of each bat atiteration iter.

The pseudo-code of the BA is depicted in the following form,where f min

m and f maxm are respectively set to 0 and 2 in this study

and aBA and cBA are constants which both of which are set to 0.9.

The original BA

Initialize the bat populationCalculate the objective function for each batWhile the termination criterion is not satisfied do

For m = 1 to NPOP doUpdate the velocity and the position of each bat as

follows:

Viterm ¼ Viter�1

m þ f iterm Gbestiter�1 � Xiter�1

m

� �ð22Þ

Xiterm ¼ Xiter�1

m þ Viterm ð23Þ

f iterm ¼ f min

m þ randð:Þ f maxm � f min

m

� �ð24Þ

Generate a new solution for each bat locally usingrandom walk:

If randmð:Þ > riterm then

Generate a local solution around the Pbestiteri where

m – i is a randomly selected solution as follows:

Xiterm;new ¼ Xiter

m þ eAitermean Pbestiter

i � Xiterm

� �ð25Þ

ElseGenerate a local solution around the randomly

selected solution m – i as follows:

Xiterm;new ¼ Xiter

m þ eAitermean Xiter

i � Xiterm

� �ð26Þ

End if

If ðrandmð:Þ < Aiterm Þ&&ðFðXiter

m;newÞ < FðXiterm Þ Then

Xiterm ¼ Xiter

m;new

Increase riterm and decrease Aiter

m as follows:

Aiterm ¼ aBAAiter�1

m ; riterm ¼ r1

mð1� expð�cBAðiter þ 1ÞÞÞ ð27Þ

End IfEnd For

End While


From the aforementioned steps of the BA, it can be seen from(22)–(27) that BA has used the same dynamics of PSO as in [32],
and a similar process in expression (27) as a cooling schedule inSA for updating Aiter
m [33]. Despite some advantages and featuresof BA like simplicity, robustness, easy implementation and a goodcombination of the major advantages of PSO and SA, the BA insome cases is converged to local optima due to the lack of diversityof the bats. In order to overcome this deficiency, the new self-adap-tive learning mechanism of BA is used which will be described inthe next subsection.

3.2. Self-adaptive learning for the original BA

In this paper, a new self-adaptive learning approach is proposedto probabilistically conduct four BA updating strategies of velocityparallel to optimizing the OMMG problem. The main idea of thesefour strategies is to achieve an appropriate velocity by distributingthe bats in the problem search domain in such a way that thediversification (exploration) and intensification (exploitation) arebalanced. The acceptable balance between these two processes isvery essential to the overall performance of a meta-heuristic opti-mization algorithm. Too little diversification and too much intensi-fication could cause the system to be trapped in the local optima ofthe problem search space. This makes it too hard or even impossi-ble to obtain the global optimum solution. For this purpose, threesolutions q1 – q2 – q3 – m from the existing population are se-lected randomly and one of the following velocities updating strat-egies is chosen based on the Roulette Wheel Mechanism (RWM)and probabilistic approach according to [34] in order to generatethe new solution Xiter

m for equation (22) and (23) as follows:

Velocity updating strategy 1:

Viterm;1 ¼ Viter�1

m;a þ 0:3f iterm þ 0:4

� �ðGbestiter�1 � Xiter�1

m Þ

þ ð0:6randð:Þ þ 0:4ÞðGbestiter�1 �Worstiter�1Þm ¼ 1; :::;Niter

1 ; a ¼ 1; . . . ;4 ð28Þ


Viterm;2 ¼ Viter�1

m;a þ Xiterq1þ randð:ÞðXiter

q2� Xiter

q3Þ

� �m

¼ 1; . . . ;Niter2 ; a ¼ 1; . . . ;4 ð29Þ


Viterm;3¼ randð:ÞViter�1

m;a þð0:3randð:Þþ0:2Þf iterm ðGbestiter�1�Xiter�1

m Þ;m¼1;. . . ;Niter

3 ; a¼1; .. . ;4 ð30Þ


Viterm;4 ¼ randð:ÞViter�1

m;a þ 0:5ð0:3randð:Þ

þ 0:2Þf iterm ðGbestiter�1 � roundð1þ randð:ÞÞMeaniter�1Þ;

m ¼ 1; . . . ;Niter4 ; a ¼ 1; . . . ;4 ð31Þ

As a means to implement the new version of BA technique, first,the probability of all of the aforementioned methods being chosenby the bats is assumed to be proba = 0.25 (a = 1, . . . , 4). Besides, anadjustable parameter called accumulator is designed as ACUMa = 0(a = 1, . . . , 4).

In each iterate of the optimization algorithm the bats are sortedon the basis of their objective function values while m = 1 repre-sents the bat with the best fitness function value and the m = NPOPstands for the bat with the worst fitness function amount. After-

ward, a weight factor is allocated to each of the bats in the popu-lation. The better solutions get the larger weight factors asfollows [34]:

WFm ¼logðNPOP �mþ 1Þ

logð1Þ þ � � � þ logðNPOPÞ ; m ¼ 1; . . . ;NPOP ð32Þ

The accumulator of each velocity updating strategy is updatedas follows [34]:

ACUMa ¼ ACUMa þWFmm mm ¼ 1; . . . ;Na ð33Þ

where Na is the number of bats selecting ath velocity updatingmethod and WFmm (mm = 1, . . . , Na) are the weight factors corre-sponding to them. The probability is computed as [34]:

proba ¼ ð1� hÞproba þ hACUMa

Iter max; ða ¼ 1; . . . ;4Þ ð34Þ

where h is set to 0.161 in this paper. Finally, the normalized proba-bility values are calculated as follows:

proba ¼ proba=ðprob1 þ prob2 þ prob3 þ prob4Þ; ða ¼ 1; . . . ;4Þð35Þ

Each particle considering the probability of each velocity updatingstrategy and using RWM chooses one of the abovementioned meth-ods to improve its solution.

4. Implementation of the suggested algorithm on the OMMGproblem

In Section 2, the OMMG problem has been described as animportant optimization problem for MGCC and a new IBA is pro-posed in Section 3 to solve this problem. In order to find optimumsize of BES and optimum set point of DGs, BES and upstream powergrid, an iterative method based on IBA is proposed in this sectionwith 10 steps as follows:

Step1. Define all information available to all DGs and BES: Inthis step, the input data including the DGs data, i.e.bid, operation and maintenance cost and generationcapacity, power output of WT and PV, minimum/maxi-mum injectable or absorbable power of grid and BES,bid of grid and utility, limit of BES’s size, IR and LTparameters of BES, FCBES and MCBES, charge and dis-charge efficiency of BES, electrical load demand, ORs,start-up and shut-down cost data for FC and MT shouldbe defined.

Step2. Generate the initial population randomly: As mentionedbefore, each bat has the role of a solution for the inves-tigated OMMG problem. Therefore, each agent (or solu-tion) consists of the size of BES, output powergeneration of FC and MT, absorption/injection powerby BES and utility, status of BES, FC and MT in the oper-ation horizon. Consequently, in this paper, an initialpopulation consisting of NPOP individuals Xm is ran-domly produced within the allowable ranges as follows:

Population ¼

X1

X2

. . .

Xm

. . .

XNPOP

2666666664

3777777775¼

x1;1 . . . x1;nv

x2;1 . . . x2;nv

. . .

xm;1 . . . xm;nv

. . .

xNPOP;1 . . . xNPOP;nv

2666666664

3777777775

ð36Þ

where


xm;1 . . . xm;nv½ � ¼

CBES;max;Pm;FC;1; . . . ;Pm;FC;NT ;Pm;MT;1; . . . ;

Pm;MT;NT ;Pm;grid;1; . . . ;Pm;grid;NT ;Pm;BES;1;

. . . ;Pm;BES;NT ;

um;BES;1; . . . ;um;BES;NT ;um;FC;1; . . . ;um;FC;NT ;

um;MT;1; . . . ;um;MT;NT

26666664

37777775

and Xm ¼ randmð1;nvÞðXmax � XminÞ þ Xmin.It should be noted that all of the constraints (11)–(21) should besatisfied in each step of the algorithm. In order to handle these con-straints the function Handle_Constraints should be applied.

Function Handle_Constraints

For m = 1 to NPOP doFor t = 1 to NT do

1. Power balance and power generation capacity handlingCalculate the value of power mismatch as follows:

P violatem;t ¼ Pm;FC;tuFC;t þ Pm;MT;tuMT;t þ PiPV ;t þ PiWT ;t þ Pm;BES;tum;BES;t

þ Pm;grid;t � PDemand;t

Select one of the FC or MT units or BES or grid randomlyWhile P_violatem,t–0 do

Subtract P_violatem,t from the selected unit.Check the feasibility of unit for upper and lower

limits as follows:If Pm,FC,t < PFC,min or Pm,MT,t < PMT,min or

Pm,grid,t < Pgrid,min or Pm,BES,t < PBES,t Then Pm,FC,t = PFC,min orPm,MT,t = PMT,min or Pm,grid,t = Pgrid,min or Pm,BES,t = PBES,t

Else If Pm,FC,t > PFC,max or Pm,MT,t > PMT,max orPm,grid,t > Pgrid,max or Pm;BES;t > PBES;t Then Pm,FC,t = PFC,max or

Pm,MT,t = PMT,max or Pm,grid,t = Pgrid,max or Pm;BES;t ¼ PBES;t

End If.Calculate P_violatem,t

Select another FC or MT unit or BES or gridrandomly.

End While2. ORs handling

Calculate ft using (2).If

PFC;maxuFC;t þ PMT;maxuMT;t þ Pgrid;max þ PBES;tuBES;t < ORtþPDemand;t

ft ¼ ft þ Penalty FactorðORt þ PDemand;t � ðPFC;maxuFC;t þ PMT;maxuMT ;t

þ Pgrid;max þ PBES;tuBES;tÞÞ

End IfEnd For (it refers to index t)Calculate F(Xm) using (1).End For (it refers to index m)

Since the ORs constraint should be met, the value of Penalty_Factorhas been considered as 10.

Step3. Select iter = 1.Step4. Select Viter

m ¼ 0; m ¼ 1; . . . ;NPOP for all the control vari-ables, i.e. DGs power output, BES and grid power andsize of BES.

Step5. Calculate the objective function for the initial popula-tion using (1).

Step6. Sort the population in descending order and select thebest and worst solution among all individuals.

Step7. Move the population by updating mechanism of IBAproposed in the previous section. The new bats set mustsatisfy the quality and inequality constraints (11)–(21).

Step8. Calculate the objective function for each individual ofthe population using (1).

Step9. Update iter, iter = iter + 1.Step10. Check the convergence criterion.

For the proposed algorithm, there are three kinds ofstopping criteria: (i) Iteration number is larger than apredefined number; (ii) total run time is longer than apredefined time; and (iii) the variation of objective func-tion (1) for the best solution is smaller than the prede-fined value during the optimization process. In thisstudy, if the current iteration number obtains the preor-dained maximum iteration number, the algorithm isstopped and the final best solution is defined as theresponse of the problem; else go to Step 6.

5. Numerical examples, comparisons and discussions

5.1. Performance assessment of the proposed IBA

In order to demonstrate the robustness and convergence char-acteristics of the proposed IBA algorithm, three renowned complexand non-smooth test functions like Generalized Rastrigin, General-ized Grienwangk and Generalized Ackley are utilized as bench-mark test functions. The formulation of these test functions isdescribed as follows [34]:

(1) Generalized Rastrigin: The first test function is highly com-plex and multimodal with deep local optima that are regu-larly distributed in the problem search space. A function isdefined multimodal if several local optima exist in its searchspace. Its global optimum is at X⁄ = [0, . . . , 0] whereF1(X⁄) = 0. Besides, its mathematical form is as follows:

F1ðXÞ ¼XD

i¼1

x2i � 10 cosð2pxiÞ þ 10

� �;

X ¼ ½x1; . . . ; xD�; �5:12 6 xi 6 5:12 ð37Þ

(2) Generalized Griewank: The second test function is multi-modal with deep local optima whose variables are indepen-dent. Further, finding the global optimum for this testfunction is more difficult even for lower dimensions. So, aweak algorithm may fail in local optima. The global opti-mum of this function is at X⁄ = [0, . . . , 0] where F2(X⁄) = 0.The mathematical form of the Generalized Grienwangk isas follows:

F2ðXÞ ¼1

4000

XD

i¼1

x2i �

YD

i¼1

cosxiffiffi

ip� �

þ 1; X

¼ ½x1; . . . ; xD�; �600 6 xi 6 600 ð38Þ

(3) Generalized Ackley: The third benchmark function is multi-modal and has one narrow global minimum valley and manyminor local minimum. The global optimum of this functionis at X⁄ = [0, . . . , 0] where F3(X⁄) = 0. The mathematical formof the Generalized Ackley is as follows:

F3ðXÞ ¼ � 20 exp �0:2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1D

XD

i¼1

x2i

vuut0@

1A� exp

1D

XD

i¼1

cosð2pxiÞ !

þ 20þ expð1Þ; X ¼ ½x1; . . . ; xD�; �32 6 xi 6 32ð39Þ

Fig. 1. Empirical distribution of normalized SP for Rastrigin test function.


The results of 30 independent runs of the IBA technique and BAalong with Teaching–Learning-Based Optimization (TLBO) and Arti-ficial Bee Colony (ABC) applied to each of the above test functionsare extracted to be able to compare them comprehensively. The re-sults of ABC are extracted by running the code given in the websitededicated to this algorithm (http://mf.erciyes.edu.tr/abc/). Thesealgorithms were chosen because of their easy application sincenone of them had any adjustable parameter and their results de-pend only on the number of population and maximum number offunction evaluation. Each test function is solved for 10, 50 and100 dimensions. The four criteria, i.e. best value of error, mean va-lue of error, Standard deviation (Std) of error and Successful Perfor-mance (SP) are considered to evaluate the performance of theoptimization algorithms [34]. The number of population in all ap-plied algorithms for all test functions is set to 50 and the maximumnumber of function evaluation is equal to 104D.The best, mean and Std of error for different dimensions of allbenchmark functions obtained by IBA and other applied algorithmsare tabulated in Table 1. The best obtained results from differentalgorithms are typed in bold in this table. By comparing the results,it can be seen that for all considered dimensions and all test func-tions, the proposed algorithm provides the best results in all threeaspects, demonstrating better efficiency and stability than the othermethods. Accordingly, it is observed that the IBA has a promisingsolution with high quality and robustness in terms of lower valueof best, mean, and Std for error criterion throughout 30 trial runsfor the selected benchmark problems which need robust, fast, opti-mal and near real time convergence solutions.The quality of convergence of IBA in the solving process of algo-rithm is clearly demonstrated in Fig. 1 for the Generalized Rastriginfunction. In this figure, the empirical distribution curve is shownindicating the overall quality of convergence for all populationmembers. From the figure, the members of IBA could find the desir-able solutions faster than other algorithms and also, all of the pop-ulation could reach the predefined success criterion at the end ofthe optimization process. It is obvious that using the proposedstrategies in the IBA ensures that the diversity of the populationis preserved to discourage premature convergence.

Table 1Comparison of the results obtained by different algorithms for Rastrigin, Griewank and Ac

Function D Criteria of error ABC

Rastrigin 10 Best 2.5549e�17Mean 5.6131e�17Std 1.7318e�17

50 Best 8.5532e�16Mean 1.3370e�15Std 2.3200e�16

100 Best 3.5392e�15Mean 4.4481e�15Std 6.6007e�16

Griewank 10 Best 1.0163Mean 26.2855Std 51.6823

50 Best 39.0123Mean 48.7198Std 11.3615

100 Best 93.7310Mean 97.4628Std 7.8362

Ackley 10 Best 4.441e�15Mean 7.923e�15Std 1.341e�15

50 Best 7.9048e�14Mean 1.1664e�13Std 1.3275e�14

100 Best 2.7089e�13Mean 3.6668e�13Std 7.0771e�14

5.2. Description of MG test system under study, technical supposingand input data

To assess the validity and effectiveness of the suggested frame-work, it is tested on a typical low voltage MG test system which isdepicted in Fig. 2. The MG is comprised of different DGs such as theMT, FC, PV, WT and also Li-ion BES. All coefficients and productionlimits which are utilized in the proposed approach are listed inTable 2. The forecasted real time market energy prices, load de-mand, PV power output and WT power output for 24 h time hori-zon are portrayed in Fig. 3. More information associated with theimplemented MG can be found in [6,15,25]. In this example, it isassumed that all of the DGs generate active power at unity powerfactor, neither requesting nor generating reactive power. More-over, the operating reserve requirement is set to the 5% of the loaddemand in each time step. The fixed and maintenance cost forinstallation and operation of BES is assumed to be 465 (€ct/kW h)

kley test functions.

TLBO BA IBA

1.696e�223 4.173e�37 09.454e�217 8.672e�34 00 3.714e�33 00 1.3284e�33 03.5284e�59 7.3622e�32 02.4645e�58 1.6061e�31 00 6.1719e�33 05.7270e�41 7.0951e�32 04.0474e�40 9.6353e�32 0

7.0828 7.9345 0.00528.5000 8.7141 0.14930.4460 0.2717 0.206448.8282 48.5205 0.002348.8991 48.6607 0.10660.0397 0.0874 0.179798.7851 98.1444 0.001098.9015 98.3915 0.06010.0443 0.1272 0.0578

8.882e�16 1.51e�14 8.8818e�164.37e�15 1.673 8.8818e�165.024e�16 0.8421 04.441e�15 3.185 8.8818e�164.654e�15 5.658 8.8818e�168.523e�16 1.178 08.8818e�16 4.3757 8.8818e�164.3698e�15 5.3069 8.8818e�165.0243e�16 0.7201 0

http://mf.erciyes.edu.tr/abc/

Fig. 2. A typical MG test system.

Table 2The limits and bids of the DGs, utility and BES.

Type Min. power (kW) Max. power (kW) Bid (€ct/kW h) OM (€ct/kW h) Start-up/shut-down cost (€ct)

MT 6 30 0.457 0.0446 0.96FC 3 30 0.294 0.08618 1.65PV 0 25 2.584 0.2082 0WT 0 15 1.073 0.5250 0BES �30 30 0.380 – 0Utility �30 30 – – –


and 15 (€ct/kW h). The lifetime and interest rate for financing theinstalled BES are respectively 3 and 0.06. The tax is selected as10% in this study. The charge rate and discharge rate of BES arethe same and set at 90%. The minimum capacity of BES is set to10% of the full capacity. The full capacity is fixed at 500 kW h. Itmeans that CBES,max is a variable which should be optimized inthe range of [50,500]. The OMMG studies are performed for a timehorizon of one day with hourly time step.

The algorithms are implemented in MATLAB on a PC with2.4 GHz CPU and 1 GB RAM. To verify the performance of the pro-posed algorithm, the algorithms are repeatedly solved for 30 inde-pendent trial runs. The necessary parameters of IBA algorithmincluding the population size (NPOP) and Iter_max are found tobe 30 and 100, correspondingly. For the purpose of comparison,Genetic Algorithm (GA) and PSO are also employed to solve thesuggested problem. For the GA, population size, crossover rate,and mutation rate are chosen to be 60, 0.8 and 0.05, respectively.For the PSO, population size, cognitive parameter and socialparameter are selected to be 60, 2 and 2, respectively. Besides,the inertia weight factor is linearly decreased from 0.9 to 0.4 dur-ing the iteration process. In this study, three different cases areanalyzed to depict the superiority of the suggested framework:

Case A: Considering the MG without BES.Case B: Considering the MG including BES without initial

charge.

Case C: Considering the MG including BES with the initialcharge equal to the size of BES.

5.3. Case A

This case study was conducted to compare the results of theproposed method with those of other techniques like PSO andGA. In this case, it is supposed that the MG is without presenceof BES and all of the DGs should satisfy the forecasted load demandduring the examined period. On the basis of daily load demandcurve in Fig. 3(b) and the maximum available power generationof the DGs either RESs or non-RESs presented in Fig. 3(c) and (d)and Table 2, we show the numerical results of the optimal dispatchunder the operation of the MG in Fig. 4 obtained by IBA. This figureillustrates the optimal power generation of the utility power gridand DGs under various hour load demands. The total operation costof OMMG is 825.8849 (€ct/day). Because no BES acts as an ancillaryservice under this operation, the available power output of the DGsand utility must be greater than the power demand of MG as oper-ating reserve to ensure stable system operation. The availableoperating reserve by dispatchable DGs, i.e. MT and FC and up-stream network is depicted in Fig. 5. It is clear that without thepresence of BES, the MGCC has fewer OR values to satisfy the sud-den faults which may occur in the MG. Overall, because the BES isnot considered in the employed MG, the MGCC should purchasepower from the utility power grid in most hours of the day and sell

Fig. 3. Forecasted values for (a) market energy prices, (b) load demand, (c) output power of PV, and (d) output power of WT.

Fig. 4. Optimal output of each DG and utility power grid obtained by IBA for case A.


them back to grid in only four time steps 12–15. Furthermore, dueto the lower bid of FC compared to the MT, the MGCC purchasesmore power from the FC. The maximum ratio of FC power outputto MT power output is five which occurred in hour 23.

In order to compare the proposed technique with other meth-ods, the results are tabulated in Table 3. The best, average, andthe worst values of operation cost for 30 runs, and CPU execution

time to carry out the simulation in all methods are also listed inthis table. It is clear that the worst value of the operation cost ob-tained by the proposed method is better than the best solutions ofall other methods. This means that each algorithm that can attainthe lower cost function is more effective. Moreover, the IBA obtainslower average operation cost than other algorithms, thus resultingin the higher solution quality compared with the others.

Fig. 5. Operating reserve amounts of 24 h time horizon for case A.

Table 3Comparison of operation cost and simulation time for case A out of 30 trial runs.

Solution methodology Best solution (€ct) Average solution (€ct) Worst solution (€ct) Mean simulation time (min)

GA 1041.8376 1196.3251 1361.2437 0.417PSO 968.0190 1081.8351 1241.7459 0.330BA 933.8145 989.3718 1106.9860 0.289IBA 825.8849 825.8849 825.8849 0.104


5.4. Case B

To some extent, the Li-ion BES is added to the MG test system inthis case study; however, it is the fundamental equipment of theMG. The main benefit of the BES in MG is to maintain stability,facilitate integration of the RESs, improve power quality, and arbi-trage [1,35,36]. The Li-ion BES starts the time period with nocharge, so in each time step of the day, the discharging action ofthe BES is restricted to how much it is charged in previous hours.In this case study, in order to investigate the efficiency of selectinga BES with suitable and optimal capacity, the maximum size of bat-tery (CBES,max) is taken as the control variable. The minimum capac-ity of BES is set to the 10% of the full capacity. The full capacity isfixed to 500 kW h. It means that CBES,max is a variable which shouldbe optimized in the range of [50,500]. This means that after deter-mining these variables by the algorithm, the energy stored in BES isunder ½CBES;min;CBES;max� limits. In [6], the CBES,max is not consideredas the variable. CBES,max is changed 100 kW h in each step and theproblem is run step by step until the optimal size of battery isdetermined. It is clear that the main disadvantage of this idea isits high execution time. Based on the above discussion, the OMMGhas been solved for the MG test system to optimize total operationcosts in order to find the optimal size of BES and best dispatch forthe MT, FC, BES and utility. The numerical results for optimal dis-patch of DGs, BES and utility obtained by IBA are portrayed inFig. 6. It must be noted that the optimal size of BES in this casestudy is 150 kW h. According to this figure and Fig. 3, the spreadbetween the peak and off-peak real time market prices providesan opportunity for BES that economically stores energy by pur-chasing power from the upstream power grid overnight and thenselling that power back into the upstream power grid during thepeak load demand. The total operation cost of OMMG in this caseis 497.0082 (€ct/day) which is lower than the operation cost forcase A, i.e. 825.8849 (€ct/day) in which the BES is not considered.The available operating reserve by dispatchable DGs, i.e. MT andFC, BES and upstream network is shown in Fig. 7. In this case,BES helps the MG and can supply the operating reserve which

was previously supplied by MT and FC and upstream network incase A.

5.5. Case C

For the third case, where BES are included with the initial chargeequal to the size of BES, the outputs of DGs, BES and upstreampower grid in the MG with BES of optimal size of 250 kW h areshown in Fig. 8. Considering the low cost power provided by theBES, it is more economical for MGCC to buy power from BES duringmost hours of the day. Considering this system with BES of optimalsize of 250 kW h, the total operation costs will be 424.1339 (€ct/day). It is clear that installing BES in the MG with optimal size of250 kW h considering the value of 250 kW h for its initial chargecan decrease the total costs 497.0082-424.1339 = 72.8743 €ct inone day compared to including BES with optimal size of 150 kW hwithout initial charge (case B).

In order to show the capability of the proposed IBA methodwith regard to the original BA, the convergence plot of these tech-niques for solving OMMG for this case study is depicted in Fig. 9.According to this figure, it is evident that the proposed algorithmnot only converges to a better solution, but also has a high conver-gence rate which is helpful for solving the complex optimizationproblems. Once again the superiority of the proposed algorithmin solving optimization problems is proved.

It can be concluded that the proposed method is more effective,faster and as a consequence more robust than other methods in allcases. Also, results of this study may be used in designing the BESwith optimum size for MG considering the needs of MGCC.

According to the above discussions, it can be concluded that theproposed framework, as an OMMG, is comprehensive and also gen-eric enough to be applied for representation of the intermittency ofRESs in the presence of optimal BES sizing considering simulta-neous cost and emission objectives with few adjustments. So, thestochastic model of WT and PV power output can be fed as someinput random variables into the stochastic programming algo-rithms such as point estimated method, scenario approach or

Fig. 6. Optimal output of each DG, BES and utility power grid obtained by IBA for case B.

Fig. 7. Operating reserve amounts of 24 h time horizon for case B.

Fig. 8. Optimal output of each DG, BES and utility power grid obtained by IBA for case C.


Fig. 9. Convergence plot related to IBA and BA algorithms for case C.


Monte Carlo simulation [37–39]. It would consequently be possibleto run the proposed approach with this adjustment and obtain thePareto results of the multi-objective OMMG using Pareto domi-nance method [40]. The proposed technique can also open a win-dow for using BES in the characteristics of final optimal size andcan give the decision maker or MGCC a more practical viewpointto understand the BES effects on the technical and economical con-cerns. As a complement to the above discussions, this feature of thesuggested framework can be claimed as one of its considerableadvantages over the other methods.

6. Concluding remarks

In this paper, an efficient framework for MG operation manage-ment studies is proposed with regards to operation, maintenanceand financial points. The fixed and maintenance cost of BES was ta-ken into account in the optimization of MG studies as well asaddressing an appropriate robust and effective meta-heuristicIBA approach in MG operation solving are some of the major supe-riorities in the presented structure. Considering various technicalbenefits and advantages of BES in the MG led to introducing invalu-able BES sizing in the way of operation studies. In response, a newversion of BA called IBA was applied as an efficacious method forhandling these criteria in optimization process. The offered frame-work was tested over a day in a typical MG depicted in Fig. 2 andits usefulness was widely approved. Several conclusions are madefrom the simulation of the problem as follows.

First, the comparison results of the case study A and three com-plex benchmark test functions (Generalized Rastrigin, GeneralizedGrienwangk and Generalized Ackley) demonstrate the superiorityof the IBA in terms of the computational effort, robustness, conver-gence speed, and the performance of the solutions.

Second, the quantitative results of the case study B show thatconsidering a BES with optimal size for the MG could decreasethe cost of the MG. The decrease in the total costs is because theBES can store the surplus powers of RESs and redispatch themappropriately. Also, it could make the DGs operate at a stable situ-ation and lower their cost by reducing the start-up and shut-downfrequency.

Third, from the comparison results of case studies A, B and C,one can easily say that installing an optimal size of 150 kW h BESwithout initial charge will decrease the cost about 40% per daycompared with the MG without BES. In addition, installing an opti-mal size of 250 kW h BES with the initial charge of 250 kW h willdecrease the cost about 15% per day compared to the MG consist-ing of optimal size of 150 kW h BES without initial charge. By con-sidering the discharging and charging efficiencies for BES, the

optimal solution will also minimize the frequency of dischargingor charging for BES. This will increase the LT of BES.

Future works will concentrate on modeling the intermittency ofRESs in the presence of optimal BES sizing for an unbalanced MGoperation management considering simultaneous cost and emis-sion objectives.

Acknowledgement

The authors would like to thank Islamic Azad University,Marvdasht, Iran for their finance support.

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