newly developed enhanced imperialistic …...newly developed enhanced imperialistic competitive...

Appl. Math. Inf. Sci.8, No. 1, 309-320 (2014) 309

Applied Mathematics & Information SciencesAn International Journal

http://dx.doi.org/10.12785/amis/080138

Newly Developed Enhanced Imperialistic CompetitiveAlgorithm for Design Optimization of an AutonomousHybrid Green Power SystemM. H. Etesami and M. M. Ardehali∗

Energy Research Center, Department of Electrical Engineering, Amirkabir University of Technology (Tehran Polytechnic), 424-HafezAvenue, 15875-4413 Tehran, Iran

Received: 21 Jun. 2013, Revised: 28 Oct. 2013, Accepted: 29 Oct. 2013Published online: 1 Jan. 2014

Abstract: The importance of economics for owning hybrid green power systems (HGPS) warrants development of optimizationmethodologies with more effective search capabilities for determination ofglobal minimum for costs. The objective of this studyis to present several newly developed enhancements for imperialistic competitive algorithm (ICA) for design optimization of anautonomous HGPS with considerations for economics and reliability. HGPS examined consists of photovoltaic (PV) modules in apanel, wind turbines (WT), and storage batteries (SB). Utilizing an IEEE load profile and actual solar irradiation and wind speed data,the economics is evaluated based on annualized cost of system (ACS) and reliability constraint specified in terms of loss of powersupply probability (LPSP). The simulation results show that enhanced ICA(EICA) developed in this study has a better convergencerate, as compared with other population based optimization methods such asICA and genetic algorithm (GA). It is found that the newenhancements developed for EICA result in lower computation time for determining the optimal configuration of HGPS equipment by40 and 79 % for ICA and GA, respectively. For LPSP of 2 %, it is determined that EICA results in lower ACS by 11.60 and 6 % incomparison with ICA and GA, respectively. For computation time, convergence occurs in 33, 55, and 160 minutes for EICA, ICA, andGA algorithms, respectively.

Keywords: Hybrid green power system, imperialistic competitive algorithm, design optimization, economics

1 Introduction

Green power technologies such as solar photovoltaic (PV)and wind turbine (WT) systems are considered as themost efficient and cost effective solutions for sustainableenergy development due to their zero environmentalemission during operation and decreasing manufacturingcosts [1,2].

For green power generation, it is determined thatstand-alone solar or a wind energy system cannot providea continuous electrical energy due to stochasticperformance and weather variations [3], therefore, theindependent use of these systems necessitatesconsiderable redundancy for reliability purposes. Forbetter reliability, it is possible to benefit from both solarand wind energy systems in a hybrid form, when the localclimate conditions have enough potential in the level ofsolar irradiation and wind speed. Hybrid green powersystems (HGPS) usually include PV panels and WTs to

compensate for autonomy deficiencies. Also, properstorage devices are indispensable in supplying oscillatoryload, when the HGPS generation is lower than load [4].The load profile is extremely important in HGPS designoptimization, as the requirement of lower loss of powersupply probability (LPSP), implying lower outageprobability, results in increasing capital costs. HGPSdesign optimization can lead to reduction in energystorage requirements, which could be a major economicrestraint [5], and lessens the capital cost, while theconsumer power supply continuity under varyingatmospheric conditions is satisfied with acceptable levelof reliability.

Clearly, the complexities in analysis of HGPS designnecessitate employment of an appropriate designoptimization method [6]. The number of modules in a PVpanel and WTs, energy storage battery (SB) capacity andrelated peripheral equipment must be configured

∗ Corresponding author e-mail:[email protected]

c© 2014 NSPNatural Sciences Publishing Cor.

http://dx.doi.org/10.12785/amis/080138

310 M. H. Etesami, M. M. Ardehali: Newly Developed Enhanced Imperialistic...

optimally, so that HGPS can provide a reliable serviceand operate unattended over its useful life span [3, 7].Also, for design optimization of autonomous HGPS, datafor solar irradiation, wind speed, and load profile to bemet are necessary [8]. As noted by [9], for annual powersupport design, the region annual data bank and not anyother periodic data should be used. To realize the fullpotential from utilization of green power systems, it isnecessary to optimize the economics of owning andoperating these systems. However, the mathematicalrelations governing the performance of green powersystems, required for technical and economic analyses,are multi-variable and non-linear. Therefore, it isnecessary to consider meta-heuristic methodologies, asalternatives to conventional mathematical approaches.

Meta-heuristic methodologies have been proven to beeffective for optimization; however, the determination ofglobal minimum always remains questionable due toinherent limitations in search capabilities of suchmethodologies [10, 11]. The ability of meta-heuristicoptimization methods to find optimal solution fordifferent applications has been examined in severalstudies. In general, meta-heuristic optimization methodshave been developed utilizing population and individualbased algorithms. Individual based methods such assimulated annealing [12] and tabu search [13] are fastenough for real-time applications but may be incapablefor finding global minimum [14]. Population basedmethods such as genetic algorithm (GA) [15–17], particleswarm optimization algorithm [18–20], and imperialisticcompetitive algorithm (ICA) [21–27], have the ability ofescaping from local minima at additional computationcosts and, therefore, such algorithms are usuallynon-applicable to real-time problems [14] and, they aresuitable for design optimization of systems, such asHGPS, where the optimal configuration of equipment isrequired for economic analyses.

While ICA has not been applied for designoptimization of HGPS in the literature, the objective ofthis study is to present several newly developedenhancements for ICA for design optimization of anautonomous HGPS with considerations for economicsand reliability. It is anticipated that ICA convergence ratecould be improved via several enhancements based onextra heuristic mathematical operations for more effectiveskipping from local minima and reduced prematuretermination caused by high rate of convergence. Actualsolar irradiation and wind speed data for Ardebil provinceof Iran are used in conjunction with IEEE reliability testsystem (RTS) load profile. Subject to LPSP as reliabilityconstraint, annualized cost of HGPS system (ACS) isminimized as a function of five sizing variablesconsidered in design optimization of this study, includingthe number of modules in PV panel, number of WTs,number of SBs, PV panel tilt angle, and WTs height.

The remaining of this study is organized as follows.Problem formulation is discussed in section 2. Section 3provides description for optimization procedure based on

ICA and EICA. Parametric values are given in section 4and, then, results and discussion are presented in section5. Finally, section 6 explains the conclusions andrecommendations for future work.

2 Problem formulation

HGPS design optimization requires individualcomponents modeling outlined in this section. As shownin Figure1, a PV panel and WTs are used simultaneouslyto supply load. When there is sufficient power producedand hourly load is satisfied, surplus power is used tocharge SB. In case of insufficient power to supply loaddue to lower solar irradiation or wind speed, SB begins todischarge. When maximum SB capacity is reached duringcharge mode, the excess energy is lost through dumpload. To extract the maximum available power from thePV panel and WTs, maximum power point trackers(MPPT) are used. The chopper, as regulator, sets thecommon DC bus output voltage in its nominal band. Thepower produced by PV panel or WTs is transferred to DCbus where the DC/AC converter is used for connection toload.

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2.1 Photovoltaic power

The performance of a crystalline silicon PV module is afunction of the physical variables of material,temperature, and solar irradiation. The maximum poweroutput delivered by each module contained in PV panel isgiven by [28,29]

Pmodule = FF.Voc.Isc

=

VocnMPP.

K.Tq

− ln( VocnMPP.

K.Tq

+ .072)

1+ VocnMPP.

K.Tq

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Appl. Math. Inf. Sci.8, No. 1, 309-320 (2014) /www.naturalspublishing.com/Journals.asp 311

All variables or constants are defined in [30] andparametric values are discussed later. If an equivalentarray of Nh.Nv modules is considered for PV panel,aggregated output power is [30]

PPV = Nh.Nv.Pmodule.ηMPPT .ηoth (2)

whereηoth is the factor representing the other lossessuch as those caused by cable resistance and accumulativedust. For PV output power calculation, solar irradiation ontilted surface is calculated based on hourly data for solarirradiation on horizontal surface for the particular location.Also, PV module temperature is determined while windspeed effect is observed [30].

2.2 Wind turbine power

The output power of a WT can be described by [30]

PWT =

0 v < vci or v > vco

Pr.v−vcivr−vci

vci ≤ v ≤ vr

Pr vr ≤ v < vco

(3)

Based on wind speed at a reference heightvre, thevelocity at a specific hub heightv for the location isestimated based on

v = vre.(HWT

Hre)ζ (4)

2.3 Storage battery power

As noted earlier, SB power can compensate forfluctuations in solar irradiation and wind power toimprove the continuity in supplying load. The storedenergy in each SB unit must be more thanESB min and lessthanESB max and, it should not exceed maximum rate ofits delivery due to its chopper transferability limit.

It must be noted that when the power available fromHGPS exceedsNSB.ESB max, surplus energy is lost viadump load, then, for the particular hour

Pdump load = PPV +PWT −PAC load(t)

ηcon(t)(5)

It is assumed that at the beginning, SB is in fullycharged and its output voltage is nominal.

2.4 Reliability

LPSP is defined as the probability that a power supplydeficit results when HGPS is unable to supply load. Fromti time tot f [30]

LPSP =∑

t fti Time(Pavailable(t)< Pload(t))

t f − ti(6)

where LPSP=0% implies the load is always suppliedwhereas an LPSP=100% means that the load is neversupplied.

The power required to meet the load is expressed as

Pload(t) =PAC load(t)

ηconv(t)+ϕ.Pdump load(t) (7)

whereϕ is a status coefficient equal to one in case ofexcess power generation and zero otherwise.

The power supplied from HGPS can be expressed by

Pavailable(t) = PPV +PWT +σ .PSB (8)

where σ is either zero or one for SB charging ordischarging, respectively.

2.5 Economics

The economic evaluation based on ACS is the bestcriterion for HGPS analysis [30]. ACS for HGPS includesthe annualized capital costCacap, annualized replacementcostCarep for SB bank, and annualized maintenance costCamain. The miscellaneous equipment includes controller,inverter and rectifier for WT with AC output.

3 Optimization

3.1 Overview of ICA

ICA has a remarkable capability for finding globaloptimal solutions for a wide range of applications withnoticeable convergence rate characteristic [21, 22]. ICAwas originally proposed in [23] to solve continuousproblems which uses imperialism and imperialisticcompetition process as a source of inspiration. Unlikemost optimization methods that mimic natural behavior,ICA follows socio-political pattern. Through convergenceprocess, countries or so-called colonies assimilate towardtheir respective imperialist [23]. Solid-line blocks inFigure 2 shows the computation sequence required forimplementing ICA. Note that dashed-line blocksrepresent the added steps for the enhanced ICA (EICA),as discussed later in this section.

3.1.1 Initialization

Initially, ICA population is categorized into two differentgroups namely imperialists and colonies considering ACSas fitness index. For HGPS with five variables, a countryis defined as [25]

country = [NPV ,NWT ,NSB,β ′,HWT ] (9)

where the variables are representative of number of PVmodules, number of WTs, number of SB units, PV panel


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installation angle, and WTs height. respectively. The ACSfor a country is given by

ACS(country)

= ACS(NPV ,NWT ,NSB,β ′,HWT ) (10)

To start the optimization process, initial countries ofsizeNcountry is produced. Then, based on lowest values forACS, the most powerful countries asNimp is selected outof Ncountry to form the imperialists according toimperialistic fraction coefficientΛ . The remaining areconsidered as colonies where each colony belongs to oneof imperialism, therefore

Nimp = Λ .Ncountry (11)

Ncountry = Nimp +Ncol (12)

Next, the normalized ACS of nth imperialist isdetermined by

ACSimp,n = ACSimp,n −max{ACSimp,i} (13)

where ACSimp,n is the ACS for the nth imperialist.Then, suitability of each imperialist is defined by

Simp,n =|ACSimp,n

∑Nimpi=1 ACSimp,i

| (14)

Note that colonies are allocated to imperialists basedon imperialists suitability indices. The initial number ofcolonies of the nth imperialism is

NCimp,n = round{Simp,n.Ncol} (15)

whereNcol is the total number of initial colonies [25].Utilizing aggregative operator on allNCimps results in

Nimp

∑i=1

NCimp,i = Ncol (16)

3.1.2 Assimilation

As in Figure 3, for two-dimensional optimizationproblem, a colony is attracted by its respective imperialistwith respect to both axes. The direction of movement isbased on the vector from the colony to the imperialist andl is a random variable with uniform distribution. Then

Imperialist= [N∗PV,N

∗WT,N

∗SB,β ′∗,H∗

WT] (17)

d =| [N∗PV ,N

∗WT ,N

∗SB,β ′∗,H∗

WT ]

− [NPV ,NWT ,NSB,β ′,HWT ] | (18)

l ∼U(0,λ .d) (19)

where assimilation coefficientλ > 1 causes thecolonies to get closer to the imperialist position from bothsides, which leads to better exploration aroundimperialist, andd is the distance between the colony andthe imperialist. For widening the scope around theimperialist, a random deviation in directional angleθ isadded to the direction of movement (Figure3), whereθ isa parameter with uniform distribution,

θ ∼U(−τ,τ) (20)

where τ adjusts the deviation from the originaldirection.

3.1.3 Position exchange

Through assimilation process, a colony may possess aposition with better minimum and lower ACS than that ofits imperialist,



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ACS([NPV ,NWT ,NSB,β ′,HWT ])

< ACS([N∗PV ,N

∗WT ,N

∗SB,β ′∗,H∗

WT ]) (21)

As a result, an exchange between their positionsoccurs. In the next iteration, the previous imperialist turnsup as a colony and related colonies change theirtrajectories toward the newly found imperialist,

Imperialistnew position

= [NPV ,NWT ,NSB,β ′,HWT ] (22)

3.1.4 Imperialism total power determination

The total power of imperialism is mainly affected by thepower of an imperialist country. However, the power ofthe colonies of imperialism also has an effect given by

T ACSimpm,n = ACSimp,n

+ξ .mean{ACScolonies o f imperialism,n} (23)

where T ACSimpm,n is the total ACS of the nthimperialism andξ is a positive small number as total ACScoefficient.

3.1.5 Imperialistic competition

During any iteration, the imperialists endeavor to possesscolonies of other imperialists. At the beginning, theweakest colony that belongs to the weakest imperialism isselected based on its ACS and, then, the ownershipprobability of each imperialism is calculated according tothe following approach. The possession likelihood relatedto any imperialism is commensurate with its total power.The normalized total ACS of nth imperialism is simplycalculated by

T ACSimpm,n

= T ACSimpm,n −max{T ACSimpm,i} (24)

Then, the ownership probability of any imperialism isgiven by

OPn = |T ACSimpm,n

∑Nimpi=1 T ACSimpm,i

| (25)

The distribution of the segregated colony amongimperialism is based on the following strategy. First,vectorA is formed as

A = [OP1,OP2,OP3, · · · ,OPNimp ] (26)

and then, vectorRa with the same dimension asA isgenerated in the way that its parameters originate fromuniformly distributed random numbers,

Ra = [r1,r2, · · · ,rNimp ],r1,r2, · · · ,rNimp ∈U(0,1) (27)

and vectorD is formed by subtractingRa from A

D = A−Ra = [D1,D2, · · · ,DNimp ]

= [OP1− r1,OP2− r2, · · · ,OPNimp − rNimp] (28)

According to vectorD, the segregated colony isassigned to the imperialism whose relevant index inD ismaximum.

Iteratively, ICA continues until predefined number ofiterations is satisfied or convergence criteria are achieved.

It should be noted in ICA, the fitness for colonies andimperialist is evaluated based on ACS subject to a desiredLPSP.

3.2 Proposed algorithm: EICA

The high convergence rate can lead ICA to get stuck inlocal minima, frequently, as it is discussed later. Asshown by dashed-line blocks in Figure2, the followingenhancements increase EICA capability in finding globalsolution probability via more effective exploration ofsearch space.

3.2.1 Fitness evaluation

For EICA, it is possible to evaluate the fitness for coloniesand imperialists based on both ACS and LPSP, whereby,a more thorough examination of search space is achieved.EICA allocation policy, in its first generation, is definedbased on primary allocation penalty coefficientψ ′ in caseof LPSP violation which performs as a weighting factor in




ACSEICA calculation of each imperialist substituted in Eq.(20).

ACSEICAimp,n = (

ACSimp,n

∑Nimpi=1 ACSimp,i

)

+ψ ′(LPSPimp,n

∑Nimpi=1 LSPSimp,i

) (29)

The same process is adapted to total ACSEICA

calculation as total ACSEICA penalty coefficient ψthrough imperialistic competition substituted in Eq. (31).

T ACSEICAimpm,n = ACSimp,n +ξ

.mean(ACS+ψ.LPSP)colonies o f imperialism n (30)

Also, such an approach is considered for segregatedcolony specification in terms of imperialistic competitionpenalty coefficientψ ′′,

ACSEICAcol,n = ACScol,n +ψ ′′.LPSPcol,n (31)

3.2.2 Clustering

Through any iteration, EICA clusters all countries intotwo categories of closer and further ones according to theclassification constantχ . Then, the revolution andpenetration enhancements, as discussed later, are imposedon further and closer colonies, respectively. Thisapproach serves as an equalizer between exploration andexploitation rate.

3.2.3 Revolution

Revolution is defined as a basic change in power ororganizational structure that occurs in a relatively shortperiod of time. Revolution causes a country to abruptlychange its socio-political characteristics. Thus, duringanyiteration, in EICA, base on revolution coefficient ofℜ(%), some colonies experience a stochastic change intheir positions, which may not necessarily be toward theirrelated imperialist. The revolution increases theexploration rate in EICA and prevents prematureconvergence of countries to local minima. In other words,revolution provides a condition in which some coloniesare being authorized to have relative freedom indivergence to some extent. Note that a very high value ofrevolution coefficient can lead to convergence diminutionto a great extent and, therefore, inferior final solutionscould be anticipated. For example after a revolution, if thefirst and third variables are substituted, the countrycurrent position is revised as

countrycurrent position




3.2.4 Unification of similar imperialism

While all colonies and imperialists are moving toward theglobal minimum, some imperialists might reach closepositions with respect to each other. When the number ofdesign variables that have violated the predeterminedthreshold distance exceeds unification constant , theimperialists integrate to establish a new unifiedimperialism, which is a combination of both. All thecolonies of two imperialists become the colonies of thenew imperialism and the new imperialist is located in oneof two imperialists positions. For instance, in case of twoimperialistsi and j

ε = [|∆NWT |, |∆NPV |, |∆NSB|, |∆β ′|, |∆HWT |] (34)

NCnew imp = NCimp i +NCimp j (35)

3.2.5 Penetration

This enhancement is inspired from crossover strategy inGA which results in better convergence rate. Throughassimilation process, because of high impression thatexists between an imperialist and its countries, thepenetration intensity coefficientκ(%) randomly allowsfor some variables to be substituted from imperialist arrayinto a colony array.



Imperialist = [N∗PV ,N

∗WT ,N

∗SB,β ′∗,H∗

WT ] (37)

countrynew position

= [NPV ,N∗WT ,NSB,β ′,H∗

WT ] (38)

Through each EICA iteration, a random percentage ofcolonies according to the penetration coefficientκ ′ ischosen with the purpose of undergoing the penetrationprocess.



3.2.6 Dynamic assimilation

The rate of colonies assimilating toward relatedimperialists changes through EICA optimization process.In other words, the assimilation coefficientλ is indynamic mode and decreases gradually in line with EICAconvergence through which the number of imperialistsNimp declines, progressively.

l ∼U(0,λ .(Nimp

Λ .Ncountry).d) (39)

As a result, the search power increases around theimperialist, where the probability of global solutionexistence is more than any other location.

Furthermore, when there is optimization problem withmore than three design variables, as it is in this study, theimplementation of the random angleθ to a moving colonybecomes difficult. The dynamic assimilation enhancementin EICA addresses this problem, where, for all colonies ofthe respective imperialist in imperialism, the parameterdarray is multiplied by a random array, whereby a search ina more chaotic manner around each imperialist is achievedduring the dynamic assimilation process,

colonynew position

= [N∗PV ,N

∗WT ,N

∗SB,β ′∗,H∗

WT ]

+ |d|− |l.rand(1,5)| (40)

Note that any variable limit violation occurrenceduring assimilation process requires that the relatedvariable is realigned to satisfy its admissible range.

3.2.7 Dynamic total ACSEICA coefficient

An enhancement to EICA is applied toξ coefficient inEq. (30) of ICA. In case of intense competition betweentwo or more imperialists, which often occurs in situationswhere most imperialists have collapsed, the total powerbecomes more significant in determination of imperialismpossessing the segregated colony than the power ofimperialist alone, then

T ACSEICAimpm,n

= ACSEICAimp,n +ξ .(

Λ .Ncountry

Nimp)

.mean{ACSEICAcolonies o f imperialism,n} (41)

3.2.8 New imperialist advent

Whenever the assimilation process leads to exclusiveauthority, the advent of new imperialists occursperiodically as an enhancement in EICA. This avoids

premature occurrence of convergence and, as a result, theexploration scope increases. Some colonies allotted to thenew imperialist grant it competition power against the lastimperialism at least for limited number of iterations.

NCnew imp =ϒ .NCbest imp (42)

where the advent coefficientϒ is an indicator fornumber of allocated colonies, and

NCbest imp = NCcol −NCnew imp (43)

3.2.9 Dual mode coding

The proposed EICA simultaneously operates in bothmodes of discrete and continuous, as HGPS designvariables include two continuous variables (β ′ and H),and three discrete variables (NPV ,NWT ,NSB).

3.2.10 Weak imperialist augmentation

In ICA, weak imperialists lose their colonies rapidly. Thischaracteristic may lead to disregard for some parts ofsearch space which decreases global point findingprobability. To surmount this problem, weak imperialistattraction probability is augmented to some extent both inprimary allocationµ ′ and imperialistic competitionµcoefficients. Consequently, it is anticipated to have moreextensive search area for EICA and better solutions,

ACSEICAimp,n = ACSEICA

imp,n −µ ′.max{ACSEICAimp,i } (44)

T ACSEICAimpm,n

= T ACSEICAimpm,n −µ .max{T ACSEICA

impm,i} (45)

3.2.11 Termination criteria

As EICA eventually causes the countries to converge tothe global minimum, different criteria can be used fortermination. One way is to use predefined maximumiteration, referred to as maximum decadesε ′ used in thisstudy. Also at the end, it is expected that only oneimperialist with most impression and most authoritycontinues to reign and all other imperialism collapse. As aconsequence of this world order, all the parametersrelated to either the imperialism or the colonies are thesame and the entire world is handled via a uniqueimperialist. Such ideality achievement can be defined as atermination for EICA, where best solution throughdifferent iterations does not improve for certainconsecutive decades, or according to a threshold for a




difference between mean ACSEICA of whole imperialistand colony is reached,

|mean{ACSEICAimp }−mean{ACSEICA

col }|

< T hreshold (46)

3.2.12 EICA sensitivity analysis

The variation of different parameters values includingconstants and coefficients used in EICA are provided inFigure4, where the chosen values are those that result inminimum value for ACSEICA and they are listed in Table1. It should be noted that during tuning process of eachparameter, all other parameters are held fixed. EICAparameters tuning is according to a 53 sample-day periodof year or one day a week.

Table 1: EICA parametric values resulting in optimum value forACS

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4 Parametric values

4.1 HGPS

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F>>> =F>>> HF>>> ?F>>> EF>>>

Fig. 4: Sensitivity analysis of EICA parameters includingconstants and coefficients: vertical axis represents the ACS(×103) ($) and horizontal axis provides the range of valuesexamined.

depicted in Figure6 (c). Costs and economic parametersfor HGPS components are given in Table4. For ACScalculations, interest and inflation rates are both equal to6%. The ACS to be minimized for HGPS designoptimization is expressed by [30]

MinACS =Cacap(NPV +NWT +NSB +H +Mis)

+Carep(NSB)

+Camain(NPV +NWT +NSB +H +Mis) (47)

Subject to

NPV ,NWT ,NSB ≥ 0 (48)

Hmin ≤ HWT ≤ Hmax (49)



0≤ β ′ ≤ 90 (50)

ESB min ≤ ESB ≤ ESB max (51)

|∆ESB| ≤ |∆ESB max| (52)

LPSPcal ≤ LPSPDesired (53)

!

"

#

$

%

&

'

% ! !% "

#$%& '())& *+,'-

./0

)1 /

23(

23

*4#

-

(

5$621) 78( )*+,-(*./0./(*1( !(23(2(1.45/6*4(*1(+647(30,,7(8# 9:(Fig. 5: Power output of WT as a function of wind speed [30].

Table 2: PV module characteristics for HGPS [30]%

<=$% >(!?%@>A% B1,%@CA% >(!?%@>A% B(!?%@CA% 5(!?%@DA%

5)#<E,.<1/!##0F$%10#0,)F% &G% H;I% GJ% I;J8% G99%

Table 3: Specifications of a SB unit [31]%

6!-$7%*!)!*+-8%9: !;<!=>%

9?@AB1/+->%%

C!=+<1<%*./D$E0+./%

*!)!*+-8%%

9?@AB1/+->%

C+/+<1<%0-.E!F$%#$D$#%

9: !;<+/>%

9?@AB1/+->%

G0$,1#%#+,$%

98$!E>%

:,,+*+$/*8%

9H>%

I% &% &% 3J% IK%

%

Table 4: Costs and economic parameters for HGPS components[9,30]

%

%?,0+0!#%.!10+!#%

.)*+%%@AB%

C$1#!.$/$,+%.)*+%%@AB%

D!0,+$,!,.$%.)*+%0,%302*+%E$!2%%@AB%

F03$+0/$%@E$!2B%

!%/)-G#$%% H;I::% %%%J% HI% %%%%KI%

"#$ 9;I::% %%%J% <I% %%%%KI%

%&$$ L::% %%M::% N:% %%%%N:%

)O$2%@AP/B% KI:% %%J% H>I% %%%%KI%

D0*.$##!,$)G*%.)/1),$,+*%%

L;:::% %%J% L:% %%%%KI%

%

In Eq. (2), althoughηMPPT is a variable according todifferent working conditions, a constant value ofηMPPT = 95% is assumed for simplifying the calculations

Figure 6: (a) Hourly vertical and horizontal solar irradiation during a year [9], (b) Hourly

0

100

200

300

400

500

600

700

800

900

1000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time (hr)

Ra

dia

tio

n(W

/m2)

Vertical Horizental

(a)

0

5

10

15

20

25

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time (hr)

Win

dsp

eed

(m/s

)

(b)

15

20

25

30

35

40

45

50

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Time (hr)

Dem

an

d(k

W)

(c)

Fig. 6: (a) Hourly vertical and horizontal solar irradiation duringa year, (b) Hourly wind speed during a year (at a height of 15 m),(c) Hourly IEEE RTS load profile [9].

and,ηoth = 1 [30]. The HGPS is studied based on usingan hourly time step (∆ t = 1hr) for one year. Convertersoperate atηcon(t) = 1 for both AC load or powerresources.

4.2 EICA

To initialize EICA, 60 primary countries are generatedrandomly (Ncountry = 60) andΛ = 25% of countries areselected as imperialistsNimp = 15. Maximum iteration isε ′ = 30 and it is used as termination criterion. The valuesof assimilation coefficientλ and τ are arbitrary but inmost studies are about 2 andΠ/4, respectively, whichresult in satisfactory convergence of countries to theglobal minimum [23], but according to sensitivityanalysis λ = 2.5 leads to better solutions. Based onsensitivity analysis results (Figure4), penetration andrevolution coefficients values that minimize ACSEICA areℜ = 0.9 andκ ′ = 1, respectively. New imperialist adventis in action after any imperialist collapses, immediatelyand, the number of colonies assigned to it isϒ = 0.2 ofthe dominant imperialist colonies. While unification




constant isΦ = 3, thresholds for activating unification areconsidered as

ε = [1,11,5,5◦,4] (54)

All other EICA parametric values resulting in optimumvalues for ACSEICA are provided in Table1.

5 Results and discussion

The proposed EICA, as a population based optimizationmethod, is used and its performance is compared withthose of ICA and GA for design optimization of HGPS.In this simulation study, the optimal configuration ofequipment is determined, while ACSEICA is minimizedand reliability constraint is met. The design variablesinclude the number of modules in the PV panel, numberof WTs, number of SBs, PV panels slope angle, and WTsinstallation height.

During application of EICA, LPSP is calculatedaccording to Eq. (6) and ACS for HGPS is estimated viaEq. (9). Then, there are two indices determined for eachcountry, where EICA is used to determine thecompetency of each.

Simulation results for design optimization of HGPSbased on ACS for LPSP=2% is shown in Table5, wherethe optimal configuration of equipment is given for EICA,ICA, and GA.

Table 5: Optimal sizes of HGPS equipment determined usingdifferent algorithms

!"!#$%$"& '(%)#)*!%)+,&#$%-+.&/ 0 1$2)"$.&& 3-!,4$&5)%-&"$2($6%&%+&7839&:;<&=&:;<&

>?@&

=>?@ A B

>?@ CD B&E

2@ & FGH

> A&

=>?@ IHD B

>?@ AEJ FEH

2@ CHEK BCD<K

>0B&

=>?@ CG& B

>?@ CAJ BG&

2@ CDC BE<A

C&:#<&

=>?@ DE B

>?@ GK FCJ<A

2@ DD FD

DE&:F<&

=>?@ EA B

>?@ JJ BEH

2@ &D BCD<G

930&:GHIJ<&:K<&

=>?@ ID<EHA B

>?@ CH&<JG BCC<A

2@ II<DK BA

/ 0 6!L&:;<&

=>?@ C<II B

>?@ C<II H<H

2@ C<DK FEE<G

The convergence of all examined algorithms to findminimum values for ACS are shown in Figure7, where itis observed that convergence time for EICA, ICA, andGA are 33, 55, and 160 minutes, respectively. It isobserved that the problem with ICA getting trapped in alocal minimum has occurred during 30 iterations inFigure 7. As in Figure 8 for variation of ACS as afunction of LPSP after 10 iterations, EICA achieves the

lowest ACS values for all LPSP values ranging from 1 to10%.

!

"

#

$

%&&

%&!

%&"

%&#

%&$

%%&

% ' ( ) %% %' %( %) % !% !' !( !) !

#$%&'$()*

+,

- .

/01

!2

.3

2

*+ ,-+ .,-+

/Fig. 7: Convergence for examined optimization algorithms.

!

"!

"

#!

#

$!

$

%!

%

& ' ( ) " # $ % &!

#$%$ &'(

)*

% &

+ ,

"-(&

.(

*+ ,-+ .,-+

Fig. 8: Variation of ACS and LPSP for examined optimizationalgorithm.

It is determined that EICA results in lower ACS by11.60 and 6% as compared with ICA and GA, respectively,for LPSP=2%. The annual cumulative dump load lossesfor EICA, ICA and GA final configuration are determinedas 63, 116, and, 63 MWh, respectively.

A major advantage of EICA compared with otheroptimization algorithms, is fewer referrals to fitnessfunction during consecutive iterations due to its high rateof convergence which is a time andmemory-storage-consuming process, as it is 892, 1734,and 3120 for EICA, ICA and GA, respectively. Thischaracteristic, particularly in industrial applicationswitha large number of variables, reduces the requiredcomputation time.

6 Conclusions and recommendations

In this study, several enhancements for ICA are developedand EICA is applied for design optimization of HGPS.The new enhancements of EICA include revolution,penetration, unification, and new imperialist advent inaddition to dynamic design of parameters. It is concludedthat EICA has a better performance in exploration of the



search space and convergence rate leading to optimalconfiguration of HGPS equipment with the lowest ACSand comparable annual cumulative dump load losses, ascompared with ICA and GA. Also, in comparison withICA and GA, EICA requires the lowest convergence time.For future works, it is proposed to investigate the abilityof EICA for minimization of environmental emissions fornon-autonomous HGPS.

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M. H. Etesami receivedhis B.Sc. and M.Sc. degreein electrical engineeringfrom Amirkabir University ofTechnology, Tehran, Iran, in2010 and 2012, respectively.His main interests includedispersed generation, powerelectronics, power systemanalysis, and optimization

techniques.

M. M. Ardehali Ph.D.,P.E., is an associate professorand the director of EnergySystems Laboratory atthe Department of ElectricalEngineering at AmirkabirUniversity of Technology(Tehran Polytechnic). Hereceived his PhD in energyconversion from University of

Iowa in 1995 and completed postdoctoral studies at IowaState University in 1997. With numerous publications andpatents, Dr. Ardehali is a registered professional engineerin several states in the US and specializes in control andapplications of artificial intelligence for energy systemsincluding power generation facilities.


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