optimal design of grid-connected hybrid renewable energy systems...

Scientia Iranica D (2017) 24(6), 3148{3156

Sharif University of TechnologyScientia Iranica

Transactions D: Computer Science & Engineering and Electrical Engineeringwww.scientiairanica.com

Optimal design of grid-connected hybrid renewableenergy systems using multi-objective evolutionaryalgorithm

Z.S. Shi, R. Wang�, X.Y. Zhang, Y. Zhang and T. Zhang

College of Systems Engineering, National University of Defense Technology, ChangSha, Hunan, P.R. China, 410073.

Received 21 October 2015; received in revised form 17 October 2016; accepted 30 May 2017

KEYWORDSGrid-connectedsystem;Renewable energy;Hybrid system;Preference-inspiredalgorithm;Coevolutionary;Multi-objectiveoptimization.

Abstract. The optimal design of grid-connected Hybrid Renewable Energy Systems(HRESs) is studied by using multi-objective evolutionary algorithm in this paper. With thetotal system cost and fuel emissions to be minimized, a two-objective optimization modelof the hybrid system is established. Then, a modi�ed preference-inspired co-evolutionaryalgorithm is, for the �rst time, applied to �nd the optimal con�guration of a grid-connectedhybrid system. As an example, a grid-connected hybrid system, including PV panels, windturbines, and diesel generators, has been designed and good results are obtained whichshow that the proposed method is e�ective.

© 2017 Sharif University of Technology. All rights reserved.

1. Introduction

The rising energy consumption, the depletion of limitedfossil fuels, and the increasing concern for global warm-ing have enhanced the use of renewable energy sources,such as solar and wind energy. Renewable energysources can decrease the dependence on conventionalresources and reduce the greenhouse gas emissions,making them potential for electric power generationin the future. However, they are also unpredictableand intermittent, hindering their wide application inpractice. A good solution to overcome the drawbacks ofrenewable sources is the appropriate design of a HybridRenewable Energy System (HRES), integrating variousenergy sources. Compared with single-source energysystems that include solar or wind energy alone, HRESshave many advantages, e.g. higher reliability, lowercost, and less fuel emissions.

*. Corresponding author. Tel.: +86 18874962006,E-mail address: [email protected] (R. Wang)

doi: 10.24200/sci.2017.4578

An HRES can operate in either Grid-Connected(GC) or Stand-Alone (SA) mode according to theavailability of utility grid [1]. Stand-alone systems cangenerate electricity without utility grid, so that is whythey are said to be stand-alone and, hence, they aresuitable for remote areas where the grid is not available.Along with the prevalence of HRESs, an increasingnumber of studies about optimal HRES design havebeen reported in the literature. The optimal design ofan HRES is a Multi-objective Optimization Problem(MOP) [2] in most cases, which is too complex to solvee�ciently by traditional optimization methods. Hence,various evolutionary algorithms have been applied tooptimally design the HRES with di�erent objectives [3-9]. However, most of the present studies focus on stand-alone hybrid systems without considering the utilitygrid.

A grid-connected HRES is an independent powersystem connected to the electricity grid and the gridacts as a storage unit with unlimited capacity [1],so the battery storage device is unnecessary in thissystem. A grid-connected system is mainly used tocater to the local load demand, and surplus genera-

Z.S. Shi et al./Scientia Iranica, Transactions D: Computer Science & ... 24 (2017) 3148{3156 3149

tion will be fed into the grid. Unlike the abundantnumber of literature reviews on stand-alone systems,there are only a few studies on grid-connected hybridsystems. Caballero et al. [10] proposed a method forthe optimal business design of a small grid-connectedhybrid PV-wind energy system aiming to minimize thelife-cycle cost of the system under a certain level ofreliability. In this method, the excess energy generatedby the hybrid system is supplied to the grid at a�xed sale price or through a Net Metering scheme.Dalton et al. [11] studied a large-scale grid-connectedhotel by an analysis of the technical and �nancialviability of di�erent types of hybrid power supplycon�gurations. They utilized the HOMER softwareto assess the net present cost, renewable fraction,and payback time of the system. Based on ParticleSwarm Optimization (PSO), Pablo et al. [12] evaluatedthree Energy Management Systems (EMSs) of a grid-connected hybrid system for long-term optimization.The three EMSs try to seek the optimality of cost,e�ciency, and lifetime, respectively. Lashkar et al. [13]proposed a multi-objective optimization methodologyto solve the reactive power-planning problem in powersystem. They combined the �-constraint approach,mixed integer non-linear programming model, andimplemented simulation experiments to simultaneouslyoptimize the objectives of total fuel cost, power losses,and system loadability. Bernal and Dufo [14] conductedan economic and environmental research on PV solarenergy installations in a grid-connected system.

As a matter of fact, the optimal design of agrid-connected HRES is similar to that of a stand-alone system. The optimization objectives needed tobe considered include the economic and environmentalindexes, i.e., the cost and fuel emissions. Note thatthe cost here consists of the initial investment cost

and the net cost of purchasing electricity which isequal to the total cost generated by purchasing thede�cient energy from the grid minus total bene�tfrom selling excess energy to the grid. In this paper,the total system cost and fuel emissions of one yearas two objectives will be taken to establish a grid-connected hybrid system model including PV panels,wind turbines, and diesel generators. To �nd theoptimal con�guration of the hybrid system which is aMOP, the modi�ed preference-inspired co-evolutionaryalgorithm using goal vectors (PICEA-g [15]) is adoptedto solve the problem. PICEA-g has better perfor-mance than other classical Multi-Objective Evolution-ary Algorithm (MOEA), such as NSGA-II [16] andMOEA/D [17]. Meanwhile, the modi�ed PICEA-g hasbeen testi�ed to be e�ective, especially for bi-objectiveproblems [18], and it is applied to size a grid-connectedHRES for the �rst time in this study.

The rest of the paper is organized as follows.Section 2 describes the problem under consideration.The model of the studied hybrid system is establishedin Section 3. Section 4 introduces the optimization al-gorithm, i.e. modi�ed PICEA-g. Experimental study ispresented in Section 5, and �nally, Section 6 concludesthis paper.

2. Problem description

The considered grid-connected hybrid renewable en-ergy system includes PV panels, wind turbines, dieselgenerators, accessory devices, and utility grid whichcan act as a back-up system. A particular con�gurationof the employed system is shown in Figure 1. Accordingto this �gure, the system energy ow can be explainedas follows. The available energy generated by PVpanels and wind turbines is directly used to cater to

Figure 1. A grid-connected hybrid system con�guration.

3150 Z.S. Shi et al./Scientia Iranica, Transactions D: Computer Science & ... 24 (2017) 3148{3156

the load demand. When the power generation exceedsthe power demand, the excess power will be fed intothe utility grid; thus, it provides additional incomefor consumers by their surplus energy sales. On thecontrary, when the energy from the renewable sourcesis not enough to satisfy the load demand, the dieselgenerators start to work. In case the diesel generatorscannot meet the surplus load demand, the de�cientelectricity will be drawn from the grid resulting in anincrease of system cost of purchasing electricity.

A grid-connected system may be vulnerable con-fronted by system abnormalities and a good systemdesign needs to be stable and reliable. In this study, thepower balance of the system will always be maintainedas the grid faults, disturbances blackouts, or otherequipment failures, which are out of consideration.

3. Modeling of the hybrid system

The mathematical model of the hybrid system canbe established based on the problem description. Itis essential to analyze individual components beforeconstructing the model of their combination. In thissection, we �rst analyze the main system componentsand establish their individual model including PVpanels, wind turbines, and diesel generators, and thenthe optimization objectives and the system model arepresented.

3.1. Mathematical models of systemcomponents

The utilization of solar energy includes primarily solarthermoelectric power generation and solar photovoltaicpower generation. Although many studies have focusedon solar thermoelectric power generation [19,20], pho-tovoltaic generation is becoming prevalent owing to itseconomic and environmental advantages. Therefore,solar photovoltaic generation is considered in thisstudy. Generally, the output power of PV panelsdepends mainly on the e�ective solar radiation, thecharacteristics, and the slope angle of the PV panel.Mathematically, the output of PV panels at an instanttime t, considering that the ambient temperature canbe calculated by the following equations [21]:

TC(t) = TA(t) +NCOT� 20

800Sp(t; �); (1)

ISC(t) = [ISC,STC +KI(TC(t)� 25)]Sp(t; �)

1000; (2)

VOC(t) = VOC,STC �KV � TC(t); (3)

PM(t; �) = NPV � VOC(t) � ISC; (t; �) � FF (t); (4)

where TC(t) and TA(t) are the cell temperature andambient temperature at time t, respectively. NCOT is

the Nominal Cell Operating Temperature provided bythe manufacturer, ISC,STC and VOC,STC are the moduleshort-circuit current and open-circuit voltage underStandard Test Conditions, and KI and KV are theircorresponding temperature coe�cients. PM(t) is thepower of a PV array consisting of NPV PV panels, andFF(t) is the �ll factor. � is the slope angle of the panel,Sp is the e�ective solar radiation perpendicular to thetilted panel and it is determined by the horizontalcomponent of solar radiation (S) as follows [22].

Sp =S

sinh� sin(h+ �); (5)

sinh = sin' sin � + cos' cos � cos �; (6)

where h is solar elevation angle, ' is geography of thelatitude, � is hour angle, � is solar declination relatedto earth's inclination to the plane of its orbit and thedaily time [6].

The output power of a wind turbine can beexpressed by the following equation:

PWT(�; t) =

8>>><>>>:0; � < Vc12CP�AWT�3; Vc � � < Vr

PWTR; Vr � � < Vf

0; � � Vf

(7)

where Cp is power coe�cient of the wind turbine, �is the air density, AWT is the rotor swept area, PWGRis the rated power of the wind turbine, and � is thewind velocity at hub elevation. Cut-in wind speed, Vc,and cut-o� Vf wind speed are set as 4 m/s and 20 m/s,respectively. Vr is the rated wind speed taken as 14 m/sin this study [5].

Given wind speed �r at reference height Hr andthe wind speed at the hub elevation of a wind turbine,Hwg can be calculated by the power law, which iswidely used by the researchers:

� = �r

�Hwg

Hr

� ; (8)

where is the wind speed power law coe�cient and itsvalue is usually set to be one-seventh of relatively atsurfaces.

The diesel generator acts as an emergency in casethe power from renewable sources cannot meet the loaddemand. Its fuel consumption, Fcons, can be expressedby a linear function of the power output as follows [5]:

Fcons = AdgPr dg +BdgPdg; (9)

where Pr-dg and Pdg are the generator's rated andoutput powers, respectively, Adg and Bdg are thecoe�cients of fuel consumption curve, and their valuescan be 0.08145 l/kW h and 0.246 l/kW h in this paperaccording to the references.


3.2. System optimization modelBased on the individual model of each component men-tioned above, we can establish a bi-objective systemoptimization model. The objectives to be minimizedin this paper are system total cost and fuel emissions.System total cost, Ctot, consists of two parts: theannualized cost (ACS) and net cost of purchasingelectricity Cgrid. ACS is the sum of annualized initialinvestment cost, (Cainv), operation and maintenancecost (Caom), and replacement cost (Carep) of eachcomponent as follows [4]:ACS=Cainv(comps)+Caom(comps)+Carep(comps);

(10)

Ctot = ACS+Cgrid; (11)

where the components include PV panels, wind tur-bines, turbine towers, and diesel generators. Thesecomponents usually have a long lifespan on the average;therefore, they need not to be replaced during theproject lifetime of 25 years considered in this study.

As for the fuel emissions, the number of kg CO2is utilized as a measure. Both the diesel generators andpower generation forming the grid will produce CO2 inthe system. The total fuel emissions are given by:

Femission =TXt=1

Fcons(t) � Ef + Emissiongrid; (12)

where Ef is the emission factor depending on thecharacteristic of the diesel generator and fuel used,and its value is generally 2.5 kg/lit. Emissiongrid isthe emissions produced by the power generation of thegrid to supply the de�cient load demand, that is to say,the more electricity is supplied by the grid, the moreemissions are produced by the system.

Decision variables are composed of the number ofPV panels, Npv, the number of wind turbines, Nwg,the number of diesel generators, Ndg, PV panel slopeangle, �, and turbine tower height, Hwg. Consideringthe constraints of decision variables and the objectivesmentioned above, the multi-objective optimizationproblem, i.e. the system optimization model, can beexpressed as follows:

Min Fobj = (Ctotal; Femission); (13)

subject to

(Npv; Nwg; Ndg) � 0; (14)

Hlow � Hwg � Hhigh; (15)

0� � � � 90�; (16)

where Hlow and Hhigh are the wind turbine towers oflower and upper height limits (m). Additionally, themaximum values of Npv, Nwg, and Ndg in the opti-mization process are set as 30, 20, and 10, respectively.

4. Optimization algorithm

The optimal design of a grid-connected hybrid systemis a multi-objective constraint optimization problem,as shown in Eqs. (13)-(16). Traditional search andoptimization approaches, such as Newton method,are no longer e�ective. Multi-Objective Evolution-ary Algorithms (MOEAs) are well-suited for solvingMOPs owing to their population-based nature whichcan �nd a set of trade-o� solutions in a single run.Numerous MOEAs have been proposed over the pasttwo decades and Preference-Inspired Co-EvolutionaryAlgorithm (PICEA) is one of them. According to theidea of PICEA, di�erent preference sets might lead todi�erent regions of a MOP's Pareto front. Therefore,a promising representative of the trade-o� solutions(so-called Pareto front) can be achieved, if multiplespeci�ed sets of hypothetical preferences are evolvedduring the search process [15,23-25].

Preference-Inspired Co-Evolutionary Algorithmsusing goal vectors (PICEA-g) are instantiation ofPICEA [15] and perform well on MOP benchmarks.Like most of evolutionary algorithms, PICEA-g con-sists of six steps: population initialization, populationevaluation, �tness assignment, selection-for-survive, so-lution reproduction, and selection-for-variation. How-ever, PICEA-g di�erentiates itself from others by itscoevolution features. Speci�cally, two populationsare evolved during the search, i.e. a population ofpreferences (goal vectors) and the usual populationof candidate solutions. The preferences are mainlyused to guide candidate solutions e�ectively towardsthe entire Pareto optimal front. Such an interac-tion is speci�cally realized in the �tness assignmentprocedure. A candidate solution gains �tness bymeeting several goal vectors in objective space, butthe �tness contribution has to be shared evenly withother solutions to satisfy the same goal vector. Thegoal vector will gain �tness only by being satis�ed bya candidate solution; therefore, the more it is satis�ed,the lower its �tness value is.

Although PICEA-g shows advantages over otherevolutionary algorithms, the employed �tness assign-ment method is only weakly Pareto dominance compli-ant [15]. Thus, Shi et al. [18] proposed an enhanced�tness assignment method for PICEA-g. The new�tness assignment method considers both the explicit�tness value of goal vectors and the Pareto dominancerank of candidate solutions. This ensures that thedominated solutions will never have higher �tnessthan non-dominated solutions. The modi�ed PICEA-gwith enhanced �tness assignment method (termed asPICEA-ng) has been demonstrated e�ective and moredetails can be found in [18].

The PICEA-ng is implemented within a (� +�) elitist approach as shown in Figure 2. First, a


Figure 2. �+ � elitist approach [13].

population of N candidate solutions, CS, and a setof Ngoal goal vectors, GV , are initialized. The twopopulations are then co-evolved for maxGen genera-tions. In each generation, gt and parents CS(gt) will bepaired up to produce N o�spring, CSc(gt), by geneticoperators (speci�cally, the simulated binary crossover(SBX) and Polynomial Mutation (PM) operators [16]).Meanwhile, Ng, new goal vectors, and GVc(gt) arerandomly re-generated according to the pre-de�nedbounds. Since, in the algorithm, all solutions arenormalized within [0,1], the goal vector bounds can beset as [1.2,1.2,...,1.2]. Then, CS(gt) and CSc(gt) aswell as GV (gt) and GVc(gt) are pooled, respectively.The combined population will be sorted based ontheir �tness value, respectively. Finally, the samenumber of individuals with the parent population isselected by the truncation selection as the new parentpopulations [15].

PICEA-g algorithm is applied to address theMOP mentioned above. The chromosome of a candi-date solution is composed of �ve genes in the form:[NpvjNwgjNdgjHwgj�]. In the optimization process,round operation is conducted to keep the number ofsystem devices as integer ones. General parametersettings are given in Table 1, where pc is recombinationprobability, pm is mutation probability, �c and �m

Table 1. General parameter settings.

N Ng MaxGenpc

(SBX)�c

(SBX)pm

(PM)�m

(PM)50 50 100 1 15 1/nvar 20

are distribution indices for SBX and PM operators,respectively. nvar is the number of decision variables.In this study, nvar = 5. The values of these parametersare set based on previous literature.

5. Experimental study

As an example of application, the optimal design ofa grid-connected hybrid system to supply power foran area in Spain (latitude 41.65�) is carried out inthis section. First, the input data are introduced toconduct the experiment. Then, experimental resultsand analyses are presented.

5.1. Input dataThe input data set includes the hourly solar irradiationon horizontal surface, the hourly mean values of windspeed and ambient temperature, the hourly load de-mand during one year, and the speci�cations of system


Figure 3. Monthly average load pro�le.

Figure 4. Hourly meteorological data.

components as shown in Figures 3 and 4 and Tables 2and 3. The load (only DC load is considered here), solarradiation, and wind speed are assumed to be constantduring the simulation time step of one hour [26].

The hourly mean values of solar irradiation andwind speed data at 10 meters height as well as theambient temperature in Figure 4 are the average dataof the last ten years [6]. The technical characteristicsof system components are given in Tables 2 and 3,where initial investment cost, Cinv, and operation andmaintenance cost, Com, are used to calculate ACS. WTtower stands for wind turbine tower.

Additionally, the limit of turbine tower height isbetween 5 and 30 meters, the rotor length is 2 meters,and the rated power is 8892 W. As for the diesel

Table 2. PV panels speci�cations.

Voc(V)

Isc(A)

Vmax

(V)Imax

(A)NCOT(�C)

21 7.22 17 6.47 43

Table 3. The cost speci�cations of system components.

ItemInitial

investmentcost Cinv

Maintenancecost Com

Lifetime(year)

PV panel 3000 $ 30 $ 25

Wind turbine 3013 $ 50 $ 25

WT tower 250 $/m 2.5 $/m 25

Diesel generator 1514 $ 0.17 $/h 25

generator, its rated power is 2 kW and its Com is relatedto the operation time. In addition, the e�ciency of theinverter is set to be 90%. The nominal interest rate andannual in ation rate considered are 3.75% and 1.5%,respectively. The fuel price used by the diesel generatoris 1.2 $/lit [26]. The prices of selling electricity back tothe grid and buying electricity from it are assumed tobe equal and they are both 0.1/$kW h. The producedequivalent CO2 emissions are set as 0.5 kg per unitpower, when we purchase electricity from the grid inthis study.

5.2. ResultsWith the input data, the PICEA-ng algorithm hasbeen applied to address the optimization problem. Theoptimization result is shown in Figure 5, which isthe representation of the last generation in objectivespace. As can be observed from the result, thetotal system cost and fuel emissions have a signi�cant

Figure 5. Pareto front of the last generation.


Table 4. Three typical optimal solutions.

Solution Npv Nwg Ndg Hwg � Femission(kg) Ctot ($)

1 30 10 0 26.10 47.29 2434.79 8051.492 3 7 0 19.83 57.63 3978.92 2835.723 0 1 0 25.53 56.10 5555.77 1675.14

negative relationship, i.e. a more cost-e�ective systemwill produce more fuel emissions.

Along with the obtained Pareto set, a decision-maker has to select a suitable solution by incorporatinghis/her a posteriori preference information. As anexample, three typical solutions are selected from thePareto set according to the fuel emissions objective(the minimal, medium, and maximum one) as shownin Table 4.

Compared with the previous work [26], this pa-per studied a grid-connected hybrid renewable energysystem using the modi�ed PICEA-g algorithm. In thegrid-connected hybrid system, the utility grid serves asthe storage device, so that the battery bank can beexcluded. Although the system model and objectivesare di�erent, good results of the problems by meansof the preference-inspired co-evolutionary approach areobtained. It is worthy to note that the number ofdiesel generators is zero in the grid-connected systemcon�gurations, i.e. there is no diesel generators in theoptimal con�gurations. The reason may be that thecost of diesel generators is high, and they emit toomany greenhouse gases compared with acquiring thesame electricity from the grid.

6. Conclusions

The modi�ed Preference-Inspired Co-Evolutionary Al-gorithm (PICEA-ng), which has high performanceand simplicity compared with other evolutionary al-gorithms, has been used for the �rst time to theoptimal design of grid-connected hybrid renewableenergy systems in this article. With simultaneousminimization of total system cost and fuel emissions,we established the grid-connected system model, whichis a two-objective optimization problem. As a casestudy, a grid-connected hybrid system, including PVpanels, wind turbines, and diesel generators, has beendesigned to �nd the optimal con�guration and goodresults are obtained by the proposed method.

It is worth mentioning that the optimizationmodel is limited to a static environment, where somenoisy parameters can be considered in the input data orobjective functions to describe uncertain problems forfuture research. Moreover, various prices of selling theexcess power back to the grid and buying the electricityfrom the grid might be considered to study theirin uence on the optimal design of a grid-connected

hybrid system. Lastly, other advanced evolutionaryalgorithms, e.g. [27,28,29], can be employed to solvethe optimal design of HRES. In another aspect, theproblem itself can be formulated as a standard multi-objective problem to benchmark the performance ofdi�erent multi-objective evolutionary algorithms.

Acknowledgment

The National Natural Science Foundation of China(No. 61403404, 71571187), the National Universityof Defense Technology (No. JC 14-05-01) and theDistinguished Natural Science Foundation of HunanProvince (No. 2017JJ1001) supported this work.

References

1. Kaundinya, D.P., Balachandra, P. and Ravindranath,N.H. \Grid-connected versus stand-alone energy sys-tems for decentralized power-A review of literature",Renew. Sust. Energ. Rev., 13(8), pp. 2041-2050 (2009).

2. Wang, R., Fleming, P.J. and Purshouse, R.C. \Generalframework for localised multi-objective evolutionaryalgorithms", Information sciences, 258(2), pp. 29-53,(2014).

3. Katsigiannis, Y.A., Georgilakis, P.S. and Karapidakis,E.S. \Multi objective genetic algorithm solution to theoptimum economic and environmental performanceproblem of small autonomous hybrid power systemswith renewable", IET Renew Power Gener., 4(5), pp.404-419 (2010).

4. Yang, H., Zhou, W., Lu, L. and Fang, Z. \Optimal siz-ing method for stand-alone hybrid solar-wind systemwith LPSP technology by using genetic algorithm",Sol. Energy, 82, pp. 354-367 (2008).

5. Dufo-Lopez, R. and Bernal-Agustin, J.L. \Multi-objective design of PV-wind-diesel-hydrogen-batterysystems", Renew Energ., 33(12), pp. 2559-2572 (2008).

6. Shara�, M. and ELMekkawy, T.Y. \Multi-objectiveoptimal design of hybrid renewable energy systemsusing PSO-simulation based approach", Renew Energ.,68, pp. 67-79 (2014).

7. Wang, R. and Zhang, T. \Multi-objective optimaldesign of hybrid renewable energy systems usingMOEA/D", International Conference on RenewableEnergy Research and Applications, IEEE, Milwaukee,USA, pp. 161-167 (2014).

8. Giannakoudis, G., Papadopoulos, A.I., Seferlis, P. andVoutetakis, S. \Optimum design and operation under


uncertainty of power systems using renewable energysources and hydrogen storage", Int. J. Hydrogen En-ergy, 35(3), pp. 872-891 (2010).

9. Jahromi, A.E. and Rad, Z.B. \Optimal topologicaldesign of power communication networks using geneticalgorithm", Sci. Iranica, Trans. E: Ind. Eng., 20(3),pp. 945-957 (2013).

10. Caballero, F., Sauma, E. and Yanine, F. \Busi-ness optimal design of a grid-connected hybrid PV(photovoltaic)-wind energy system without energystorage for an Easter Island's block", Energ., 61, pp.248-261 (2013).

11. Dalton, G.J., Lockington, D.A. and Baldock, T.E.\Feasibility analysis of renewable energy supply op-tions for a grid-connected large hotel", Renew Energ.,34(4), pp. 955-964 (2009).

12. Pablo, G.T., Francisco, L.I., Carlos, A.G.V., Antonio,J.L.M., Luis, M.F.R. and Francisco, J. \Long-termoptimization based on PSO of a grid-connected renew-able energy/battery/hydrogen hybrid system", Int. J.Hydrogen Energy, 39(21), pp. 10805-10816 (2014).

13. Lashkar Ara, A., Kazemi, A., Gahramani, S. andBehshad, M. \Optimal reactive power ow using multi-objective mathematical programming", Sci. Iranica,Trans. D: Comput. Sci. Eng. Electr. Eng., 19(6), pp.1829-1836 (2012).

14. Bernal-Agustin, J.L. and Dufo-Lopez, R. \Economicaland environmental analysis of grid connected photo-voltaic systems in Spain", Renew. Energ., 31(8), pp.1107-1128 (2006).

15. Wang, R., Purshouse, R.C. and Fleming, P.J.\Preference-Inspired Coevolutionary Algorithms forMany-Objective Optimization", IEEE Trans. Evol.Comput., 17(4), pp. 474-494 (2013).

16. Deb, K., Pratap, A., Agarwal, S. and Meyarivan, T.\A fast and elitist multiobjective genetic algorithm:NSGA-II", IEEE Trans. Evol. Comput. 6(2), pp. 182-197 (2002).

17. Zhang, Q. and Li, H. \MOEA/D: A Multiobjec-tive Evolutionary Algorithm Based on Decomposi-tion", IEEE Trans. Evol. Comput., 11(6), pp. 712-731(2007).

18. Shi, Z.C., Wang, R. and Zhang, T. \PICEA-g usingan enhanced �tness assignment method", 2014 IEEESymposium on Computational Intelligence in Multi-Criteria Decision-Making (MCDM), IEEE, Orlando,USA, pp. 72-77 (2014).

19. Muthu, G., Shanmugam, S. and Veerappan, A.R.\Numerical modeling of year-round performance ofa solar parabolic dish thermoelectric generator", J.Electronic Materials, 44(8), pp. 2631-2637 (2015).

20. Baranowski, L.L., Warren, E.L. and Toberer, E.S.\High-temperature high-e�ciency solar thermoelectricgenerators", J. Electronic Materials, 43(6), pp. 2348-2355 (2014).

21. Koutroulis, E., Kolokotsa, D., Potirakis, A. andKalaitzakis, K. \Methodology for optimal sizing ofstand-alone photovoltaic/wind-generator systems us-ing genetic algorithms", Sol. Energy, 80(9), pp. 1072-1088 (2006).

22. Abedi, S., Alimardani, A., Gharehpetian, G.B., Riahy,G.H. and Hosseinian, S.H. \A comprehensive methodfor optimal power management and design of hybridRES-based autonomous energy systems", Renew. Sust.Energ. Rev., 16(3), pp. 1577-1587 (2012).

23. Wang, R., Purshouse, R.C. and Fleming, P.J.\Preference-inspired co-evolutionary algorithms usingweights for many objective optimisation ", EuropeanJournal of Operations Research, 243(2), pp. 423-441(2015).

24. Wang, R., Purshouse, R.C., Giagkiozis, I. and Flem-ing, P.J., \The iPICEA-g a new hybrid evolution-ary multi-criteria decision making approach using thebrushing technique", European Journal of OperationsResearch, 243(2), pp. 442-453 (2015).

25. Wang, R., Maszatul, M. Mansor, Purshouse, R.C. andFleming, P.J. \An analysis of parameter sensitivities ofpreference-inspired co-evolutionary algorithms", Inter-national Journal of Systems Science, 46, pp. 423-441(2015).

26. Shi, Z.C., Wang, R. and Zhang, T. \Multi-objectiveoptimal design of hybrid renewable energy systemsusing preference-inspired coevolutionary approach",Sol. Energy, 118, pp. 96-116 (2015).

27. Wang, R. Zhang, Q.F. and Zhang, T. \Decompositionbased algorithms using Pareto adaptive scalarizingmethods", IEEE Trans. Evol. Comput., 20, pp. 821-837 (2016).

28. Li, M., Yang, S., Zheng, J., and Liu, X. \ETEA: AEuclidean minimum spanning tree-based evolutionaryalgorithm for multiobjective optimization", Evolution-ary Computation, 22(2), pp. 189-230 (2014).

29. Li, M., Yang, S., Zheng, J., and Liu, X. \Pareto ornon-Pareto: Bi-criterion evolution in multi-objectiveoptimization", IEEE Trans. Evol. Comput., 20(5), pp.645-665 (2016).

Biographies

Zhichao Shi received his BSc degree from the NankaiUniversity in 2013 and MSc degree from the NationalUniversity of Defense Technology in 2015, both in P.R.China. He is currently pursuing his PhD degree in theDepartment of Electrical and Computer Engineering,University of Alberta, Canada. His main researchinterests include renewable energy system planning,optimization methods, and computational intelligence.

Rui Wang received his BSc degree from the NationalUniversity of Defense Technology (NUDT), P.R. China,in 2008 and his PhD degree from the University ofShe�eld, U.K, in 2013. He is currently a Lecturer at


the NUDT. His main research areas are evolutionarycomputation, multi-objective optimization, machinelearning, and optimization methods on energy internetnetwork. He won the Operational Research SocietyPhD prize Runners-up for the best PhD dissertationin 2016.

Xiaoyu Zhang is currently pursuing the PhD degreeat the College of Information System and Management,National University of Defense Technology. Her mainresearch interests include machine learning and opti-mization.

Yan Zhang received his BSc from the Sichuan Uni-versity (SCU), P.R. China, in 2010. He received hisMSc and PhD degrees from the National University

of Defense Technology (NUDT), P.R. China, in 2012and 2016, respectively. He is currently a ResearchAssistant at the Science and Technology University onship integrated power system technology laboratory,the Naval University of Engineer. His main researchareas are optimal scheduling and model predictivecontrol of micro-grids.

Tao Zhang received his BSc, MSc, and PhD degreesfrom the National University of Defense Technology(NUDT), P.R. China, in 1998, 2001, and 2004, respec-tively. He is currently a Professor at the College ofInformation System and Management, the NUDT. Hismain research areas are multi-criteria decision-making,optimal scheduling, data mining, and optimizationmethods on energy internet network.

optimal design of grid-connected hybrid renewable energy systems...

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