An Efficient Sizing Method With Suitable Energy Management Strategy for Hybrid Renewable Energy Systems

An efficient sizing method with suitable energy managementstrategy for hybrid renewable energy systems

Mohammad Ali Yazdanpanah-Jahromi*,†, Seyed-Masoud Barakati and Said Farahat

University of Sistan and Baluchestan, Zahedan, Iran

SUMMARY

This paper propose a new method for designing a stand-alone hybrid wind-photovoltaic-diesel-batterysystem that minimizes the inequality coefficient and annualized cost of system and maximizes the correla-tion coefficient using multi-objective particle swarm optimization algorithm. The proposed method usesdata from solar radiation, temperature, and wind speed that are collected from the city of Zabol, locatedin south-east of Iran. The results are presented as an optimal Pareto front set and the optimal number ofdevices, as well as objective functions, that is, inequality coefficient, annualized cost of system, and corre-lation coefficient. Additionally, a study of the operating hours of diesel generator in optimal configuration iscarried out. Simulation results show the match rate between demand, supply, and energy storage. Theoptimal number of wind turbines, photovoltaic modules, and batteries ensuring that the system total costis minimized, while guaranteeing a highly reliable source of load power is obtained. The proposed sizingmethod can be applied to any other locations with different weather data, load demands, and differentcharacteristics. Copyright © 2013 John Wiley & Sons, Ltd.

key words: large-scale optimization; hybrid power systems; wind-PV-power systems; multi-objectiveoptimization; sizing method; electricity match rate (EMR)

1. INTRODUCTION

Ever-increasing need for energy, global environmental concerns, and growth of population calls for com-bining multiple renewable energy resources in a practical fashion. Wind power has recently become thefastest growing renewable energy resource and is projected to lead the growth of the renewable powerportfolio in the near term [1]. Solar energy, both as a thermal and as an electric source, has been also wellsuited as an environmentally friendly power source. Additionally, wind turbine (WT) and photovoltaic(PV) have been considered as promising power generating sources because of their complementary powergeneration characteristics, that is, there is more sunlight during lowwind and more wind at night time. Thereliability of hybrid systems must be considered during the planning and design stages, although design-ing hybrid systems with both solar and wind components increases the reliability of such systems [2].Adoption of renewable energy technologies poses risks of compromising system reliability because ofthe intermittent nature of renewable sources. The social cost of emissions helps to justify hybrids’implementation. Many simulation studies have been performed to justify the hybrid systems. Hybridstand-alone electric generating systems are usually more reliable and less costly than systems that use onlya single source of energy [3]. Additionally, energy storage devices are necessary in the hybrid systemsbecause of the intermittent nature of wind and solar energies. Traditionally, deep-cycle lead-acid batteriesare used to store direct current electrical energy in electrochemical form [4]. In order to generate the powerfrom renewable energy continuously, there is a need for back-up systems. A diesel generator is usuallyused as a back-up system to supply the load demand and to charge the batteries.

*Correspondence to: Mohammad Ali Yazdanpanah-Jahromi, University of Sistan and Baluchestan, Zahedan, Iran.†E-mail: [email protected]

Copyright © 2013 John Wiley & Sons, Ltd.

INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMSInt. Trans. Electr. Energ. Syst. (2013)Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/etep.1790

The optimal design of stand-alone hybrid renewable energy systems includes proper capacity plan-ning and sizing, to ensure the lowest investment and optimal deployment of hybrid energy resources.The optimal design should consider the coordination among hybrid energy sources, energy storagesystems, and load demand profiles. Various optimization techniques in sizing of hybrid energyresources have been reported in literature. Classical optimization techniques may be computationallyintensive or may not take into account all relevant parameters. Because some of the practical probleminvolves objective functions that are not continuous and/or differentiable, the classical optimizationtechnique has limited scope in practical application [5]. Some other optimization method is conceptu-ally different from the traditional method. These methods are labeled as modern or nontraditionalmethod of optimization [5]. Modern optimization methods on the other hand provide nondominatedsolutions with minimal computational requirements. Genetic algorithm and particle swarm optimiza-tion (PSO) are emerging as valuable, robust, simple, and effective tools for traction in industrial pro-cess automation and online control adaption [6]. An optimized wind-PV hybrid power system usingPSO algorithm resulting in higher capacity and better efficiency has been proposed in [7]. Thenondominated sorting genetic algorithm II (NSGA-II) that is used to simultaneously minimize powerlosses in transmission network and cost has been proposed by Dhillon (2009) in [8]. The use of geneticalgorithm in unit sizing of PV/wind generator systems has been discussed in [9]. Juhari et al. (2009)have discussed sizing and determined the optimum combination of a hybrid PV-wind-hydro-dieselenergy system [10]. Erdinc and Uzunoglu (2012) have reviewed different optimum sizing approachesthat are available in literature [11]. PSO is especially suited to deal with complex engineeringdesigns because of its fast convergence performance and simple operations [12]. In this paper, amulti-objective PSO (MOPSO) algorithm has been proposed to handle the problem.Hybrid systems are usually designed with the lowest total cost and pollutant emissions for the life of

the installation. Boomsma et al. (2012) have presented a framework to evaluate investment time frameand capacity for renewable energy scenarios [13]. Some other researchers have developed preprocess-ing techniques and heuristic algorithms for timetabling and labor scheduling, obtaining excellentresults [14]. Two different hierarchical approaches, fuzzy logic and physical model-based optimiza-tion, to control the heat transfer fluid output temperature and attempt to maximize profit by findingthe optimal operating point have been performed in [15].Proper design of stand-alone renewable energy system by maximizing the power reliability and cost

minimization has been considered in recent years. One parameter that helps to elucidate the system’sreliability is the loss of power supply probability. Optimal configurations for different hybrid systemshave been obtained by the loss of power supply probability technique and minimum annualized cost ofsystem (ACS) [16–21]. Some others have sized the hybrid power systems based on minimization ofthe levelized cost of energy and the carbon dioxide emission [22,23]. The levelized cost of energycan be defined as a metric that describes the cost of every unit of energy generated by a project. Amulti-objective design of hybrid systems by minimizing the total cost, pollutant emission, and unmetload has been presented in [24]. The different sizing methodologies developed in recent years havebeen reviewed by Luna-Rubio et al. (2012) [25]. Match evaluation method (MEM), which is usedin this article, can be another sizing method [26]. The MEM is based on the coordination criteriabetween generation and consumption intervals.In this paper, a wind-PV-diesel-battery (WPDB) hybrid power generation system is suggested. The

WPDB hybrid systems consist of many components. Ways to match various components are the mainchallenge in such systems. More coordination between the components increases the system effi-ciency. When the output power of renewable energy resources cannot meet the load demand, the strat-egy will be used to start the diesel generator or use the battery power. The WPDB components havenonlinear characteristics. Therefore, to have an optimal power generation, a nonlinear optimizationproblem must be solved.Correctly designed of hybrid systems can greatly increase the rate of hybrid adoption and could jus-

tify by the additional social benefits of emissions reduction. The design of hybrid WPDB system hasbeen studied extensively in recent years [18,19,22,23]. However, these references do not calculate theelectricity match rate (EMR). Some of the studies have used monthly average weather conditions suchas solar insolation and wind speed for a year. However, it is not accurate and not suitable to size thehybrid system based on monthly average because of the intermittent nature of renewable energy

M. A. YAZDANPANAH-JAHROMI ET AL.

Copyright © 2013 John Wiley & Sons, Ltd. Int. Trans. Electr. Energ. Syst. (2013)DOI: 10.1002/etep

sources [17]. Some of the researchers have determined the optimal number of hybrid componentsbased on iteration techniques [16]. These techniques take a lot of computational times. Changing theweather data such as solar insolation and wind speed is also difficult in these techniques.In this paper, a new optimum sizing methodology for hybrid systems based on the coordination

between electricity generation and consumption periods with the lowest cost is developed. TheEMR technique, considered to be the criterion for sizing, is deployed in a WPDB hybrid system.The EMR sizing technique is based on MOPSO algorithm. For this technique, hourly average solarirradiation, temperature, wind speed, and demand data for a small village in Sistan and Baluchestanprovince, Iran, are collected for 1 year. The data are used for system modeling and optimization. Itis assumed that the hourly generation and hourly demand are constant. In this technique, three param-eters are used: inequality coefficient (IC), correlation coefficient (CC), and ACS. IC and CC control theEMR, whereas ACS represents the system cost. IC provides a measure of how well a time series ofestimated values compares with a corresponding time series of observed values [27]. In other words,IC provides a relative measure of forecast accuracy in terms of deviation from the perfect forecast[28]. CC measures of how well the predicted values from a forecast model “fit” with the real-life data[29]. IC gives the match magnitude, whereas CC deals with trend matching. Hence, IC and CC areselected together, to check the EMR between supply and load demand profiles. These two objectivestogether provide a good match rate for hybrid systems. The calculation of IC will always result in avalue between zero and one, with zero denoting a perfect match and one indicating no match. TheCC can range in values between �1 and 1. The results of 1 denote perfect positive correlation, and�1 shows perfect negative correlation. A value of zero represents no correlation between the variables.The ACS checks the total system cost. The economical approach, according to the concept of ACS, isdeveloped. For the proposed hybrid WPDB system, the ACS is composed of annualized capital cost(ACC), annualized replacement cost, annualized maintenance cost, and annualized fuel cost.The optimum combination of IC, CC, and ACS parameters results in the most efficient hybrid

WPDB system. The optimization is achieved by an iterative process using a system model and realweather and load demand data to investigate the efficiency of the proposed methodology. The simula-tion is carried out on the basis of the algorithm developed for the proposed hybrid system using theclimate data of the mentioned area, located in south-east of Iran. Using the EMR objective functions,the configuration of the proposed hybrid system, which gives the highest match rate requirements, canbe obtained. The decision variables included in the optimization process are the number of PV mod-ules, WTs, and batteries. This proposed algorithm is most suitable for global optimization of renewableenergy systems with variable nature. The results show a set of possible solutions as a Pareto front. Thedesigner can select the solution he or she considers most suitable from the Pareto front obtained, study-ing for each solution its IC, CC, and ACS. The designer can also limit the acceptable upper and lowerbound of each objective.The remainder of the paper is organized as follows. Section 2 introduces the mathematical model of

hybrid components. Sections 3 and 4 formulate the hybrid system design problem. The proposedMOPSO algorithm is detailed in Section 5. The operation strategy is discussed in Section 6. Simulationresults and analysis are presented in Section 7. Finally, conclusions are drawn, and future research di-rection is suggested.

2. MATHEMATICAL MODEL OF HYBRID SYSTEM

The proposed hybrid power generation system consists of WT, PV array, battery bank, diesel, controller,inverter, cables, and other accessory devices. Mathematical modeling of the hybrid components isperformed before applying optimal sizing algorithm to ensure the hybrid system meets the load demand.A brief description for modeling of the proposed hybrid system is presented in the following sections.

2.1. Modeling of photovoltaic generator

Photovoltaic technology is identified as the most environment friendly technology [30]. The simula-tion of PV array performance has been carried out by considering the modeling of the maximum power

MODELING OF RENEWABLE ENERGY COMPONENT


point tracking. This model can predict the output power of PV panels in different temperatures andvarious irradiation levels. The output power of a PV panel can be calculated by using the followingequations [31]:

I Vð Þ ¼ lx

1-exp - 1b� � � 1� exp

V

b�Vx�1b

� �� (1)

Vx ¼ s� Ei

EiN�TCV � T � TNð Þ þ s�V max � s� V max � V minð Þ� exp Ei

EiN� ln V max � Voc

V max � V min

� �� (2)

lx ¼ p� Ei

EiN� lsc þ TCi�T � TN½ � (3)

P Vð Þ ¼ V �lx1� exp �1

b

� � � 1� expV

b�Vx�1b

� �� (4)

where P(V) is the output power of the PV panel in watts (W); I(V) is the output current of the PV panelin amperes (A); V is the output voltage of the PV in volts (V); Isc and Voc are the short-circuit currentand the open-circuit voltage at 25°C and 1000W/m2, respectively; Vmax is the maximum open-circuitvoltage at 25°C and 1200W/m2 (usually, Vmax is close to 1.03 Voc); Vmin is the minimum open-circuitvoltage at 25°C and 1200W/m2 (usually, Vmin is close to 0.85 Voc); T is the solar panel temperature(C); Ei is the effective solar irradiation impinging the cell in watts per square meter (W/m2); Tw is the25°C standard test condition; TCi is the temperature coefficient of ISC in A/°C; TCV is the temperaturecoefficient of Voc in V/°C; Ix and Vx are the short-circuit current and the open-circuit voltage, respectively,at any givenEi and T; s is the number of PV panels in series; p is the number of PV panels in parallel; and bis the characteristic constant based on the I-V curve. The characteristic constant, b, usually varies from0.01 to 0.18 and can be calculated using Equation (5) with iterative procedures [32]:

bnþ1 ¼ Vop � Voc

Voc� ln 1� IopIsc� 1� exp �1

bn

� � � (5)

where Vop is the nominal voltage in volts, and Iop is the nominal current of the selected module in amperes.For calculating the available energy of PV array at a specific site, which its solar radiation profile has beenshown in Figure 1, the following equation is used [32]:

0 1000 2000 3000 4000 5000 6000 7000 8000 90000

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (Hour in a year)

Inso

lati

on (

kW/m

2)

Figure 1. Meteorological conditions of solar radiation.



EPV ¼ Pout Exð Þ� SolarWindowð Þ� TotalDayð Þ (6)

where EPV is the yearly production of the PV energy in kilowatt hour (kWh),“SolarWindow” is the totaltime hours that the sun hits the PV module at an average hourly solar irradiation, the product of“TotalDay” is to change from daily to monthly or yearly quantities, and Pout(Ex) is the PV module poweroutput at an average hourly solar irradiation (Ex). The “KyoceraKC200 GHT-2” PV module type is usedin this simulation procedure. The P-V and I-V curves for 36 PVs in series (s=36 and p=1) have beenshown in Figure 2.

2.2. The Wind Turbine Model

Adjusting the measured wind speed to the hub height (h), by using the wind speed data at a referenceheight (hr) from the database, is an important stage before calculating the output power of WT. Thiscan be carried out through the wind power law equation as describe in Equation (7) [33]:

v tð Þ ¼ vr tð Þ h

hr

� �γ

(7)

where ν is the wind speed at the desired height h, νr is the wind speed measured at known height hr, γ isthe wind shear exponent coefficient, which varies with pressure, temperature, and time of day. Acommonly used value for γ in open lands is 1/7.The variation in wind speed are best described by the Weibull probability distribution function

(PDF), f, with two parameters, the shape factor β, and the scale factor η [34]. The PDF calculatesthe probability that the wind speed will be occurred between zero and infinity during the entire chosenperiod. Note that the PDF curve shape and the height of it provide in some way that the area under thePDF curve is unity. There are various notations for the Weibull PDF in literature. In this paper, theWeibull PDF is defined as follow [34]:

f vð Þ ¼ βη

v

η

� �β�1e� v

ηð Þβ

(8)

where β is the shape factor, and v is the wind speed. Figures 3 and 4 are the plot of f versus v for dif-ferent values of η and β in Equation 8, respectively. The value of β controls the curve shape and hence

0 200 400 600 800 1000 1200 14000

0.5

1

1.5

2

2.5x 104

Voltage (V)

Pow

er (

W)

0 200 400 600 800 1000 1200 14000

5

10

15

20

25

Voltage (V)

Cur

rent

(A

)

Figure 2. P-V and I-V curve for 36 photovoltaics in series.



is called the shape factor. The larger shape factor indicates a relatively narrow distribution of windspeeds around the average, whereas the lower shape factor indicates a relatively wide distribution ofwind speeds around the average. The scale factor (η) defines where the bulk of the distribution liesand how stretched out [32]. For wind speed profile, which is shown in Figure 5, the Weibull PDF isshown in Figure 6.The PDF is the key information needed to estimate the total kilowatt hour produced in a year by a

WT at a given site. Using the WT power curve, the annual output energy can then be calculated. Apower curve is a graph that presents the output power of WT at any wind speed. This curve is afunction of the turbine design and normally obtained from the WT manufacturer. The power curveof the selected WT is shown in Figure 7. The energy available for a WT at a specific site can be cal-culated as follows [35]:

EWT ¼ daysð Þ hoursð Þ�Pc f v; β; ηð Þ (9)

where EWT is the generated energy of WT in kilowatt hour for a specific site, Pc is the output power ofWT, f(v) is the Weibull PDF for wind speed ν, β is the shape factor, and η is the scale factor. The

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Wind Speed (m/s)

Wei

bull

pdf

Shape Factor=1Shape Factor=2Shape Factor=3Shape Factor=4Shape Factor=5

Figure 3. Weibull probability distribution function with scale factor η= 10 and shape factor β = 1, 2, 3, 4, 5.

0 5 10 15 20 250

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Wind Speed (m/s)

Wei

bull

pdf

Scale Factor=6Scale Factor=7Scale Factor=8Scale Factor=9Scale Factor=10Scale Factor=11Scale Factor=12

Figure 4. Weibull probability distribution function with shape factor β = 2 and scale factorη= 6, 7, 8, 9, 10, 11, 12.



0 1000 2000 3000 4000 5000 6000 7000 8000 90000

5

10

15

20

25

30

Time (Hour of day)

Win

d Sp

eed

(m/s

)

Figure 5. Meteorological conditions of wind speed.

0 5 10 15 20 250

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Wind Speed (m/s)

f(V

)

Figure 6. Weibull probability density function [f(v)].

0 5 10 15 20 250

2

4

6

8

10

12

Wind Speed (m/s)

Pow

er O

utpu

t (K

W)

Figure 7. Power curve of selected wind turbine (the symbols represent the data sampled from the powercurve graphs given by the manufacturer).



multiplication of days by hours gives the total hours in the period of simulation. “ARE442”, a small WTtype, is employed in this simulation. Figure 8 shows the total energy output for the selected WT in 1 year.

2.3. Battery Performance Model

Batteries are the most widely used devices for energy storage. Lead–acid batteries are usually used forstand-alone hybrid wind-PV-diesel generation systems. Surplus electrical energy is stored in a batterybank, which supplies power to the load when the total power output of WTs and PVs is insufficient. Sothe correct battery sizing is critical. There are different models in literature for battery behaviorsimulation. The modeling of battery based on state of charge (SOC) is the most commonly used model.SOC is an important parameter in system assessments [18]. Temperature can also affect battery capac-ity. The available battery capacity [C’

bat (Ah)], in a given temperature [Tbat (K)], can be calculated usingEquation (10) [16]:

C’bat ¼ C}

bat� 1þ δc� Tbat � 298:15ð Þð Þ (10)

where δc is temperature coefficient. The value of 0.6% per degree is usually used for δc, unless other-wise specified by the manufacturer.For the proposed hybrid WPDB system, it is supposed that the WT has the direct current output. If

the cable losses in the system are neglected, the battery current rate at time t can be expressed asEquation (11) [18]:

Ibat tð Þ ¼PPV tð Þ þ PWind tð Þ � PACLoad tð Þ

ηinverter� PDCLoad

Vbat tð Þ (11)

where ηinverter is the inverter efficiency, which is considered as 92% in this study.The SOC at any hour t is depending on the battery current, the charge or discharge time, and the pre-

vious SOC. By all the aforementioned consideration, the battery SOC can be defined as follows [18]:

SOC t þ 1ð Þ ¼ SOC tð Þ� 1� σ:Δt24

þ Ibat tð Þ�Δt�ηbatC’bat

� �(12)

where ηbat is the battery efficiency, which 90% for charging stage and 100% in discharging process arerecommended. σ is the self-discharge rate; 0.2% per day is recommended, andΔt is the desire time inter-val. When theWT and PVmodules supply power more than the load demand, the overcharging process isoccurred. On the other hand, when the load demand is more than the total output energy of supply sources,the battery SOCmay decrease to the minimum level, which is defined as SOCmin = 1�DOD,where DODis the depth of discharging of battery. In this study, for longevity of battery lifetime, the value of DOD is

0 5 10 15 20 250

1000

2000

3000

4000

5000

6000

7000

8000

9000

Wind Speed (m/s)

Ene

rgy

(kW

h/Y

ear)

Figure 8. Total wind turbine energy output for 1 year.



considered 50%. In order to prevent the batteries against destruction, it is important to control the batteriesSOC at the following constrain:

SOCmin ≤ SOC≤ SOCmax (13)

where SOCmax is the maximum SOC for batteries (SOCmax = 1). The “US Battery US250” battery type isused for this simulation. The selected battery has a voltage of 6V and a capacity of 250Ah.

2.4. Load Model

The total output power of the proposed hybrid system (WT, PV, battery, and diesel generator) shouldmeet the power load demand. The hourly load data used in this study is shown in Figure 9. This is theyearly variation of domestic load profile in the region.

3. SIZING MODEL BASED ON MATCH EVALUATION METHOD

The maximization of EMR between demand and supply in hybrid renewable energy systems is an es-sential issue in power generation. In other words, the generating periods for renewable resourcesshould closely match the consumption periods. For quantifying the deviation between two set of datavariables, the least squares (LS) approach is used. The following equation describes LS [36]:

LS ¼ ∑n

t¼0Dt � Stð Þ2 (14)

where Dt and St are the demand and supply at time t, respectively. The value of LS is always a positivevalue, and zero value shows a perfect match. Spearman’s Rank CC is one of the objectives that candescribe the correlation between supply and demands. CC can vary from �1 to 1. “One” shows theperfect positive match, “�1” shows the perfect negative correlation, and “0” represents no match.The CC can be expressed as Equation (15) [37]:

CC ¼∑n

t¼0Dt � dð Þ� St � sð Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

∑n

t¼0Dt � dð Þ2�∑

n

t¼0St � sð Þ2

s (15)

whereDt is the demand and St is the supply at time t, and d and s are the demand and supply average overperiod n, respectively. The CC is used to describe the trend matching between the time series of two data

0 1000 2000 3000 4000 5000 6000 7000 8000 90002

4

6

8

10

12

14

Time (Hour of day)

Loa

d (k

W)

Figure 9. Yearly variation of domestic load profile.



sets. It does not explain the relative match magnitudes of the individual variables. Thus, if the size of apower supply doubled, however the excess supply would be far greater, the CC would stabilize the same.Moreover, if two profiles are perfectly in phase with each other, but of very different magnitudes, wouldresult in perfect correlation but not a perfect match rate. For a perfect match rate, both phase and magni-tude must be considered. Hence, another criterion is needed to determine the match magnitude. The IC,describes the inequality in the magnitude domain because of three sources: unequal tendency (mean), un-equal variation (variance), and imperfect covariation (covariance) [37]. Therefore, IC and CC are selectedtogether, to check the EMR between supply and load demand. The resultant IC can range in value between0 and 1. The smaller IC denotes the larger match rate. Value of 0 represents a perfect match, and 1 showsno match. The IC can be given by the following equation [37]:

IC ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n ∑

n

t¼0Dt � Stð Þ2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n ∑

n

t¼0Dtð Þ2 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n ∑

n

t¼0Stð Þ2

svuut(16)

where Dt and St are the demand and supply at time t, respectively; and n is the total time period. Value ofIC between 0 and 0.4 shows good match, and value greater than 0.5 represents weak match [38]. IC is thebest criterion for matching between supply and demand. However, CC is also good criteria, but it is not aswell as IC [38]. In this work, MEM is used for sizing purpose. The algorithm has been implemented on thebasis of the MEM technique. Load is needed to be matched with different supplies in a way that resultantsupply (N1.S1+N2S2+…+Nn.Sn) meets the load with high EMR. Themain objective of the proposed op-timal algorithm is to find the optimal values of “N1, N2,…, Nn”. St in Equations 15 and 16 is the sum oftwo parts,NPV.SPV,NWT.SWT, andNbatt.Sbatt orNPV.SPV,NWT SWT, and SDiesel that respectively denote theenergy supply sources, PV modules, WTs, and battery or PV modules, WTs, and diesel generator. NPV isthe total number of PV modules, NWT is the total number of the WTs, and Nbatt is the number of battery.The initial assumption of the hybrid system configuration will be subjected to the following constrains:

Min NPV;NWT;Nbattð Þ≥1 (17)

Max NPV;NWT;Nbattð Þ ¼ max Dð Þ=min Snð Þ (18)

where max(D) and min(Sn) are, respectively, the maximum and minimum values of demand and supplyover considered period. An initial population of 200 particles, comprising the 1st generation, is generatedrandomly and the constraints described by (17) and (18) are evaluated for each particle. If any of the initialpopulation particles violates the problem constraints, then it is replaced by a new particle, which is gen-erated randomly and fulfills these constraints.

4. COST ANALYSIS BASED ON ANNUALIZED COST OF SYSTEM CONCEPT

A cost analysis of the system is performed according to the concept of ACS. The ACS is composed ofindividual annualized capital cost (ACC) of components, annualized operation and maintenance cost(AOC), annual replacement cost (ARC), and annual fuel cost. It supposes that the life of the projectis 20 years. ACS can be calculated as follows:

ACS ¼ ACC PVþWindþ Tower þ Dieselþ Batteryð Þ þ AOC PVþWindþ Tower þ Batteryð ÞþARC Batteryð Þ þ AFC Dieselð Þ

(19)

4.1. Annualized capital cost

The annualized capital cost (ACC) of each component has taken into account the installation cost. TheACC of each component can be calculated by using Equation (20):



ACC ¼ Ccap�CRF i; nproj� �

(20)

where Ccap is capital cost of each component ($), nproj is the component lifetime (year), and CRF iscapital recovery factor, defined as Equation (21):

CRF i; nproj� � ¼ i: 1þ ið Þnproj

1þ ið Þnproj � 1(21)

where i is the annual interest rate, consisting of nominal interest rate (iloan, the rate at which a loan canbe obtained) and the annual inflation rate, f, calculated as follows:

i ¼ iloan � f

1þ f(22)

In this study, the iloan and f are considered to be 5% and 2%, respectively.

4.2. Operation and maintenance cost

The operation and maintenance cost is the maintenance and repair cost of each hybrid component cal-culated by using Equation (23):

AOC nð Þ ¼ AOC 1ð Þ� 1þ fð Þn (23)

where AOC(n) is the maintenance cost of nth year, and the AOC(1) is the component maintenance costfor the first year of the project.

4.3. Annual replacement cost

Annual replacement cost is the annual cost value for replacing the components during the projectlifetime. The components that have a lifetime less than the lifetime of the project needs to be replacedduring the project lifetime. In this study, components that need replacement are batteries. Othercomponents do not need for replacement because their lifetime is the same as the project lifetime.The ARC is calculated as the following Equation (24):

ARC ¼ Crep�SFF i; nrep� �

(24)

where Crep is the replacement cost of units, SFF is the Sinking Fund Factor that depends on lifetime ofunits (nrep) and interest rate (i). SFF is a ratio that calculates the future value of a series of equal annualcash flow and can be calculated as the following Equation (25):

SFF i; nrep� � ¼ i

1þ ið Þnrep � 1(25)

4.4. Annual fuel cost

The cost of fuel for diesel generator is calculated by using the following Equation (26):

AFC ¼ Tfc�CRF i; nð Þ (26)

where Tfc is total fuel consumption for 20 years.The fuel (gas oil) price is considered 0.16049 $/kWh. The expected carbon dioxide emission is

0.669 kg/kWh. The output power of diesel generator is 5 kW. Other cost parameters used in this paperare shown in Table I.

5. MULTI-OBJECTIVE OPTIMIZATION PROCEDURE USING MULTI-OBJECTIVEPARTICLE SWARM OPTIMIZATION

Implementation of MOPSO and NSGA-II for various engineering and business applications have beencarried out in recent years. MOPSO is an evolutionary computation optimization technique (a search



method based on a natural system) [39,40]. MOPSO is a form of swarm intelligence, and it is moti-vated by social behavior of organism such as flock of birds. In bird flocking, if a member finds asuitable way to move for food or protection, other individuals in the swarm will follow its movement.This behavior can be modeled by swarms of particle. Each particle, having both position and velocity,is first randomly initialized. Then, its fitness value is calculated according to the fitness measureprespecified. If the position is better than the best position (Pbest) encountered by itself and its neigh-bors, the current value is set as the new Pbest. The particle that has the best fitness value of all particlesis chosen as the global best (Gbest). The position and the velocity of each particle are updated accordingto its own flight experience and that of its companions. Finally, stopping criteria such as maximum it-erations can be used to stop the algorithm.Nondominated sorting genetic algorithm II is another multi-objective evolutionary algorithm that

was first proposed by Deb et al. in 2000 [41]. NSGA-II is a revised version of NSGA, which was pro-posed by Srinivas and Deb in 1994 [42]. NSGA-II uses a fast nondominated sorting approach, an elitiststrategy, and no niching parameter. Diversity is preserved by the use of crowded comparison in thetournament selection and in the phase of population reduction [43]. The MOPSO and NSGA-II shareseveral common points. For instance, both of them improve the solution quality through continuesadjustment parameters; the fitness value of each individual evaluates by the prespecified criteria; bothbegin with a population generated randomly. However, there are several aspects that make their innerworking different from one another. The philosophy of MOSPO is “to follow the leader”, whereas thatof NSGA-II is “survival of the fittest”. In MOPSO, the particles update their states with the internalvelocity, and there are no genetic operators such as crossover and mutation. The mechanism of infor-mation sharing significantly differs from one another. In MOSPO, just local and global positions aretransparent to other individuals, which is a form of one-way communication. However, in NSGA-II,the whole population moves toward the promising region because individuals share information witheach other. The control parameters are fewer in MOPSO compared with NSGA-II. So, in MOSPO, allthe particle tend to converge to the best solution quickly, comparing with NSGA-II [6].These two multi-objective optimization algorithms can find Pareto-optimal solution in one single simu-

lation run. The objectives of sizing stand-alone hybrid power system are usually in conflict with each other.The sizing of the hybrid wind/PV systems is much more complicated than the single source power gener-ation systems. This is due to multiple variables and parameters that have to be taken into account in systemoptimization. Long-term system performance, cost parameters, and EMR objectives must be considered inorder to reach the best compromise for both power match rate and cost. Both algorithms were applied to theproposed system. It was found that with the same number of iteration and population, MOPSO convergedfaster than NSGA-II [26]. Therefore, MOPSO was selected for this optimization procedure.The MOPSO algorithm achieves system optimization by dynamically searching for the optimal con-

figuration based on maximizing the EMR and minimizing ACS and IC parameters and maximizing theCC parameter. It is noted that ACS, IC, and CC parameters, essential for the optimization process, con-flict with one another. By employing the MOPSO algorithm for each configuration, a set of possiblesolutions (Pareto set) are obtained.A proper sizing algorithm is the one that can find the optimal size of each component in each con-

figuration to maximize the EMR between demand and supply. The numbers of PV panels, WTs, andbattery are considered design variables for proper sizing. The minimum value (lower limit) of designvariables is selected to be one to be sure that there is at least one of each resource in the system. Theflowchart for applying the MOPSO algorithm is shown in Figure 10.

Table I. The costs and lifetime aspect for the proposed hybrid components.

ComponentsInitial capital

cost ($)Maintenance cost in the

first year ($)Replacement

cost ($)Life time(year)

Photovoltaic module 800.00 65.00 Null 20.00Wind turbine and its tower 1404.86 101.50 Null 20.00Battery 126.35 25.00 126.35 5.00Diesel 500.00 1000.00 Null 20.00Other components 900.00 90.00 Null 20.00



6. OPERATION STRATEGY OF PROPOSED HYBRID WIND-PV-DIESEL-BATTERY SYSTEM

One of the crucial factor for optimization is to determinate the best time for starting and stopping thediesel generator. A suitable operation strategy can optimize the fuel consumption, which is one of themain concerns for the entire operation cost of a diesel generator over its lifetime. The optimized modelachieves the optimal size for hybrid components based on the maximum EMR and minimum ACS.The operating strategy is as follows:

• If the total power generated from WTs (PWT) and PV panels (PPV) is more than the load demand(PL), the excess power is used to charge the batteries. In this case, the sizing optimization will becarried out with only two supplies (PV and wind).

• If the total generated power (PWT+PPV +Pbatt) is less than the load demand and SOC of batteriesis higher than SOCmin, the batteries will supply the extra power. The sizing optimization will becarried out with PV, wind, and battery.

• If the batteries SOC are equal or less than SOCmin, the diesel generator will start and supply thepower in order to protect the batteries against excessive draining. Surplus power from diesel willcharge the batteries as amount as SOCmax. In this case, the calculation of sizing optimization willbe carried out with PV-wind including one diesel generator.

The decision parameters for the optimization algorithm are the numbers of PV modules, WTs, andbatteries. The simulation assumes ambient air temperature, high WT installation, hourly solar

Initial Guess of NPV, NWT and NBatt

Fitness FunctionEvaluation:

Minimization of IC andACS and also

Maximization Of CC

DieselGeneration

All CombinationOptimized

Optimum Number ofUnits:

NWT, NPV and NBatt

Selection Operation:Minimum ACS

Crossover and MutationOperation of MOPSO

(or NSGA-II)

Hourly Meteorological Data for One Year(Wind Speed, Solar irradiation and Load

Demand Data)

Wind TurbineModel and

Calculation Of PWT

PV System Modeland Calculation

Of PPV

The PV ModuleTemperature

(TPV)

Desire High(HWT)

BatteryPerformance

Model

N

New Generation ofConfiguration

Y

Figure 10. Flowchart of the optimization procedure for the multi-objective particle swarm optimization(MOPSO) algorithm.



irradiation on a horizontal surface, existence of wind, and load demand for 1 year. The output power ofPV array and WT is calculated according to the models described before. The battery storage system ispermitted to discharge up to a limit defined by the maximum DOD. The proposed strategy determinesthe best value for diesel generator starting and stopping points, which are the keys to achieve an opti-mum operation. The system design is optimized by employing the MOPSO algorithm, which dynam-ically searches for the optimal configuration in somehow to maximize the EMR in the lowest ACS.The proposed strategy of operating the hybrid WPDB system is presented as a flowchart in Figure 11.

7. OPTIMIZATION RESULTS AND DISCUSSION

The output power of PV array and WT is calculated according to the model that was described previ-ously. The maximum power point tracker method has been employed in the PV systems. The actualcollected solar radiation, temperature, wind speed, and load demand data from south-east of Iran areused for simulation. The optimization process, which dynamically searches for the optimal configura-tion by minimizing the IC and ACS and maximizing the CC, is deployed. The results of optimal solu-tion obtained for optimal capacities of WT and PV generation from MOPSO and the Pareto front arepresented in Table II. As mentioned, for having good EMR, IC values must be as low as possible. Thevalues lower than 0.4 are acceptable for providing a good match rate between supply and demand [38].The ACS cost should be as low as possible. Higher CC is another criterion for this process. It is worthmentioning that CC deals with trend matching, whereas IC shows the match magnitude. Hence, IC and

Read Hourly Wind Speed, SolarIrradiation And Load Demand DATA

PL>PWT+PPV

SOC<SOCmax

Charge theBatteries

Calculate IC, CCand ACS as:

S1=PV, S2=Wind

PL>PBatt+PWT+PPV

OrSOC<SOCmin

Diesel Start andSupply the Power.

Surplus Power WillCharge the Batteries

The BatteriesSupply the Power

and Will BeDischarged.

Calculate IC, CC andACS as:

S1=PV, S2=Wind andS3=Diesel

Calculate IC, CCand ACS as:

S1=PV, S2=Windand S3=Battery

Calculation of AvailableOutput Energy for Wind

Turbine (PWT)

Y

Y

N

Dump theExcess Power

N

Y

N

Calculation of AvailableOutput Energy for PV

Module (PPV)

Figure 11. Operation strategy of proposed hybrid system.



CC values are selected together to ensure the match rate between supply and demand. The IC param-eter is especially of greater importance than CC or ACS. Furthermore, the CC parameter is of greaterimportance when compared with ACS. Therefore, the Pareto front has been plotted for IC and CC, ICand ACS, and CC and ACS, as shown in Figures 12, 13, and 14, respectively. When a prespecifiediteration count (N=Nmax) is reached, MOPSO is terminated (Nmax = 300 and a population size ofNpop = 200 are considered).The 20 best sizing selections out of 30 runs searching for the best configuration have been obtained

and rounding up. The solutions found by these optimization algorithms are shown in Table II. Theseresults show the optimum combination of equipment needed to supply the energy to the load at thelowest cost possible.

Table II. Pareto front/optimal solutions obtained from multi-objective optimization.

Solution

Obtained results from MOPSO algorithm

IC CC ACS NPV NWIND Nbatt NPV-New NWI-New Nbatt-New

1 0.1041 0.8924 2207.1 1.0102 1.0266 1.0242 2 2 22 0.1055 0.8934 2301.8 1.0116 1.4203 1.0000 2 2 13 0.0980 0.9022 2373.2 1.0680 1.1641 1.3246 2 2 24 0.0903 0.9116 2347.7 1.0065 1.3256 1.8844 2 2 25 0.0886 0.9111 2559.4 1.0000 1.0024 1.7803 1 2 26 0.1018 0.8948 2206.2 1.0105 1.0000 1.0942 2 1 27 0.0900 0.9123 2354.1 1.0050 1.4004 1.7371 2 2 28 0.1046 0.8900 2559.1 1.0042 1.2515 1.0000 2 2 19 0.0942 0.9086 2392.2 1.0442 1.5754 1.6031 2 2 210 0.0923 0.9078 2240.6 1.0288 1.0000 1.4954 2 1 211 0.0921 0.9077 2339.5 1.0126 1.0176 1.4582 2 2 212 0.1044 0.8965 2312.6 1.1620 1.1443 1.7070 2 2 213 0.0914 0.9109 2358.6 1.0051 1.4805 1.5452 2 2 214 0.0917 0.9086 2265.7 1.0378 1.0525 1.6334 2 2 215 0.0928 0.9069 2263.2 1.0242 1.0000 1.4500 2 1 216 0.0911 0.9116 2363.4 1.0146 1.4500 1.6829 2 2 217 0.0907 0.9105 2295.1 1.0017 1.2249 1.5408 2 2 218 0.0923 0.9106 2362.2 1.0289 1.4499 1.6508 2 2 219 0.0899 0.9104 2350.4 1.0110 1.0000 1.6529 2 1 220 0.0941 0.9096 2460.7 1.0050 1.9275 1.4536 2 2 2

MOPSO, multi-objective particle swarm optimization; IC, inequality coefficient; CC, correlation coefficient; ACS, annualizedcost of system.

0.0885 0.089 0.0895 0.09 0.0905 0.091 0.0915 0.092 0.09250.914

0.9135

0.913

0.9125

0.912

0.9115

0.911

0.9105

CC

Figure 12. 2D Pareto front for the last generation inequality coefficient (IC) versus correlation coefficient(CC).



New parameters values for the rounded sizing numbers are shown in Table III. One can concludethat there are variations in optimization parameter functions. As shown in Table II, all the obtainedresults for PV sizing numbers are near 1. Rounding these values to the greater one, disturb the matchrate. The optimal sizing numbers, which is shown in Table III, show that the values 1, 2, and 2 for PVmodules, WT, and battery, respectively, give us the best match rate.

0.088 0.09 0.092 0.094 0.096 0.098 0.1 0.102 0.104 0.1061580

1590

1600

1610

1620

1630

1640

1650

IC

AC

S

Figure 13. 2D Pareto front for the last generation inequality coefficient (IC) versus annualized cost ofsystem (ACS).

0.915 0.91 0.905 0.9 0.895 0.89 0.8852190

2200

2210

2220

2230

2240

2250

2260

Figure 14. 2D Pareto front for the last generation correlation coefficient (CC) vs. annualized cost of system(ACS).

Table III. The final goal function values for sizing numbers and the total hours the diesel operates in 1 year.

NPV-New NWT-New Nbatt-New IC CC ACSDiesel operating hours for 1 year

(total year hours = 8760)

2 2 2 0.2565 0.7592 2670.9 32302 1 2 0.2477 0.7569 2426.2 32691 2 2 0.0938 0.9110 2520.9 49072 2 1 0.2577 0.7514 2591.9 3906

IC, inequality coefficient; CC, correlation coefficient; ACS, annualized cost of system.



One scope of using hybrid renewable energy systems is to use green energies such as solar and windinstead of fossil fuels. So the total hours the diesel generator operates in 1 year (8760 h) can be one ofthe criteria in the selection of optimal solutions. The total hours the diesel operates in 1 year is alsogiven in Table III.Table III shows that 2, 2, and 2 sizing numbers for PV modules, WT, and battery, respectively, give

the minimum hour’s diesel operating, and 1, 2, and 2 have the maximum one.It depends to the designer to select one of the obtained optimal sizing numbers for the hybrid com-

ponents, by considering the fuel cost, the necessity of match rate, and the cost consideration.

8. CONCLUSION

A new methodology to size an optimal stand-alone hybrid WPDB bank using a MOPSO algorithm hasbeen presented in this paper. The developed methodology is applied to a selected site to size the hybridWPDB systems. The methodology minimizes the IC and ACS, while simultaneously maximizing CC.The actual collected solar radiation, temperature, wind speed, and load demand data are used for sim-ulation. The application of the methodology offers several solutions, which are presented under opti-mal Pareto front. For the hybrid system, a control strategy has been designed to achieve a higher matchrate between supply and demand intervals. Simulation results show that a configuration with one PV,two WTs, and two battery units have a high EMR with the expense of long operating hours for thediesel generator. Another configuration with two units of each PV, WTs, and battery has short dieseloperating hours and acceptable match rate, but its ACS is the highest. The designers can select the bestconfiguration among the Pareto set, which fits their desire. In the future work of this study, other moredecision variables and different design scenarios may be incorporated into system designs.

9. LIST OF SYMBOLS AND ABBREVIATIONS

9.1. Symbols

α Wind shear exponent coefficientβ Shape factorη Scale factorσ Self-discharge rate of batteryδc Temperature coefficientAOC(1) Maintenance cost of that component for the first year of the projectB characteristic constant based on I-V curveC’bat Available battery capacity

Ccap Capital cost of each component ($)Crep Replacement cost of units ($)Crep Replacement cost of unitsD Mean demand over time period nDt Demand at time tDt Load demand at time tEi Effective solar irradiation impinging the cell in (W/m2)Epv Yearly expected production of photovoltaic energy in kilowatt hour (kWh)Ewt Expected energy production of wind turbine in kilowatt hour (kWh) for a specific sitef Annual inflation ratef(v) Weibull PDF for wind speed (ν)H1 Known heightH2 Desired heighti Annual interest rateiloan Nominal interest rateIop Nominal current in amperes (A)



Isc Short-circuit current at 25°C and 1000W/m2

Ix Short-circuit current at any given Ei and TI(V) Output current of the photovoltaic panel (A)ηbat Battery efficiencyηinverter Inverter efficiencynrep Lifetime of unitsN Component lifetime (year)NPV Total number of PV modulesNWT Total number of the WTsP Number of photovoltaic panels in parallelP Output power of the photovoltaic panel (W)PL Load demandPout(Ex) PV module output power at an average hourly solar irradiation (Ex)PPV Total generated powert of PV panelsPWT Total generated power of wind turbinesS Number of photovoltaic panels in seriesS Supply over time period nSolarWindow Total time hours that the sun hits the PV module at an average hourly solar irradiationSPV Supplied energy of PV modulesSWT Supplied energy of WTSt Supply at time tT Solar panel temperature (°C)Tbat Battery temperatureTCi temperature coefficient of ISC in (A/°C)TCV Temperature coefficient of Voc in (V/C)Tfc Total fuel consumptionTotalDay Change from daily to monthly or yearly quantitiesTw 25°C standard test condition (STC)V1 Wind speed measured at H1

V2 Wind speed at H2

V Output voltage of the photovoltaic (V)Vmax Maximum open-circuit voltage at 25°C and 1200W/m2 (usually it is close to 1.03 Voc)Vmin minimum open-circuit voltage at 25°C and 200W/m2 (usually, Vmin is close to 0.85 Voc)Voc Short-circuit current at 25°C and 1000W/m2

Vop Nominal voltage in volts (V)Vx Open-circuit voltage at any given Ei and T

9.2. Abbreviations

ACS Annualized cost of systemACC Annualized capital cost of componentsAFC Annual fuel costAOC Annualized operation and maintenance costARC Annual replacement costCC Spearman’s rank correlation coefficientCRF Capital recovery factorEMR Electricity match rateIC Inequality coefficientLS Least squaresMEM Match evaluation methodPDF Weibull probability distribution functionSFF Sinking Fund FactorDOD Depth of discharging of batterySOC Battery based on state of charge



REFERENCES

1. Tarroja B, Mueller F, Eichman JD, Samuelsen S. Metrics for evaluating the impacts of intermittent renewablegeneration on utility load-balancing. Journal of Energy 2012; 44:546–562.

2. Abedi S, Alimardani A, Gharehpetian GB, Riahy GH, Hosseinian SH. A comprehensive method for optimal powermanagement and design of hybrid RES-based autonomous energy systems. Renewable and Sustainable EnergyReviews 2012; 16(3):1577–1587.

3. Vafaei M. Optimally-sized design of a wind/diesel/fuel cell hybrid system for remote community.Master of AppliedScience Electrical and Computer Engineering University of Waterloo, 2011.

4. Bindner H, Cronin T, Lundsager P, Manwell JF, Abdulwahid U, Baring-Gould I. Lifetime Modelling of Lead AcidBatteries. Risø National Laboratory Information Service Department: Denmark, 2005.

5. Rao SS. Engineering Optimization: Theory and Practice, 4th edn. John Wiley & Sons, Inc: Canada, 2009.6. El-Gammal Adel AA, Sharaf AM. A hybrid PV-FC-diesel-battery efficient schemes for four-wheel PMDC electric

vehicle drive system. International Journal of Renewable Energy Research 2012; 2(1):53–77.7. Zhao YS, Zhan J, Zhang Y, Wang DP, Zou BG. The optimal capacity configuration of an independent wind/PV

hybrid power supply system based on improved PSO algorithm. IEEE, 2006, pp. 1–7.8. Dhillon J. Multi-objective optimization of power dispatch problem using NSGA-II. Master of Engineering Power

Systems & Electric Drives, Thapar University, Patiala, 2009.9. Koutroulis E, Kolokotsa D, Potirakis A, Kalaitzakis K. Methodology for optimal sizing of stand-alone photovoltaic/

wind-generator systems using genetic algorithms. Solar Energy 2006; 80(9):1072–1088.10. Razak JA, Sopian K, Ali Y, Alghoul MA, Zaharim A, Ahmad I. Optimization of PV-wind-hydro-diesel hybrid

system by minimizing excess capacity. European Journal of Scientific Research 2009; 25:663–671.11. Erdinc O, Uzunoglu M. Optimum design of hybrid renewable energy systems: overview of different approaches.

Renewable and Sustainable Energy Reviews 2012; 16(3):1412–1425.12. Wang L, Singh C. PSO-based multi-criteria optimum design of a grid-connected hybrid power system with

multiple renewable source of energy. Proceedings of the 2007 IEEE Swarm Intelligence Symposium (SIS),2007, pp. 1–8.

13. Boomsma TK, Meade N, Fleten SE. Renewable energy investments under different support schemes: a real optionsapproach. European Journal of Operational Research 2012; 220(1):225–237.

14. Alvarez-Valdes R, Crespo E, Tamarit JM, Villa F. GRASP and path relinking for project scheduling under partiallyrenewable resources. European Journal of Operational Research 2008; 189(3):1153–1170.

15. Cirre CM, Berenguel M, Valenzuela L, Klempous R. Reference governor optimization and control of a distributedsolar collector field. European Journal of Operational Research 2009; 193(3):709–717.

16. Yang H, Zhou W, Lua L, Fang Z. Optimal sizing method for stand-alone hybrid solar–wind system with LPSPtechnology by using genetic algorithm. Solar Energy 2008; 82(4):354–367.

17. Nelson DB, Nehrir MH, Wang C. Unit sizing and cost analysis of stand-alone hybrid wind/PV/fuel cell powergeneration systems. Renewable Energy 2006; 31(10):1641–1656.

18. Wei Z. Simulation and optimum design of hybrid solar-wind and solar-wind-diesel power generation systems.Doctor of Philosophy, The Hong Kong Polytechnic University, 2007.

19. Xu D, Kang L, Cao B. The elitist non-dominated sorting GA for multi-objective optimization of standalone hybridwind/PV power systems. The International journal of Applied Sciences 2006; 6(9):2000–2005.

20. Elbaset AA. Design, modeling and control strategy of PV/FC hybrid power system. Electrical Systems 2011;7(2):270–286.

21. Bakelli Y, Arab AH, Azoui B. Optimal sizing of photovoltaic pumping system with water tank storage using LPSPconcept. Solar Energy 2011; 85(2):288–294.

22. Bilala BO, Samboua V, Kébé CMF, Ndiaye PA, Ndongo M. Methodology to size an optimal stand-alone PV/wind/diesel/battery system minimizing the levelized cost of energy and the CO2 emissions. Energy Procedia 2012;14:1636–1647.

23. Yang H, Lu L, Zhou W. A novel optimization sizing model for hybrid solar-wind power generation system. SolarEnergy 2007; 81(1):76–84.

24. Dufo-Lopez R, Bernal-Agustin JL. Multi-objective design of PV–wind–diesel–hydrogen–battery systems.Renewable Energy 2008; 33(12):2559–2572.

25. Luna-Rubio R, Trejo-Perea M, Vargas-Va’zquez D, Rı’os-Moreno GJ. Optimal sizing of renewable hybrids energysystems: a review of methodologies. Solar Energy 2012; 86(4):1077–1088.

26. Yazdanpanah-Jahromi MA, Farahat S, Barakati SM. A novel sizing methodology based on match evaluationmethod for optimal sizing of stand-alone hybrid energy systems using NSGA-II. The Journal of Mathematics andComputer Science 2012; 5:134–145.

27. AEMO. Victorial annual planning report: Australian energy market operator limited (AEMO), 2010.28. Henderson N. Report to reliability panel on demand forecast: AEMO, 2010.29. Hsieh CY. Climate change prediction by wireless sensor technology. International Electrical Engineering Journal

(IEEJ) 2012; 3(2):620–624.30. Mohammadi M, Hosseinian SH, Gharehpetian GB. GA-based optimal sizing of microgrid and DG units under pool

and hybrid electricity markets. Electrical Power and Energy System 2012; 35(1):83–92.31. Ortiz Rivera EI. Modeling and analysis of solar distributed generation. Ph.D. Dissertation, Department of Electrical

and Computer Engineering, Michigan State University, 2006.



32. Rios Rivera M. Small wind/photovoltaic hybrid renewable energy system optimization. Master of Science,Electrical Engineering, Puerto Rico, Mayagüez Campus, 2008.

33. Borowy BS, Salameh ZM. Methodology for optimally sizing the combination of a battery bank and PV array in awind/PV hybrid system. IEEE Transactions on Energy Conversion 1996; 11:367–375.

34. Patel MR. Wind and Solar Power Systems: Design, Analysis, and Operation, 2nd edn. Taylor & FrancisGroup, New York, 2006.

35. Ramos Robles CA. Determination of favorable conditions for the developement of a wind power farm in PUERTORICO. Master Of Science, Electrical Engineering, PUERTO RICO, 2005.

36. Scheaffer L, Mulekar S, MvClave T. Probability and Statistics for Engineers, 5th edn. Richard Stratton: Canada, 2011.37. Born FJ. Aiding renewable energy integration through complimentary demand-supply matching. Doctor of

Philosophy, Energy Systems Research Unit, University of Strathclyde, 2001.38. Waqas S. Development of an optimisation algorithm for auto sizing capacity of renewable and low carbon energy

systems. Master of Science, Department of Mechanical Engineering, University of Strathclyde Engineering, 2011.39. Kennedy J, Eberhart R. Particle swarm optimization. Proceeding, IEEE International Conf. on Neural Network, Vol.

4, pp. 1942–1948, 1995.40. Shi Y, Eberhart R. Empirical study of particle swarm optimization. Proceedings of the 1999 Congress on Evolutionary

Computation, Vol. 3, 1999.41. Deb K, Agrawal S, Pratab A, Meyarivan T. A fast elitist non-dominated sorting genetic algorithm for multi-objective

optimization: NSGA-II. Parallel Problem Solving From Nature VI Conf, 2000, pp. 849–858.42. Srinivas N, Deb K. Multiobjective optimization using nondominated sorting in genetic algorithms. Evolutionary

computation 1994; 2(3):221–248.43. Deb K. Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley and Sons: Chichester, England.



Documents

An Efficient Sizing Method With Suitable Energy Management Strategy for Hybrid Renewable Energy Systems