Optimal size and cost analysis of stand-alone hybrid wind/photovoltaic power-generation systems

5/28/2018 Optimal size and cost analysis of stand-alone hybrid wind/photovoltaic power-generation systems

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Optimal Size and Cost Analysis of Stand-Alone Hybrid

Wind/PV Power Generation Systems

Journal: Civil Engineering and Environmental Systems

Manuscript ID: Draft

Manuscript Type: Original Article

Date Submitted by the Author: n/a

Complete List of Authors: Yazdanpanah Jahromi, Mohammad Ali; University of Sistan and

Balushestan, Mechanical Engineering DepartmentFarahat, Said; University of Sistan and baluchestan, MechanicalEngineering DepartmentBarakati, Seyed Masoud; University of Sistan and Balushestan, Power

Electronic Engineering

Keywords:hybrid wind/PV systems, multi-objective optimization, sizing method,electricity match rate (EMR), match evaluation method (MEM),management strategy

URL: http:/mc.manuscriptcentral.com/gcee

Civil Engineering and Environmental Systems


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Manuscript # GCEE-2012-0150

(Optimal Size and Cost Analysis of Stand-Alone Hybrid Wind/PV Power

Generation Systems)

Amendments concerning the comments of Reviewer # 1

We thank the respected reviewer for the comments that he/she raised that helped us to enhancethe quality of the paper. These comments are addressed separately below.

1)Comment #1:

The models used in this paper have already been presented by the authorsin the Journal of Mathematics and Computer Science TJMCS Vol.5 No. 2 (2012) 134-145.This

paper has to be cited and parts of the manuscript submitted to CEES, where the models aredescribed, can be adequately shortened.

Amendments/Replies: Based on this comment of the respected reviewer, there are a

few points which should be clearly highlighted. The mentioned previously work has

been published in late December 2011. We have submitted the currents work in 18

December 2012 in

Civil Engineering and Environmental Systems, and we didnt know

about our previous work publication since then. The mentioned reference is now

included in the manuscript as reference [15]. We removed or added some texts to

improve the quality of the paper in the revised version of the paper. Examples are:

A text has been added to the end of second paragraph in Section 1 to include thementioned reference.

We found that Figures 3 and 4 (of the original paper) is out of the scope of thispaper. So we removed these figures.

We added a text and an equation to Section 2.2, after equation (8).

Sections 2.3, 5.4 and 7 have been added to the article. Two text has been added to the first paragraph in section 8 to clarify how the

solutions have been obtained.

We added two paragraphs to the end of Section 8. A study of operating hours ofdiesel generator in optimal configuration is carried out and given in Table 9.

2) Comment #2:The choice of the two technical objectives (IC and CC) is very critical, in factdue to the statistical variations of the load. A perfect generation, that overlaps the loads yearlyprofile, doesnt represent an optimal solution as it introduces an high number of unavailabilityhours . To overcome this problem a storage system has to be considered in the optimizationalgorithm.

Amendments/Replies: We have include a diesel generator and a battery as backup andstorage systems, respectively, to even out the irregularities. Moreover, a propermanagement strategy is designed to control the starting and stopping operation times ofdiesel generator. The mathematical modelling of battery storage system is given insection 2.3. Annual replacement cost (ARC), and annual fuel cost (AFC) is two costparameters which appear after adding diesel generator and battery to the system.These two cost parameter are included in Equation (19) and their description given in

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sections 5.3 and 5.4. The operation strategy for the proposed hybrid system isexpressed in section 7.

3) Comment #3: The assumption of 10 year in the life time of the project is an evidentlimitation considering the big difference between the life time of wind generator and PV

modules.

Amendments/Replies: We appreciate the suggestions of the respected reviewer. The

life time of the project is assumed to be 20 years. All the hybrid components is assumed

to have a life time of 20 years, except the battery life time which considered to have a

life time of 5 years. Life time specification for all hybrid components is included in Table

6.

4) Comment #4:

It is not clear how the solutions have been generated. The authors combinea system (wind turbine) with components of a PV system, i.e. PV modules. These solutions are

practically useless as an inverter can accept only a certain number of PV modules. It meansthat the PV optimization requires also the consideration of inverters.

Amendments/Replies: We have addedtwo text to clarify how the solutions have beenobtained. The first one, is included in the last section of 4 as:

- In this work, match evaluation method (MEM) is used for sizing purpose. Thisis first uses in [15]. Stin Equation 11 and 12 is the sum of two or sometimesthree parts; NPV.SPV, NWT.SWT, and Nbattery.Sbattery, or NPV.SPV, NWT.SWT, andSdiesel which respectively denote the energy supply sources, PV modules,WTs, and battery, or PV modules, WTs, and diesel generator. NPV is thenumber of PV modules, NWTis the number of WTs, and NBattery is the numberof battery. The management strategy controls the starting and stoppingoperation times of diesel generator.

The second one is include in the first paragraph in section 8 as follows:- Load is needed to be matched with different supplies in a way that resultant

supply (N1.S1+ N2S2+ +Nn.Sn) meet the load with high electricity matchrate (EMR). Main objective of the proposed optimal algorithm is to find theoptimal values of N1, N2, , Nn.

At the first paragraph of section 5 (just before section 5.1), we revised the followingparagraph:

- Four main parts are considered in this revision article: wind turbine togetherwith its tower, PV module, battery and other devices. The other devices whichare not included in the decision variables, are equipment including inverter,controller, and cables.

5) Comment #5:

The analysis needs further investigation, specifically concerning the followingaspects:

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1. Which is the criteria for selecting the wind turbines ? Further important parameters have tospecified such as cut-in wind speed, cut-out wind speed, rated wind speed.2. Does the selection consider the pdf wind speed distribution ?3. Which is the criteria for selecting the PV modules? And what about the inverters ? Furtherimportant parameters have to specified such as the thermal coefficient of maximum power, andthe thermal coefficient of open circuit voltage.

4. Does the selection consider the impact of ambient temperature on photovoltaic production?

Amendments/Replies: we appreciate the suggestion of the reviewer 1, and we havetaken the above comment on-board when revising the manuscript.

1- At the section of 8, we revised the following text:- In order to determine the best values of parameters, evaluating convergence,

several executions of the design program have been worked out. Each hybridsystem has included one type of PV modules and one type of WTs togetherwith diesel and battery storage systems. The results of these studies, suggestthe choice of Kyocera Solar (KC200) PV module and Bornay (Inclin 3000)

wind turbine for the proposed hybrid power system, compared to the otherconfigurations. The reason of this selection is that this configuration providesthe lowest cost in larger EMR. Other configurations, either have not optimalIC range (0 0.4IC ), or optimal CC range ( 1, 1CC = + ), or have higher cost

than the selected configuration.

In addition, detailed specification of the WTs are included in the article as Table 4.

2- Thanking this comment of the reviewer, we added the following text in the paper tothe second paragraph in Section 2.2:

- The Weibull PDF is basely depend on the shape factor, the scale factor, and

the wind speed (equation 8). The shape factor will typically range from 1 to 3[28]. The selection of shape factor is usually based on the experience andmultiple observations of sites where wind speed data have been recorded.The can be calculated using equation (9) [29].

1(1 )

=

+

(9)

- where is the mean wind speed and is the gamma function. Therefore, and are independent of WT specifications and they are constant for all WTs.For wind speed profile which shown in Figure 4, the Wiebull PDF has been

plotted in Figure 5, with a shape Factor of 2.5.

3- As noted earlier, several executions of the design program have been done. LargerEMR in lower ACS is the criteria for selecting the mentioned configuration. The reasonof this selection is that this configuration provides the lowest cost in larger EMR. Otherconfigurations, either have not optimal IC range ( 0 0.4IC ), or optimal CC range( 1, 1CC = + ), or have higher cost than the selected configuration.

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4- Yes. The model predict the output power of PV panels in different meteorologicalconditions of ambient temperature and solar radiation. The monthly ambienttemperature and solar radiation is added as Figures 1 and 2.

Because of large number of inputs and complicated procedure, we prefer to simulatethe system based on monthly data (in August). Finally we would like to thank thisrespected reviewer for his/her comments that helped us to improve the quality of thepaper.

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Manuscript # GCEE-2012-0150

(Optimal Size and Cost Analysis of Stand-Alone Hybrid Wind/PV Power

Generation Systems)

Amendments concerning the comments of Reviewer # 2

We thank the respected reviewer for the comments that he/she raised that helped us to enhancethe quality of the paper. These comments are addressed separately below.

1) Comment #1:

The manuscript needs improvements before it can be considered forpublication. There are some pieces of information it seems that the authors have forgotten toinclude, the presentation of their results needs to be improved for clarity, and they need a nativeEnglish speaker to read through the manuscript and correct the language. The paper needs tobe reviewed for clarity to tune up recurring grammatical issues.

Amendments/Replies:We added some texts to improve the quality of the article in therevised version of it. Examples are:

Two text has been added to the first paragraph in section 8 to clarify how thesolutions have been obtained.- Load is needed to be matched with different supplies in a way that resultant

supply (N1.S1+ N2S2+ +Nn.Sn) meet the load with high electricity matchrate (EMR). Main objective of the proposed optimal algorithm is to find theoptimal values of N1, N2, , Nn

- In order to determine the best values of parameters, evaluating convergence,several executions of the design program have been worked out. Each hybridsystem has included one type of PV modules and one type of WTs togetherwith diesel and battery storage systems.

We have added a text as follow in the last section of 4 as:- In this work, match evaluation method (MEM) is used for sizing purpose. This

is first uses in [15]. Stin Equation 11 and 12 is the sum of two or sometimesthree parts; NPV.SPV, NWT.SWT, and Nbattery.Sbattery, or NPV.SPV, NWT.SWT, andSdiesel which respectively denote the energy supply sources, PV modules,WTs, and battery, or PV modules, WTs, and diesel generator. NPV is thenumber of PV modules, NWTis the number of WTs, and NBattery is the numberof battery. The management strategy controls the starting and stoppingoperation times of diesel generator.

Sections 2.3, 5.4 and 7 have been added to the article. We added two paragraphs to the end of Section 8. A study of operating hours of

diesel generator in optimal configuration is carried out and given in Table 9.

Correct. Thank you. We now have revised the WHOLE manuscript carefully andtried to avoid any grammar or syntax error. We believe that the language is nowacceptable for the publication.

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2) Comment #2: The references for the prices of the equipment used should be noted. Thesevalues change with time (and are currently different than what is noted in the paper - in fact Ibelieve the Sky stream turbine's cost quoted is closer to its educational price, rather thanMSRP). There is another challenge that Southwest Wind power has recently gone out ofbusiness and sold several of these products off. I don't think this should impact this paper beingpublished, as the real focus of the paper is the process not the specifics, but the text should

clarify where information has been collected from and mention that these values vary with time.

Amendments/Replies: Correct. The required information is now included in themanuscript, and we have change all the WTs in revised version. The references for theprices and detailed technical characteristics are included in the first paragraph ofsection 3. Other cost parameters are given in Tables 6 and 7. At the end of section 5,the following text is added:

- It is worth mentioning that the price of these components change over time.

3) Comment #3:

In this reviewers opinion, Figures 3 and 4 are not needed. This informationis basic background material which doesn't add value to the current paper. The paper should,

however, provide the details of the shape factor and scale factor which fit the Zabol data asplotted in Figure 6. The paper is incomplete without this detail.

Amendments/Replies: We appreciate the suggestion of reviewer 2. We removed thesefigures. We added the following text in the paper to the second paragraph in Section2.2:

- The Weibull PDF is basely depend on the shape factor, the scale factor, andthe wind speed (equation 8). The shape factor will typically range from 1 to 3[28]. The selection of shape factor is usually based on the experience andmultiple observations of sites where wind speed data have been recorded.The can be calculated using equation (9) [29].

1(1 )

=

+

(9)

- where is the mean wind speed and is the gamma function. Therefore, and are independent of WT specifications and they are constant for all WTs.For wind speed profile which shown in Figure 4, the Wiebull PDF has beenshown in Figure 5, with a shape Factor of 2.5.

4) Comment #4:

Figure 8's description should be modified to note that this is the energyoutput by wind speed for one month and also include which month it is. An annual plot wouldbe useful to show as well.Amendments/Replies:Monthly and yearly plots is included in Figures 7 and 8 for thegiven WTs in Table 2. The corresponding text in now added under the figures.

5) Comment #5:

It is not explained in the text why there are values such as "7247/27" inTables 4 and 5. What is the division symbol being used to represent in these values? Theresults of the optimization should be very clearly explained.

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Amendments/Replies:Sorry. We correct them in the revised version of manuscript.

6) Comment #6:

Figure 14 is the most important figure in this study, and it is unfortunately

quite difficult to interpret. Perhaps the scale could be changed to zoom in on the results.Arrows overlaying the direction of the optimal solutions would help. Perhaps color coding thetop several designs would also make this more intuitive to interpret.

Amendments/Replies: Some ranges that there are no values have removed in 3DPareto front for the best configuration which is now Figure 15 in revised version. Arrowsto overlay the direction of optimal solutions are now included in Figures 12, 13, 14, and15.

7) Comment #7:

An additional result of this study that would be quite interesting to see is aplot showing the resulting generation and demand over some period of time from the optimizedsystem designs and an evaluation of the amount of backup generation or storage that would be

needed to make each scenario work for a stand-alone application (if that is an objective of thework).

Amendments/Replies: In the current paper, in a novel approach a battery and also adiesel generator have been added to different hybrid systems as back-up and storagesystems, respectively. A suitable management strategy controls the starting andstopping time of diesel generator which is a critical factor for optimization. The algorithmand the management strategy are hourly basis. Study of operating hours of dieselgenerator in optimal configuration is carried out. Other simulation results is out of theobjectives of this work.

Because of large number of inputs and complicated procedure, we prefer to simulatethe system based on monthly data (in August). Finally we would like to thank thisrespected reviewer for his/her comments that helped us to improve the quality of thepaper.

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Optimal Size and Cost Analysis of Stand-Alone Hybrid Wind/PV

Power Generation Systems

Mohammad Ali Yazdanpanah Jahromia, Said Farahatb, Seyed Masoud

Barakatic

aDepartment of Mechanical Engineering, University of Sistan and Baluchestan,

Zahedan, Iran

bDepartment of Mechanical Engineering, University of Sistan and Baluchestan,

Zahedan, Iran

cDepartment of Power Electronic Engineering, University of Sistan and Baluchestan,

Zahedan, Iran

Corresponding author. Tel.: ++98-917-392-3846; fax: +0-541-244-7092; e-mail: [email protected]

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Optimal Size and Cost Analysis of Stand-Alone Hybrid Wind/PV

Power Generation Systems

Designof sustainable energy systems for the supply of electricity need correct

selection and sizing to reduce investment costs. In this article, a new sizing

methodology is developed for stand-alone hybrid wind/PV power systems, using

multi-objective optimization algorithms. MOPSO algorithm and NSGA-II are

selected related to their match with nature of renewable energy sizing problem. A

match evaluation method (MEM) is developed based on renewable energy

supply/demand match evaluation criteria, to size the proposed system in lowest

cost.

As an example of application of this technique, six different wind turbines

and also six different PV modules have been considered. The sizing methodology

determines a multi-objective design, obtaining the best solutions that the applied

algorithm has found simultaneously considering three objectives: inequality

coefficient (IC), correlation coefficient (CC), and annualized cost of system

(ACS). The optimal number of wind turbines, PV modules and batteries ensuring

that the system total cost is minimized while guaranteeing a highly reliable

source of load power is obtained. A management strategy has been designed to

achieve higher electricity match rate (EMR). Based on the proposed technique,

the algorithm developed for different cases, using the climatic condition data of

the city Zabol, located in south-east of Iran. Additionally, a study of operating

hours of diesel generator in optimal configuration is carried out.

Keywords: Hybrid wind/PV systems; multi-objective optimization; sizing

method; electricity match rate (EMR); match evaluation method (MEM),

management strategy

1. Introduction

Nowadays, the renewable energy and estimation of energy production are popular

research areas and they should be further investigated. Fast depletion of conventional

energy resources, rise in the fuel prices, harmful emissions from the burning of fossil

fuels and growing in energy demand have made power generation from conventional

energy sources unsustainable. Standalone hybrid power systems are promising

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alternatives particularly in remote areas as an isolated small power producing units for

the supply of power. Energy security under varying weather condition and the

corresponding system cost are the two major issues in designing of hybrid power

generation systems. Hybrid power systems can address the limitations of reliability,

efficiency, cost and emission on individual renewable energy supply options. The two

technologies that have seen the most significant growth are wind turbine (WT) and solar

photovoltaic (PV). Wind power has recently become the fastest growing renewable

energy resource and is projected to lead the growth of the renewable power portfolio in

the near term [1]. Solar energy, both as a thermal and an electric options, is well suitable

for the built environment. The solar energy distribution is mostly periodic and the wind

speed may present stochastic patterns. These both together, present supplementary

availability. Hence the combined exploitation of the available wind and solar potential

caused reliable power generation. The reliability of hybrid systems are important to both

planning and utilization stages. Designing energy systems including solar and wind

energies together, to some extent, reduce the depth of the problem [2]. M. Vafaei (2011)

showed that hybrid stand-alone power generation systems are usually more reliable and

less costly than systems that use only single source of energy [3].

Design and modelling are important aspects of the analysis of hybrid power

systems. There are many studies carried out by various researchers in the field of

renewable energies. The design of hybrid systems is usually done by searching the

configuration and/or control with the lowest total cost throughout the useful life of the

installation or pollutant emissions. Optimal sizing of the hybrid components is one of

the main issues related with the application of such hybrid alternative energy systems.

Proper sizing ensures the load demand supply in all conditions with the lowest total

cost. Hence, the economic disadvantages of renewable energy systems compared to

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conventional energy sources can partially be overcome. By increasing number of hybrid

components, the sizing procedure will be more complex. Variation of load demand in

different time intervals that may not match with the generation power of renewable

energy sources further promotes the complex structure of the sizing procedure. The

sizing methodologies for hybrid power systems available in the literature cover a large

spectrum of approaches. Energy system reliability is one of the key aspects regarding

stochastic nature of renewable sources. One parameter that helps to elucidate the system

reliability is loss of power supply probability (LPSP) technique. Optimal configuration

was calculated by LPSP technique and minimum annualized cost of system (ACS) in

[4-10]. One other sizing method commonly used is based on levelized cost of energy

(LCE) as used in [11, 12]. The LCE can be defined as a metric that describes the cost of

every unit of energy generated by a project. Some other sizing method, deal with

pollutant emission and unmet load. A multi-objective design of hybrid systems by

minimizing the total cost, pollutant emission and unmet load is presented in [13]. Luna-

Rubio et al. (2012) reviewed different sizing methodologies developed in the recent

years in [14]. Match evaluation method (MEM) which is used in this article is another

sizing method [15]. The MEM is based on the coordination criteria between generation

and consumption intervals.

The design process is generally very complex. The classical optimization

techniques are not able to take into account all the characteristics associated to the posed

problem consuming excessive CPU time. Nevertheless, modern optimization methods

obtain a set of non-dominated solutions with little computational effort. Most of these

methods are based on certain characteristics and behavior of biological, swarm of

insects, molecular, and neurobiological systems. Particle swarm optimization (PSO)

algorithm and genetic algorithm (GA) are the two of modern stochastic optimization

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methods that can find Pareto-optimal solution in one single simulation run. Y. S.

Zhoaand et al. (2006) proposed an optimized wind/PV hybrid power system using PSO

algorithm to have higher capacity and faster search efficiency [16]. J. Dhillon (2009)

proposed the non-dominated sorting genetic algorithm (NSGA-II) to simultaneously

minimize the total system real power losses in transmission network and cost, by

satisfying power balance equation [17]. Using of genetic algorithm (GA) in unit sizing of

photovoltaic/wind generator systems is discussed in [18]. O. Erdinc and M. Uzunoglu

(2012) reviewed different optimum sizing approaches in literatures [19].

In this article, a new optimum sizing methodology for stand-alone hybrid

systems is developed based on MEM at the lowest investment. The electricity match

rate (EMR) technique, which is considered to be the criteria for sizing, is employed in

different wind/PV hybrid systems. In this procedure, three objectives are proposed.

They are inequality coefficient (IC), correlation coefficient (CC) and annualized cost of

system (ACS). IC and CC control the EMR while ACS checks the system cost. IC

provides a measure of how well a time series of estimated values compares to a

corresponding time series of observed values [20]. In other word, IC provides a

relative measure of forecast accuracy in terms of deviation from the perfect forecast

[21]. CC measure of how well the predicted values from a forecast model "fit" with the

real-life data [22]. IC gives the match magnitude while CC, deals with trend matching.

Hence, IC and CC are selected together, to check the EMR between supplies and load

demand. These two objectives together, can obtain good match rate for hybrid systems.

More coordination between the components increases the system efficiency. When the

output power of renewable energy resources cannot meet the load demand, the strategy

will be used to start the diesel generator or use the battery power. The optimization

algorithm selects the optimal size of hybrid components based on above procedure. The

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optimum combination of hybrid wind-PV system can make the best compromise

between the three considered objectives: IC, CC and ACS. The MEM sizing technique

is implemented based on multi-objective particle swarm optimization (MOPSO)

algorithm. The results are validated by NSGA-II. Six different kinds of wind turbine

(WT) and also six different kinds of PV module, with different output powers and costs

are considered for this optimization procedure to investigate the efficiency of the

proposed methodology. The simulation is carried out based on the basis of the algorithm

developed for different cases using the climatic condition data of the city Zabol, located

in south-east of Iran. Using the EMR objective functions, the configuration of the

proposed hybrid system which gives the highest EMR requirements can be obtained.

The decision variables included in the optimization process are the number of PV

module, WT, and battery. The optimization is conducted by an iterative simulation

using a system model and real weather and load demand data.

2. Modelling of Hybrid Wind/PV System

In order to predict the performance of a hybrid power system, individual components

need to be modelled first, and then the generation power can be evaluated to meet the

load demand. The proposed hybrid power generation system consists of WT, PV array,

inverter, cables and other accessory devices. Weather data from the city of Zabol

obtained from a nearby meteorological station is used for more precise estimation of the

local potential of both solar and wind energy. A brief description for modelling of wind-

PV-battery system is presented in forthcoming subsection.

2.1. Mathematical Model of PV Module

PV technology is identified as most environment friendly technologies [23]. Simulation

of PV array performance has been done by considering the modelling of the maximum

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power point tracking (MPPT) controller. This model can predict output power of PV

panel in different temperatures and various irradiation levels. The PV panel model

depending on the solar radiation and the temperature can be calculated as [24]:

1I(V)= . 1 exp( )1 .

1-exp(- )b

Ix VbVx b

(1)

maxmax max min

max min

. . .( ) . .( ).exp( .ln( ))oci iNiN iN

V VE EV x s TCV T T sV s V V

E E V V

= +

(2)

[ ]. . .( )i sc NiN

EIx p I TCi T T

E= + (3)

. 1( ) .[1 exp( )]

1 .1 exp( )

V Ix V P V

bVx b

b

=

(4)

wherePis the output power of the photovoltaic panel [W],I(V)is the output current of

the photovoltaic panel [A], V is the output voltage of the photovoltaic [V], Isc and Voc

are the short-circuit current and the open-circuit voltage at 25 [C] and 1000 [W/m2],

respectively, Vmax, is the maximum open-circuit voltage at 25 [C] and 1200 [W/m2]

(usually Vmax is close to 1.03Voc), Vminis the minimum open-circuit voltage at 25 [C]

and 200 [W/m2], (usually, Vminis close to 0.85Voc), Tis the solar panel temperature [C],

Ei, is the effective solar irradiation impinging the cell in [W/m2],Twis 25 [C] standard

test condition (STC), TCi is the temperature coefficient of Voc in [V/C], Ix and Vx is

short circuit current and open circuit voltage, respectively, at any given Ei and T ;s is

the number of photovoltaic panels in series, pis the number of photovoltaic panels in

parallel,bis characteristic constant based on I-Vcurve. The characteristic constant, b,

usually varies from 0.01 to 0.18 and can be calculated using (5) with iterative procedure

[25].

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11

.ln(1 .(1 exp( )))

op oc

nop

oc

n

V Vb

IV

Isc b

+

=

(5)

For calculating the available energy of PV module at a specific site the following

Equation is used [25]:

( ).( ).( )PV out xE P E SolarWindow TotalDay= (6)

whereEpvis the expected production of photovoltaic energy in [kWh], SolarWindow

is the total time hours that sun hit the PV module at an average hourly solar irradiation,

the product of TotalDay is to change from daily to monthly or yearly quantities,

Pout(Ex) is the PV module output power at an average hourly solar irradiation (Ex).

Figure 3 shows the P-V and I-V curves for each photovoltaic module given in Table 1

by using available solar radiation and ambient temperature which is given in Figures 1

and 2, respectively, for the selected site.

2.2. Mathematical Model of Wind Turbine

Adjusting the measured wind speed to the hub height, by using the wind speed data at a

reference height from the database, is an important phase before calculating the output

power of WTs. This can be done through the following expression [26]:

22 1

1

( )H

V VH

= (7)

where V2, is the wind speed at the desired height H2, V1 is wind speed measured at

known height H1, is wind shear exponent coefficient which varies with pressure,

temperature and time of day. A commonly used value for open land is one-seventh

(1/7).

The variations in wind speed are best described by the Weibull probability

distribution function (PDF), f(v), with two parameters, the shape factor , and the

scale factor [27]. The PDF calculates the probability that the wind speed will be

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occurred between zero and infinity during the entire chosen time period. Note that the

PDF curve shape and the height of it provide in some way that the area under the PDF

curve is unity. There are various notations for Weibull PDF in articles. In this article,

the Weibull PDF is defined as [27]:

( )1( ) ( )

vv

v e

= (8)

where is the shape factor, is scale factor, and v is the wind speed. The value of

controls the curve shape and hence is called the shape factor. The larger shape factor

indicates a relatively narrow distribution of wind speeds around the average while the

lower shape factor indicates a relatively wide distribution of wind speeds around the

average. The scale factor () defines where the bulk of the distribution lies and how

stretched out [25]. The Weibull PDF is basely depend on the shape factor, the scale

factor and the wind speed. The shape factor will typically range from 1 to 3 [28]. The

selection of shape factor is usually based on the experience and multiple observations of

sites where wind speed data have been recorded. The can be calculated using Equation

(9) [29].

1(1 )

= +

(9)

where is the mean wind speed and is the gamma function. Therefore,and are

independent of WT specifications. For wind speed profile which shown in Figure 4, the

Wiebull PDF has been plotted in Figure 5, with a shape Factor of 2.5. The wind speed

distribution (PDF) is the key information needed to estimate the total kWh produced in

a period of time by a WT at a given site. And then, using the WT power curve the

annual energy output can be calculated. A power curve is a graph that presents the

output power of wind turbine at any wind speed. This curve is a function of the turbine

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design and normally obtained from the wind turbine manufacturer. The power curves of

the WTs which given in Table 2, can be seen in Figure 6.The energy available for a WT

at a specific site can be calculated using (10) [30].

25

1

( )( ). ( , , )WT cE days hours P f

=

= (10)

where Ewt is the expected energy production of WT in kWh for a specific site. The

product of days by hours, gives the total hours in the period of simulation, Pc is the

output power of wind turbine;f(v)is the Weibull PDF for wind speed (), is the shape

factor, and is the scale factor. Monthly (August) and yearly total energy outputs for

each WT are presented in Figures 7 and 8, respectively.

2.3. Modelling of Battery Storage System

Stochastic nature of renewable sources make their supply really intermittent and

unreliable. This characteristic necessitate the use of energy storage system in renewable

power systems. Batteries are the most widely used devices for energy storage. Lead-

acid batteries are usually used for stand-alone hybrid wind-PV-diesel generation

systems [27]. Batteries are required to even out irregularities in the solar and wind

power distributions. Surplus electrical energy is stored in a battery bank which supplies

power to the load when the total power output of WTs and PVs is insufficient. So the

correct battery sizing is critical. There are different models in literatures for battery

behaviour simulation. The modelling of battery based on state of charge (SOC) is the

most commonly used model. SOC is an important parameter in system assessments

[31]. Temperature can also affect battery capacity. The available battery capacity ( 'batC

[AH]), in a given temperature ( batT [K]), can be calculated using (11) [32].

' '' .(1 .( 298.15)),bat bat c bat C C T= + (11)

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where c is temperature coefficient. The value of 0.6% per degree is usually used for c ,

unless otherwise specified by the manufacturer.

For the proposed hybrid WPDB system, it is supposed that the WTs has the DC

outputs. If the cable losses in the system are neglected, the battery current rate at time t

can be expressed as (12) [31].

( )( ) ( )

( )( )

ACLoadPV Wind DCLoad

inverterbat

bat

P tP t P t P

I tV t

+

=

(12)

where inverter 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 previous state of charge. By all above consideration the battery SOC

can be defined as [31]:

'

( ). ..( 1) ( ).(1 )

24

bat bat

bat

I t ttSOC t SOC t

C

+ = +

(13)

where bat is the battery efficiency, which 90% for charging stage and 100% in

discharging process are recommended. is the self-discharge rate; 0.2% per day is

recommended. When the wind turbine and PV module supply power more than the load

demand, the overcharging process is occurred. On the other hand, when the load

demand is more than the total output energy of supply sources, the battery SOC may

decrease to the minimum level which is defined as SOCmin= 1 -DOD, whereDODis

the depth of discharging of battery. In this study, for longevity of battery lifetime, the

value ofDODis considered 60%. In order to prevent the batteries against destruction, it

is important to control the batteries SOCat the following constrain:

in maxSOC SOC SOC (14)

where SOCmaxis the maximum state of charge for batteries (SOCmax = 1).

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2.4. Load Model

The output power of the proposed hybrid system should meet the power load demand.

The hourly load data in August used in this study is shown in Figure 9. This is the

Monthly variation of domestic load profile in the region.

3. The Components Characteristics

There are six possible different PV generators and also six possible different WTs. The

specifications of these components used to design and to optimize the hybrid wind/PV

are presented in Tables 1 and 2, respectively [25]. Detailed technical characteristics of

WTs, PVs and battery which is given by the Manufacturers are given in Tables 3, 4 and

5, respectively [25, 33]. Each hybrid system will include one kind of PV as well as one

kind of WT with battery and diesel.

[Table 1. Solar module power at standard test condition rating and price]

[Table 2. Small wind turbines rating and price]

[Table 3. Solar module specifications at standard test condition rating]

[Table 4. Detailed specifications of the wind turbine]

[Table 5. Battery characteristic][Figure 1. Meteorological conditions of solar radiation in August]

[Figure 2. Ambient temperature in August]

[Figure 3. P-V and I-V Curves]

[Figure 4. Meteorological conditions of wind speed in August]

[Figure 5. Weibull probability density function (f(v))]

[Figure 6. Wind turbine power curves (The symbols represent data sampled from the

power curve graphs given by the manufacturer)]

[Figure 7. Total wind turbine energy outputs by wind speed in August]

[Figure 8. Total wind turbine energy outputs by wind speed for one year]

[Figure 9. Monthly (August) variation of domestic load profile]

4. Sizing Model Based on Match Evaluation Method (MEM)

There are challenges in term of finding the correct capacity for hybrid power generation

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systems. The maximization of EMR between demand and supply intervals is an

important subject in hybrid power systems. For quantifying the magnitude of deviation

between two set of data variables, the least squares (LS) approach can be used. The

following Equation describes LS [34]:

2

0

( )n

t t

t

LS D S=

= (15)

whereDtand Stare demand and supply at time t, respectively. The LS in Equation (15)

is always a positive

quantity. Zero value of LS indicates a perfect match. Spearman's

Rank correlation coefficient (CC) is one of the objectives which can describe the

correlation between supply and demands. Calculation of this coefficient will always

result in a value between -1 and 1. Result of 1 shows the perfect positive match while

-1 indicates perfect negative match. In perfect negative match ( 1CC = ), as one

variable tends to increase the other will decrease at the same rate and vice versa for the

perfect positive match ( 1CC = + ). Value of 0 represents no match. The correlation

coefficient, CC, can express as [35]:

0

2 2

0 0

( ).( )

( ) . ( )

n

t t

t

n n

t t

t t

D d S s

CC

D d S s

=

= =

=

(16)

whereDtand Stare the load demand and supply at time t, respectively; dand sare the

mean demand and supply over time period n, respectively. The CC is used to describe

the trend matching between the time series of two data sets. It does not explain the

relative match magnitudes of the individual variables. Thus, if the size of a power 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 another, but of very

different magnitudes, would result in perfect correlation, but not a perfect match rate. For

a perfect match rate, both phase and magnitude must be considered. Hence, another

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criterion is needed to determine the match magnitude. The inequality coefficient (IC),

describes the inequality in the magnitude domain due to three sources: unequal tendency

(mean), unequal variation (variance) and imperfect co-variation (co-variance) [35].

Therefore, IC and CC are selected together, to check the EMR between supplies and load

demand. The resultant IC can range in value between 0 and 1.The smaller IC denotes the

larger match rate. Value of 0 represents a perfect match while 1 shows no match.

The IC can be given by the following Equation [35]:

2

0

2 2

0 0

1( )

1 1( ) ( )

n

t t

t

n n

t t

t t

D Sn

IC

D S

n n

=

= =

=

+

(17)

whereDtand Stare demand and supply at time t, respectively. nis the total time period.

Values of IC between 0 - 0.4 represents good match and value above 0.5 shows weak

match [36]. IC is more important criterion than CC in determining the

strength of

matching between supplies and demand. However CC is also good but it is not as well as

IC. In this work, match evaluation method (MEM) is used for sizing purpose. This is first

uses in [15]. St in Equation 11 and 12 is the sum of two or sometimes three parts;

NPV.SPV,NWT.SWT, and Nbattery.Sbattery, or NPV.SPV,NWT.SWT, and Sdiesel which respectively

denote the energy supply sources, PV modules, WTs, and battery, or PV modules, WTs,

and diesel generator.NPVis the number of PV modules,NWTis the number of WTs, and

NBattery is the number of battery. The management strategy controls the starting and

stopping operation times of diesel generator.

5. Cost Analysis Based on ACS Concept

A cost analysis of the system is performed for each configuration according to the

concept of annualized cost of system (ACS) [4, 6, 37]. An optimum combination of a

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hybrid wind-PV-battery energy system must satisfy both the reliable and economical

requirements. For all configurations, the ACS is composed of the sum of individual

annualized capital cost of components (ACC), annualized operation and maintenance

cost (AOC), annual replacement cost (ARC), and annual fuel cost (AFC). Four main

parts are considered: wind turbine together with its tower, PV module, battery and other

devices. The other devices which are not included in the decision variables, are

equipment including inverter, controller, and cables. The ACS is expressed by:

( )

( )

( ) ( )

ACS ACC PV Wind Tower Diesel Battety Other

AOC PV Wind Tower Battey Other

ARC Battery AFC Diesel

= + + + + +

+ + + +

+ +

+

(18)

5.1. Annualized Capital Cost

The annualized capital cost (ACC) of each component has taken into account the

installation cost, and can be calculated using (19).

. ( , )cap

CC C CRF i n= (19)

where Ccapis capital cost of each component, US$; and CRFis capital recovery factor, a

ratio that calculate the present value of an annuity (a series of equal annual cash flows).

CRFcan define as:

(1 )( , )

(1 ) 1

n

n

i iCRF i n

i

+=

+

(20)

where n is the component lifetime, year; i is the annual interest rate related to the

nominal interest rate (iloan, the rate at which a loan could be obtained) and the annual

inflation rate,f, by the Equation given below:

1loani fi

f

=

+ (21)

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5.2. Operation and Maintenance Cost

The operation and maintenance cost is the maintenance and repair cost of hybrid

components. The maintenance cost of each component, which has taken the inflation

ratefinto account, can be calculated as follows:

(1)*(1 )nAOC AOC f= + (22)

where AOC(1) is the maintenance cost of that component for the first year of the

project.

5.3. Annual Replacement Cost

The components which have a lifetime less than the project lifetime need to be replaced

during the lifetime of the project. TheARCcan be calculated from Equation (23).

* ( , )rep rep

ARC C SFF i n= (23)

Where Crep, is replacement cost of units, US$, is sinking fund factor, a ratio to

calculate the future value of a series of equal annual cash flows, depends on lifetime of

units (nrep) and interest rate (i), as given below.

( , )(1 ) 1

rep nrepiSFF i n

i=

+ (24)

5.4. Annual Fuel Cost (AFC)

The cost of fuel for diesel generator is calculated using the following Equation (25).

* ( , )fcAFC T CRF i n= (25)

where fcT is total fuel consumption for lifetime of the project.

The fuel (gas-oil) price is considered 0.16049 $/kWh. The expected CO2emission is

0.669 kg/kWh. The output power of diesel generator is 500 W.

The initial capital cost of different PV modules and WTs, are given in Table 1 and 2,

respectively [25]. Other cost parameters used in this paper are shown in Tables 6 and 7

[3, 31]. It is worth mentioning that the price of these components change over time.

SFF

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[Table 6. The cost and lifetime aspect for the proposed hybrid components]

[Table 7. Cost parameters]

6. Multi-Objective Optimization Procedure Using MOPSO

The sizing of the hybrid wind/PV systems is much more complicated than the single

source power generation systems. It is because of more variables and parameters that

have to be considered in system optimization. Long-term system performance,

economical parameters and EMR objectives must be considered in order to reach the

best compromise for both power match rate and cost. PSO and GA are the most suitable

algorithms in term of global optimization, stochastic nature of renewable sources, and

particular nature of sizing method. Implementation of MOPSO and NSGA-II has been

done in various engineering and business applications in recent years.

In this article, a multi-objective PSO (MOPSO) algorithm is employed to size

the hybrid stand-alone wind/PV power generation systems. The PSO algorithm was

originally proposed by Kennedy and Eberhart in 1995 [38]. Generally, PSO is based on

a simple concept, short time computation, easy implementation and few memory

requirements. It works by maintaining a population of candidate solutions to the

problem. Each solution is considered as a particle. The particles move through the

search space. In every iteration of the algorithm, the fitness of each candidate solution is

evaluated. Best value of fitness achieved so far is remembered as its personal best

fitness. The global best fitness and the candidate solution that achieved this fitness are

also remembered. The local and global bests are updated in each iteration, in order to

achieved better fitness. For the purpose of this article, six different WTs and also six

different PV modules, with different characteristics and costs are considered. Backup

and storage systems such as diesel generator and battery storage is needed to have better

EMR and also even out irregularities. The system configurations will be optimized by

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employing the MOPSO algorithm, which dynamically searches for the optimal

configuration to maximize the EMR and also minimize the ACS. IC, CC and ACS, are

the three objective functions of this optimization process which conflicting to each

other. By mathematically formulating of multi-objective design problem and applying it

to each configuration of hybrid system, the best combination of components

(minimizing IC and ACS and also maximizing the CC) can been obtained. The

solutions are validated by NSGA-II. These multi-objective optimization algorithms can

find Pareto-optimal solution in one single simulation run. With the same number of

iteration and population, the MOPSO algorithm has higher speed than NSGA-II.

Proper sizing algorithm is the one which can find the optimal size of each

component in each configuration to maximize the EMR between demand and supplies.

The number of PV panels, WTs and batteries are design variables. The minimum value

(lower limit) of design variables is selected 1 to be sure that there is at least one of each

supply in the system and the upper bound of them is set as max( ) in( )nD

S ,where max(D)and

min(Sn)are the maximum and minimum values of demand and supplies over considered

time period, respectively. The input data for the simulation are ambient air temperature,

WT installation high, hourly solar irradiation on a horizontal surface, wind speed, and

load demand data for one month. By employing the MOPSO algorithm to each

configuration, a set of possible solutions (Pareto set) will be obtained. The flow chart of

the optimization process is presented in Figure 10.

[Figure 10. Flow chart of optimization process using MOPSO (or NSGA-II)]

The optimization process starts with taking input values of hourly data for WT

and PV module output powers, and load demand profile. Then a for loop is run to call

MOPSO algorithm (or NSGA-II) several times (n) with objectives of minimizing IC

and ACS, and also maximizing CC. The results of optimum capacity generated by

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MOPSO algorithm (or NSGA-II) in decimal values are then converted to closest integer

values in order to get whole value of each sizing of supply sources. Optimum sizing

results along with corresponding IC, CC and ACS values are recorded for each run and

stored in arrays, which update in each iteration. When a pre-specified iteration count (

axn n= ) is reached, the algorithm is terminated. The max 200n = , and a population size

of 200popn = , are considered. A set of possible solutions (Pareto set) with relative

number of each supply will be finally provided.

7. Operation of Proposed Hybrid System

In order to have continuous power generation, there is need for backup and

storage systems such as diesel generator and battery storage. Diesel generator fuel

consumption is an important subject for entire operation cost. Hence, one of the critical

factor for optimization is managing the starting and stopping time of diesel generator.

The operation strategy could be explained in detail as fallow.

If the total power generated from wind turbines (PWT) and PV panels (PPV) is morethan the load demand (PL), the excess power is used to charge the batteries. In this

case, the sizing optimization will be done with only two supplies.

If the total generated power (PWT+PPV) is less than the load demand, and SOC ofbatteries is higher than SOCmin, the batteries will supply the extra power. If the

batteries SOC are equal or less than SOCmin, the diesel generator will start and

supply the power in orderto protect the batteries against excessive draining. Surplus

power from diesel will charge the batteries as amount as SOCmax. In this case, the

calculation of sizing optimization is divided in two categories: PV-wind-battery and

PV-wind including one diesel generator. The decision parameters for the

optimization algorithm are the numbers of PV modules, wind turbines, and batteries.

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The proposed management strategy is presented as a flowchart in Figure 11. The

optimized model gives the optimal size for hybrid components based on MEM and

minimum ACS. To calculate the CO2emission and fuel cost of diesel generator, they

are calculated correspond with the generating kWh, every time diesel generator started.

[Figure 11- Flowchart of operation strategy]

8. Optimization Results and Discussion

The output power of PV arrays and WTs, have been calculated according to the model

which described before, by specifications of PV modules and WTs, given in Tables 1

and 2. The sizing of optimal hybrid wind/PV systems was achieved using multi-

objectives PSO algorithm and GA approaches. The algorithm has been implemented

using data collected of the city Zabol, south-east of Iran, based on the MEM. Load is

needed to be matched with different supplies in a way that resultant supply (N1.S1 +

N2S2 + +Nn.Sn) meet the load with high electricity match rate (EMR). Main objective

of the proposed optimal algorithm is to find the optimal values of N1, N2, , Nn. The

obtained solutions for goal functions are presented as optimal Pareto front. The

inequality coefficient (IC), correlation coefficient (CC) and annualized cost of system

(ACS) were computed, using the developed program for each combination. It can be

noted that the increasing of IC implies the decreasing of CC. It is the same for both IC

vs. ACS and CC vs. ACS. In order to determine the best values of parameters,

evaluating convergence, several executions of the design program have been worked

out. Each hybrid system has included one type of PV modules and one type of WTs

together with diesel and battery storage systems. The results of these studies, suggest

the choice of Kyocera Solar (KC200) PV module and Bornay (Inclin 3000) wind

turbine for the proposed hybrid power system, compared to the other configurations.

The reason of this selection is that this configuration provides the lowest cost in larger

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EMR. Other configurations, either have not optimal IC range ( 0 0.4IC ), or optimal

CC range ( 1, 1CC= + ), or have higher cost than the selected configuration. Owing to

above considerations, the Pareto front has been plotted for IC vs. CC, IC vs. ACS, and

also CC vs. ACS, as shown in Figures 12, 13 and 14, respectively. The evolution of the

3D Pareto front can be observed in Figure 15.

[Figure 12. 2D Pareto front for the last generation. Inequality coefficient (IC) vs.

correlation coefficient (CC)]

[Figure 13. 2D Pareto front for the last generation. Inequality coefficient (IC) vs.

annualized cost of system (ACS)]

[Figure 14. 2D Pareto front for the last generation. Correlation coefficient (CC) vs.

annualized cost of system (ACS)]

[Figure 15. 3D Pareto front for the best configuration]

The results obtained by the optimization algorithms for the best configuration

are summarized in Table 8. They are the optimum combination of hybrid components

(PV, WT, and battery) needed to supply the energy to the load demand at the lowest

cost possible. The 11 best sizing selections from 30 runs for the best configuration have

been obtained. The calculations of the goal functions have also been done for these

sizing numbers.

[Table 8. Pareto front/optimal solutions obtained from multi-objective optimization]

As mentioned earlier, IC is more important factor than CC and ACS. Table 8

show that the values 6, 2 and 3 for PV modules, WTs, and battery units, respectively,

give us better match rate respect to others. But this configuration has the highest ACS

which can be very important in practical system installation. One scope of using hybrid

renewable energy systems is to use green energies like solar and wind instead of fossil

fuels. So the total hours the diesel generator operates in one month (744 hours) can be

one of the criteria in the selection of optimal solutions. Table 9 shows the total hours the

diesel operates in one month (August).

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[Table 9. Total hours the diesel operates in one month for each sizing solutions]

It can be seen that the sizing number of 4, 1, and 2 for PV module, WT and

battery gives the maximum diesel generator operating hours in lowest ACS and number

of 6, 2, and 3 for them, gives the minimum one in highest ACS. It depends to the

designer to select one of the obtained optimal sizing numbers for the hybrid

components, by considering the fuel cost, the necessity of match rate, and the cost

consideration

9. Conclusion

This study has been dedicated to determining the optimum stand-alone hybrid wind/PV

power generating systems. A new sizing methodology has been developed based on the

match evaluation method (MEM), considering resource uncertainties associated with

wind speed, solar irradiation and load demand. A diesel generator and a battery is used

to even out the irregularities. A management strategy has been designed to achieve

higher match rate between supply and demand intervals. The optimization process

provides optimum capacity of as many numbers of supplies as required to match with a

load demand in lowest investment, so it can handle large scale design problems. This

sizing methodology is useful for better energy utilization, eliminating exhaustive search

and avoid excessive computation times. This work is undertaken with triple objective

function: inequality coefficient (IC), correlation coefficient (CC), and annualized cost of

system (ACS). Studies have been done on different configurations of stand-alone hybrid

wind/PV systems. Six different wind turbines (WTs) and also six different PV modules,

with different characteristics have been considered. Sizing parameters have been

determined by the multi-objective particle swarm optimization (MOPSO) algorithm.

The results are also validated by NSGA-II. Obtained results suggest the choice of

Kyocera Solar (KC200) PV module and Bornay (Inclin 3000) wind turbine for the

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proposed hybrid power system, among all configurations. The algorithm has been run

for the best configuration. Obtained solutions are non-dominated and they form the

Pareto front. Simulation results show that a configuration with 6 PVs, 2 wind turbines,

and 3 battery units has a high electricity match rate (EMR) and lower operating hours

for the diesel generator with the expense of high ACS. Another configuration with 4 PV

modules, 1 wind turbine, and 2 battery units has long diesel operating hours in

acceptable match rate, and its ACS is the lowest. The designers can select the best

configuration among the Pareto set which fits their desire. It is worth mentioning that

the proposed methodology can be effectively employed for any composition of hybrid

energy systems in any locations taking account of the meteorological data and the

consumers demand.

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Documents

Optimal size and cost analysis of stand-alone hybrid wind/photovoltaic power-generation systems