Research Article Optimal Site Selection for a Solar Power Plant in the Central Anatolian Region of

14 Pages·2017·2.47 MB·English

Hindawi
International Journal of Photoenergy
Volume 2017, Article ID 7452715, 13 pages
https://doi.org/10.1155/2017/7452715
Research Article
Optimal Site Selection for a Solar Power Plant in the Central
Anatolian Region of Turkey
Ozge Pinar Akkas, Mustafa Yasin Erten, Ertugrul Cam, and Nihat Inanc
DepartmentofElectricalandElectronicsEngineering,KirikkaleUniversity,Kirikkale,Turkey
CorrespondenceshouldbeaddressedtoMustafaYasinErten;[email protected]
Received 17 November 2016; Revised 14 February 2017; Accepted 19 March 2017; Published 7 June 2017
AcademicEditor:Md.RabiulIslam
Copyright©2017OzgePinarAkkasetal.This is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Primary energysources arerunning outduetotheincrease inelectrical energyconsumption.Environmental problemscaused
by primary energy sources are also increasing. Using more renewable energy resources (RES) can be considered as one of the
most powerful solutions to address these problems. Today, required photovoltaic power systems (PVPS) and wind energy
systems (WES) are widely used as RES for addressing these problems. Because of their high costs, feasibility studies are
required for locating large systems associated with these resources. In this study, various suggestions are determined about
location selection, which is an important stage in the PVPS’s establishment. Hence, the criteria for selecting the
appropriate location are analyzed by the multicriteria decision making (MCDM) methods and the results are evaluated for
5 cities in the Central Anatolian Region of Turkey. In conclusion, it is determined which city is the most suitable place
for installation of solar power plants.
1. Introduction MCDM is a subbranch of a decision process. The deci-
sionprocessconsistsofthedeterminationofdifferentcriteria
Solar energy is one of the most important RES, and it is for modelling goals, evaluation of alternatives, and getting
becoming more popular day by day for many reasons such results.Toevaluatethealternatives basedoncriteria,differ-
as the purification of raw materials and the reduction of ent methods are used, such as analytic hierarchy process
dependence on foreign oil and gas. Moreover, solar energy (AHP), analytic network process (ANP), Technique for
is an inexhaustible reliable source and it is harmless to the Order Preference by Similarity to Ideal Solution (TOPSIS),
ecological environment. Thechoiceofthe appropriate solar EliminationandChoiceTranslating RealityEnglish(ELEC-
energy location, which is important in their setup, depends TRE), The Preference Ranking Organization Method for
on many factors. These factors should be optimized to Enrichment Evaluation (PROMETHEE), and Vise Kriteri-
get more energy as well as to reduce initial investment jumskaOptimizacijaIKompromisnoResenje(VIKOR)[6].
andoperation costs. These operationsshould be considered TherearemanystudiesthatusetheMCDMmethodsto
during the first phase of solar energy installation to locate solvelocationproblemsintheliterature.Kengpoletal.devel-
the plant accurately. Hence, many studies are performed in oped a decision support system for solar power plant site
theliteraturelocatingthepowerplantsintothemostappro- selectioninThailand.Theyappliedfuzzy analytic hierarchy
priate places [1–4]. Multicriteria decision making (MCDM) process (Fuzzy AHP) model for the problem [7]. Uyan
methodsareusedintheoptimizationofsystemswithmulti- worked for suitable site selection in solar farms using geo-
pleparameterstakenintoconsiderationatthesametime[5]. graphical information system (GIS) and AHP. Karapinar
Forthispurpose,varioussubmethodshavebeenusedtomeet Region in Konya/Turkey was chosen as the study area [8].
therequirements. Asakerehetal.usedaFuzzyAHPandGIStolocatethemost
2 InternationalJournalofPhotoenergy
appropriatesitesforsolarenergyfarmsinShodirvanregion 2.1. Solar Energy Potential. The location where the solar
inIran[9].ElQuolitiusedAHPtodeterminethesuitablesite power plant will be installed is highly related with the solar
for solar power generation in the Western Region of Saudi energy potential of the location. The information about the
Arabia. Fourteen site selection criteria are determined in solar energypotential ofa location can be determined from
the study [10]. Sozen et al. presented an approach for the theglobalradiationvalues(kWh/m2-day),sunshineduration
location of solar plants by data envelopment analysis (hours),andPV-typeareaenergygeneration(kWh/year).In
(DEA)andusingtheTOPSISmethod.Theyapplieditto30 this study, these values of the cities are obtained from solar
different cities in different regions of Turkey [11]. Lee et al. energy potential atlas (GEPA) of Directorate General of
proposed a multiple-criteria decision-making model that RenewableEnergyinTurkey[14].InFigures1–5,eachcity’s
incorporates the interpretive structural modeling (ISM), globalradiationvalues,sunshineduration,andtotalamount
fuzzy ANP, and VIKOR to select the most suitable photo- ofenergy/PVareaareshown.
voltaic solar plant location and applied it in a case study Thedatainthefiguresareusedasinputstotheproposed
in evaluating photovoltaic solar plant locations in Taiwan methods.Sincethecitiesareinthesameregionandareclose
[12]. Sindhu et al. used hybrid combination of AHP and toeachother,thesuitablelocationoftheinstallationcannot
fuzzy TOPSIS to select an appropriate site in India [13]. beestimatedfromthefigureseasily.However,theyarevery
In this study, four different MCDM methods are usefulwhileusingtogetherwithothermethods.Forthisrea-
used to select the most suitable city among 5 cities in son,theyhavebeenthoroughlyexamined.
theCentralAnatolianRegionofTurkeyfortheestablishment
of solar power plant in order to get maximum power out- 2.2.FeederCapacityoftheDistributionCenter.Whenanelec-
put and have minimum cost. Aksaray, Konya, Karaman, tric energy production facility is installed in a region, the
Nevşehir, and Niğde, which have the highest solar radia- infrastructure of the region should be examined. Therefore,
the transformer capacities, the number of lines, cable sec-
tion, are selected for comparison. Three main criteria are
defined for solar power plant location selection. These cri- tions,andsoforthareconsidered astheparameters. Inthis
context, the allocated capacity should also be considered.
teria rely on solar energy potential, feeder capacity, and
surface slope. This study differs from other studies in The allocated capacity of the transformer center for solar
and wind energy power plants within unlicensed electricity
terms of comparative use of all the MCDM methods. This
generation is obtained with the notification of Directorate
situation has not been studied previously in the literature,
General of Turkish Electricity Transmission Corporation
especially when choosing suitable locations for PVPS. In
(TEİAŞ) [15]. The cities of Aksaray, Konya, Karaman,
addition, associating such a study with cities that have not
Nevşehir, and Niğde have a number of 10, 38, 5, 2, and 1
been selected before is another contribution of this study.
In conclusion of the study, it is observed that Karaman is allocatedcapacitiesofthefeeders,respectively.
determined as the most suitable city for the establishment
2.3. Surface Slope. Another main criterion is surface slope.
ofthesolarplantstation.
The slope of the surface where a solar power plant will be
installedisusuallykeptbelow5%[16].Thedatainthestudy
[17] is considered for the average slope data of the cities.
2. Problem Definition
Aksarayhas2%,Konyahas 1%,Karaman has3%,Nevşehir
has 7%, and Niğde has 5% of surface slope coefficient. This
It has become important to determine the installation loca- suggeststhatthecitiesofNevşehirandNiğdeareproblematic
tionofsolarenergysystemsthatareintheforegroundamong
intermsofinstallation.However,thesecities,whicharegood
theRES.Sincethelifetimeofsuchsystemsisalongtimein25
intermsoftheamountofsunlight,havenotbeenextracted
years,thelocationofasolarpowerplantthatcanobtainmax-
fromtheanalysis.
imum energy is significant. Moreover, it is not possible to
change the place of the system after installation because of
3. Methods
theconstructioncosts.
There are different criteria that can be used to deter-
In this study, the AHP, ELECTRE, TOPSIS, and VIKOR,
mine the solar power plant location. Solar energy poten-
submethods of theMCDM, are used todecide which of the
tial, feeder capacity of the distribution center, and surface
above-mentionedcitiesissuitableforthePVPSinstallation.
slope are the main criteria that have been used for the
Thesemethodsaredescribednextforabetterunderstanding
selection of the solar power plant location. These main cri-
ofthesimulations.
teriahavesubcriteriatoexaminetheproblemindetail.Sub-
criteria of energy potential criterion are photovoltaic (PV) 3.1. Analytic Hierarchy Process (AHP). AHP can be
solar radiation, sunshine duration, and the total amount of explained as the decision and the estimation method that
energy/PVarea.Thefeedercapacityofthedistributioncenter is used for the identification of the decision hierarchy,
has subcriteria of total capacity andavailable quota. Subcri- and it gives percentage distribution of the decision points
teriaofthepowerplantsurfacearethesurfaceslope,iceload, in terms of factors which affect the decision [18]. Its solu-
and wind potential. Each subcriterion has its own weight tion consists of 5 steps. Firstly, the decision-making prob-
factor for the related main criterion. In the following, the lem is defined. The decision points and affecting factors
above-mentioned main criteria for the related cities will are determined to define the decision-making problem.
be, respectively, explained. The number of decision points is denoted by m, and the
InternationalJournalofPhotoenergy 3
8.00 14.00
y)
da 7.00 12.00
2obal radiation values (kWh/m- 654321......000000000000 1.98 2.56 4.23 5.20 6.30 6.78 6.81 6.05 5.12 3.73 2.36 1.77 Sunshine duration (hour) 102486.....0000000000 4.19 5.51 6.88 8.03 9.46 11.28 11.97 11.36 9.79 7.36 5.53 3.93
Gl
0.00 0.00
January February March April May June July August September October November December January February March April May June July August September October November December
Months Months
(a) (b)
30000
ear) 2286000000
y
h/ 24000
W
k 22000
a ( 20000
e
ar 18000
V
P 16000
y/
g 14000
er
n 12000
e
of 10000
unt 8000
o
m 6000
a
al 4000
Tot 2000
0
0 10 20 30 40 50 60 70 80 90100
m2
Monocrystalline Cadmium
silicon tellurium
Polycrystalline Amorphous
silicon silicon
Thin copper film
strip
(c)
Figure1:Konyaprovince(a)globalradiationvalues,(b)sunshineduration,and(c)totalamountofenergy/PVarea.
number of factors affecting them is denoted by n. In the matrix A, and shows the intensity of importance of mth
second step, comparison matrix among factors is formed. factor over nth factor. The relative importance of pairwise
It is a square matrix of size nxn. The components on comparisons is measured according to a numerical scale
the diagonal of the matrix take the value of “1.” The from1 to 9 as shown in Table 1 [19]. When factor m com-
resulting comparison matrix is shown in pared to n is assigned with the number shown in Table 1,
thefactorncomparedtombecomesitsreciprocal.
a11 a12 … a1n In the third step, percentage importance distribution of
A= a21 a22 … a2n , 1 timhepofartcatonrcseliesvedlewteirthmriensepde.ctCtoomeapcahrifsaocntorm.Tathreixcoslhuomwnsvtehce-
⋮ ⋮ ⋮ ⋮
torBthathaskcomponentsisformedtodetermineweights
am1 am2 … amn or the percentage importance distribution of all factors by
using column vectors that form the comparison matrix.
where a is the element of mth row, nth column of ThecolumnvectorBisshownin
mn
4 InternationalJournalofPhotoenergy
8.00 14.00
y)
2bal radiation values (kWh/m-da 7654321.......00000000000000 2.16 2.69 4.38 5.35 6.45 6.98 6.91 6.15 5.22 3.86 2.52 1.91 Sunshine duration (hour) 11022468......000000000000 4.46 5.85 7.14 8.44 9.84 11.51 12.02 11.47 10.11 7.77 5.95 4.31
o
Gl 0.00 0.00
January February March April May June July August September October November December January February March April May June July August September October November December
Months Months
(a) (b)
30000
ear) 2286000000
y
h/ 24000
W
k 22000
a ( 20000
e
ar 18000
V
P 16000
gy/ 14000
ner 12000
e
of 10000
nt 8000
u
mo 6000
al a 4000
ot 2000
T
0
0 10 20 30 40 50 60 70 80 90100
m2
Monocrystalline Cadmium
silicon tellurium
Polycrystalline Amorphous
silicon silicon
Thin copper film
strip
(c)
Figure2:Karamanprovince(a)globalradiationvalues,(b)sunshineduration,and(c)totalamountofenergy/PVarea.
ThematrixCisformedbycombiningthecolumnvector
b11 Basshownin
Bi= b⋮21 2 c11 c12 … c1n
bn1 C= c21 c22 … c2n , 4
⋮ ⋮ ⋮ ⋮
ThecomponentsofthecolumnvectorBarecalculatedas cm1 cm2 … cmn
shownin
wherec istheelementofmthrow,nthcolumnofmatrixC.
mn
a The percentage importance distribution that shows the
bmn= 〠k mna 3 relative importance of each factor can be obtained with the
m=1 mn help of matrix C. The column vector W called weighting
InternationalJournalofPhotoenergy 5
8.00 14.00
y)
da 7.00 12.00
2-obal radiation values (kWh/m 654321......000000000000 2.03 2.65 4.23 5.11 6.37 6.84 6.92 6.06 5.10 3.76 2.39 1.81 Sunshine duration (hour) 102468.....0000000000 4.41 5.48 6.74 7.85 9.51 11.39 12.16 11.57 10.06 7.61 5.65 3.90
Gl
0.00 0.00
January February March April May June July August September October November December January February March April May June July August September October November December
Months Months
(a) (b)
30000
ear) 2286000000
y
h/ 24000
W
k 22000
ea ( 20000
V ar 18000
y/P 16000
erg 14000
n
e 12000
nt of 10000
u 8000
o
m 6000
a
al 4000
ot
T 2000
0
0 10 20 30 40 50 60 70 80 90100
m2
Monocrystalline Cadmium
silicon tellurium
Polycrystalline Amorphous
silicon silicon
Thin copper film
strip
(c)
Figure3:Niğdeprovince(a)globalradiationvalues,(b)sunshineduration,and(c)totalamountofenergy/PVarea.
vectorisobtainedbytakingthemeanofrowcomponentsof 〠k c
matrixC.Wisshownin(5).Thecalculationofcomponents w = n=1 mn 6
m k
ofvectorWisshownin(6).
In the fourth step, consistency of factor comparison
w1 is measured. Consistency ratio (CR) determines whether
W= w2 , 5 the comparisons that are made by AHP method are true
⋮ or not. Firstly, column vector D is obtained by multiply-
ing comparison matrix A with weighting vector W as
wn shown in
6 InternationalJournalofPhotoenergy
8.00 14.00
y)
da 7.00 12.00
2-Global radiation values (kWh/m 654321......000000000000 1.87 2.48 4.03 4.95 6.20 6.61 6.71 5.94 4.95 3.56 2.22 1.68 Sunshine duration (hour) 102468.....0000000000 4.07 5.32 6.43 7.65 9.16 11.17 12.05 11.48 9.68 7.27 5.35 3.57
0.00 0.00
January February March April May June July August September October November December January February March April May June July August September October November December
Months Months
(a) (b)
28000
ar) 26000
e 24000
y
Wh/ 22000
a (k 20000
are 18000
V 16000
P
y/ 14000
g
ner 12000
e
of 10000
unt 8000
o
m 6000
a
al 4000
ot
T 2000
0
0 10 20 30 40 50 60 70 80 90100
m2
Monocrystalline Cadmium
silicon tellurium
Polycrystalline Amorphous
silicon silicon
Thin copper film
strip
(c)
Figure4:Nevşehirprovince(a)globalradiationvalues,(b)sunshineduration,and(c)totalamountofenergy/PVarea.
a11 a12 … a1n w1 takinMgetahnevmaleuaenroelfaEteFdetloemtheenctsomaspsahroiswonni(nλ)isobtainedby
D= a21 a22 … a2n x w2 7
⋮ ⋮ ⋮ ⋮ ⋮ 〠k EF 9
λ= i=m m
am1 am2 … amn wn k
Then,consistencyindex(CI)andthe(CR)arecalculated
Main value related to each evaluation factor (EF) is
asshownin(10)and(11).
obtainedbydividingcolumnvectorDtothecorresponding
ThevalueofCRmustbesmallerthan0.10tobeconsis-
elementsofcolumnvectorWasshownin
tentwithcomparisonmatrix[20].
Random index (RI) in (11) takes different values by
d
EF = m  m=1,2,…,k 8 the number of criteria. The values of RI according to n,
m wm which is the number of criteria, are shown in Table 2.
InternationalJournalofPhotoenergy 7
8.00 14.00
y)
da 7.00 12.00
2-Global radiation values (kWh/m 654321......000000000000 1.90 2.48 4.13 5.03 6.22 6.67 6.76 6.00 5.03 3.66 2.29 1.71 Sunshine duration (hour) 102468.....0000000000 4.11 5.40 6.80 7.97 9.36 11.27 12.12 11.53 9.81 7.36 5.45 3.73
0.00 0.00
January February March April May June July August September October November December January February March April May June July August September October November December
Months Months
(a) (b)
28000
ar) 26000
ye 24000
Wh/ 22000
a (k 20000
are 18000
V 16000
P
y/ 14000
g
ner 12000
e
of 10000
nt 8000
u
o
m 6000
a
al 4000
Tot 2000
0
0 10 20 30 40 50 60 70 80 90100
m2
Monocrystalline Cadmium
silicon tellurium
Polycrystalline Amorphous
silicon silicon
Thin copper film
strip
(c)
Figure5:Aksarayprovince(a)globalradiationvalues,(b)sunshineduration,and(c)totalamountofenergy/PVarea.
In this study, the value of RI is taken as 0.58 from the After each comparison operation, column vector S that
table since there are 3 criteria. shows percentage distribution and has a size of mx1 is
obtained.ThecolumnvectorSisshownin
CI= λ−k, 10
k−1 s11
CR= CI 11 S = s21 12
RI m ⋮
In the final step, percentage importance distribution sm1
(PID)atmdecisionpointsisfoundforeachfactor.Inother
words, the comparisons and matrix operations are repeated The decision matrix K is formed with mxn size, and it
ktimes.However,thesizeofthecomparisonmatrixthatwill consists of n column vector S which has the size of mx1. It
be used as the decision points of each factor will be mxm. isshownin
8 InternationalJournalofPhotoenergy
Table1:RatingscaleofAHPmethod.
Intensityofimportance Definition Explanation
1 Equalimportance Twofactorscontributeequallytotheobjective.
3 Moreimportant Experienceandjudgementslightlyfavouroneovertheother.
5 Muchmoreimportant Experienceandjudgementstronglyfavouroneovertheother.
7 Verymuchmoreimportant Experienceandjudgementverystronglyfavouroneovertheother.
9 Absolutelymoreimportant Theevidencefavouringoneovertheotherisofthehighestpossiblevalidity.
2,4,6,8 Intermediatevalues Whencompromiseisneeded.
Table2:ThevaluesofRI.
x11 x12 … x1n
k1 R0I k6 1R.2I4 X = x21 x22 … x2n 16
mn ⋮ ⋮ ⋮ ⋮
2 0 7 1.32
3 0.58 8 1.41 xm1 xm2 … xmn
4 0.90 9 1.45 X is formed by the help of matrix A. The elements of
5 1.12 10 1.49 matrixXarecalculatedasshownin
a
s11 s12 … s1n xmn= 〠mmna2 , 17
K= s⋮21 s⋮22 …⋮ s⋮2n 13 where m is the number of thk=e1dkencision points, n is the
number of the columns, and a is the element of matrix A.
sm1 sm2 … smn Inthethirdstep,theweightedstandarddecisionmatrix,
Y,isformed.ThematrixYisusedtoreflectimportancedif-
Asaresult,thecolumnvectorLisobtainedbymultiply-
ferences of the criteria to the solution. The matrix Y is
ing the decision matrix with column vector W (weighting
obtained by multiplying matrix X with a weighting vector
vector)asshownin(14).ThecolumnvectorLgivestheper-
w asshownin
centagedistributionofdecisionpoints,andthesumofitsele- i
mentsis1. w1x11 w2x12 … wnx1n
s11 s12 … s1n w1 l11 Y = w1x21 w2x22 … wnx2n 18
mn ⋮ ⋮ ⋮ ⋮
L= s⋮21 s⋮22 …⋮ s⋮2n x w⋮2 = l⋮21 14 w1xm1 w2xm2 … wmxmn
sm1 sm2 … smn wn lm1 In the fourth step, consistency (Ckl) and inconsistency
(D )setsaredetermined.MatrixYisusedtodeterminethe
kl
3.2. Elimination and Choice Translating Reality English consistency sets. The decision points are evaluated in terms
(ELECTRE). The method depends on dual superiority of the criteria. Equation (19) is used in this evaluation pro-
comparisons among the decision points for each evaluation cess.Everyconsistencysetcorrespondstooneinconsistency
factor. This method basically consists of 8 steps [21]. setinthismethod.Inconsistencysetconsistsoftheelements
Firstly, the decision matrix A is formed. There are decision thatarenotintheconsistencyset.
points and evaluation factors in rows and columns of the
decision matrix. The matrix A is the initial matrix that is Ckl= n,ykn≥yln 19
formed by the decision maker. The number of decision
In the fifth step, consistency (C) and inconsistency (D)
points and the number of the evaluation factors are repre-
matrices are formed with the help of the consistency and
sented by m and n in the A matrix. The resulting deci-
mn inconsistency sets. The elements of the consistency matrix
sion matrix is shown in
are found with (20), and the elements of the inconsistency
a11 a12 … a1n matrixarefoundwith(21).
A = a21 a22 … a2n 15 ckl= 〠 wn, 20
mn ⋮ ⋮ ⋮ ⋮ n∈C
kl
am1 am2 … amn maxykn−yln
d = n∈Dkl 21
In the second step, standard decision matrix, X, is kl maxy −y
kn ln
formed.Itisshownin n
InternationalJournalofPhotoenergy 9
ThematrixCisobtainedwith(20)asshownin(22),and Inthesecondstep,standarddecisionmatrixRisformed.
thematrixDisobtainedwith(21)asshownin(23). ThematrixRisshownin
− c12 c13 … c1m r11 r12 … r1n
C= c21 − c23 … c2m , 22 R = r21 r22 … r2n 27
⋮ ⋮ ⋮ ⋮ ⋮ mn ⋮ ⋮ ⋮ ⋮
cm1 cm2 cm3 … − rm1 rm2 … rmn
− d12 d13 … d1m TheelementsofthematrixRarecalculatedwiththehelp
ofthematrixAasshownin
D= d21 − d23 … d2m 23 a
d⋮m1 d⋮m2 d⋮m3 …⋮ ⋮− rmn= 〠mmk=n1a2kn 28
In the sixth step, consistency superiority (F) and incon- Inthethirdstep,standardweighteddecisionmatrixVis
sistencysuperiority(G)matricesareformed. formed.Firstly,weightvalues(w )relatedtoevaluationfac-
n
ThematrixFis inthesize ofmxm,andtheelements of tors aredetermined.Then,elements foreachcolumninthe
thematrixFareobtainedbythecomparisonofaconsistency matrixRaremultipliedwithrelatedw value.ThematrixV
n
threshold value c and the elements of consistency matrix isshownin
¯
c .Consistencythresholdvalueisfoundwith
kl w1r11 w2r12 … wnr1n
¯c = m m1−1 k〠m=1〠l=m1ckl 24 Vmn= w⋮1r21 w⋮2r22 …⋮ w⋮nr2n 29
TheelementsofthematrixF fkl takeavalueof1or0, w1rm1 w2rm2 … wnrmn
andtherearenovaluesonthediagonalofthematrixbecause
∗ −
Inthefourthstep,ideal A andnonideal A solutions
the diagonal elements show the same decision point. If
c ≥ c ⇒f =1,andifc < c ⇒f =0 areformed.Thebiggestvalueoftheweightedevaluationfac-
kl ¯ kl kl ¯ kl torsofmatrixVischosentoformanidealsolutionset.Equa-
ThematrixGisinthesizeofmxm,anditisformedinthe tion(30)showsthefindingoftheidealsolutionset.
samemannerasmatrixF.Inconsistencythresholdvalue d
¯
isfoundwith A∗= max v n∈N ,  min v n∈N 30
mn mn
m m
1 m m
d = 〠〠d 25 The smallest value of weighted evaluation factors of
¯ m m−1 kl matrixVischosentoformanonidealsolutionset.Equation
k=1l=1 (31)showsthefindingofthenonidealsolutionset.
TheelementsofthematrixG g takeavalueof1or0,
kl
andtherearenovaluesonthediagonalofthematrixbecause A−= min v n∈N ,  max v n∈N 31
mn mn
the diagonal elements show the same decision point. If m m
d < d ⇒g =1,andifd ≥ d ⇒g =0 Inthefifthstep,discriminationmeasurementsarecalcu-
kl ¯ kl kl ¯ kl
lated.Thedeviationvaluesrelatedtothedecisionpointsare
Intheseventhstep,totaldominancematrix(E)isformed.
calculated with the help of Euclidean distance approach.
EisobtainedwiththemultiplicationofmatricesFandKand
∗ −
consistsof1’sand0’s.Finally,theorderofimportanceofthe Ideal discrimination Sm and nonidealdiscrimination Sm
decisionpointsisdetermined. measurementvaluesarefoundwith
3.3. Technique for Order Preference by Similarity to Ideal S∗ = 〠n v −v∗ 2, 32
Solution (TOPSIS). In the first step of this method, the m n=1 mn n
decision matrix A is formed. There are decision points in
the rows of the decision matrix and evaluation factors at S−m= 〠nn=1 vmn−v−n 2 33
thecolumnsofthedecisionmatrix.ThematrixAisaninitial
Inthefinalstep,therelativeproximityoftheidealsolu-
matrixthatisformedbythedecisionmaker[22].Theresult-
tion is calculated. The ideal and nonideal discrimination
ingdecisionmatrixisshownin
values are used to calculate relative proximity of the ideal
a11 a12 … a1n solutionforeachdecisionpoint.Thecalculationisshownin
A = a21 a22 … a2n 26 C∗ = S−m 34
mn ⋮ ⋮ ⋮ ⋮ m S− +S∗
m m
am1 am2 … amn In(34),thevalueofC∗ isbetween0and1asshownin
m
10 InternationalJournalofPhotoenergy
Table3:Comparisonmatrixforsolarenergypotential. Table5:Comparisonmatrixforsurfaceslope.
Solarenergy Aksaray Konya Karaman Nevşehir Niğde Aksaray Konya Karaman Nevşehir Niğde
potential Aksaray 1 1/3 2 8 5
Aksaray 1 1/3 1/7 3 1/5 Konya 3 1 5 9 7
Konya 3 1 1/5 5 1/3 Karaman 1/2 1/5 1 6 3
Karaman 7 5 1 9 3 Nevşehir 1/8 1/9 1/6 1 1/3
Nevşehir 1/3 1/5 1/9 1 1/7 Niğde 1/5 1/7 1/3 3 1
Niğde 5 3 1/3 7 1
Table6:Decisionmatrix.
Table 4: Comparison matrix for maximum capacity that can be
allocated. Solarenergypotential Surfaceslope Capacity
Aksaray 4 8 8
Maximum
Konya 6 10 10
capacitythat Aksaray Konya Karaman Nevşehir Niğde
Karaman 10 6 6
canbeallocated
Nevşehir 2 2 4
Aksaray 1 1/3 3 5 8
Niğde 8 4 2
Konya 3 1 5 7 9
Karaman 1/3 1/5 1 2 5
Nevşehir 1/5 1/7 1/2 1 3
Niğde 1/8 1/9 1/5 1/3 1 Table7:MatrixE.
Aksaray Konya Karaman Nevşehir Niğde
0≤C∗ ≤1 35 Aksaray — 0 0 1 0
m Konya 1 — 0 1 0
IfC∗ equals1,itshowstheabsoluteproximityofrelated Karaman 1 1 — 1 1
m
decision point to the ideal solution, and if C∗ equals 0, it Nevşehir 0 0 0 — 0
m
shows the absolute proximity of the related decision point Niğde 1 0 0 1 —
tothenonidealsolution.
3.4.ViseKriterijumskaOptimizacijaIKompromisnoResenje
(VIKOR).Thismethodsolvestheproblemsbycalculatingthe Table8:Proximityvaluesbasedonidealsolution.
bestandtheworstvaluesofallthecriteriafunctions.Thebest
(f ∗)andtheworst(f −)valuesarefoundwith[22,23] C∗
m m
Aksaray 0.34
f ∗=maxf , 36
m mn Konya 0.56
f −=minf , 37 Karaman 0.83
m mn Nevşehir 0.07
wheremrepresentscriteriaandnrepresentsalternatives. Niğde 0.62
Then,thevaluesofS andR arecalculatedwith[22,23]
n n
n w fm∗−fmn changes between 0 and 1. Generally, the value of v is taken
Sn= 〠 mfm∗−fm− , 38 as0.5.
m=1 Finally,thecalculatedvaluesofS ,R ,andQ areranked
n n n
w fm∗−fmn inadecreasingorder.Qnwiththesmallestvalueisexpressed
Rn=max mfm∗−fm− , 39 asthebestoptionamongalternatives.
4. Simulation and Results
wherew representstheweightofthemthcriteria.
m
Afterthat,thevalueofQ thatrepresentsthemaximum
groupbenefitisfoundwith(4n0)foreachalternative. In this study, a simulation is implemented by using the
MATLAB program to establish the location of the solar
Q = v Sn−S∗ + 1−v Rn−R∗ , 40 power plants for the suggested cities with the help of the
n S−−S∗ R−−R∗ methods that are described next. The results obtained from
the methods according to the problem definition have been
where S∗=minnSn, S−=maxnSn, R∗=minnRn, and explainedinthissection.
R−=maxnR . v refers to the weight for the strategy that
n
ensures maximum group utility, and (1−v) refers to the 4.1.AHPResults.Inthismethod,thematricestobefoundfor
weight of the minimum regret in dissent. The value of v thethreemaincriteriadescribedinthepreviouschapterswill