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Multicriterial Analysis on Selecting Solar Radiation Concentration Ration for Photovoltaic Panels Using Electre-boldur Method
Available online at www.sciencedirect.com
ScienceDirect Procedia Technology 22 (2016) 773 – 780
9th International Conference Interdisciplinarity in Engineering, INTER-ENG 2015, 8-9 October 2015, Tirgu-Mures, Romania
Multicriterial Analysis on Selecting Solar Radiation Concentration Ration for Photovoltaic Panels Using Electre-Boldur Method George Sebastian Naghiua, Ioan Giurcaa,*, Ioan Aúchileanb, Gheorghe Badeaa a
Technical University of Cluj-Napoca, Faculty of Building Services Engineering, Boulevard December 21, no. 128-130, Cluj-Napoca, 400604, Romania b SC ACI Cluj SA, Avenue DorobanĠilor, no. 70, Cluj-Napoca, 400609, Romania
Abstract The selection of the optimal solution regarding the concentration ratio is a complex process, as it depends on a very high number of criteria. The production of renewable energy using the concentrated solar radiation is a field of high scientific level worldwide, while in Romania the research in this field is only in its early stages. The purpose of this document is to present a classification method for photovoltaic systems taking into account the concentration ration. The paper tries to fill in a gap in the field of choosing the photovoltaic systems from the concentration ratio perspective. Based on the study performed, we recommend using the variant A4, namely the technical solution consisting of a photovoltaic system with a 1000x concentration ratio. © by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license © 2016 2016The TheAuthors. Authors.Published Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the “Petru Maior” University of Tirgu-Mures, Faculty of Engineering. Peer-review under responsibility of the “Petru Maior” University of Tirgu Mures, Faculty of Engineering Keywords: photovoltaic energy; photovoltaic systems; multi-criteria methods; Electre method; Electre-Boldur method.
1. Introduction 1.1. Context The emergence of the new type of high-performance multi-junction photovoltaic cells, which allows the efficient conversion of concentrated solar radiation separately for the spectrum components, led to the development of
* Corresponding author. Tel.: +40-0723 371 760. E-mail address: [email protected]
2212-0173 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the “Petru Maior” University of Tirgu Mures, Faculty of Engineering doi:10.1016/j.protcy.2016.01.048
774
George Sebastian Naghiu et al. / Procedia Technology 22 (2016) 773 – 780
photovoltaic systems specific for these cells. The selection of the optimal solution regarding the concentration ratio of the photovoltaic panels is a complex process, as it depends on a very high number of criteria, such as: the efficiency of the photovoltaic cell at different concentration ratios, the cost of photovoltaic cell, the amount of the costs of photovoltaic cell compared to the total cost of the system, the cost of the land required for the investment, etc. 1.2. The current stage of international research The production of renewable energy using the concentrated solar radiation is a field of high scientific level worldwide. The technology level in this field is a very advanced one, while research is performed in order to optimize and decrease the investment costs and also the output energy costs, together with the decrease of the land areas required for the installation of photovoltaic panels. According to the data provided by National Renewable Energy Laboratory from United States of America [1], one can find on the market about 30 different types of photovoltaic cells, having an efficiency between 9.2% - 45,7% and concentration ratio between 1% - 1024% [2], thus noticing an highly increased dynamic of the research results in this field during the last years. 1.3. The current stage of Romanian research In Romania, the research in this field is in its early ages. It is expected the research to be increased in the years to come, taking into consideration the high development potential of the concentrated photovoltaic systems, due to the accelerated increase of the multi-junction photovoltaic cells’ efficiency. The main individual criterion and multi-criteria methods used for substantiating the decision in the field of fittings for construction are the following: the method of ordinal individual criterion ranks, the method of ordinal multi-criteria ranks, the method of real ranks, the method of the complex quality index, the method of the complex quality and economic efficiency index, the global performance assessment method, the utility method, maximum score method [3], optimal degree of foreign ownership under uncertainty method, the relative distance comparison model in relation with the maximum performance, the relative distance comparison model in relation with the average performance, advanced multi criteria analysis, comparative analysis method, the AHP method [4], the Electre method [5], Electre-Boldur method [6], the Onicescu method, the Promethee method. 1.4. The purpose described in the article The purpose of this document is to present a classification method for photovoltaic systems taking into account the concentration ration. We wish to be able to use this method as a research and innovation tool, useful for selecting the optimal system during the stage of technological development of the new photovoltaic systems and during the stage of development of the opportunity and feasibility studies, and of the business plans on the development of new production capacities of photovoltaic energy. 1.5. The added value of the present article This paper tries to fill a gap in the field of selection of the photovoltaic systems considering the concentration ratio criterion. Nomenclature P X
an alternative is preferred to another one Number of suns (or the concentration ratio of the solar radiation incident on the surface of the PV cell)
George Sebastian Naghiu et al. / Procedia Technology 22 (2016) 773 – 780
2. Materials and methods 2.1. Materials Nowadays, on the market, there are a lot of photovoltaic systems, thus both the designer and the beneficiary found it difficult to choose the photovoltaic systems. These difficulties are caused, on the one hand, by the diverse range of products on the market, and on the other hand by their different technical performances, as well as by the different investment and operation costs. In this context, in this paper we analyze the following technical solutions: • • • • •
photovoltaic system with 1X concentration factor, alternative A1; photovoltaic system with 3X concentration factor, alternative A2; photovoltaic system with 300X concentration factor, alternative A3; photovoltaic system with 1000X concentration factor, alternative A4; photovoltaic system with 3000X concentration factor, alternative A5.
Pursuant to the analysis of the five photovoltaic systems, one notices that these photovoltaic systems consist of different components, which obviously hampers the analysis process of the technical solutions. Also, pursuant to the analysis of the five photovoltaic systems, one notices that these photovoltaic systems have their advantages and disadvantages, therefore the various alternatives must be very carefully analyzed. Considering that the various photovoltaic systems have different components, considering that they have a series of advantages and disadvantages, and considering that they have different investment and operation costs, in practice both designers and beneficiaries encounter problems when it comes to select photovoltaic systems. In this context, when selecting photovoltaic systems, we propose: • • • •
to minimize the surface of photovoltaic cells for the production of 1 kWh of electricity, criterion C1; to maximize the ratio capacity/surface for the photovoltaic cell, criterion C2; to minimize the cost of the photovoltaic cell, criterion C3; to minimize the ratio between the cost of the photovoltaic cell / the cost of the photovoltaic system, criterion C4.
2.2. Methods In this paper, the technical criteria shall be chosen based on the ELECTRE-Boldur Method. ELECTRE acronym stands for the initials of the method’s name: ELimination Et Choix Traduisent la REalité {Elimination and Choice Expressing Reality} [7]. The ELECTRE Method was elaborated in 1965, at S.E.M.A. Paris (Societe d'Economie et de Mathematique Appliquees), by a team of French researchers led by B. Roy. The ELECTRE-Boldur Method was proposed by teacher Gheorge Boldur-LăĠescu. In order to simplify and make the method operational in the meaning of the theory of utility, the author proposed the use of certain normalized concordance and discordance coefficients. These coefficients, marked c*(.,.), d*(.,.) are calculated based on utilities “Uij” estimated for the consequences “aij” from the decision/making matrix ’’A’’, according to the procedure Neumann-Morgenstern [8]. In our opinion, applying the ELECTRE-Boldur method involves ten steps, as presented below: Step 1: Establishing the decision-making variants. In this stage, the set of alternatives that can be applied shall be identified, while the data shall be written in the alternatives matrix A = [Ai]. Where i = 1...n, represents the number of alternatives. Step 2: Establishing the decision-making criteria. Here we shall identify the criteria (objectives) that shall be used for the selection of the alternatives, while the data shall be written in the decision criteria matrix C = [Cj]. Where j = 1...m, represents the number of criteria. Step 3: Filling in the performance matrix, where the performance of the alternatives shall be identified for each criterion, and the data shall be written in the performance matrix P = [Pij].
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Step 4: Calculating the utilities and filling in the utility matrix. The calculation of utilities shall be made based on the performance of alternatives while using the method created by von Neumann and O. Morgenstern in 1947 [9]. One shall estimate the utility for each criterion alone or for the entire decision table, thus obtaining the multicriterion utility matrix U = [Uij] [8]. Depending on the nature of the criteria, the utilities will be calculated according to the following formulas [10]: Maximizing criteria:
uij =
aij − a min j a max j − a min j
(1)
Minimizing criteria:
uij =
a max j − aij a max j − a min j
(2)
Where: uij represents the usability of the i variant according to the j criterion; amax j - the maximum performance obtained by the analyzed variants, according to the j criterion; amin j - the minimum performance obtained by the analyzed variants, according to the j criterion; aij - the performance obtained by the i variant according to the j criterion. One utility corresponds to each consequence [10]. Step 5: Establishing the importance coefficients corresponding to the decision-making criteria. An importance coefficient, Kj, shall be associated to each criterion “j” [6]. The criteria set for the comparative analysis of objects, objectives, projects or activities usually don’t have the same importance. The quantization of the importance (ratio) of the criteria is made by the calculation of some “weighting coefficients” Kj. It begins with a qualitative analysis of the criteria, by comparing every two criteria and establishing which of them is more important [11]. Then, the importance factors are set based on FRISCO formula, elaborated by a well-known creation group based in San Francisco - U.S.A., which was acknowledged worldwide as being the most performing one and widespread used [12-14].
kj =
p + Δp + m + 0,5 NCRT + Δp ' 2
(3)
where: Kj represents the weighting coefficients; p - the sum of points gained by that element; ǻp - the difference between the score of the element used and the score of the element on the last place; m - the number of surpassed criteria, namely the number of criteria with a lower score than those of respective element; NCRT - the number of criteria used; ǻp’ - the difference between the score of the element used and the score of the element on the first place (negative value). In order to establish the importance level compared to the other criteria, the criteria shall be ordered according to their score. Each of them shall have a number for the importance level, corresponding to the place taken in this ranking table. If two or more criteria gain the same number of points, the number of the place taken shall be the same place and it shall be calculated as the arithmetic mean of the places taken by these criteria [11].
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Step 6: Normalizing the importance coefficients corresponding to the decision-making criteria. The normalization of importance coefficients is made by dividing the obtained value by one of the importance coefficients with the sum of the importance coefficients’ values. It is obvious that in this case the sum of normalized importance coefficients is 1.
kj* =
kj
(4)
m
¦ kj j =1 m
Where [6]
¦ kj* = 1 . j =1
Step 7: Calculating the concordance coefficients and filling in the concordance coefficients matrix. The calculation of concordance correlation coefficients “c*” is made based on the following formula [8]: m
c * (Vi, Vl ) = ¦ (Ui − Ul ) ⋅ kj *
(5)
j =1
After being calculated, the concordance correlation coefficients shall be written in the concordance correlation coefficients matrix, and then, we shall determine for each line the minimum value of the concordance correlation coefficients [6]. Step 8: Calculating the discordance coefficients and filling in the discordance coefficients matrix. If the sum of importance coefficients “Kj” is higher than 1, then we have a simplified instance of the algorithm, as we can notice that [8]:
d * (Vi,Vl ) = c * (Vl,Vi)
(6)
where: d* represents the deviation coefficients. The elements of the lines of concordance correlation coefficients matrix become elements of the columns of deviation coefficients matrix. After the deviation coefficients matrix is completed, we shall determine for each line the maximum value of deviation coefficients [6]. Step 9: Filling in the matrix of differences between the concordance coefficients and the discordance coefficients and establishing the top of alternatives. We shall build a matrix similar to the concordance correlation coefficients matrix and deviation coefficients matrix, where the values of the new matrix are the result of the difference between the two matrixes mentioned above, using the following formula [6].
Δ ≡ max i(c * (Vi,Vl )) − min i(d * (Vi,Vl )
(7)
The ranking of the alternatives shall be made arranging in decreasing order the values calculated in the matrix of the differences between the concordance correlation coefficients and deviation coefficients. Step 10: Choosing the optimal alternative. The optimal alternative shall be the one for which we calculate the highest value for the differences between the concordance correlation coefficients and deviation coefficients [6].
max Δ max optimal ranking
(8)
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3. Results and discussions 3.1. Results The final results are mentioned in the case study regarding the selection of the concentration ratio of solar radiation for the photovoltaic panels. In order to solve this case study, we shall take the ten hereinabove mentioned steps, while the calculations are performed based on formula 1-8. For this case study, the set of alternatives is specified in Table 1, the set of decision criteria is specified in Table 2, and the performances obtained for each alternative according to the decision criteria are specified in Table 3. In this case study, the data from table 1, table 2 and table 3 have been taken over directly from paper [14]. Table 1. The set of alternatives [15]. No.
Alternative’s symbol
Description
1
A1
1X Photovoltaic system
2
A2
3X Photovoltaic system
3
A3
300X Photovoltaic system
4
A4
1000X Photovoltaic system
5
A5
3000X Photovoltaic system
Table 2. The set of decision criteria [15]. MU
Status (maximization or minimization)
Photovoltaic cell surface necessary to produce 1 kWh of electric power
cm2
Minimization Maximization
No.
Criterion’s symbol
Criterion description
1
C1
2
C2
Capacity/surface ration, for the photovoltaic cell
Wh/cm2
3
C3
Cost of the photovoltaic cell
€/Wh
Minimization
4
C4
Photovoltaic cell cost / system cost ratio
%
Minimization
Table 3. Consequence matrix [15]. No.
1
Criterion’s symbol
MU
2
Alternative’s symbol A1
A2
A3
A4
A5
C1
cm
71,428.571
23,809.524
72,464
22,727
8,772 114.000
2
C2
Wh/cm2
0.014
0.042
13.800
44.000
3
C3
€/Wh
0.650
0.400
0.478
0.125
0.063
4
C4
%
1.538
3.000
3.555
13.600
27.105
Based on the utility matrix and on the relation no. 5, we determined the concordance coefficients, and the data were transcribed in the concordance coefficients’ matrix (Table 4). Table 4. Concordance coefficients’ matrix. A1 A1
A2
A3
A4
A5
Minim
0.0178
0.0246
0.1471
0.3117
0.0178
A2
0.2786
A3
0.2879
0.0649
0.0623
A4
0.5704
0.2919
0.2825
A5
0.6883
0.4097
0.4004
0.1293
0.2939
0.0623
0.1225
0.2872
0.0649
0.1647
0.1647
0.1178
0.1178
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George Sebastian Naghiu et al. / Procedia Technology 22 (2016) 773 – 780
Based on the utility matrix and by using relation no. 6, we also determined the discordance coefficients, and the data were transcribed in the discordance coefficients’ matrix (Table 5). Table 5. Discordance coefficients’ matrix. A1 A1
A2
A3
A4
A5
Maxim
0.2786
0.2879
0.5704
0.6883
0.6883
0.0649
0.2919
0.4097
0.4097
A2
0.0178
A3
0.0246
0.0623
A4
0.1471
0.1293
0.1225
A5
0.3117
0.2939
0.2872
0.2825
0.4004
0.4004
0.1178
0.1471
0.1647
0.3117
Based on the hereinabove mentioned methodology, we finally calculated the differences between the concordance correlation coefficients and deviation coefficients based on formula 7, and we put the results in Table 6. The ranking of technical solutions was made by arranging in decreasing order the value of the differences between the concordance correlation coefficients and deviation coefficients. Table 6. The matrix of differences between the concordance correlation coefficients and deviation coefficients. Alternative’s symbol
Minimum value of concordance
Maximum value of deviation
Difference - D
Rank
A1
0.0178
0.6883
-0.6704
5
A2
0.0623
0.4097
-0.3474
4
A3
0.0649
0.4004
-0.3355
3
A4
0.1647
0.1471
0.0176
1
A5
0.1178
0.3117
-0.1939
2
According to the relation 8 the optimal alternative is that alternative for which one obtains the maximum differences between the concordance coefficients and the discordance coefficients, and in this case it is alternative A4. The results are suggestively presented in Fig. 1.
Delta difference
0,1000 0,0000 -0,1000 -0,2000 -0,3000 -0,4000 -0,5000 -0,6000 -0,7000 -0,8000
A1
A2
A3
A4
A5
Alternative
Fig. 1. Differences between the concordance coefficients and the discordance coefficients.
3.2. Discussions Analyzing the results and the ranking detailed in Table 6, as well as the data mentioned in Fig. 1, we may notice that:
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George Sebastian Naghiu et al. / Procedia Technology 22 (2016) 773 – 780
• • • • •
on the first place there is alternative A4, namely the technical solution with a 1000X photovoltaic system; on the second place there is alternative A5, namely the technical solution with a 3000X photovoltaic system; on the third place there is alternative A3, namely the technical solution with a 300X photovoltaic system; on the fourth place there is alternative A2, namely the technical solution with a 3X photovoltaic system; on the fifth place there is alternative A1, namely the technical solution with a 1X photovoltaic system. Therefore, based on the calculation algorithm, eventually one obtains the following classification: A4 P A5 P A3 P A2 P A1. When establishing the top of alternatives, the only subjective element is the establishment of the weights of the importance coefficients corresponding to the decision-making criteria. 4. Conclusions As a result of the above calculations, it is reccomended the implementation in practice of the alternative A4, namely the technical solution with a 1000X photovoltaic system. Considering that when establishing the top of alternatives by applying the ELECTRE-Boldur method the final result may be influenced by the weights of the importance coefficients corresponding to the decision-making criteria, in order to eliminate this inconvenient, in our paper we established the importance coefficients corresponding to the decision-making criteria based on the Frisco formula. As we already mentioned above, this paper tries to fill a gap in the field of selection between different photovoltaic systems from the point of view of concentration ratio. References
[1] Best research-cell efficiencies [image on the Internet]. Available from: http://www.nrel.gov/ncpv/images/efficiency_chart.jpg. [2] NREL. NREL Demonstrates 45.7% Efficiency for Concentrator Solar Cell New design for ultra-efficient III-V multijunction cell pushes the limits of solar conversion, News Release NR-4514 [Internet]. 2014 [updated 2014 December 16; cited 2015 June 17]. Available from: http://www.nrel.gov/news/press/2014/15436.html. [3] Ilina M, Lungu C. Analiza structurii sortimentale úi a calităĠii microcentralelor termice (The analysis of assortment and quality heating boilers). Buletin Informativ - Radet 2000; 1:19-22. [4] Carmen NC, Sofia EC, Stefan B. An AHP approach to evaluate the implementation of WEEE management systems. In: GavriluĠă N, Răducanu R, Iliescu M, Costin H, Mastorakis N, Olej V, Strouhal J, editors. Recent Researches in Environment, Energy Planning and Pollution. Iaúi, România. Athens: WSEAS Press; 2011. p. 233-8. [5] Munteanu A. Optimizarea constructivă a reĠelei electrice de distribuĠie din incinta consumatorului (Optimizing design of electric distribution network inside the consumer) [PhD thesis]. Cluj-Napoca: Universitatea Tehnică din Cluj-Napoca; 2003. [6] Cârlan M, Oltean M, Bendea C, AlbuĠ D, Blaga A., Sas A. Adopting an optimal maintenance strategy by using multicriterial decisional models. Journal of Sustenable Energy 2010;1(1). [7] ùuteu S. Modele de fundamentare a deciziilor. Suport de curs (Models for Substantiating Decisions. Lecture) [monograph online]. ClujNapoca: Universitatea Tehnică din Cluj-Napoca; 2007. p. 18-20 [cited 2015 June 17]. Available from: NetLibrary. [8] Dobre I, Bădescu AV. Modelarea deciziilor economico-financiare (Modeling of economic and financial decisions) [monograph online]. Bucureúti: Academia de Studii Economice din Bucureúti; 2002 [cited 2015 June 17]. Available from: NetLibrary. [9] Ogarca G. Metode úi tehnici de perfecĠionare a abordării deciziilor în întreprinderile din industria panificaĠiei din zona Oltenia (Methods and techniques to improve decision approach in the bakery industry enterprises Oltenia) [PhD thesis]. Bucureúti: Academia de Studii Economice din Bucureúti; 2007. p. 241-2. [10] Petca I. Curs Management (Management Course) [internet]. Sibiu: Academia ForĠelor Terestre din Sibiu; nd. Partea V - Luarea deciziilor în organizaĠia militară (5th Part - Decision making process in the military organization). [cited 2009 December 03]. Available from: http://www.actrus.ro. [11] Cruceru R, Ciobanu I. Analiza multi-criterială a unor investiĠii în turismul românesc (Multi-criteria analysis of an investment in Romanian tourism). Revista Recent 2008; Vol. 9, No. 1 (22):30-1. [12] Boomer J. Finding out what knowledge management is-and isn’t. Accounting Today 2004; 18(14):9-22. [13] Grecu V, Chiliban BM, Kifor C-V, Oprean C. An ict system for decisional support în university management. In: International Conference on Engineering & Business Education, Innovation and Entrepreneurship. Windhoek: Polytechnic of Namibia; 2013. p. 15-22. [14] Bobancu ù. Creativitate úi inventică. Curs (Creativity and invention. Course). Braúov: Editura UniversităĠii Transilvania; 2009. p. 63. [15] Naghiu G, Giurca I. Analiza multicriterială privind alegerea raportului de concentrare a radiaĠiei solare (Multi-criteria analysis regarding the selection of concentration ratio of solar radiation). In: Badea G, editors. ConferinĠa ùtiinĠa Modernă úi Energia. Cluj-Napoca: Risoprint; 2015. p. 207-17.
ScienceDirect Procedia Technology 22 (2016) 773 – 780
9th International Conference Interdisciplinarity in Engineering, INTER-ENG 2015, 8-9 October 2015, Tirgu-Mures, Romania
Multicriterial Analysis on Selecting Solar Radiation Concentration Ration for Photovoltaic Panels Using Electre-Boldur Method George Sebastian Naghiua, Ioan Giurcaa,*, Ioan Aúchileanb, Gheorghe Badeaa a
Technical University of Cluj-Napoca, Faculty of Building Services Engineering, Boulevard December 21, no. 128-130, Cluj-Napoca, 400604, Romania b SC ACI Cluj SA, Avenue DorobanĠilor, no. 70, Cluj-Napoca, 400609, Romania
Abstract The selection of the optimal solution regarding the concentration ratio is a complex process, as it depends on a very high number of criteria. The production of renewable energy using the concentrated solar radiation is a field of high scientific level worldwide, while in Romania the research in this field is only in its early stages. The purpose of this document is to present a classification method for photovoltaic systems taking into account the concentration ration. The paper tries to fill in a gap in the field of choosing the photovoltaic systems from the concentration ratio perspective. Based on the study performed, we recommend using the variant A4, namely the technical solution consisting of a photovoltaic system with a 1000x concentration ratio. © by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license © 2016 2016The TheAuthors. Authors.Published Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the “Petru Maior” University of Tirgu-Mures, Faculty of Engineering. Peer-review under responsibility of the “Petru Maior” University of Tirgu Mures, Faculty of Engineering Keywords: photovoltaic energy; photovoltaic systems; multi-criteria methods; Electre method; Electre-Boldur method.
1. Introduction 1.1. Context The emergence of the new type of high-performance multi-junction photovoltaic cells, which allows the efficient conversion of concentrated solar radiation separately for the spectrum components, led to the development of
* Corresponding author. Tel.: +40-0723 371 760. E-mail address: [email protected]
2212-0173 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the “Petru Maior” University of Tirgu Mures, Faculty of Engineering doi:10.1016/j.protcy.2016.01.048
774
George Sebastian Naghiu et al. / Procedia Technology 22 (2016) 773 – 780
photovoltaic systems specific for these cells. The selection of the optimal solution regarding the concentration ratio of the photovoltaic panels is a complex process, as it depends on a very high number of criteria, such as: the efficiency of the photovoltaic cell at different concentration ratios, the cost of photovoltaic cell, the amount of the costs of photovoltaic cell compared to the total cost of the system, the cost of the land required for the investment, etc. 1.2. The current stage of international research The production of renewable energy using the concentrated solar radiation is a field of high scientific level worldwide. The technology level in this field is a very advanced one, while research is performed in order to optimize and decrease the investment costs and also the output energy costs, together with the decrease of the land areas required for the installation of photovoltaic panels. According to the data provided by National Renewable Energy Laboratory from United States of America [1], one can find on the market about 30 different types of photovoltaic cells, having an efficiency between 9.2% - 45,7% and concentration ratio between 1% - 1024% [2], thus noticing an highly increased dynamic of the research results in this field during the last years. 1.3. The current stage of Romanian research In Romania, the research in this field is in its early ages. It is expected the research to be increased in the years to come, taking into consideration the high development potential of the concentrated photovoltaic systems, due to the accelerated increase of the multi-junction photovoltaic cells’ efficiency. The main individual criterion and multi-criteria methods used for substantiating the decision in the field of fittings for construction are the following: the method of ordinal individual criterion ranks, the method of ordinal multi-criteria ranks, the method of real ranks, the method of the complex quality index, the method of the complex quality and economic efficiency index, the global performance assessment method, the utility method, maximum score method [3], optimal degree of foreign ownership under uncertainty method, the relative distance comparison model in relation with the maximum performance, the relative distance comparison model in relation with the average performance, advanced multi criteria analysis, comparative analysis method, the AHP method [4], the Electre method [5], Electre-Boldur method [6], the Onicescu method, the Promethee method. 1.4. The purpose described in the article The purpose of this document is to present a classification method for photovoltaic systems taking into account the concentration ration. We wish to be able to use this method as a research and innovation tool, useful for selecting the optimal system during the stage of technological development of the new photovoltaic systems and during the stage of development of the opportunity and feasibility studies, and of the business plans on the development of new production capacities of photovoltaic energy. 1.5. The added value of the present article This paper tries to fill a gap in the field of selection of the photovoltaic systems considering the concentration ratio criterion. Nomenclature P X
an alternative is preferred to another one Number of suns (or the concentration ratio of the solar radiation incident on the surface of the PV cell)
George Sebastian Naghiu et al. / Procedia Technology 22 (2016) 773 – 780
2. Materials and methods 2.1. Materials Nowadays, on the market, there are a lot of photovoltaic systems, thus both the designer and the beneficiary found it difficult to choose the photovoltaic systems. These difficulties are caused, on the one hand, by the diverse range of products on the market, and on the other hand by their different technical performances, as well as by the different investment and operation costs. In this context, in this paper we analyze the following technical solutions: • • • • •
photovoltaic system with 1X concentration factor, alternative A1; photovoltaic system with 3X concentration factor, alternative A2; photovoltaic system with 300X concentration factor, alternative A3; photovoltaic system with 1000X concentration factor, alternative A4; photovoltaic system with 3000X concentration factor, alternative A5.
Pursuant to the analysis of the five photovoltaic systems, one notices that these photovoltaic systems consist of different components, which obviously hampers the analysis process of the technical solutions. Also, pursuant to the analysis of the five photovoltaic systems, one notices that these photovoltaic systems have their advantages and disadvantages, therefore the various alternatives must be very carefully analyzed. Considering that the various photovoltaic systems have different components, considering that they have a series of advantages and disadvantages, and considering that they have different investment and operation costs, in practice both designers and beneficiaries encounter problems when it comes to select photovoltaic systems. In this context, when selecting photovoltaic systems, we propose: • • • •
to minimize the surface of photovoltaic cells for the production of 1 kWh of electricity, criterion C1; to maximize the ratio capacity/surface for the photovoltaic cell, criterion C2; to minimize the cost of the photovoltaic cell, criterion C3; to minimize the ratio between the cost of the photovoltaic cell / the cost of the photovoltaic system, criterion C4.
2.2. Methods In this paper, the technical criteria shall be chosen based on the ELECTRE-Boldur Method. ELECTRE acronym stands for the initials of the method’s name: ELimination Et Choix Traduisent la REalité {Elimination and Choice Expressing Reality} [7]. The ELECTRE Method was elaborated in 1965, at S.E.M.A. Paris (Societe d'Economie et de Mathematique Appliquees), by a team of French researchers led by B. Roy. The ELECTRE-Boldur Method was proposed by teacher Gheorge Boldur-LăĠescu. In order to simplify and make the method operational in the meaning of the theory of utility, the author proposed the use of certain normalized concordance and discordance coefficients. These coefficients, marked c*(.,.), d*(.,.) are calculated based on utilities “Uij” estimated for the consequences “aij” from the decision/making matrix ’’A’’, according to the procedure Neumann-Morgenstern [8]. In our opinion, applying the ELECTRE-Boldur method involves ten steps, as presented below: Step 1: Establishing the decision-making variants. In this stage, the set of alternatives that can be applied shall be identified, while the data shall be written in the alternatives matrix A = [Ai]. Where i = 1...n, represents the number of alternatives. Step 2: Establishing the decision-making criteria. Here we shall identify the criteria (objectives) that shall be used for the selection of the alternatives, while the data shall be written in the decision criteria matrix C = [Cj]. Where j = 1...m, represents the number of criteria. Step 3: Filling in the performance matrix, where the performance of the alternatives shall be identified for each criterion, and the data shall be written in the performance matrix P = [Pij].
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Step 4: Calculating the utilities and filling in the utility matrix. The calculation of utilities shall be made based on the performance of alternatives while using the method created by von Neumann and O. Morgenstern in 1947 [9]. One shall estimate the utility for each criterion alone or for the entire decision table, thus obtaining the multicriterion utility matrix U = [Uij] [8]. Depending on the nature of the criteria, the utilities will be calculated according to the following formulas [10]: Maximizing criteria:
uij =
aij − a min j a max j − a min j
(1)
Minimizing criteria:
uij =
a max j − aij a max j − a min j
(2)
Where: uij represents the usability of the i variant according to the j criterion; amax j - the maximum performance obtained by the analyzed variants, according to the j criterion; amin j - the minimum performance obtained by the analyzed variants, according to the j criterion; aij - the performance obtained by the i variant according to the j criterion. One utility corresponds to each consequence [10]. Step 5: Establishing the importance coefficients corresponding to the decision-making criteria. An importance coefficient, Kj, shall be associated to each criterion “j” [6]. The criteria set for the comparative analysis of objects, objectives, projects or activities usually don’t have the same importance. The quantization of the importance (ratio) of the criteria is made by the calculation of some “weighting coefficients” Kj. It begins with a qualitative analysis of the criteria, by comparing every two criteria and establishing which of them is more important [11]. Then, the importance factors are set based on FRISCO formula, elaborated by a well-known creation group based in San Francisco - U.S.A., which was acknowledged worldwide as being the most performing one and widespread used [12-14].
kj =
p + Δp + m + 0,5 NCRT + Δp ' 2
(3)
where: Kj represents the weighting coefficients; p - the sum of points gained by that element; ǻp - the difference between the score of the element used and the score of the element on the last place; m - the number of surpassed criteria, namely the number of criteria with a lower score than those of respective element; NCRT - the number of criteria used; ǻp’ - the difference between the score of the element used and the score of the element on the first place (negative value). In order to establish the importance level compared to the other criteria, the criteria shall be ordered according to their score. Each of them shall have a number for the importance level, corresponding to the place taken in this ranking table. If two or more criteria gain the same number of points, the number of the place taken shall be the same place and it shall be calculated as the arithmetic mean of the places taken by these criteria [11].
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Step 6: Normalizing the importance coefficients corresponding to the decision-making criteria. The normalization of importance coefficients is made by dividing the obtained value by one of the importance coefficients with the sum of the importance coefficients’ values. It is obvious that in this case the sum of normalized importance coefficients is 1.
kj* =
kj
(4)
m
¦ kj j =1 m
Where [6]
¦ kj* = 1 . j =1
Step 7: Calculating the concordance coefficients and filling in the concordance coefficients matrix. The calculation of concordance correlation coefficients “c*” is made based on the following formula [8]: m
c * (Vi, Vl ) = ¦ (Ui − Ul ) ⋅ kj *
(5)
j =1
After being calculated, the concordance correlation coefficients shall be written in the concordance correlation coefficients matrix, and then, we shall determine for each line the minimum value of the concordance correlation coefficients [6]. Step 8: Calculating the discordance coefficients and filling in the discordance coefficients matrix. If the sum of importance coefficients “Kj” is higher than 1, then we have a simplified instance of the algorithm, as we can notice that [8]:
d * (Vi,Vl ) = c * (Vl,Vi)
(6)
where: d* represents the deviation coefficients. The elements of the lines of concordance correlation coefficients matrix become elements of the columns of deviation coefficients matrix. After the deviation coefficients matrix is completed, we shall determine for each line the maximum value of deviation coefficients [6]. Step 9: Filling in the matrix of differences between the concordance coefficients and the discordance coefficients and establishing the top of alternatives. We shall build a matrix similar to the concordance correlation coefficients matrix and deviation coefficients matrix, where the values of the new matrix are the result of the difference between the two matrixes mentioned above, using the following formula [6].
Δ ≡ max i(c * (Vi,Vl )) − min i(d * (Vi,Vl )
(7)
The ranking of the alternatives shall be made arranging in decreasing order the values calculated in the matrix of the differences between the concordance correlation coefficients and deviation coefficients. Step 10: Choosing the optimal alternative. The optimal alternative shall be the one for which we calculate the highest value for the differences between the concordance correlation coefficients and deviation coefficients [6].
max Δ max optimal ranking
(8)
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3. Results and discussions 3.1. Results The final results are mentioned in the case study regarding the selection of the concentration ratio of solar radiation for the photovoltaic panels. In order to solve this case study, we shall take the ten hereinabove mentioned steps, while the calculations are performed based on formula 1-8. For this case study, the set of alternatives is specified in Table 1, the set of decision criteria is specified in Table 2, and the performances obtained for each alternative according to the decision criteria are specified in Table 3. In this case study, the data from table 1, table 2 and table 3 have been taken over directly from paper [14]. Table 1. The set of alternatives [15]. No.
Alternative’s symbol
Description
1
A1
1X Photovoltaic system
2
A2
3X Photovoltaic system
3
A3
300X Photovoltaic system
4
A4
1000X Photovoltaic system
5
A5
3000X Photovoltaic system
Table 2. The set of decision criteria [15]. MU
Status (maximization or minimization)
Photovoltaic cell surface necessary to produce 1 kWh of electric power
cm2
Minimization Maximization
No.
Criterion’s symbol
Criterion description
1
C1
2
C2
Capacity/surface ration, for the photovoltaic cell
Wh/cm2
3
C3
Cost of the photovoltaic cell
€/Wh
Minimization
4
C4
Photovoltaic cell cost / system cost ratio
%
Minimization
Table 3. Consequence matrix [15]. No.
1
Criterion’s symbol
MU
2
Alternative’s symbol A1
A2
A3
A4
A5
C1
cm
71,428.571
23,809.524
72,464
22,727
8,772 114.000
2
C2
Wh/cm2
0.014
0.042
13.800
44.000
3
C3
€/Wh
0.650
0.400
0.478
0.125
0.063
4
C4
%
1.538
3.000
3.555
13.600
27.105
Based on the utility matrix and on the relation no. 5, we determined the concordance coefficients, and the data were transcribed in the concordance coefficients’ matrix (Table 4). Table 4. Concordance coefficients’ matrix. A1 A1
A2
A3
A4
A5
Minim
0.0178
0.0246
0.1471
0.3117
0.0178
A2
0.2786
A3
0.2879
0.0649
0.0623
A4
0.5704
0.2919
0.2825
A5
0.6883
0.4097
0.4004
0.1293
0.2939
0.0623
0.1225
0.2872
0.0649
0.1647
0.1647
0.1178
0.1178
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Based on the utility matrix and by using relation no. 6, we also determined the discordance coefficients, and the data were transcribed in the discordance coefficients’ matrix (Table 5). Table 5. Discordance coefficients’ matrix. A1 A1
A2
A3
A4
A5
Maxim
0.2786
0.2879
0.5704
0.6883
0.6883
0.0649
0.2919
0.4097
0.4097
A2
0.0178
A3
0.0246
0.0623
A4
0.1471
0.1293
0.1225
A5
0.3117
0.2939
0.2872
0.2825
0.4004
0.4004
0.1178
0.1471
0.1647
0.3117
Based on the hereinabove mentioned methodology, we finally calculated the differences between the concordance correlation coefficients and deviation coefficients based on formula 7, and we put the results in Table 6. The ranking of technical solutions was made by arranging in decreasing order the value of the differences between the concordance correlation coefficients and deviation coefficients. Table 6. The matrix of differences between the concordance correlation coefficients and deviation coefficients. Alternative’s symbol
Minimum value of concordance
Maximum value of deviation
Difference - D
Rank
A1
0.0178
0.6883
-0.6704
5
A2
0.0623
0.4097
-0.3474
4
A3
0.0649
0.4004
-0.3355
3
A4
0.1647
0.1471
0.0176
1
A5
0.1178
0.3117
-0.1939
2
According to the relation 8 the optimal alternative is that alternative for which one obtains the maximum differences between the concordance coefficients and the discordance coefficients, and in this case it is alternative A4. The results are suggestively presented in Fig. 1.
Delta difference
0,1000 0,0000 -0,1000 -0,2000 -0,3000 -0,4000 -0,5000 -0,6000 -0,7000 -0,8000
A1
A2
A3
A4
A5
Alternative
Fig. 1. Differences between the concordance coefficients and the discordance coefficients.
3.2. Discussions Analyzing the results and the ranking detailed in Table 6, as well as the data mentioned in Fig. 1, we may notice that:
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• • • • •
on the first place there is alternative A4, namely the technical solution with a 1000X photovoltaic system; on the second place there is alternative A5, namely the technical solution with a 3000X photovoltaic system; on the third place there is alternative A3, namely the technical solution with a 300X photovoltaic system; on the fourth place there is alternative A2, namely the technical solution with a 3X photovoltaic system; on the fifth place there is alternative A1, namely the technical solution with a 1X photovoltaic system. Therefore, based on the calculation algorithm, eventually one obtains the following classification: A4 P A5 P A3 P A2 P A1. When establishing the top of alternatives, the only subjective element is the establishment of the weights of the importance coefficients corresponding to the decision-making criteria. 4. Conclusions As a result of the above calculations, it is reccomended the implementation in practice of the alternative A4, namely the technical solution with a 1000X photovoltaic system. Considering that when establishing the top of alternatives by applying the ELECTRE-Boldur method the final result may be influenced by the weights of the importance coefficients corresponding to the decision-making criteria, in order to eliminate this inconvenient, in our paper we established the importance coefficients corresponding to the decision-making criteria based on the Frisco formula. As we already mentioned above, this paper tries to fill a gap in the field of selection between different photovoltaic systems from the point of view of concentration ratio. References
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