An integrated multi-objective optimization model for determining the optimal solution in implementing the rooftop photovoltaic system

Renewable and Sustainable Energy Reviews 57 (2016) 822–837

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

An integrated multi-objective optimization model for determining the optimal solution in implementing the rooftop photovoltaic system Choongwan Koo a,b, Taehoon Hong b,n, Minhyun Lee b, Jimin Kim b a b

Division of Construction Engineering and Management, Purdue University, West Lafayette, IN 47906, United States Department of Architectural Engineering, Yonsei University, Seoul 03722, Republic of Korea

art ic l e i nf o

a b s t r a c t

Article history: Received 29 May 2014 Received in revised form 7 September 2015 Accepted 18 December 2015

The photovoltaic (PV) system has been highlighted as a sustainable clean energy source. To successfully implement the PV system in a real project, several impact factors should be simultaneously considered. This study aimed to develop an integrated multi-objective optimization (iMOO) model for determining the optimal solution in implementing the rooftop PV system. This study was conducted in six steps: (i) establishment of database; (ii) generation of the installation scenarios in the rooftop PV system; (iii) energy simulation using the software program 'RETScreen'; (iv) economic and environmental assessment from the life cycle perspective; (v) establishment of the iMOO process using a genetic algorithm; and (vi) systemization of the iMOO model using a Microsoft-Excel-based VBA. Two criteria were used to assess the robustness and reliability of the developed model. In terms of effectiveness, the optimal solution was determined from a total of 399,883,120 ( ¼91  49  19  80  59) possible scenarios by comprehensively considering various factors. In terms of efficiency, it was concluded that the time required for determining the optimal solution was 150 s. The developed model makes it possible for final decision-maker such as construction managers or contractors to determine the optimal solution in implementing the rooftop PV system in the early design phase. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Rooftop photovoltaic system Existing building Integrated multi-objective optimization Trade-off problem Genetic algorithm Economic and environmental assessment

Contents 1. 2.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 2.1. Reviews on the impact factors of the rooftop PV system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 2.2. Reviews on the optimization objectives of the rooftop PV system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 824 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825 3.1. Step 1: establishment of database . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825 3.2. Step 2: generation of the installation scenarios in the rooftop photovoltaic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826 3.3. Step 3: energy simulation using the software program 'RETScreen' . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826 3.4. Step 4: economic and environmental assessment from the life cycle perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827 3.5. Step 5: establishment of an integrated multi-objective optimization using a genetic algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827 3.6. Step 6: systemization of the iMOO model using a Microsoft-Excel-based VBA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827 Model application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828 Results and discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 5.1. Generation of the installation scenarios in the rooftop photovoltaic system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 5.2. Validation of the simulated electricity generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 5.3. Economic and environmental assessment from the life cycle perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 5.4. Determination of the optimal solution in the iMOO model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 5.4.1. Optimization results in the iMOO model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 5.4.2. Trade-off analysis between the target variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831 5.4.3. Comparison chart for intuitive decision-making . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 833

Correspondence to: Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea. Tel.: þ 82 2 2123 5788; fax: þ 82 2 365 4668. E-mail address: [email protected] (T. Hong).

http://dx.doi.org/10.1016/j.rser.2015.12.205 1364-0321/& 2015 Elsevier Ltd. All rights reserved.

C. Koo et al. / Renewable and Sustainable Energy Reviews 57 (2016) 822–837

6. Conclusions . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . Appendix A. . Acronyms . . . . . . . . . . . . . . Appendix A. Supplementary material. References . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction The rapid increase in the use of fossil fuels has caused energy depletion and environmental pollution. World primary energy consumption in 2010 registered a 5.6% increase, which was the highest rate since 1973. If the annual increase rate of energy consumption is assumed to be 1.4% from 2008 to 2035, some experts estimate that fossil fuel reserves will be fully depleted within 50 years [1–8]. To overcome this challenge, the interests in new renewable energy (NRE) have increased [9–12]. According to a press release, renewable energy power plants accounted for about 60% of newly installed power plants in the European Union and more than 50% in the United States [13–17]. In particular, a photovoltaic (PV) energy is expected to play an important role in renewable and sustainable energy development [18–22]. The interests in PV energy have rapidly increased in the wake of the nuclear-power-plant accident in Fukushima, Japan [23]. The PV market was only 7.2 GW in 2009, but it has increased more than twofold—to 16.6 GW in 2010. As of 2011, the installation capacity of global PV system went up to 40 GW [24–27]. In South Korea, various energy policies (such as Renewable Portfolio Standard and Renewable Energy Certificates) have been promoted to activate the distribution of the PV system [28–31]. In addition, PV system has greater potential in South Korea because South Korea is one of the leading countries in a semiconductor technology (which is related to crystalline silicon used in 94% of PV modules) [32]. Even if the PV system has several advantages (such as governmental financial support, the decreases in the unit cost of the PV system, and high potential as a sustainable clean energy source), its initial investment cost is still high, which has been an obstacle to its continuous growth. To overcome this challenge, it is required to analyze the whole life-cycle cost of a potential PV system before its implementation. That is, based on the holistic analysis from the life-cycle perspective, a final decision-maker (e.g., owner, construction manager, designer, and contractor) should be able to determine whether or not the economic feasibility of the PV system can be achieved. To do this, one of the most significant steps is to estimate the amount of electricity generation from the PV system. There are several impact factors that should be considered in estimating the amount of electricity generation from the PV system, which include (i) the regional climates (i.e., the geographical factors such as latitude and monthly meridian altitude, and the meteorological factors such as monthly average daily solar radiation (MADSR) and monthly average temperature) and (ii) the building characteristics (i.e., the azimuth of the installed panel (AoP), the slope of the installed panel (SoP), and the rooftop area limit). In addition, it is required to take into account the regulation such as the Mandatory Renewable Energy Installation Program (which makes it compulsory to supply over 10% of energy consumptions in a public building as the minimum electricity generation limit). As mentioned above, in order to determine the economic feasibility of the PV system before its implementation, it is necessary to consider the various impact factors affecting the amount of annual electricity generation (AEG) from the PV system as well as its initial investment cost (IIC) with government subsidy. In addition, in order to conduct the whole life-cycle cost analysis on

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834 834 834 835 835

the PV system from the various perspectives, it is required to analyze the net present value (NPV) as an absolute index and the saving-to-investment ratio (SIR) as a relative index. As such, there are several objectives that should be considered in implementing the PV system (i.e., the IIC, the AEG, the NPV, the SIR, and the AEG per unit panel (AEG/EA)), which have the trade-off relationships. In order to analyze the complex relationships among the several objectives, the research team has conducted a series of studies. First, Hong et al. [33] developed a GIS (geographic information system)-based optimization model for estimating the amount of electricity generation from the rooftop PV System. This study conducted a comprehensive sensitivity analysis on how the AEG/ EA in the rooftop PV system depended on the complex correlations among the impact factors. Based the results, this study finally developed a GIS-based optimization model for estimating the AEG/EA in the rooftop PV system. The results showed that (i) a 1.12-fold difference in the AEG depended on the regional climates; (ii) a 1.62-fold difference in the AEG depended on the AoP; and (iii) a 1.37-fold difference in the AEG depended on the SoP. Second, Koo et al. [34] developed an economic and environmental optimization model for a rooftop PV system by implementing various processes and the associated equations. The results showed that as follows: (i) the number of the installed panels (NoP) depended on the type of the panel (ToP) and the SoP, which resulted in the different the IIC, the AEG, the NPV, the SIR, and the AEG/EA; (ii) a trade-off relationship between the NPV and the SIR occurred in the specific zone. Based on the previous studies conducted by the research team, it can be concluded that several types of parameters should be simultaneously considered to analyze the economic feasibility of the PV system. That is, a multi-objective optimization problem should be well defined in a dynamic, complex, and multidimensional decision space. Therefore, this study aimed to develop an integrated multi-objective optimization (iMOO) model for solving the aforementioned trade-off problems, which makes it possible to determine the optimal solution in implementing the PV system. Using the optimal solution, this study can achieve the five objectives: (i) minimization of the IIC (with government subsidy); (ii) maximization of the AEG; (iii) maximization of the NPV; (iv) maximization of the SIR; and (v) maximization of the AEG/EA.

2. Literature review 2.1. Reviews on the impact factors of the rooftop PV system There are a lot of impact factors affecting the amount of electricity generation from the PV system, which should be considered to determine the optimal solution in implementing the rooftop PV system. Many previous studies on the PV system considered these impact factors [33–62], which can be categorized into two parts: (i) the regional climates (i.e., the geographical factors and the meteorological factors) and (ii) the building characteristics (i.e., the on-site installation factors, the rooftop area limit, and the budget limit). In particular, the previous studies have mainly focused on the building characteristics (e.g., the AoP and the SoP)

Gong and Kulkarni [50], Weinstock and Appelbaum [53], Farahat et al. [58]. Gong and Kulkarni [50], Spertino et al. [61], Dufo-Lopez et al. [62]. ()m US$ ( )

()

The type of the panel (ToP) and inverter (ToI) Width and length limit Budget limit Rooftop area limit Budget limit

()° The slope of the installed panel (SoP)

Building characteristics On-site installation factors The azimuth of the installed panel (AoP)

()°

()° ( ) kWh/m2/ day ( ) °C Monthly meridian altitude Monthly average daily solar radiation (MADSR) Monthly average temperature Meteorological factors

Hong et al. [33], Koo et al. [34], Hummon et al. [40], Levinson et al. [41], Siraki and Pillay [42], Tang and Wu [43], Tiris and Tiris [45], Weinstock and Appelbaum [53]. Hong et al. [33], Koo et al. [34], Kaldellis and Zafirakis [36]. Hong et al. [33], Koo et al. [34], Kaldellis and Zafirakis [36], Siraki and Pillay [42], Kesler et al. [44], Cucchiella and D’Adamo [46], Leloux et al. [47]. Hong et al. [33], Koo et al. [34], Leloux et al. [47], Braun et al. [56], Dincer and Meral [57], Farahat et al. [58], Hoffmann and Koehl [59]. Hong et al. [33], Koo et al. [34], Sánchez and Izard [35], Kaldellis and Zafirakis [36], Gunerhan and Hepbasli [37], Jafarkazemi and Saadabadi [38], Gopinathan et al. [39], Hummon et al. [40], Levinson et al. [41], Siraki and Pillay [42], Tang and Wu [43], Kesler et al. [44], Cucchiella and D’Adamo [46], Leloux et al. [47], Gómez-Gil et al. [48], Ubertini and Desideri [49], Gong and Kulkarni [50], Hussein et al. [51], Mousazadeh et al. [52], Weinstock and Appelbaum [53], Masa-Bote and Caamaño-Martín [54]. Hong et al. [19], Hong et al. [20], Hong et al. [33], Koo et al. [34], Kaldellis and Zafirakis [36], Gunerhan and Hepbasli [37], Jafarkazemi and Saadabadi [38], Hummon et al. [40], Siraki and Pillay [42], Tang and Wu [43], Kesler et al. [44], Tiris and Tiris [45], Leloux et al. [47], Gómez-Gil et al. [48], Ubertini and Desideri [49], Gong and Kulkarni [50], Hussein et al. [54], Mousazadeh et al. [52], Weinstock and Appelbaum [53], Masa-Bote and Caamaño-Martín [54], Drury et al. [55]. Kesler et al. [44], Cucchiella and D’Adamo [46], Leloux et al. [47], Gong and Kulkarni [50], Ordóñez et al. [60]. ( ) °N Latitude Regional climate

Geographical factors

Reference Unit

C. Koo et al. / Renewable and Sustainable Energy Reviews 57 (2016) 822–837

Impact factors

Table 1 Reviews on the impact factors of the rooftop PV system.

824

in order to investigate the performance of the rooftop PV system (refer to Table 1). First, some studies have been conducted to maximize the performance of the rooftop PV system by considering the AoP as the impact factor. Sánchez and Izard [35] explored the feasibility of the PV system with non-optimal AoP. The results showed that the southwest orientation had more stable electricity output throughout a year [35]. Second, other studies have been conducted to maximize the performance of the rooftop PV system by considering the SoP as the impact factor. Kaldellis and Zafirakis [36] conducted an experimental study to evaluate the performance of the PV system by considering the different SoP during the summer period in Greece. The results showed that the angle of 15° was determined to be the optimal value for the entire summer period in Athens area [36]. Gunerhan and Hepbasli [37] investigated the optimal SoP in implementing the solar collectors in Turkey. The results showed that the optimal SoP depended on the days of a year, and thus, it is recommended to adjust the SoP once a month [37]. Third, the others have been conducted to maximize the performance of the rooftop PV system by considering both the AoP and the SoP as the impact factor. Jafarkazemi and Saadabadi [38] evaluated the effect of the AoP on the optimal SoP and the solar radiation. The solar radiation was estimated within the range of the AoP (  90° to 90°) and the SoP (0° to 90°). The results showed that the optimal SoP changed as the AoP got away from the south, in order to absorb more solar radiation [38]. Gopinathan et al. [39] estimated the monthly mean daily global radiation on the PV system with the different values of the AoP (180°, 160°, 140°, 120°, and 100°) and the SoP (latitude 10°, latitude, latitude þ10°, latitude þ20°, and latitude þ30°) in three locations in the Southern Africa. The results showed that the optimal SoP in summer months was 10° less than the latitude for all orientations and the optimal SoP in winter months varied from latitude þ30° to latitude  10° depending on the AoP [39]. As mentioned above, several previous studies were conducted by considering the different values of the AoP and the SoP as the impact factor in implementing the PV system, however, they failed to fully examine the complex relationships between all of the impact factors including the rooftop area limit, the electricity generation limit, and the budget limit. In order to successfully implement the rooftop PV system in a real project, it is necessary to simultaneously consider the several impact factors mentioned above. 2.2. Reviews on the optimization objectives of the rooftop PV system A final decision-maker should be able to consider the various target values, i.e., the optimization objectives (e.g., the IIC, the AEG, the NPV, the SIR, and the AEG/EA) in order to determine the optimal solution in implementing the rooftop PV system. Several previous studies were conducted to achieve this goal [34,62–91], which can be categorized into two parts: (i) economic objectives (e.g., the IIC, the NPV, and the SIR) and (ii) environmental objectives (e.g., the AEG and the CO2 emissions) (refer to Table 2). First, some studies have been conducted to optimize the economic value in implementing the rooftop PV system. González et al. [63] used a genetic algorithm (GA) to determine the optimal sizing of hybrid grid-connected photovoltaic–wind power system, which focused on the minimization of the NPV in implementing the hybrid system. The results showed that hybrid system would be able to reach the payback period within 18 years [63]. Makhloufi (2015) compared the GA method with two classical methods (i.e. worst month method and loss of power supply probability method) in order to minimize the cost of the remote PV system. The results showed that the GA and worst month methods had similar optimization results when the SoP was set between 0° and 60°. However, the system using the worst month method was

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825

Table 2 Reviews on the optimization objectives of the rooftop PV system. Optimization objectives Economic objectives

Total system cost Initial investment cost (IIC) Total annual cost Life cycle cost

Environmental objectives System output pollutant emissions

Unit

Reference

US$ ( )

Makhloufi [64], Freitas et al. [66], Arabali et al. [73], Sheng et al. [74], Khatib et al. [75], Amer et al. [76]. Liu et al. [72], Maleki and Askarzadeh [77], Fetanata and Khorasaninejad [78], Shi et al. [79]. González et al. [63], Kornelakis [67], Zhao et al. [80], Kaabechea and Ibtiouen [81], Ma et al. [82], Sulaiman et al. [83], Ioannou et al. [84], Kamjoo et al. [85], Kornelakis and Marinakis [86], Sharafi and ELMekkawy [87]. Koo et al. [34].

US$ ( )

Net present value (NPV) US$ ( )

Saving to investment () ratio (SIR) Levelized cost of energy US$ ( ) /kW h Electricity generation ( ) kW h Pollutant emissions CO2 emissions Fuel emissions

( ) kg ( ) kg CO2 ( ) kg

designed larger than that using the GA method when the SoP was set over 60° [64]. Second, other studies have been conducted to optimize the environmental value in implementing the rooftop PV system. Bojić et al. [65] used EnergyPlus and GenOpt to determine the optimal SoP of the PV system, which focused on the maximization of the amount of electricity generation in four locations in France. This study analyzed the amount of electricity generation based on the number of the optimal tilts of the PV system, resulting that the amount of electricity generation from the PV system with two optimal tilts per year was larger than that from the PV system with the only one optimal tilt per year [65]. Third, the others have been conducted to simultaneously consider the economic and environmental values, which focuses on developing the multi-objective optimization model for the rooftop PV system. Freitas et al. [66] developed the multi-objective optimization model using a GA to optimize the layout of the PV system, which aimed to both maximize the AEG and minimizes the IIC. The results showed that the optimal PV layout had about 20% less energy cost compared to the conventional configuration [66]. Kornelakis [67] developed the multi-objective optimization model using Particle Swarm Optimization to determine the optimal design of the PV system, which aimed to both maximize the NPV and minimize the CO2 emissions. This study considered several adjustable variables such as the ToP, the type of the inverter (ToI), the SoP, and the placement of the PV modules [67]. As mentioned above, several previous studies were conducted by considering the various target values (i.e., the optimization objectives) in implementing the PV system, however, there still exist some limitations: (i) most of the previous studies only focused on either economic or environmental objectives at a time and (ii) even if some of the previous studies tried to consider both economic and environmental objectives at the same time, they only covered the single objective within a specific category (i.e., economic objective or environmental objective). However, from the economic perspective, it is required to simultaneously consider the absolute and relative values of the PV system. Similarly, from the environmental perspective, it is necessary to simultaneously cover the entire amount of electricity generation from the PV system as well as the amount of electricity generation from the unit PV panel.

3. Materials and methods To solve the trade-off problems in determining the optimal solution of the PV system, this study was conducted in six steps:

Dufo-López et al. [62], Amer et al. [76], Shi et al. [79], Ma et al. [82], Malheiro et al. [88]. Bojić et al. [65], Freitas et al. [66], Sulaiman et al. [83], Chao et al. [89], Ioannou et al. [84], Notton et al. [90], Saad et al. [91]. Zhao et al. [80]. Dufo-López et al. [62], Kornelakis [67]. Shi et al. [79].

(i) establishment of database; (ii) generation of the installation scenarios in the rooftop PV system; (iii) energy simulation using the software program 'RETScreen'; (iv) economic and environmental assessment from the life cycle perspective; (v) establishment of an integrated multi-objective optimization process using a genetic algorithm; and (vi) systemization of the iMOO model using a Microsoft-Excel-based Visual Basic for Applications (VBA) (refer to Fig. 1). Through an extensive literature review and interviews with experts in the field of PV systems of Parsons Brinckerhoff, Oerlikon Solar, and Hilti Corporation, this study established the database and the reference model for estimating the amount of electricity generation from the PV system. 3.1. Step 1: establishment of database As shown in Table 3, the database was established, which consists of two parts: (i) regional meteorological and geographical information; and (ii) physical information on the PV panels [92–95]. This information was used to generate the installation scenarios in step 2 and to conduct the energy simulation in step 3. First, this study collected the regional meteorological and geographical information for 16 administrative divisions in South Korea. The temporal scope of this study was established as of 2011.

 The regional MADSR was collected from New and Renewable Energy

 

Data Center [92] (refer to Supplementary Data, SD Table S1). For the region where the MADSR was not measured, the data from the geographically closest region was used; The regional monthly average temperature was collected from the Korea Meteorological Administration [93–94] (refer to SD Table S2); and, The regional latitude was collected from the geographical information provided by Google Earth™ and the meridian altitude at noon of winter solstice was calculated using Eq. (1) [95] (refer to SD Table S3).

τ ¼ 90 3  φ  ε

ð1Þ

where τ is the minimum incidence angle of the sun (the meridian altitude at noon of winter solstice by region), φ is the regional latitude, and ε is the tilt angle of the Earth's axis (23.5°). Second, this study collected the basic information on the panels and inverters in the rooftop PV system through market research (such as capacity, efficiency, miscellaneous losses, width, length, unit cost, repair cycle, and repair rate) (refer to SD Tables S4 and S5).

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C. Koo et al. / Renewable and Sustainable Energy Reviews 57 (2016) 822–837

Fig. 1 Research framework.

3.2. Step 2: generation of the installation scenarios in the rooftop photovoltaic system Based on the previous studies [33,34], which conducted the sensitivity analysis from two perspectives (i.e., the unit panel and the rooftop PV system), it was concluded that there were the complex correlations among the impact factors affecting the amount of electricity generation from the rooftop PV system. These impact factors can be divided into three categories: (i) defined parameters; (ii) adjustable parameters; and (iii) constraint parameters.

 Defined parameters: As the target building is selected, the 



defined parameters can be determined: (i) the region where the target building is located; and (ii) the AoP. Adjustable parameters: Various installation scenarios in the rooftop PV system can be generated by combining the adjustable parameters: (i) the SoP; (ii) the ToP; (iii) the ToI; (iv) the number of installed panels along the length of the rooftop area (NoP_L); and (v) the number of installed panels along the width of the rooftop area (NoP_W). Constraint parameters: Some scenarios should be excluded from all the possible scenarios in the rooftop PV system by considering the constraints: (i) rooftop length (RL); (ii) rooftop width (RW); (iii) minimum electricity generation limit (GL); and (iv) maximum budget limit (BL).

Considering three kinds of parameters simultaneously, this study can generate various installation scenarios in the rooftop PV

Table 3 Basic information affecting the electricity generation of the rooftop PV system. Main classification

Sub classification

Unit

Regional geographical information

Latitude Meridian altitude at noon of winter solstice Monthly average daily solar radiation (MADSR) Monthly average temperature Capacity Efficiency Miscellaneous losses Width Length

( ) °N ()°

Regional meteorological information Physical information on the photovoltaic panel

( ) kW h/ m2/day ( ) °C ()W ()% ()% ( ) mm ( ) mm

system. Based on the scenarios, this study conducted both the energy simulation in step 3 and the LCC and life cycle CO2 (LCCO2) analyses in step 4. In addition, the results of these analyses were used to establish an iMOO process in step 5. 3.3. Step 3: energy simulation using the software program 'RETScreen' The reference model can be established by using the actual electricity generation data of the target building, which can be used to verify the effect of various installation scenarios in the rooftop PV system. A software program 'RETScreen' was used to establish the reference model. This program was co-developed by specialists from

C. Koo et al. / Renewable and Sustainable Energy Reviews 57 (2016) 822–837

the Department of Natural Resources in Canada and the United Nations Environment Programme [96–97]. As of 2010, more than 20,000 copies have been downloaded worldwide [98–103] and it can provide the high prediction accuracy within an error rate of 0–6% [104–105]. To verify the feasibility of the simulated electricity generation, this study used the tolerance limits provided by the American Society of Heating, Refrigerating, and Air-Conditioning Engineers, which is the Coefficient of Variation of the Root Mean Square Error (CV(RMSE)) as a measure of uncertainty. Using Eq. (2), this study calculated the value of CV(RMSE), and if it is within 25%, the simulation result was considered feasible [106]. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n P ðAEGi  SEGi Þ2  1n CVðRMSEÞ ¼

i¼1

n P i¼1

 100

ð2Þ

AEGi  1n

where CV(RMSE) stands for the coefficient of the variation of the root mean square error; AEG stands for the actual electricity generation; SEG stands for the simulated electricity generation; and n is the number of data (months). 3.4. Step 4: economic and environmental assessment from the life cycle perspective The LCC and LCCO2 analyses were conducted to evaluate the economic and environmental effects of the rooftop PV system. Various assumptions were established as follows: (i) the analysis approach; (ii) the real discount rate; (iii) the analysis period; and (iv) the significant cost of ownership [107]. SD Table S6 shows the assumptions on key elements for the LCC and LCCO2 analyses.

 Analysis approach: The present worth method was adopted,



 

which can be expressed largely as two indices: (i) the NPV as an absolute index; and (ii) the SIR as a relative index. If 'NPVZ0' (refer to Eq. (3)) or 'SIR Z1' (refer to Eq. (4)), it is considered that the project can be profitable, so break-even point can be achieved. Real discount rate: Based on basic information provided by the Bank of Korea Economic Statistics System and the Korean Statistical Information Service, the real discount rate can be calculated by using SD Eq. (S1): the interest growth rate (3.30%); the electricity price growth rate (0.66%); and the carbon dioxide emission trading price growth rate (2.66%). Analysis period: Based on interviews with experts in the field of PV systems, the analysis period was set to 25 years (i.e., the service life of the PV panel). Significant cost of ownership: This study considered the initial construction cost, the initial benefit, the operation and maintenance cost, and the operation and maintenance benefit. In particular, CO2 emission reduction was converted into economic value by using the profit from the sale of carbon credits [108].

NPVn ¼

n X BEGt þ BETt t¼0

SIRn ¼

ð1 þ r Þ

t

n X BEGt þ BETt t¼0

ð1 þ iÞ

t



n X CIt þ CRt t¼0

,

ð1 þ r Þt

n X CIt þ CRt t¼0

ð1 þ iÞt

ð3Þ

ð4Þ

where NPVn stands for the net present value during n years; SIRn stands for the savings-to-investment ratio during n years; BEGt stands for the benefit from the electricity generation in year t; BETt stands for the benefit from the emission trading in year t; CIt stands for the cost of the initial investment in year t; CRt stands for the cost of the repair work in year t; i stands for the real discount rate; and n stands for the period of the LCC and LCCO2 analyses.

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3.5. Step 5: establishment of an integrated multi-objective optimization using a genetic algorithm Koo et al. [109] developed the concept of an iMOO model to solve the time-cost trade-off problem, which can be used in the following ways: (i) to solve the multi-objective optimization problems with a more intuitive, simplified, applicable and flexible approach; and (ii) to define the trade-off problems with more than two optimization objectives using the multi-dimensional concept (please refer to Koo et al. [109] if further understanding is required). In this study, the iMOO model was adopted to determine the optimal solution in implementing the rooftop PV system, depending on the following three concepts.

 Hyperplane: This can be established based on the two extreme

 

points: (i) the maximum extreme point (Z þ ); and (ii) the minimum extreme point (Z-). The two extreme points can be found using SD Eq. (S2) and (S3). Standardization: All of the points within the whole criteria space, which means various installation scenarios in the rooftop PV system, should be standardized using SD Eq. (S4) and (S5). Fitness function: This can be determined by considering the characteristics of the optimization objectives. This study basically adopted the 'weighted Euclidean distance' (refer to SD Eq. (S6)). Although there are many methods of calculating the weight value (e.g., analytic hierarchy process, heuristic method, or statistical methods, etc.), the detailed descriptions of the methods are outside the scope of this study. It will be discussed in depth in future research. The fitness function can be established by using five optimization objectives (refer to Eq. (5)): (i) minimization of the IIC; and (ii) maximization of the AEG, the NPV, the SIR, and the AEG/EA. The optimization process is not stopped until the fitness function reaches the minimum value, when the optimal solution in the rooftop PV system can be found. This study defined the value of the fitness function as the iMOO score.

Fitness Function ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðSA  0Þ2 þ ð1  SB Þ2 þ ð1  SC Þ2 þ ð1  SD Þ2 þ ð1  SE Þ2

ð5Þ where SA, SB, SC, SD, and SE stand for the standardized values for the optimization objectives of the IIC, the AEG, the NPV, the SIR, and the AEG/EA, respectively; and the value of the fitness function stands for the iMOO score. Through the standardization process using SD Eqs. (S2)–(S5), a new coordinate axis between 0 and 1 should be created to define the fitness function and to find the optimal solution. Table 4 shows the extreme values for five target variables (i.e., Zmax and Zmin) to convert the actual values into the standardized values. Meanwhile, this study used a GA through a software program 'Evolver 5.5' to establish the optimization process. In a GA, optimization parameters including the adjustable parameters and the constraint parameters should be defined as a gene in a chromosome [110–112]. As shown in Fig. 2, the chromosome was established using five adjustable parameters defined in step 2 (i.e., the SoP, the ToP, the ToI, the NoP_L, and the NoP_W) and four constraint parameters defined in step 2 (i.e., the RL, the RW, the GL, and the BL). 3.6. Step 6: systemization of the iMOO model using a MicrosoftExcel-based VBA As explained in steps 1 to 5, various processes and the associated equations should be used to develop the iMOO model for determining the optimal solution in implementing the rooftop PV system. Thus, the aforementioned considerations should be integrated

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Table 4 Establishment of the Zmax and Zmin of five target variables. Classification

Zmax

Zmin

Optimization objective

IICa (US$) AEGb (kW h/yr) NPVc (US$) SIRd AEG/EAe (kW h/yr/unit)

179,487 252,510 352,865 2.256 317.25

28,230 43,376 43,352 1.533 43.12

Minimization Maximization Maximization Maximization Maximization





#ce:italic>Note:#/ce:italic> a

IIC stands for the initial investment cost. AEG stands for the annual electricity generation. NPV stands for the net present value. d SIR stands for the saving-to-investment ratio. e AEG/EA stands for the annual electricity generation per unit panel. b c

maximum and minimum values of the target variables should be found in advance (refer to 'Part (E)' of Fig. 4). Part (F), LCC and LCCO2 Analysis: For more intuitive decisionmaking, the results of the economic and environmental assessment can be presented in the form of charts from the life cycle perspective (refer to 'Part (F)' of Fig. 4); and, Part (G), Trade-off Analysis: For more intuitive decision-making, a two-dimensional chart can be provided to clearly explain the complex relationship among the target variables. This chart can make it possible for decision-makers to understand the results of the economic and environmental assessment (refer to 'Part (G)' of Fig. 4).

4. Model application In order to verify the feasibility of the developed iMOO model, the model application was conducted. First, this study selected the type of building, the regional factors, and the target building. SD Table S7 shows the detailed descriptions of 'Y' elementary school facility.

 The type of building: The Mandatory Renewable Energy Installa-

 Fig. 2 Description of chromosome in a genetic algorithm.

into a system, and the optimization process should be subsequently applied to the system. This study developed the iMOO model using a 'Microsoft-Excel-based VBA' [113]. Fig. 3 shows the decision making process in the iMOO model. In addition, Fig. 4 shows the graphical user interface of the iMOO model, which consists of seven parts as detailed below.



 Part (A), Optimization Objective: The fitness function can be









established by using the target variables selected by the final decision-maker (e.g., the IIC, the AEG, the NPV, the SIR, and the AEG/EA) (refer to 'B' of Fig. 3 and 'Part (A)' of Fig. 4). Part (B), Defined Parameters: The values of the defined parameters (i.e., the region and the AoP) depend on the characteristics of the target building (refer to 'B' of Fig. 3 and 'Part (B)' of Fig. 4). The regional meteorological and geographical information are retrieved from the database to conduct the energy simulation. Part (C), Adjustable Parameters: The applicable ranges of the adjustable parameters (i.e., the SoP, the ToP, the ToI, the NoP_L, and the NoP_W) depend on the characteristics of the target building (refer to 'B' of Fig. 3 and 'Part (C)' of Fig. 4). The values of the adjustable parameters can be finally determined in a GA, which can be used for determining the optimal solution in implementing the rooftop PV system. Part (D), Constraint Parameters: The limit ranges of the constraint parameters (i.e., the RL, the RW, the GL, and the BL) depend on the characteristics of the target building (refer to 'B' of Fig. 3 and 'Part (D)' of Fig. 4). The constraint parameters can be used to exclude some scenarios from all possible scenarios in the rooftop PV system. Part (E), Standardization: In order to establish the fitness function in the iMOO model (refer to Eq. (5)), the values of the target variables should be standardized from 0 to 1. To do this, the

tion Program and Eco-School Project are compulsory regulations enforced by the Ministry of Trade, Industry and Energy in South Korea. As an elementary school is included in the above program, this study selected the elementary school as the type of building. The regional factors: Seoul, the capital of South Korea and the region with the highest CO2 emission density with regard to elementary school facilities, was selected as the target region. Seoul's geographical factors (i.e., latitude and monthly meridian altitude) and meteorological factors (i.e., MADSR and monthly average temperature) are shown in SD Tables S1–S3. The target building: 'Y' elementary school was selected based on the following criteria: (i) educational facility, where the energy-saving rate in implementing the NRE system was determined to be over 5.44% (which was the average energy-saving rate in the Eco-School Project as of 2009); and (ii) educational facility, where the PV system was implemented at least a year ago and thus the actual electricity generation data from the PV system can be collected.

Second, this study established the iMOO process using a GA. Table 5 shows the detailed descriptions of the optimization process.

 The optimization objective: This study selected the following five







variables as the target variables in the optimization process: (i) the IIC; (ii) the AEG; (iii) the NPV; (iv) the SIR; and (v) the AEG/EA. Accordingly, the fitness function can be established using the five target variables (refer to Eq. (5)). The AoP: The unit panels of the rooftop PV system are generally installed toward the south (orientation ¼0°). Because 'Y' elementary school facility is south-southeast-facing, the unit panels of the rooftop PV system in the target building was set toward the southern direction (orientation ¼0°). Therefore, the AoP was determined as one of the defined parameters in the optimization process. The SoP: The SoP has a great effect on the amount of electricity generation from the rooftop PV system. Therefore, the SoP was defined as one of the adjustable parameters in the optimization process. This study assumed that the unit panels of the rooftop PV system can be installed within the range from 0° to 90°. The ToP and the ToI: The database was established by using 49 types of PV panels and 19 types of PV inverters, including the PV panel installed in 'Y' elementary school (refer to SD Tables S4

C. Koo et al. / Renewable and Sustainable Energy Reviews 57 (2016) 822–837

Fig. 3 Decision making process in the iMOO model.

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C. Koo et al. / Renewable and Sustainable Energy Reviews 57 (2016) 822–837

Fig. 4 Graphical user interface of the iMOO model.

Table 5 Establishment of the optimization process using a genetic algorithm. Classification

Variables

Detailed description

Optimization objective The Fitness function can be established with: (i) the initial investment cost (IIC); (ii) the annual electricity generation (AEG); (iii) the net present value (NPV); (iv) the saving-to-investment ratio (SIR); and (v) the annual electricity generation per unit panel (AEG/EA) Defined parameter Installation region (R) The azimuth of the installed panel (AoP) Adjustable parameter The slope of the installed panel (SoP) The type of the panel (ToP) The type of the inverter (ToI) Constraint parameter

Basic information

 

The rooftop area limit (RL and RW) The minimum electricity generation limit (GL) The maximum budget limit (BL) Latitude Monthly meridian altitude Monthly average daily solar radiation (MADSR) Monthly average temperature

and S5). The database was used to generate the various installation scenarios in the optimization process. Therefore, the ToP and the ToI were defined as one of the adjustable parameters in the optimization process. The NoP_L and the NoP_W: If the SoP and the ToP were determined, the NoP_L and the NoP_W could be calculated (refer to Koo et al. [34]). The rooftop area limit (RL and RW): The rooftop area of 'Y' elementary school facility is 1540 m2. To simplify the optimization process, the rooftop area was set as '40  40 square (width(m)  length(m))'. Therefore, the RL and the RW were defined as one of the constraint parameters in the optimization process.

Target: minimization

Seoul, in South Korea S: 0˚ Dividing the range from 0° to 90° by 1° Profile of PV panels (refer to SD Table S4) Profile of PV inverters (refer to SD Table S5) 1540 m2 ( E40 m  40 m) 28,043.30 (kWh/yr) US$ 1,000,000 Regional value (refer to SD Table S3) Regional value (refer to SD Table S3) Regional value (refer to SD Table S1) Regional value (refer to SD Table S2)

 The minimum electricity generation limit (GL): According to the



Mandatory Renewable Energy Installation Program, the NRE system should be implemented to supply over 10% of energy consumptions in a public building (including educational facility). 'Y' elementary school has consumed a total of 280,433 kWh in 2010. Thus, the GL was set at 10% of the total consumption (i.e., 28,043.30 kW h) (refer to SD Table S7), which was defined as one of the constraint parameters in the optimization process. The maximum budget limit (BL): The BL was established at US$ 1,000,000 in the model application. Thus, this study can simulate the iMOO model within the range of the maximum number of panels, which can be applicable to the target building.

C. Koo et al. / Renewable and Sustainable Energy Reviews 57 (2016) 822–837

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5. Results and discussion

5.4. Determination of the optimal solution in the iMOO model

5.1. Generation of the installation scenarios in the rooftop photovoltaic system

5.4.1. Optimization results in the iMOO model Table 7 shows the representative log of progress steps in the optimization process of the iMOO model. The iMOO score was minimized at 0.3243 when the Sop, the ToP, the ToI, the NoP_L, the NOP_W, and the NoP were established at 30°, No.13 (SM- 240 MHO), No.6 (HPC-500SL-K), 14 EA, 40EA, and 560 EA (refer to the shaded area of Table 7). Meanwhile, the model application was conducted to assess the robustness and reliability of the iMOO model from two perspectives: (i) consideration of the effectiveness of the optimal solution; and (ii) coming up with an efficient computation time.

In order to generate the possible installation scenarios, the adjustable parameter were defined within a certain range: (i) the SoP (0–90°); (ii) the ToP (Nos. 1 to 49) (refer to SD Table S4); (iii) the ToI (Nos. 1 to 19) (refer to SD Table S5); (iv) the NoP_L (0  79EA) (i.e., because the NoP_L depends on the SoP, the ToP, and the length of the rooftop area, the maximum NoP_L was determined at 79.2); and (v) the NoP_W (0  58EA) (i.e., because the NoP_W depends on the ToP and the width of the rooftop area, the maximum NoP_W was determined at 58.8). Therefore, a total of 399,883,120 (¼91  49  19  80  59) combinations can be generated as the possible installation scenarios.

 For the effectiveness, the iMOO model could determine the

5.2. Validation of the simulated electricity generation 'Y' elementary school implemented the 44 kW of the rooftop PV system on December in 2009, which replaced 17.10% (47,952 kW h; the actual electricity generation) of its annual electricity consumption (280,433 kW h). Based on the tolerance limit for energy simulation provided by the ASHRAE (refer to Eq. (2)), this study verified the feasibility of the software program 'RETScreen'. The CV(RMSE) was determined at 12.86%, which satisfied the tolerance limits (25%) [106]. Therefore, it was concluded that the simulated results (i.e., estimated electricity generation of several installation scenarios in the rooftop PV system) was feasible. 5.3. Economic and environmental assessment from the life cycle perspective Table 6 shows LCC and LCCO2 analyses results for the simulated electricity generation as a case study. The detailed descriptions of the optimization objectives (i.e., the IIC, the AEG, the NPV, the SIR, and the AEG/EA) are explained as follows: (i) by considering the initial construction cost (US$ 62,040) and the government subsidy (40%), the IIC was determined at US$ 37,224; (ii) the AEG was determined at 48,637 (kW h), achieving the GL (28,043 (kW h)); (iii) the NPV and the SIR were determined at US$ 63,490 and 1.895, respectively; and (iv) by dividing the AEG (48,637 (kW h/yr)) by the NoP (220 (EA)), the AEG/EA was determined at 221.08 (kW h/ yr/unit). The LCC and LCCO2 analyses can be conducted in the same way for a total of 399,883,120 possible scenarios.



optimal solution from a total of 399,883,120 possible scenarios by comprehensively considering various impact factors of the rooftop PV system (i.e., the adjustable parameters and the constraint parameters). For the efficiency, it was concluded that the total computational time required for determining the optimal solution on a computer (Processor, Intels Core™ i7-2600 CPU @ 3.40 GHz; RAM, 3.80 GB available) was only 150 s.

5.4.2. Trade-off analysis between the target variables In order to verify the effectiveness of the optimal solution, this study conducted the trade-off analysis between the target variables. Prior to the detailed trade-off analysis, the correlation analysis among the five target variables was conducted. (refer to Table 8): (i) the IIC has very high positive correlations with the AEG (0.977) and the NPV (0.937), a positive correlation with the AEG/EA (0.654), and a low positive correlation with the SIR (0.401); and (ii) the SIR has positive correlations with the AEG (0.580), the NPV (0.685), and the AEG/EA (0.695). Meanwhile, the IIC is optimized if it is closer to minimum value, whereas the other target variables are optimized if they are closer to maximum value. Namely, the IIC is negatively correlated with the other target variables, which means the trade-off relationship between the IIC and the other target variables. Therefore, it is necessary to conduct the trade-off analysis between two variables among five target variables. A visual chart for intuitive decision-making was developed using the software program 'MATLABs' [114]. Fig. 5 shows the surface plot with the interpolated iMOO score between the IIC (x-axis) and the SIR (y-axis) as an example. As the optimization process progresses, the colors of the corresponding coordinates were changed from red (0.75) to blue (0.35) (in web version), which indicates the iMOO score. The iMOO score was set

Table 6 LCC and LCCO2 analysis results for the simulated electricity generation. Classification

Variables

Detailed value

Optimization objective

The The The The The The The The The The The The The The The The

US$ 37,224 48,637 (kW h/yr) US$ 63,490 1.895 221.08 (kW h/yr/unit) Seoul, in South Korea S: 0˚ 30° No.7: SM-200 PD0 (refer to SD Table S4) No.13: PV-C340S/H (refer to SD Table S5) 20 EA 11 EA 40.0 m/34.51 m 40.0 m/16.06 m 28,043 (kW h/yr) /48,637 (kW h/yr) US$ 1,000,000/US$ 62,040

Defined parameters Adjustable parameters

Constraint parameters

initial investment cost (IIC) annual electricity generation (AEG) net present value (NPV) saving-to-investment ratio (SIR) annual electricity generation per unit panel (AEG/EA) installation region (R) azimuth of the installed panel (AoP) slope of the installed panel (SoP) type of the panel (ToP) type of the inverter (ToI) number of the installed panels (Length) (NoP_L) number of the installed panels (Width) (NoP_W) rooftop length limit (RL)/Applied rooftop length rooftop width limit (RW)/Applied rooftop width minimum electricity generation limit (GL)/Annual electricity generation maximum budget limit (BL)/The initial construction cost (w/o subsidy)

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Table 7 Log of progress steps in the optimization process of the iMOO model. Step

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

iMOO scoreg

Adjustable parameters SoPa

ToPb

ToIc

NoP_Ld

NoP_We

NoPf

27 31 31 34 38 36 14 17 17 20 20 21 21 24 24 24 27 29 30 30

21 22 23 23 22 22 11 12 12 12 12 12 13 12 13 13 13 13 13 13

10 10 10 10 10 10 4 4 4 4 4 4 4 4 4 4 4 4 4 6

9 10 14 14 14 14 17 16 16 15 15 15 15 15 15 15 14 14 14 14

36 36 38 39 39 40 38 37 39 38 40 40 39 39 39 40 40 40 40 40

324 360 532 546 546 560 646 592 624 570 600 600 585 585 585 600 560 560 560 560

0.5363 0.5065 0.4456 0.4385 0.4164 0.4115 0.3606 0.3512 0.3488 0.3469 0.3427 0.3406 0.3388 0.3369 0.3338 0.3333 0.3327 0.3309 0.3302 0.3243

Standardized value (0–1) IICh

AEGi

NPVj

SIRk

AEG/EAl

0.1921 0.2402 0.3995 0.4150 0.4608 0.4774 0.6227 0.5815 0.6231 0.5530 0.5919 0.5919 0.5986 0.5725 0.5986 0.6188 0.5651 0.5651 0.5651 0.5651

0.1799 0.2312 0.3949 0.4117 0.4584 0.4760 0.6508 0.6167 0.6612 0.5939 0.6360 0.6385 0.6458 0.6235 0.6522 0.6742 0.6202 0.6225 0.6234 0.6328

0.2317 0.2837 0.4418 0.4597 0.5057 0.5226 0.7066 0.6824 0.7269 0.6676 0.7101 0.7151 0.7224 0.7064 0.7356 0.7580 0.7080 0.7131 0.7152 0.7329

0.7209 0.7372 0.7372 0.7436 0.7444 0.7451 0.8167 0.8532 0.8532 0.8848 0.8848 0.8943 0.8943 0.9191 0.9191 0.9191 0.9386 0.9487 0.9528 0.9877

0.7546 0.7722 0.7064 0.7078 0.7731 0.7737 0.8562 0.9047 0.9047 0.9152 0.9151 0.9183 0.9553 0.9264 0.9637 0.9637 0.9701 0.9733 0.9746 0.9874

#ce:italic>Note:#/ce:italic> a

SoP stands for the slope of the installed panel. ToP stands for the type of the panel. c ToI stands for the type of the inverter. d NoP_L stands for the number of the installed panels on length side. e NoP_W stands for the number of the installed panels on width side. f NoP stands for the number of the installed panels. g iMOO score stands for the value of the fitness function. h IIC stands for the initial investment cost. i AEG stands for the annual electricity generation. j NPV stands for the net present value. k SIR stands for the saving-to-investment ratio. l AEG/EA stands for the annual electricity generation per unit panel. b

Table 8 Correlation analysis between the optimization objective. Variables IIC

a

AEGb

NPVc

SIRd

AEG/EAe

IIC Pearson correlation Sig. (2-tailed) N Pearson correlation Sig. (2-tailed) N Pearson correlation Sig. (2-tailed) N Pearson correlation Sig. (2-tailed) N Pearson correlation Sig. (2-tailed) N

1 – 4931 .977nn .000 4931 .937nn .000 4931 .401nn .000 4930 .654nn .000 4928

AEG

NPV nn

.977 .000 4931 1 — 4931 .990nn .000 4931 .580nn .000 4930 .740nn .000 4928

nn

.937 .000 4931 .990nn .000 4931 1 – 4931 .685nn .000 4930 .779nn .000 4928

SIR

AEG/EA nn

.401 .000 4930 .580nn .000 4930 .685nn .000 4930 1 – 4930 .695nn .000 4927

.654nn .000 4928 .740nn .000 4928 .779nn .000 4928 .695nn .000 4927 1 – 4928

#ce:italic>Note:#/ce:italic> nn

Correlation coefficient is significant at 0.01 level (both sides). IIC stands for the initial investment cost. AEG stands for the annual electricity generation. c NPV stands for the net present value. d SIR stands for the saving-to-investment ratio. e AEG/EA stands for the annual electricity generation per unit panel. a

b

to be minimized in the optimization process (refer to Table 5), where was conducted from the two perspective: (i) minimization of the IIC; and (ii) maximization of the SIR. Accordingly, the optimal solution can occur at the nearest point to the coordinate (0, 1), which indicates the Pareto Front. As a result, the optimization

Fig. 5 Surface plot with the interpolated iMOO score between IIC and SIR. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

process has been conducted in the direction of the arrow shown in Fig. 5. Finally, the optimal solution was found in the coordinate (0.5651, 0.9877), the red circle, in which the iMOO score was determined at 0.3243 (in web version). SD Figs. S1–S9 show the

C. Koo et al. / Renewable and Sustainable Energy Reviews 57 (2016) 822–837

833

Table 9 Optimal scenario and the other four alternative scenarios in the optimization process of the iMOO model. Scen.a

OSn Alto.1 Alt.2 Alt.3 Alt.4

iMOO scoreb

Adjustable parameters SoPc

ToPd

ToIe

NoP_Lf

NoP_Wg

NoPh

30 30 21 30 27

13 13 22 17 22

6 4 4 15 10

14 14 14 14 14

40 40 39 40 40

560 560 546 560 560

0.3243 0.3302 0.3720 0.4167 0.4189

Standardized value (0–1) IICi

AEGj

NPVk

SIRl

AEG/EAm

0.5651 0.5651 0.4608 0.4304 0.4774

0.6328 0.6234 0.4960 0.4401 0.4716

0.7329 0.7152 0.5710 0.4974 0.5117

0.9877 0.9528 0.8942 0.7974 0.7208

0.9874 0.9746 0.8255 0.7248 0.7677

#ce:italic>Note:#/ce:italic> a

Scen. stands for the scenario. iMOO score stands for the value of the fitness function. c SoP stands for the slope of the installed panel. d ToP stands for the type of the panel. e ToI stands for the type of the inverter. f NoP_L stands for the number of the installed panels on length side. g NoP_W stands for the number of the installed panels on width side. h NoP stands for the number of the installed panels. i IIC stands for the initial investment cost. j AEG stands for the annual electricity generation. k NPV stands for the net present value. l SIR stands for the saving-to-investment ratio. m AEG/EA stands for the annual electricity generation per unit panel. n OS stands for the optimal scenario (refer to Table 7). o Alt. stands for the alternative scenario. b

Fig. 6 Comparison chart for intuitive decision-making. (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)

other surface plots with interpolated iMOO score between two variables among the other target variables. 5.4.3. Comparison chart for intuitive decision-making A trade-off analysis between two target variables was conducted to verify the effectiveness of the optimal solution in the iMOO model.

However, it is necessary to conduct the trade-off analysis among more than three target variables, which makes it possible for the final decision-maker easily understand the results of the multi-objective optimization at a glance. Towards this end, this study developed a visual chart (i.e., a comparison chart for intuitive decision-making). In

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order to clearly explain this chart, this study selected the optimal scenario and the other four alternatives (refer to Table 9). This study established the fitness function by using five target variables (the IIC, the AEG, the NPV, the SIR, and the AEG/EA) (refer to Table 5). As shown in Fig. 6, this study selected three target variables (i.e., the IIC (part (A) in Fig. 6), the AEG (part (B) in Fig. 6), and the SIR (part (C) in Fig. 6) by considering the aforementioned correlation analysis. As explained in Eq. (5), the iMOO score can be used to determine the optimal scenario from the possible installation scenarios (i.e., a total of 399,883,120 scenarios). Namely, the scenario with the minimum value of the iMOO score was determined as the optimal scenario (part (D) in Fig. 6). The details of the optimization process can be explained as follows:

 (i) Comparison between the optimal solution and the alter-



native scenario: Even if the IICs of the optimal solution (redcolored circle and line) and alternative scenario 1 (blue-colored circle and line) had the same values (part (A) in Fig. 6), the results showed that the AEG of the optimal solution was higher than that of alternative scenario 1 (part (B) in Fig. 6). The same results were found for the SIR (part (C) in Fig. 6). Finally, the results showed that the iMOO score of the optimal solution was lower than that of alternative scenario 1 (part (D) in Fig. 6). (ii) Trade-off analysis between two alternative scenarios: Even if the IIC of alternative scenario 4 (purple-colored circle and line) was higher than that of alternative scenario 2 (green-colored circle and line) (part (A) in Fig. 6), the results showed that the AEG of alternative scenario 4 was lower than that of alternative scenario 2 (part (B) in Fig. 6). In addition, although the AEG of alternative scenario 4 (purple-colored circle and line) was higher than that of alternative scenario 3 (yellow-colored circle and line) (part (B) in Figure), the results showed that the SIR of alternative scenario 4 was lower than that of alternative scenario 3 (part (C) in Fig. 6). As a result, the iMOO scores of alternative scenarios 2–4 were calculated, and the rankings were determined by comprehensively considering the aforementioned results (part (D) in Fig. 6).

6. Conclusions This study aimed to develop an iMOO model for solving the trade-off problems among the various target variables (i.e., the IIC, the AEG, the NPV, the SIR, and the AEG/EA), which makes it possible to determine the optimal solution in implementing the PV system. Also, this study verified the feasibility of the developed model though a case study. In the model application, this study referred to the practical specification (technical standard) used in 'Y' elementary school facility and an interviews with experts in the field of PV systems of Parsons Brinckerhoff, Oerlikon Solar, and Hilti Corporation.

In order to assess the robustness and reliability of the iMOO model, the model application was conducted in terms of two criteria. First, for the effectiveness of the optimal solution, it was concluded that the optimal solution can be determined from a total of 399,883,120 ( ¼91  49  19  80  59) possible scenarios by comprehensively considering various factors. In addition, visual charts (i.e., the comparison chart for intuitive decision-making) make it possible for the final decision-maker to conduct the tradeoff analysis among more than three target variables at a glance and to easily understand the results of the multi-objective optimization. Second, for the efficient computation time, it was concluded that the time required for determining the optimal solution on a computer (Processor, Intels Core™ i7-2600 CPU @ 3.40 GHz; RAM, 3.80 GB available) was only 150 s. The iMOO model could enable architects or construction managers to easily, rapidly, and accurately determine the optimal solution in implementing the rooftop PV system in the early design phase. This could be achieved by using a visual chart for intuitive decision-making. In addition, it could be useful for contractors in competitive bidding processes to analyze the alternatives. As the iMOO model was developed using Microsoft Excelbased VBA, a final decision-maker could determine the optimal solution in implementing the rooftop PV system simply by entering the optimization parameters. Finally, the iMOO model could be applied to other NRE systems and could be extended to any other country or sector in the global environment. Meanwhile, there are some limitations in this study. First, this study applied a GA to establish the multi-objective optimization process because it is easy to understand for the final decision makers such as construction managers or contractors. Even if a GA can be used to solve the complex problems with a large search space in the several research areas, there is no guaranty that it can find the minimum value, because it could be stuck in the local optima. Thus, the research team is working on more advanced optimization approaches. Second, in this study, the first attempt was conducted to apply the iMOO model to the complex problems with more than five objectives. Although the results showed that the iMOO model can solve these complex trade-off problems, it is necessary to conduct more future research. To do this, the research team is working on the further research to apply the concept of the iMOO model to the various research areas.

Acknowledgments This work was supported by the National Research Foundation of Korea, South Korea (NRF) Grant funded by the Korea government (MSIP; Ministry of Science, ICT and Future Planning) (No. NRF-2015R1A2A1A05001657).

Appendix A. Acronyms

AEG AEG/EA AoP BL CV(RMSE) GA GL IIC

Annual Electricity Generation Annual Electricity Generation per unit panel Azimuth of the installed Panel maximum Budget Limit Coefficient of Variation of the Root Mean Square Error Genetic Algorithm minimum electricity Generation Limit Initial Investment Cost (with the government subsidy)

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iMOO LCC LCCO2 MADSR NoP NoP_L NoP_W NPV RL RW SIR SoP ToI ToP VBA

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integrated Multi-Objective Optimization Life Cycle Cost Life Cycle CO2 Monthly Average Daily Solar Radiation The Number of the installed Panels on the rooftop area The Number of installed Panels along the Length of the rooftop area The Number of installed Panels along the Width of the rooftop area Net Present Value Rooftop Length Rooftop Width Saving-to-Investment Ratio Slope of the installed Panel Type of the Inverter Type of the Panel Visual Basic for Applications

Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at http://dx.doi.org/10.1016/j.rser.2015.12.205.

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