## 3 Results and Discussion
### Case Study of Curitiba City, Brazil  
The second city to be analysed is Curitiba of Parana state in Brazil. According to [PERSON] et al. (2017), the estimated average daily irradiation for the country's Southern region is 4.53 kWh/m\({}^{2}\)-day. The Southern region presents an average daily irradiation 17.48% lower than the Northeast region. Curitiba has the following coordinates: latitude: \(-\)25.401; longitude: \(-\)49.249; altitude: 935 m; and GMT \(-\)3. Figure 8 presents the annual irradiance map of Brazil's south and highlights Curitiba city in Parana. Figure 9 demonstrates the average high and low temperatures. Due to the first case study prioritising installation cost, the weight of the investment payback time was maximised for the case study in Curitiba. Therefore, the MCDSS for photovoltaic set definition tended to have a balanced value between efficiency and cost for determining the system to be installed. The weight assigned to \"payback time\" was 100%, and for the other criteria, the weight was 75%. The proposal generated by the MCDSS can be seen in Figures 10 and 11. Figure 7: Analysis of the alternatives selected by the MCDSS for photovoltaic set definition of the City of Barreiras. As observed in Figures 10 and 11, the methods selected divergent alternatives. For the selection of photovoltaic modules, the AHP method sought the equipment with the shortest payback time among the options, as desired by the user. This photovoltaic module model had the lowest cost among the possible options. On the other hand, the TOPSIS method selected a photovoltaic module model that was quite similar but had slightly higher efficiency than the one AHP selected. The methods used to determine inverters had completely divergent responses. The AHP method selected an inverter model with the shortest payback time possible, like when choosing photovoltaic modules. However, the TOPSIS method selected the most efficient inverter model among the available options, ignoring models with shorter payback times and lower costs. Upon analysing the system, it was possible to verify that the photovoltaic system selected by the AHP method minimised the investment payback time and selected the cheapest possible system within the range offered by the alternatives. The TOPSIS method determined a slightly more efficient system than the proposal provided by AHP. Still, it did not achieve a satisfactory result for the payback time criterion as required by the user. Figure 8: Average annual irradiation in Curitiba city, Brazil. Source: [57]. Figure 9: Average high and low temperature in Curitiba city, Brazil. Source: [57]. Upon analysing the systems proposed by the decision methods, it is possible to verify that despite the evaluation graphs of the selected alternatives being completely different, the photovoltaic systems determined by AHP and TOPSIS are similar due to the restricted range of options for choosing the inverters. The annual power generated by the systems is 3036 kWh/year for the installation selected by the AHP method and 3056 kWh/year for the system chosen by the TOPSIS method, generating a positive energy balance of 36.0 kWh and 56.0 kWh, respectively. For the analysis of the maximised criterion, the investment payback time, the AHP method selected a system with a payback time value of 2.76 years. On the other hand, the TOPSIS method selected photovoltaic component alternatives so that the payback time was 2.95 years. When analysing the different criteria for efficiency, the TOPSIS method selected alternatives whose overall efficiency was higher than the proposal of the AHP method, reaching a global efficiency value of 14.8% compared to the 14.4% chosen by the AHP method. For the installation cost criterion, the AHP method selected an installation that was 6.1% cheaper than the system proposed by the TOPSIS method, whose total cost was USD 1284.49. When analysing the economic viability, the system proposed by the AHP method obtained a better IRR value, reaching 52.0%.