# Simulation of Self-Consumption Photovoltaic Installations: Profitability Thresholds
## 3 Results  
For the evaluation of PV installations with self-consumption and the study of their profitability limits, in accordance with the exposed methodology, a set of domestic PV installations has been simulated and evaluated technically and economically in which some design variables, such as the inclination of the photovoltaic collector \((\beta)\), the azimuth of the collector \((\gamma)\), the nominal power of the installation \((PP)\) and the degree of obstruction \((\zeta)\), have been systematically varied. Specifically, Table 1 shows the values considered for these variables. Thus, their systematic crossing has given rise to 2548 different cases (\(2548=7\cdot 13\cdot 7\cdot 4\)). For all these cases, a house located in Cordoba (Spain) has been considered, so the latitude and longitude of the place will be 37.85\({}^{\circ}\) N and 4.85 W, respectively, and the values of global horizontal radiation \((H)\) and the clarity index \((k_{t})\) on the representative days of each month of the year will be those listed in Table 2.  
Moreover, regarding energy demand, household consumption data representative of all Spanish households during 2019 was used. Likewise, it was considered that the average Spanish household is covered by the type of regulated contract 2.0 without hourly discrimination, which contracted a power of 3.27 kW and which consumed 2240 kWh/year [25]. For this case, the hourly profiles of demand are characterised and published by Red Electrica Espanola [43]. These data are hourly and were averaged to obtain consumption profiles on the representative days of each month proposed by [PERSON] [42]. Figure 5 shows the profiles obtained in the months of January, April, July, and October. Finally, for the economic evaluation of all the facilities, the values shown in Table 3 were used. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Variable**} & **Inclination of Collectors \((\beta)\)** & **Azimuth of Collectors \((\gamma)\)** & **Power Peak (PP, _in_ W)** & **Angle of De Obstruction \((\zeta)\)** \\ \hline Number of cases & 7 & 13 & 7 & 4 \\ Minimum Value & 0\({}^{\circ}\) & \(-180^{\circ}\) & 500 W & 0\({}^{\circ}\) \\ Maximum Value & 90\({}^{\circ}\) & 180\({}^{\circ}\) & 3500 W & 30\({}^{\circ}\) \\ Increase & 15\({}^{\circ}\) & 30\({}^{\circ}\) & 500 W & 10\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design variables and variation intervals considered for the systematic analysis of PV installations with self-consumption. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Month**} & \multirow{2}{*}{**\(H\) (kWh/m\({}^{2}\))**} & \multirow{2}{*}{\(k_{t}\)**} & **Mean** & **Representative** \\  & & & **Temperature** & **Julian Day** \\ \hline January & 2.06 & 0.46 & 9.1 & 17 \\ February & 3.08 & 0.51 & 10.7 & 47 \\ March & 3.93 & 0.50 & 13.5 & 75 \\ April & 4.81 & 0.49 & 16.3 & 105 \\ May & 5.28 & 0.48 & 19.4 & 135 \\ June & 6.74 & 0.59 & 24.4 & 162 \\ July & 7.14 & 0.64 & 27.9 & 198 \\ August & 6.50 & 0.64 & 27.6 & 228 \\ September & 5.00 & 0.58 & 24.3 & 258 \\ October & 3.30 & 0.49 & 18.6 & 288 \\ November & 2.29 & 0.46 & 13.6 & 318 \\ December & 1.73 & 0.42 & 9.6 & 344 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Daily radiation on the horizontal plane \((H)\) and \((k_{t})\) in Córdoba (Spain) [19] and representative day of each month [42]. The simulation of all the cases considered in this study was implemented in VBA-Excel, requiring a total of 1256 s (0.492 s/case) on Intel(R) Core (TM) i5-8250U CPU @ 1.60 GHz. Thus, the results of the simulation of the different PV installations with self-consumption characterised by the parameters defined above, were tabulated with respect to the azimuth and orientation of collectors as a cylindrical chart, obtaining graphic maps in which the numerical values of the different estimated variables are represented. In these maps, the obstruction level and installed power values have been kept constant.