# Simulation of Self-Consumption Photovoltaic Installations: Profitability Thresholds
## 4 Conclusions  
In this work, a complete set of scenarios of domestic self-consumption PV installations located in Cordoba (Spain) has been simulated for a base scenario shown in Table 3. The design variables that were systematically varied were the collector azimuth, inclination of collectors, power of the installation and degree of obstruction. The facilities have been simulated considering the pessimistic hypothesis of energy purchase price values (\(p_{E}=\text{EUR 0.16 kWh}\)) and compensation price (\(p_{C}=\text{EUR 0.04 /kWh}\)) corresponding to the free market. The \"Royal Decree 148/2021\" [44], which established the method to calculate the costs of the electric system, is applied from the 1 June 2021 onwards. This new scenario provides two periods for the signed power and three periods for the energy. Initially, there has been an increase in the energy price of both PVPC and free market consumers. Equally, there has been a proportional increase of the energy retribution surplus in PVPC. It is therefore necessary to study this effect with a broader perspective to determine whether it is a temporary disturbance or a trend. This analysis will be addressed in future work. For all the considered combinations of peak power and angle of obstruction, there are two extreme positions in profitability. The optimal position, \(\gamma=0^{\circ}\) and \(\beta=15^{\circ}\), in which the profitability indices reach maximum profitability, and the most unfavorable position, \(\gamma=180^{\circ}\) and \(\beta=90^{\circ}\). In the absence of obstructions, the power of 1500 Wp is optimal for all orientations, reaching an optimal \(NPV\) of EUR 1626.0 for the most favourable orientation compared to a value of doubtful profitability (EUR 48) in the most unfavourable orientation. If the level of obstruction increases, the \(NPV\) interval evolves, decreasing the maximum achievable \(NPV\), although the minimum remains at values of doubtful profitability (Table 9). The maximum \(NPV\) values obtained for each level of obstruction  
Figure 10: (**a**) Comparison of \(NPV\) obtained with the proposed model (Equation (32)) versus that obtained by simulation; (**b**) Comparison of \(Pay-back\) obtained with the proposed model (Equation (33)) versus that obtained by simulation. are compatible with suitable cost-effective installations. Likewise, it is observed that, as the degree of obstruction increases, the optimal \(NPV\) values are achieved for installations with powers lower than 1500 W. The preference for powers lower than 1500 W is also justified in cases in which it is intended to improve the profitability unit of invested capital, quantified by the \(Pay-back\) or \(NPV/investment\) indices. The study of dependency of the profitability indices with respect to the power of the facilities shows a uniform decrease in \(Pay-back\) and \(NPV/investment\). Empirical adjustment equations have been developed to estimate profitability parameters in cases of orientation comprised between extreme orientations. From these, a simple model (Equation (32)) is obtained that allows the evaluation of PV installations for self-consumption in Cordoba (Spain) as well as the study of the dependency of the technical and economic evaluation parameters of the installation with respect to other variables of design such as \(p_{E}\), \(p_{C}\), \(C_{0}\), \(i\), \(d\), \(\Delta p\), and \(n\). Although the values offered by the empirical model are approximate, its advantage lies in being able to carry out an analytical and quantitative study of the influence of the design parameters on the \(NPV\) and \(Pay-back\) indicators. This work is a starting point for future work, where climatic considerations or stochastic variations in energy demands can be considered in greater detail. Conceptualization, R.L.-L. and J.R.-F.; methodology, L.M.F.-A. and J.R.-F.; software, L.M.F.-A. ; validation, J.R.-F. and M.V.-M.; formal analysis, L.M.F.-A. and M.V.-M.; investigation, R.L.-L. and L.M.F.-A. ; resources, J.R.-F.; data curation, L.M.F.-A.