## 5 Conclusions  
The developed PSO optimization method allows a high degree of flexibility in the calculation of the optimal SAPV installation. The methodology that performs the optimal system sizing allows the collection of irradiance log data for any location and its use in the system calculation, as well as the input of detailed demand profiles. It also allows the input of parameters for specific commercial PV components, making the system solution unique and optimal for each individual user.  
Figure 24: Variation of the reliability and cost of the system with the price of fuel.  
Figure 23: Optimum power and capacity variation with fuel price.  
The PSO optimization method always converges to the same result, having used two different optimization algorithms to corroborate this fact and check the accuracy of the result. This fact, together with the computational speed of the algorithms, is sufficient to admit the feasibility of using the program in the design of larger SAPV systems.  
Sensitivity analysis of the annual irradiance data indicates that, once the optimal system has been obtained in the indicated order of magnitude, the system solution allows for a margin of error while maintaining the desired supply reliability.  
Looking at the trends and price sensitivity analyses, it can be concluded that the trend for these mixed off-grid systems, which combine photovoltaics with an external generator, is towards a pure photovoltaic system. The market trend is towards lower costs for both PV modules and batteries, so the system will evolve towards the elimination of the auxiliary generator in favor of increasing the installed power and, above all, the storage capacity, thus increasing the reliability of supply to values close to 100%.  
Finally, it should be added that, although a fully functional design method has been obtained, it can be improved in future work, allowing for improvements in the installation calculation model, taking into account, for example, maintenance costs and replacement of the components of the system, and the effect of aging on these system components, which would affect both their failure rate and the generation capacity of the PV modules and the storage capacity of the batteries.  
It can be concluded that this research makes a significant contribution to the field by providing a complete and robust study that addresses various critical aspects of SAPV system design.  
Conceptualization, E.Q.-C., A.M.-T., C.R.-P. and C.R.-B.; methodology, A.M.-T., E.Q.-C. and C.R.-B.; software, A.M.-T. and C.R.-B.; validation, E.Q.-C., A.M.-T. and C.R.-P.; formal analysis, A.M.-T. and E.Q.-C.; research, E.Q.-C., A.M.-T., C.R.-B. and C.R.-P.; resources, E.Q.-C., A.M.-T. and C.R.-B.; data curation, A.M.-T.; writing--original draft preparation, A.M.-T. and E.Q.-C.; writing--review and editing, A.M.-T., E.Q.-C., C.R.-B. and C.R.-P.; visualization, E.Q.-C., A.M.-T. and C.R.-P.; supervision, E.Q.-C., C.R.-P. and C.R.-B.; project administration, E.Q.-C., C.R.-B. and C.R.-P.; funding acquisition, E.Q.-C., C.R.-B. and C.R.-P. All authors have read and agreed to the published version of the manuscript.  
Cierrectorado de Investigacion de la Universitat Politecnica de Valencia (PAID-11-22).  
Not applicable.  
This work has been supported by Universitat Politecnica de Valencia.  
The authors declare no conflict of interest.