Mathematical Optimization of Design Parameters of Photovoltaic Module

We propose a method for finding the most appropriate photovoltaic (hereafter PV) module and the return on investment for specific household needs, leveraging mathematical optimization. Based on electricity consumption and location of the household, the algorithm finds PV module design parameters using Covariance Matrix Adaptation Evolution Strategy (hereafter CMA-ES). According to these computed design parameters, the algorithm finds the most similar PV module from the dataset of PV modules using Euclidean distance. Subsequently, savings and costs are calculated for the recommended PV system. When calculating the return on investment, the algorithm takes into account the price of electricity, initial investment and battery replacements. The objective function is defined to maximize net savings during the lifetime of the PV system, which is considered to be 20 years. Heuristics of the battery takes into account the aging of batteries and the loss of energy due to storage. Battery life is set at 10 years, as we are considering using high quality batteries. In order to extend battery life, the algorithm counts with the charge level restrictions.