Deterministic and stochastic optimization-based decision-making approaches for effectively coping with residential photovoltaic micro-systems sizing problem under net-metering schemes

Decentralized generation has gained importance in the energy industry since auto-consumption with renewable resources nowadays exhibits attractive costs. In this sense, photovoltaic generation micro-systems are a promising technology. This work faces the problem of finding the optimal capacity of the photovoltaic (PV) micro-system to be installed by a residential customer –which at the same time is connected to the public grid-, and it is able to compensate the public power electricity consumption through self-supply, with PV generation. In this sense, two approaches are proposed in this paper. The deterministic approach assumes all input variables are known with certainty and focuses on matching the expected demand with an estimated PV generation. Starting from this deterministic perspective, the stochastic approach uses a Particle Swarm Optimization (PSO) algorithm to obtain the most likely capacity of the PV power micro-system which will match consumption with generation during an established time period, while uncertain input variables are randomly modeled by means of probability distribution functions within a Monte Carlo (MC) technique. Temperature and irradiance are considered as random variables. Optimal PV power is obtained in a proposed study case, where net measured energy resulting from the optimization process reaches about 0.0003 kWh during one day. In addition, the levelized cost of energy is calculated. It shows the benefit of PV energy whose cost (0.078 US$/kWh) is lower than the nominal cost considering distributor rates. The results are successfully tested through an energy management system (EMS) developed to validate the proposed methodology.