Multi-objective mathematical programming for optimally sizing and managing battery energy storage for solar photovoltaic system integration of a multi-apartment building

This article presents a novel mathematical formulation to solve the problem of optimally sizing and managing battery energy storage for the solar photovoltaic system integration of a multi-apartment building. The aim is the maximization of the collective self-consumption maintaining control over time of the energy sold and bought and the monitoring of the state of batteries while ranging from minimum to maximum levels. This is obtained through a new mathematical programming model with three different objective functions that can be tuned simultaneously to find Pareto optimal solutions to the problem. The computational results in detailed scenarios with real data verify the model's adequacy to deal with the real problem and give a measure of the saving of bought and sold energy.