An efficient mixed-integer linear programming model for optimal sizing of battery energy storage in smart sustainable buildings

A building with an integrated photovoltaic system that roughly generates as much energy as it consumes annually is called net zero energy building. The owner of such a building still has to pay a monthly electricity bill due to frequent electricity exchange with the grid and the fact that the retail price of electricity is usually higher than the feed-in-tariff. Adding a battery energy storage system can potentially reduce the monthly net payment of the building owner since it can alleviate the necessity of importing power from the grid at the time where it is expensive. The problem of selecting the optimal size of the battery energy storage system for all-electric buildings is modeled and solved in this paper. First, a new mixed-integer nonlinear programming model is built. Then, it is reformulated to accumulate the nonlinearity of the model in only one constraint. Finally, the reformulated model is linearized to efficient mixed-integer programming models applying two approaches: McCormick relaxation and piecewise linearization. The numerical study on a typical building in Luxembourg illustrates that the proposed McCormick-based linear model can provide high accuracy results within a reasonable runtime.