Exact sizing of battery capacity for photovoltaic systems

In this paper, we study battery sizing for grid-connected photovoltaic (PV) systems. In our setting, PV generated electricity is used to supply the demand from loads: on one hand, if there is surplus PV generation, it is stored in a battery (as long as the battery is not fully charged), which has a fixed maximum charging/discharging rate; on the other hand, if the PV generation and battery discharging cannot meet the demand, electricity is purchased from the grid. Our objective is to choose an appropriate battery size while minimizing the electricity purchase cost from the grid. More specifically, we want to find a unique critical value (denoted as Emaxc) of the battery size such that the cost of electricity purchase remains the same if the battery size is larger than or equal to Emaxc, and the cost is strictly larger otherwise. We propose an upper bound on Emaxc, and show that the upper bound is achievable for certain scenarios. For the case with ideal PV generation and constant loads, we characterize the exact value of Emaxc, and also show how the storage size changes as the constant load changes; these results are validated via simulations.