Non-linear charge-based battery storage optimization model with bi-variate cubic spline constraints

Variable renewable generation demands increasing amount of flexible resources to balance the electric power system, and batteries stand out as a promising alternative. Battery models for optimization typically represent the battery with power and energy variables, while the voltage, current, charge variable space is used for simulation models. This paper proposes a non-linear battery storage optimization model in the voltage, current, charge variable space. The battery voltage is conceived as an empirical function of both state-of-charge and charge current and represented through bi-variate cubic splines. The voltage source converter losses are also approximated with a cubic spline function. Compared to energy-based storage models, the results show that this approach enables safe operation closer to the battery voltage and current limits. Furthermore, it prefers operating around high state-of-charge due to the higher efficiency in that region.