The role of storage degradation in energy management problems: An optimal control perspective

The energy management problem of grid-connected storage systems is becoming crucial due to massive integration of renewable energy sources. However, in these problems, the storage degradations are often overlooked while designing the optimal control policy. The key reason behind that is the degradation cost, which occurs at each (dis)charging storage cycle, is hard to evaluate, and it is highly dependent on the grid demand. Thus, integrating them in the energy management problem is a challenge. In this article, we address this challenge, and propose an optimal control update, which solves the energy management problem of a power grid considering the storage degradation cost. We first adopt a multi-storage setup, where each storage system has a constant efficiency function and finite storage capacity (not necessarily the same), and then evaluate necessary optimal conditions based on Pontryagin's minimum principle. We show that these conditions can further be leveraged to obtain an explicit optimal control update for a family of homogeneous storage systems. Moreover, we derive explicit control updates for the energy management problems, where the storage degradation costs obey either the additive or the multiplicative degradation cost models. Several numerical experiments are performed on the Israel electric grid to demonstrate the covered concepts and the effectiveness of the proposed approach.