Optimal Battery Control Under Cycle Aging Mechanisms in Pay for Performance Settings

We study the optimal control of battery energy storage under a general “pay-for-performance” setup such as providing frequency regulation and renewable integration. In these settings, batteries need to carefully balance the tradeoff between following the instruction signals and their degradation costs in real-time. Existing battery control strategies either do not consider the uncertainty of future signals, or cannot accurately account for battery cycle aging mechanism during operation. In this paper, we take a different approach to the optimal battery control problem. Instead of attacking the complexity of a battery degradation function or the lack of future information one at a time, we address these two challenges together in a joint fashion. In particular, we present an electrochemically accurate and trackable battery degradation model called the rainflow cycle-based model. We prove that the degradation cost is convex. Then, we propose an online control policy with a simple threshold structure and show that it achieves near-optimal performance with respect to an offline controller that has complete future information. We explicitly characterize the optimality gap and show that it is independent to the duration of operation. Simulation results with both synthetic and real regulation traces are conducted to illustrate the theoretical results.