Defining a degradation cost function for optimal control of a battery energy storage system

Optimal control of Battery Energy Storage Systems (BESSs) is challenging because it needs to consider benefits arising in power system operation as well as cost induced from BESS commitment. The presented approach relies on the methodology of Model Predictive Control (MPC) for optimal BESS operation. Variable and strongly usage dependent battery degradation costs constitute the bulk of the marginal costs for BESS operation. Battery degradation is usually modeled with nonlinear functional dependencies or an implicit cycle counting approach unsuited for an MPC implementation. In this paper an explicit cost function considering battery degradation is developed, which sufficiently captures the nonlinearities and is applicable for arbitrary battery load patterns. The resulting piece-wise affine cost function leads to a mixed-integer quadratic programming problem allowing a standard hybrid MPC formulation. As proof-of-concept, a peak shaving algorithm relying on the proposed cost function and on adaptive soft limits is developed and implemented on the Zurich 1MW BESS demonstration project, owned and operated by the utility of the Canton of Zurich (EKZ).