Deriving Sufficient Conditions for Exact Relaxation of Complementarity Constraints in Optimization Problems With Energy Storage

Energy storage is becoming increasingly important in power and energy systems. However, its strongly nonconvex complementarity constraints, which prevent simultaneous charging or discharging behavior, hinder its application in optimization-based decision making. One remedy is to relax these constraints, but the existing relaxation methods are specific to power system applications with limited universality. To bridge this gap, we provide a methodology to derive the general form of sufficient conditions for the exact relaxation of a general energy storage-concerned optimization problem (ESCOP). Specific sufficient conditions for a wide range of ESCOPs can be easily accessed via the proposed methodology. This paper provides mathematical proofs and analyses of the proposed conditions, where sufficient conditions obtained from specific forms of ESCOPs are numerically validated to guarantee exact relaxation and significantly improve the ESCOP solution efficiency.