An Analytical Feasibility Condition for The Multi-stage Robust Scheduling of Energy Storage Systems with Application on SCUC

To mitigate the growing uncertainty associated with the increasing penetration of renewable energy, energy storage systems (ESS) are increasingly installed in power systems to provide the required flexibility. The time-coupled and nonlinear constraints of ESSs bring new difficulties for the scheduling problem. Motivated by these challenges, this paper proposes a multi-stage robust optimization (MSRO) method for scheduling problems with uncertainty and ESSs. Unlike the most widely adopted affine decision rules (ADR) for MSRO in which the decisions are assumed to be linear functions with respect to the uncertainty realizations, in this paper, robust feasible intervals (RFI) are proposed in a recursive manner to guarantee the multi-stage operation feasibility (robustness). When uncertainties are observed, decisions can be optimized flexibly within the corresponding RFIs in a rolling horizon manner. In this way, the solution quality is improved since no explicit decision function assumption is required. Besides, an analytical feasibility condition is proposed by analyzing the constraint structure to accelerate the computation. A small example is given to analyze the advantages of the proposed method. Extensive computational experiments are tested on the IEEE 6-bus, 118-bus system, and the Polish 2383-bus system. Results verify the effectiveness of the proposed method.