An exact relaxation method for complementarity constraints in energy-concerned economic dispatch with reserve uncertainty

The integration of high-penetration renewable energy introduces significant volatility into power systems, complicating the optimal dispatch of energy storage systems (ESS). This paper proposes a chance-constrained optimal dispatch framework for multi-unit ESS coordination that explicitly accounts for stochastic generation uncertainty. By reformulating chance constraints into deterministic reserve capacity requirements, the model rigorously internalizes operational risk while preserving computational tractability. To overcome the computational burden of non-convex complementarity constraints, we introduce a cconvex hull reformulation that linearizes the feasible operational region of storage units. Crucially, three sufficient conditions are established to guarantee the exactness of the convex hull relaxation, thereby ensuring global optimality of the solution without introducing binary variables or compromising physical feasibility. Extensive numerical studies on multi-period benchmark systems demonstrate that the proposed method produces solutions identical to those of the original mixed-integer programming (MIP) formulations while achieving substantial reductions in computational time. These results confirm the scalability, robustness, and practical relevance of the proposed uncertainty-aware convex relaxation, making it well suited for real-time operation in large-scale power systems with high penetration of energy storage.