Sufficient Conditions for the Exact Relaxation of Complementarity Constraints for Storages in Multi-period OPF Problems

Storage-concerned Optimal Power Flow (OPF) with complementarity constraints is highly non-convex and intractable. In this paper, we propose two generalized sufficient conditions which guarantee no simultaneous charging and discharging (SCD) in the relaxed multi-period OPF excluding the complementarity constraints. Moreover, we prove that the regions on the locational marginal prices (LMPs) formed by the proposed two conditions both contain the other existing representative ones. We also generalize the application premise of sufficient conditions from the positive electricity price requirements to the negative electricity price scenarios. In contrast to participating solely in the energy dispatch, we highlight that offering reserve services can broaden the application range of relaxation conditions for storages. The case studies verify the exactness and advantages of the proposed conditions.