Integrated Scheduling of Wind Power and Pumped Hydroelectric Storage Based on an MILP Model

In this article, we develop a tractable mixed-integer linear programming framework for the annual scheduling of a hybrid offshore wind and pumped hydroelectric energy storage system. The proposed formulation uses McCormick envelopes to relax the non-convex hydraulic power relations while embedding generation dispatch within a direct current optimal power flow model. In particular, we incorporate a cumulative storage incentive into the objective function to capture the trade-off between net electricity-market revenue and intra-horizon water availability, examining its weighting multiplier through a systematic sensitivity analysis. We illustrate the performance of the proposed formulation applied to (i) a modified PJM five-bus benchmark and (ii) an IEEE 30-bus network hosting two hybrid installations, driven by historical wind profiles from Tamaulipas and locational marginal prices from the Mexican wholesale electricity market. Moreover, we assess the selected binary operating-mode sequences ex post by re-optimizing the continuous dispatch under the exact bilinear hydraulic equations. The numerical results demonstrate that coordinated dispatch enhances energy arbitrage and dynamic grid interaction. In the five-bus case, the reference cumulative storage incentive raises the average upper-reservoir elevation relative to scheduling without the incentive, but both schedules end at the minimum operating level. Thus, the incentive improves water availability within the annual horizon without preventing terminal depletion or guaranteeing long-term water reserves.