SOCP-DistFlow Based Two-Stage Robust Scheduling of Shipboard Integrated Energy Systems Under Carbon Pricing

Existing and prospective maritime carbon-pricing regimes, together with uncertain renewable generation, complicate the low-carbon operation of shipboard integrated energy systems (SIES), particularly when network voltages and coupled electrical, heating, and cooling demands must be coordinated. To address this problem, this paper develops a two-stage robust optimization framework for day-ahead unit commitment and dispatch of diesel generators, renewable energy sources, energy storage, alternative maritime power, and carbon capture systems. A shipboard-adapted second-order cone programming (SOCP) DistFlow formulation combines an impedance-ratio-dependent operational security margin with node-specific voltage envelopes. The resulting min–max–min problem is solved by column-and-constraint generation with Big-M linearization. Case studies on a 20-bus shipboard microgrid demonstrate that the framework maintains nodal-voltage feasibility under the modeled worst-case deviations and provides a favorable robustness–cost trade-off. In out-of-sample tests, no infeasible robust realization is observed among the sampled scenarios, whereas the deterministic schedule exhibits infeasibility. Under the assumed capture efficiency, carbon capture also substantially reduces net emissions relative to the no-capture case. The proposed framework supports network-feasible, low-carbon day-ahead scheduling under renewable-generation and multi-energy-load uncertainty without altering the voyage plan.