Distributionally Robust Optimal Scheduling of Hybrid Ship Microgrids Considering Uncertain Wind and Wave Conditions

A hybrid ship uses integrated generators, an energy storage system (ESS), and photovoltaics (PV) to match its propulsion and service loads, and together with optimal power and voyage scheduling, this can lead to a substantial improvement in ship operation cost, ensuring compliance with the environmental constraints and enhancing ship sustainability. During the operation, significant uncertainties such as waves, wind, and PV result in considerable speed loss, which may lead to voyage delays and operation cost increases. To address this issue, a distributionally robust optimization (DRO) model is proposed to schedule power generation and voyage. The problem is decoupled into a bi-level optimization model, the slave level can be solved directly by commercial solvers, the master level is further formulated as a two-stage DRO model, and linear decision rules and column and constraint generation algorithms are adopted to solve the model. The algorithm aims at minimizing the operation cost, limiting greenhouse gas (GHG) emissions, and satisfying the technical and operational constraints considering the uncertainty. Extensive simulations demonstrate that the expected total cost under the worst-case distribution is minimized, and compared with the conventional robust optimization methods, some distribution information can be incorporated into the ambiguity sets to generate fewer conservative results. This method can fully ensure the on-time arrival of hybrid ships in various uncertain scenarios while achieving expected operation cost minimization and limiting greenhouse gas (GHG) emissions.