Uncertain Parameters Adjustable Two-Stage Robust Optimization of Bulk Carrier Energy System Considering Wave Energy Utilization

Within the 21st century, in the Maritime Silk Road, wave energy, a clean renewable source, is drawing more interest, especially in areas with power shortages. This paper investigates wave energy in ships, particularly in a hybrid electric bulk carrier, by designing a system that supplements the existing power setup with oscillating buoy wave energy converters. The system includes diesel generators (DGs), a wave energy generation system, heterogeneous energy storage (consisting of battery storage (BS) and thermal storage (TS)), a combined cooling heat and power (CCHP) unit, and a power-to-thermal conversion (PtC) unit. To ensure safe and reliable navigation despite uncertainties in wave energy output, onboard power loads, and outdoor temperature, a robust coordination method is adopted. This method employs a two-stage robust optimization (RO) strategy to coordinate the various onboard units across different time scales, minimizing operational costs while satisfying all operational constraints, even in the worst-case scenarios. By applying constraint linearization, the robust coordination model is formulated as a mixed-integer linear programming (MILP) problem and solved using an efficient solver. Finally, the effectiveness of the proposed method is validated through case studies and comparisons with existing ship operation benchmarks, demonstrating significant reductions in operational costs and robust performance under various uncertain conditions. Notably, the simulation results for the Singapore–Trincomalee route show an 18.4% reduction in carbon emissions compared to conventional systems.