Joint Optimization for Micro-Siting and Collector System of Floating Wind and Wave Energy Considering Stochastic Displacements Under Combined Wind-Wave-Current Loads

Co-locating floating wind turbines (FWTs) with wave energy converters (WECs) offers a promising pathway to reduce the levelized cost of electricity (LCOE) for deep-sea renewable energy. However, stochastic platform displacements under coupled wind–wave–current loads aggravate wake interactions, degrade WEC shielding benefits, and increase cable fatigue risks—challenges not addressed by existing deterministic or empirical approaches. This paper proposes a bi-level distributionally robust optimization method for joint micro-siting and collector-system design of hybrid FWT–WEC plants. The upper level optimizes device layout by incorporating motion-aware wake–shielding coupling, while the lower level formulates a distributionally robust optimization (DRO) model for cable topology, sizing, and slack allocation using Wasserstein ambiguity sets constructed via kernel density estimation. Case studies demonstrate that the proposed method reduces wake losses by 53.70%, FWT heave amplitude by 42.3%, cable length by 4.81%, line losses by 12.76%, and reliability costs by 39.55%, achieving an overall LCOE reduction of 5.36% compared to conventional approaches.