Hub-Height Optimization of Offshore Wind Farm Based on the Tian Ji’s Horse Racing Algorithm and Collaborative Staggering Layout Considering Primary and Secondary Wind Directions

In offshore wind farm micro-siting, maximizing annual power generation across all wind directions often involves a trade-off among different directional conditions, especially when the primary and secondary wind directions account for most wind energy. To address this issue, this paper proposes a turbine layout strategy combining horizontal and vertical staggering. The objective function maximizes the simplified capital efficiency (power generation per unit capital cost) under the primary and secondary wind directions, for which a layout optimization model is constructed and solved using the Tian Ji’s Horse Racing Algorithm (THRO). A case study on an offshore wind farm validates the proposed approach. Results show that, compared with manual empirical layout and the GA-PSO algorithm, the proposed strategy significantly improves the simplified capital efficiency under the primary and secondary wind directions, while also enhancing overall power generation efficiency across all wind directions. This offers a new technical pathway for offshore wind farm micro-siting. Additionally, the THRO algorithm converges within 30 iterations, outperforming conventional optimization algorithms and demonstrating its effectiveness in solving such optimization problems.