Optimal Black-Start Restoration Sequencing of Hybrid Wind Farms Considering Dynamic Wake Effects and Wind Energy Variability

Following extreme disasters, hybrid wind farms comprising grid-following (GFL) and grid-forming (GFM) turbines can serve as black-start resources for power system restoration. However, wind power uncertainty, wake effects, and collection-grid restoration constraints complicate the startup sequence planning of GFL turbines within hybrid wind farms. To address these challenges, this paper proposes a multi-objective mixed-integer linear programming (MILP) model that jointly considers electrical impedance paths, wind uncertainty, and spatial wake effects. Information Gap Decision Theory (IGDT) is incorporated into active power support constraints to account for wind uncertainty through a robust adjustment of available generation capacity, while the Dijkstra algorithm is employed to convert collection-cable parameters into impedance-based cost factors for identifying minimum-impedance restoration paths and mitigating transient overvoltage risks. In addition, dynamic wake losses under non-uniform turbine layouts are quantified to capture the influence of startup sequences on local flow fields, and the resulting nonlinear terms are reformulated using the big-M linearization technique. Case studies considering different wind directions, time-varying wind speed conditions, and cable-impedance sensitivities demonstrate the effectiveness of the proposed framework. The results show that the proposed strategy provides a favorable balance between impedance-cost minimization, wake-effect mitigation, and robustness enhancement, while maintaining reliable restoration performance under diverse operating conditions.