Optimal Planning Method of Wind Farms Considering Spatiotemporal Frequency Characteristics Under Uncertain Disturbances

With the large-scale integration of wind farms, the spatial distribution characteristics of system dynamic frequency response become increasingly prominent. Existing wind farm planning methods considering frequency constraints mostly rely on predefined disturbance scenarios or system-level average frequency indicators, failing to account for the spatial randomness of disturbance locations. This leads to potential safety risks of local bus frequency limit violations when the systems planned accordingly are subjected to uncertain disturbances in actual operation. To address this issue, this paper proposes an optimal wind farm planning method based on frequency response upper bound constraints. The proposed method utilizes the algebraic connectivity index to characterize the theoretical upper bound of system frequency response under uncertain disturbances, which is then incorporated into the planning model as a constraint, thereby avoiding the risk of frequency limit violations in weak areas of the network. First, based on the closed-loop transfer function model and infinity norm theory, the theoretical upper bound of frequency response under uncertain disturbances is derived, and an upper bound evaluation index explicitly correlated with algebraic connectivity is constructed to identify the worst-case frequency response under uncertain disturbances. Second, the upper bound evaluation index is transformed into constraints for the wind farm siting and sizing model and an optimal planning method based on the frequency upper bound constraint is proposed. Simulation results on the IEEE 39-bus system show that, when a 1.2 p.u. active-power disturbance is applied at each bus individually, the proposed planning method reduces the average maximum frequency deviation by 36.78% relative to the unoptimized siting-and-sizing scheme (arithmetic mean across 39 bus-wise scenarios); for eight preset topology change scenarios, it yields a further 7.03% average reduction in maximum frequency deviation relative to the unoptimized scheme under each scenario topology.