Coupling modeling and optimization strategy of wind power reserves across different time-scales for frequency-constrained unit commitment

Under the dual‑carbon goals, the large-scale integration of renewable energy has introduced new challenges to the operational flexibility of power system. Existing research has confirmed that wind turbines (WTs) can provide reserve capacity and inertial support to the power grid. However, existing research on reserve optimization scheduling with frequency constraints fails to clarify the coupling mechanism among different time-scale reserves of WTs. To address this gap, this paper proposes a frequency-constrained scheduling strategy that accounts for the coupling characteristics of WTs reserves across different time-scales. The proposed strategy first models dynamic coupling among virtual inertia control (VIC), rotor speed control (RSC), and pitch angle control (PAC) of WTs, enabling an accurate quantification of WTs reserve capacities across different time-scales. Secondly, according to the dynamic characteristic differences of reserves provided by WTs at different time-scales during the frequency response process, a multi-stage frequency response model considering the dead band and saturation limit of frequency regulation is established. Finally, by considering wind speed uncertainty and decision-dependent uncertainty caused by WTs control decisions, a frequency-constrained robust unit commitment with coupled multi-timescale reserves of WTs (FCRUC-CMR) is developed. The proposed model is adopted to collaboratively optimize generation schedules and reserve allocation. To improve computational feasibility, a modified support vector machine decision tree (MSVMDT) algorithm is proposed to linearly approximate nonlinear frequency constraints. Case studies demonstrate that the proposed model can effectively evaluate the impact of the coupling relationships among different time-scale reserves of WTs on scheduling decisions.