Energy Storage Sizing for Wind-Storage Frequency Regulation: Kinetic Energy Recovery and Secondary Frequency Drop Suppression

High wind power penetration aggravates power system inertia scarcity, and wind turbines switching to MPPT mode after virtual inertia support induces secondary frequency drop (SFD), impairing grid frequency stability. Traditional energy storage system (ESS) sizing methods fail to couple wind turbine virtual inertia dynamics, rotor kinetic energy recovery and time-varying wind speeds, causing a trade-off between regulation performance and economy. To address this, an optimal ESS sizing method for wind-storage coordinated frequency regulation is proposed, including a doubly fed induction generator (DFIG) model for virtual inertia-power drop correlation, an incomplete compensation strategy, and a constrained three-objective optimization model co-optimizing virtual inertia and ESS parameters. The method, solved by NSGA-II with fuzzy membership functions, is validated on a 1000 MVA grid with a 245 MW DFIG wind farm. Results show it mitigates SFD, avoids ESS over-sizing, and balances performance and economy, breaking the decoupling between traditional ESS sizing and the virtual inertia dynamics of wind turbines.