## 1 Introduction
Very few published papers or documents emphasize the comprehensive frequency regulation capacity of PMSG based on rotor speed-based control under different wind speeds or enhanced inertial responses based on active power-based control when operated in MPPT mode, especially for the potential impact of frequency regulation on the mechanical components of wind turbines. Therefore, this research addresses the major issues with the goal of maximizing PMSG-WTG performance for frequency regulations in accordance with its specific operation characteristics and control structure. Concurrently, it is necessary to research a frequency regulation strategy to effectively maximize the stored KE. The authors of [24; 25] suggested an operational strategy for maximizing the amount of KE during a frequency disturbance. However, these studies have not described the optimization techniques in detail. This study proposes a new optimal control and operation strategy for a PMSG wind turbine to support system frequency in wind energy production. The machine-side converter (MSC) and grid-side converter (GSC) are designed to control the DC link voltage using vector control, and obtain maximum power output from PMSG wind turbines. The active power control operates the turbine with the MPPT and achieves the power margin through de-loaded control. Once these are achieved, the KE reserve control establishes the frequency regulation to provide stable PMSG wind turbines. To increase the contribution of wind turbines to support frequency stability via a temporary release of energy, the KE optimization method performs a KE maximization for various wind speeds using the particle swarm optimization (PSO) algorithm. The operation of PMSG wind turbines is then optimized to extract more KE, which can be released into the power system in the case of a frequency event. The optimization strategy assumes that the wind farm system performs continuous output control with monitoring and control systems for individual PMSG wind turbines. With the wind speed, this strategy calculates the maximum possible output, optimal rotational speed, and KE reserve in each wind turbine. The de-loaded power reference from an individual PMSG wind turbine that maximizes the KE reserve of the wind farm is obtained by satisfying the output command of the system operator. The frequency support capability of the PMSG system with the proposed KE reserve control strongly depends on the KE reserve obtained from the de-loaded operation and generating margin. Therefore, the frequency response of a system can be improved after organizing the de-loaded operations of individual PMSG systems with regard to the KE reserve when the wind farm is de-loaded. The KE optimization strategy, which maximizes the sum of the KE reserves at a wind farm, is adopted to determine the de-loaded power reference for each PMSG wind turbine. The rest of this work is structured as follows. Section 2 presents the system modeling and converter control. Section 3 presents the proposed control and operation strategy to support frequency regulation using PSO. Section 4 describes a comparison of the simulation results of other cases to assess the performance of the proposed strategy. Section 5 presents the concluding remarks.