## 1 Introduction  
An increase in the proportion of renewable energy in power systems is planned and expected. Among the types of renewable energy, solar and wind power have the highest proportions of use and potential for renewable energy generation. These are inverter-based resources (IBRs) and have a low contribution to the inertia of power systems. Increasing the number of IBRs will result in the replacement of traditional synchronous generators in power systems, leading to low system inertia [1]. In a low-inertia system, insufficient system inertia increases the rate of change of frequency (RoCoF). This is mainly because photovoltaic devices do not have inertia. Although the variable-speed wind turbine generator (VSWTG) has rotational inertia, it does not affect the system's inertia because it is decoupled from the system through a converter. In a traditional power system, a disturbance leads to a frequency decrease, and synchronous generators immediately respond. This generator action prevents further decreases in frequency. Initially, the missing infeed is provided by inertia, and after a few seconds, the generator's governor response is activated by droop control. However, in a high-IBR system, low inertia leads to a large initial RoCoF, which results in a small margin for the traditional generator governor. In the event of a missing large power supply, the frequency will drop below the reliability standard and a wide-area power failure may occur owing to the operation of the under-frequency relay. To prevent this issue, fast frequency response, which improves the lower frequency and the initial RoCoF through the inertial contribution of IBRs, has been introduced as a new auxiliary service. FFR can improve frequency stability during events with a large initial RoCoF. VSWTGs and energy storage systems (ESSs) are representative IBRs that can be used as FFR resources [2]. Research has been conducted on the ability of the IBR control of VSWTGs to contribute to system inertia. In some studies, the use of the rotational kinetic energy of a wind turbine using the rotational kinetic energy of a drivetrain through converter control has been introduced [3; 4; 5]. This control method requires frequency or RoCoF measurements. The electrostatic inertia method uses the capacitor potential energy as inertia by regulating the voltage on the DC-link capacitor in the converter [6]. Suboptimal power point tracking (SPPT) is also a method of mitigation, which generates additional output by changing the operating point from the operating point on the maximum power point tracking (MPPT) curve to a suboptimal point [2; 7; 8]. Torque limit control, one type of SPPT control, is a control method that instantly maximizes the electrical torque through converter control [9]. Therefore, it is suitable for use in the case of frequency-drop events. The synchronverter method, which provides control similar to that of a synchronous generator, has the advantage that it does not rely on frequency or RoCoF measurements [10]. However, FFR does not always improve system stability. Because FFR reacts as quickly as possible after a frequency drop, the resource may not be used efficiently. In particular, the FFR of a VSWTG sometimes occurs at a second frequency nadir owing to the reduced power to restore the normal operating point of the wind turbine. This study proposed a novel coordinated control strategy for FFR using ESS and permanent magnetic synchronous generator (PMSG)-type wind turbine in order to solve the disadvantage that the second frequency nadir is lower than that of the first frequency nadir. The proposed control strategy utilizes resources efficiently to improve the frequency bottom point rather than responding to the frequency drop as quickly as possible.