## 3 Proposed Optimal Strategy
### KE Optimization Method  
#### 3.2.1 Operation Scheme  
For effective utilization of the stored KE, it is essential to understand the influenced of the operating point. The operation scheme that utilizes the KE control as a fast reserve is adopted in the proposed optimal strategy. In normal operation, a PMSG wind turbine acts in the MPPT mode, which is the most economically viable mode. However, to actively participate in frequency control, the PMSG wind turbine operates at the de-loaded power extraction curve. In the event of a severe frequency drop, the de-loaded control mode is changed to the KE reserve discharging mode with a trigger signal. The output \(P_{out}\) of the wind turbine increases as \(\Delta P_{KE}\), and the KE reserve mode maintains the output command using the de-loaded control during the support time. The purpose of the proposed KE optimization method is to first, improve PMSG performance in terms of frequency regulation capability and second, maximize the KE reserve while determining the de-loaded power reference for active power control of the wind farm. When operating under frequency support control, the KE reserve obtained from the individual PMSG wind turbines can be calculated using Equation (18). Assuming that the wind farm consists of \(N\) wind turbines operating at different wind speeds, the total KE reserve of the wind farm can be expressed as  
\[KE_{res,wf}=\sum_{i=1}^{N}0.5J_{i}\left(\omega_{del,i}^{2}-\omega_{m,opt,i}^{2 }\right) \tag{19}\]  
Here, \(\omega_{del,i}\) and \(\omega_{m,opt,i}\) are the de-loaded rotational and optimal rotational speeds in the \(i^{th}\) PMSG wind turbine, respectively. The KE reserve mode can discharge a much greater amount of KE than a conventional plant of the same rating and inertia. The rotational speed deceleration resulting from the KE discharge can be calculated according to the following equation. \[J\omega_{m}\frac{d\omega_{m}}{dt}=P_{m}-\left(P_{ref}+\Delta P_{KE}\right) \tag{20}\]  
The active power control can immediately control the active power output of a PMSG wind generator (\(P_{out}=P_{ref}+\Delta P_{KE}\)) according to the command determined in the system. Because the mechanical input \(P_{m}\) of wind energy in a turbine blade of the wind generator is only determined from the given wind speed and rotational speed, \(P_{m}\) is not instantly changed from the active power control. Controlling the output of the PMSG wind turbine generator results in the rotational speed changing with the difference between the mechanical power input and active power output. If the mechanical input and actual output of the wind turbine balance, the rotational speed is stabilized and the wind turbine operates at the corresponding operation point. Figure 7 shows the modified \(q\)-axis rotational current control loop for the proposed frequency support control. The wind turbine would require a detection scheme to analyze the frequency drop. The trigger signal for switching to the KE reserve is obtained from the variance in the frequency. Figure 8 shows the triggering scheme and frequency detection employed in the proposed frequency support control. In general, when the frequency of the system decreases because of an accident, it is very difficult to determine the scale of the actual accident or severity of the frequency problem until the frequency is restored. A misjudgment by the frequency detector may cause other frequency problems due to the frequency support control of the PMSG wind turbine. To prevent this problem, the frequency detector determines the trigger signal by prioritizing the frequency change rate of the system. All wind turbines simultaneously recognize the frequency deviation using an event detector. The rate of change of frequency (ROCOF) [28] can be obtained as  
\[\frac{df_{system}}{dt}=\frac{2H_{system}}{\Delta P_{loss}\cdot f_{nominal}} \tag{21}\]Here, \(f_{\text{system}}\) is a system frequency and \(f_{\text{nominal}}\) is the nominal frequency (60 Hz).