## 3 Proposed LVRT Control System
### Pitch & Rotor Side Converter Controls  
In previous studies, pitch and RSC controls (also called WT inertia control) were proposed [25] for LVRT control in a WT. These controls can be used for effective LVRT at normal and low wind speeds. However, when the WPS operates at high wind speeds and rotor speed is similar to the rated rotor speed, the rotor speed might be over its limit. Because many WPSs include ESSs for different WP applications, it would be more efficient to use the ESS properly. Thus, we formulated coordinated pitch and RSC controls by calculating an appropriate power reference during LVRT operation. As shown in Figure 3 the WP coefficient reduces as the pitch angles increases. Even though the pitch angle has a slow mechanical response, 10\({}^{\circ}\)/s in an emergency, it has the effect of decreasing the WP reference during the LVRT. Without pitch angle control, the power reference can change from A (MPPT) to B. We can modulate the power reference to decrease further at the time of a grid fault. However, it is quite complex and can result in violations of the speed limit. Therefore, we can define the power reference with respect to the pitch angle and it can be represented as shown in Figure 4 considering the maximum pitch angle response. We considered the grid fault duration as 0.625 s and the maximum pitch angle variation to be 6.25\({}^{\circ}\)/s. Therefore, the power reference can be defined as the profile from B to C considering a linear variation of the pitch angle. In this case, the upper portion of the power reduction can be regarded as the WT LVRT response and the bottom portion as the ESS-required LVRT response (Figure 4). By defining the power reference design in this manner, we can guarantee that the WT LVRT remains within the rotor speed limit and prepare the required ESS capacity for LVRT. Before we apply the proposed method, we can analyze whether the ESS LVRT response is required or not. Because the total energy required for the LVRT response can be regarded as the entire rectangular  
Figure 2: Overall control block diagram of the generator and GSC.  
region in Figure 4, the following equation can be used to evaluate situations in which the ESS is required for a suitable LVRT response.  
\[\frac{1}{2}J\left(\omega_{limit}^{2}-\omega_{m}^{2}\right)<\int_{0}^{T_{ fault}}P_{t}dt, \tag{6}\]  
where \(T_{fault}\) is the fault duration which is defined as the grid code requires a WT to be connected. \(\omega_{limit}\) denotes the maximum rotor speed limit. If the above equation is satisfied, then an ESS LVRT response is needed; the required ESS capacity can be obtained using the following equation.  
\[ESS_{LVRT}=\frac{1}{2}\left(P_{B}+P_{C}\right)T_{fault}, \tag{7}\]  
where \(ESS_{LVRT}\) is the required ESS capacity for LVRT. B and D can be obtained by the following equations.  
\[\begin{array}{ll}P_{B}&=\frac{1}{2}\rho AC_{p}\left(\omega_{limit},\beta \right)r_{wind}^{3},\\ P_{C}&=\frac{1}{2}\rho AC_{p}\left(\omega_{limit},\beta_{max}\right)r_{wind} ^{3},\end{array} \tag{8}\]  
where \(P_{B}\) is the current MPPT power output and \(P_{D}\) is the lowest power reference during LVRT. \(\beta_{max}\) is the maximum achievable pitch angle when its value is increased in steps of \(10^{\circ}\)/s during LVRT. Thus, the RSC is controlled by following rules.  
\[P_{RSC}^{*}=\left\{\begin{array}{ll}P_{inertia},&\text{if Equation (\ref{