## 3 Proposed De-Loading Approach  
The WT system considered in this paper is a direct drive configuration, where the power converter is directly connected to the machine's stator winding. In such a system, the rotor speed is fully controlled by the converter, while the blades are controlled by a pitch angle control system.  
The reserve power for PFC is achieved by controlling both pitch angle and rotor speed simultaneously, in order to optimize the operation of the WT system. The goal is to minimize the power losses in the PMSG given in (6) and (7). This is accomplished by involving a pitch angle controller during underrated wind speeds.  
Initially, with the prediction of wind speed, the pitch angle is obtained such that the rotor speed is increased to reduce the power losses in the stator of the PMSG. Predicted wind speed is averaged to avoid blade fluctuation and an excessive number of pitch motor operations. Therefore, averaged pitch angle is selected to ensure consistent operation of the WT, while minimizing resistive losses of the machine.  
First, the measured wind speed is averaged and used to calculate the maximum power that can be achieved by the turbine. The wind forecast is needed to estimate the maximum possible power in advance (\(t+k\)) to help reduce the number of pitch operations. For a given specific reserve power, the output power is obtained and used to determine the required pitch angle instantaneously.  
The optimum operating point of pitch angle and rotor speed is determined using the steps as follows:  
1. Calculate the current and future maximum available power as \[P_{MPPT}=\frac{1}{2}C_{P}\big{(}\lambda_{opt.},0\big{)}\,A_{W}\rho_{air}V_{W}^ {3}\] (9)
2. Calculate the output power as \[P_{out}=P_{MPPT}-\Delta P+P_{PFC}\] (10) where \(P_{PFC}\) is the output power of the droop curve and \(\Delta P\) is the reserved power.
3. Set \(\beta=0\) and solve the nonlinear power equation for \(\omega_{r}\) as: \[F(\omega_{r})=0\] (11) \[F(\omega_{r})=\frac{1}{2}A_{W}\rho_{air}V_{W}^{3}\bigg{\{}c_{1} \bigg{(}\frac{c_{2}}{7}-c_{3}\beta-c_{4}\bigg{)}e^{\frac{-c_{5}}{7}}+C_{6} \lambda\bigg{\}}-P_{out}\] (12) \[\frac{1}{\gamma}=\frac{1}{\lambda+0.08\times\beta}-\frac{0.035}{1+ \beta^{3}}\] (13) \[\lambda=\frac{R_{W}\omega_{r}}{V_{W}}\] (14)
4. Increment \(\beta\) and repeat Step 3 until \(\beta_{max}\).
5. Select an optimal solution such that: \[\min_{\omega_{r,\beta}}(P_{RJoses}+P_{cond.})\]  
All solutions found by the solver in Step 3 provide the same output power as demonstrated in Figure 2. However, the optimal solution, \(S^{*}=\{\beta^{*},\omega_{r}^{*}\}\), is selected such that pitch angle is as maximum as possible. As a result, the required rotor speed of the WT is increased and obtained by the nonlinear solver in Step 3. This will minimize the resistive power in the machine as in Equation (6) and the conduction losses in Equation (7). The algorithm must consider operation limits, such as  
\[\left\{\begin{array}{c}\omega_{r,min}\leq\omega_{r}\leq\omega_{r,MPPT}\\ 0\leq\beta\leq\beta_{max}\end{array}\right. \tag{15}\]  
Figure 3 summarizes the algorithm used to generate the optimum operating point of pitch angle and rotor speed. Note that the output of the droop curve can be involved in the equation, in order  
to define the rotor speed for the amount of power necessary to be injected during a frequency drop. Otherwise, the PFC power is considered to be zero.  
The proposed algorithm with the control loop is shown in Figure 4. The pitch controller is based on a conventional method, where the pitch angle is controlled considering the pitch servo transfer function [28]. The rotor speed is controlled using a designed proportional integral (PI) controller with an inner loop to control the current.  
The controller must ensure a smooth and reliable response to frequency drop. Therefore, the controller is required to adjust the frequency variation by considering the output of a droop curve.  
Figure 3: Proposed de-loading approach.  
Figure 2: Demonstrating all possible operating points.