## 2 Frequency Regulation Model of DFIG
### De-Loading Strategy for FR Reserve Capacity
#### 2.2.4 De-Loading Strategy of DFIG  
Based on the division of the WS region and operation point selection of pitch angle, the specific de-loading strategy of DFIG in different WS regions are elaborated below. **Low WS region:** The DFIG outputs 90% maximum power by controlling the rotor speed to operate at the over-speed suboptimal trajectory, providing reserve capacity of 10% maximum power for up-regulation. The pitch angle remains at \(\beta_{2}\). **Medium WS region:** The rotor speed cannot follow the over-speed suboptimal trajectory due to the upper limit of 1.2 p.u. ; thus, the pitch angle is increased to keep 90% maximum power output, providing reserve capacity of 10% maximum power for up-regulation. The rotor speed remains at 1.2 p.u. **High WS region:** The maximum power point has reached the rated power. The DFIG outputs 90% rated power by controlling the pitch angle, providing reserve capacity of 10% rated power for up-regulation. The rotor speed remains at 1.2 p.u. In the de-loading strategy, the rotor speed and pitch angle operation strategy for providing FR reserve capacity is summed up in (3) and (4), respectively:  
\[\left\{ \begin{array}{ll}P_{m}(v_{w},\omega_{FRC},\beta_{2})=(1-d\%)P_{MPPT} (v_{w})&6.7\text{m/s}<v<9.1\text{m/s}\\ \omega_{FRC}=1.2&9.1\text{m/s}\leq v<25\text{m/s}\end{array} \right. \tag{3}\]  
\[\left\{ \begin{array}{ll}\beta_{FRC}=\beta_{2}&6.7\text{m/s}<v<9.1\text{m/s} \\ P_{m}(v_{w},1.2,\beta_{FRC})=(1-d\%)P_{MPPT}(v_{w})&9.1\text{m/s}\leq v\leq 11.8 \text{m/s}\\ P_{m}(v_{w},1.2,\beta_{FRC})=(1-d\%)P_{e}&11.8\text{m/s}<v<25\text{m/s}\end{array} \right. \tag{4}\]  
where \(\omega_{FRC}\) and \(\beta_{FRC}\) are the operating rotor speed and a pitch angle of DFIG for providing FR capacity, respectively. In addition, the operation range of the pitch angle is 0-70\({}^{\circ}\)[5]. Figure 3: Analysis of pitch angle change rule. (**a**) Blade power coefficient change at different WSs (wind speeds); (**b**) Pitch angle operation trajectory in medium WS region. **Low WS region:**  
Up-regulation: The DFIG reduces \(\omega_{r}\) so as to increase power output. When \(\omega_{r}\) reaches \(\omega_{opt}\), if the FR task allocated to DFIG by grid control center still cannot be fulfilled, the deceleration should be stopped. Then, \(\beta\) will be reduced to continue increasing power output. If the FR task still cannot be fulfilled even when \(\beta\) reaches \(0^{\circ}\), \(\beta\) stops decreasing and DFIG stays in the MPPT state, providing frequency support in another way. Down-regulation: The DFIG raises \(\omega_{r}\) so as to decrease power output. If the FR task cannot be fulfilled even when \(\omega_{r}\) reaches 1.2 p.u., the acceleration should be stopped. Then, \(\beta\) will be raised to continue decreasing power output. If the FR task still cannot be fulfilled even when \(\beta\) reaches \(70^{\circ}\) or the power output reaches \(P_{\text{min}}\), \(\beta\) stops increasing, providing frequency support in another way. **Medium WS region:**  
Up-regulation: The DFIG reduces \(\omega_{r}\) so as to increase power output. If the FR task still cannot be fulfilled even when \(\omega_{r}\) reaches \(\omega_{opt}\), the deceleration should be stopped. Then, \(\beta\) will be reduced to continue increasing power output. If the FR task still cannot be fulfilled even when \(\beta\) reaches \(0^{\circ}\), \(\beta\) stops decreasing and DFIG stays in the MPPT state, providing frequency support in another way. Down-regulation: The DFIG raises \(\beta\) so as to decrease power output. If the FR task cannot be fulfilled even when \(\beta\) reaches \(70^{\circ}\) or the power output reaches \(P_{\text{min}}\), \(\beta\) stops increasing, providing frequency support in another way. \(\omega_{r}\) always remains at 1.2 p.u. **High WS region:**  
Up-regulation: The DFIG reduces \(\beta\) so as to increase power output. If the FR task cannot be fulfilled even when the power output reaches \(P_{e}\), \(\beta\) stops decreasing, providing frequency support in another way.