## 5 Simulation Cases
### DFIG Participating in FR  
In order to verify the effectiveness of the proposed FR model for DFIG, two scenarios are set up. In Scenario 1, DFIG participates in FR, and the lack of FR demand power is compensated by the conventional unit. In Scenario 2, DFIG does not participate in FR and operates according to the proposed de-loading strategy. Other conditions of the two scenarios are the same. The power output of DFIG in two scenarios are shown in Figure 10. Following the proposed de-loading operation strategy for FR capacity, DFIG's power output in Scenario 2 varies with the change in WS. It can be seen from the figure that DFIG's power output in Scenario 1 fluctuates around the de-loading operation curve in Scenario 2, which indicates that DFIG plays an active role in system FR through regulating power output. \begin{table}
\begin{tabular}{c c} \hline
**Name** & **Parameter** \\ \hline Threshold of residence time \(T^{*}\) & 1 h \\ Charging/discharging efficiency & 0.95 \\ Battery capacity & 30 kWh \\ Initial SOC & \(SOC_{0}\)\(\sim\)U (0.2,0.8) \\ \(SOC_{\text{max}}\) & 0.9 \\ \(SOC_{\text{min}}\) & 0.2 \\ Time of arrival at workplace \(AR\) & \(AR\)\(\sim\)N (8.5,0.52) \\ Time of departure from workplace \(DP\) & \(DP\)\(\sim\)N (17.5,0.52) \\ Driving distance \(DS\) (km) & \(\ln DS\)\(\sim\)N (17.9,4.9) \\ Driving speed [28] & 28.5 km/h \\ Energy consumption & 15 (kWh/100 km) \\ \(\rho_{up}\) & 0.95 \\ \(\rho_{down}\) & 0.15 \\ Vehicle number & 1000 \\ \hline \end{tabular} SOC: state of charge.  
\end{table} 
Table 6: Parameters of EV (electric vehicle). Figure 9: Profiles of load fluctuation and wind speed in the two-area model. (**a**) Profiles of load fluctuation; (**b**) Profiles of wind speed. The FR task of DFIG in Scenario 1 is shown in Figure 11, where the blue curve represents the FR task without rotor speed protection, while the red curve represents the FR task after being processed by rotor speed protection block. It can be seen that in the time period of 2:00-5:00 and 10:30-14:30, the WS is in the low-speed region, as shown in Figure 9b; thus, the rotor speed protection will work and reduce DFIG's FR task with the decrease in WS. In the time period of 0:00-2:00 and 5:00-7:00, the WS is lower than 6.7 m/s, so DFIG completely exits FR, and its FR task is set to be zero. The FR capacity of DFIG for up-regulation and down-regulation are shown in Figure 12a,b, respectively. It can be seen that in low and medium WS region, the up-regulation capacity of DFIG is relatively less when the WS is small and rises with the increase in WS. When the WS enters high WS region, the up-regulation capacity remains at 0.1 p.u. At the same time, the down-regulation capacity of DFIG rises as well with the increase in WS, and DFIG's down-regulation capacity is more sufficient than up-regulation capacity due to the operation characteristic of DFIG and the set value of de-loading rate. The FR output of DFIG is shown in Figure 13. The comparison of FR output and FR task is shown in Figure 13a. It can be seen that the FR task is well accomplished in the down-regulation situation since the FR capacity for down-regulation is sufficient, but the FR task for up-regulation is not completely accomplished. This is because, in the situation of up-regulation, the FR output of DFIG is restrained by the FR capacity, as shown in Figure 13b. The operation state changes of DFIG are shown in Figure 14, where the rotor speed or pitch angle equaling to zero indicates that the DFIG has exited FR. The rotor speed change in the FR process is shown in Figure 14a. Corresponding to the WS profile, it can be seen that in low WS region, \(\omega_{FRC}\) in Scenario 2 changes to keep the power output at 0.9\(P_{MPPT}(v_{w})\). On this basis, \(\omega_{r}\) in Scenario 1 changes to regulate DFIG's power output for FR. In medium and high WS regions, \(\omega_{FRC}\) remains at 1.2 p.u., and \(\omega_{r}\) only decrease to participate in up-regulation except for transient over-limit. Change in \(\beta\) in the FR process is shown in Figure 14b.