# Fast Frequency Response of a Doubly-Fed Induction Generator for System Inertia Support
## 6 Dynamic Simulation Results
### Case 2: Wind Speed = 8.0 m/s  
Figure 8 displays simulation results for Case 2 (the incoming wind speed of the DFIG is 8.0 m/s) and is smaller than in Case 1 by 2.0 m/s. Thus, the available kinetic energy from a DFIG is 1.683 s, which is  
38.2% of that available in Case 1. Accordingly, \(\Delta P_{\text{con}}\) is 0.16 p.u., which is smaller than in Case 1. \(\Omega_{\text{c}}\) in the conventional strategy is set to 0.74 p.u. In addition, \(\Delta t\) in the proposed method is set to 9.5 s.  
Figure 7: Results for Case 1: (**a**) system frequencies; (**b**) active powers; (**c**) rotor speeds; (**d**) captured mechanical powers. Figure 8: Results for Case 2: (**a**) system frequencies; (**b**) active powers; (**c**) rotor speeds; (**d**) captured mechanical powers. The system frequency nadir for MPT is 59.391 Hz, which is the same as in Case 1 because no power is injected from a DFIG and all active power is compensated by synchronous generators. The system frequency nadir for the proposed strategy is 59.490 Hz, which is slightly smaller than that of the conventional strategy. This is because the output power rapidly decreases during the deceleration period and is slightly smaller compared to that of the conventional strategy, around 13.0 s (see Figure 8b). In addition, the system frequency nadirs for the proposed and conventional methods are less than those in Case 1 due to less incremental power for STFS. Similar to Case 1, in the proposed strategy, the second frequency deviation, which indicates the difference between the second frequency nadir and the nominal frequency, is 0.280 Hz, which is the same as in the conventional method because of the setting of \(\Delta t\) in Equation (14) (see Figure 8a). In addition, the NBFR in the proposed strategy is slightly smaller compared to the conventional strategy due to the lower system frequency nadir in the proposed strategy. The rotor speed in the proposed method converges to 0.83 p.u. at 29.9 s; whereas, the rotor speed in the conventional method converges to 0.74 p.u. at 42.0 s. Accordingly, the proposed method starts recovering \(\omega_{7}\) 12.1 s earlier than in the conventional method, as in the previous case (see Figure 8c). Consequently, as shown in Table 4, the released rotating kinetic energy for the proposed strategy is 0.730 s, which is 52.5% of the released rotating kinetic energy for the conventional strategy. The released rotating kinetic energy around the system frequency nadir in the proposed strategy is 0.373 s in the deceleration period, which is slightly smaller than in the conventional strategy by 0.043 s; nevertheless, the released rotating kinetic energy in the rest acceleration period is 0.373 s, which is 0.614 s less than in the conventional strategy. After supporting the system frequency, the proposed strategy releases rotating kinetic energy significantly less than in the conventional method. As in Case 1, when the proposed strategy produces the same second frequency deviation as the conventional method, the rotor speed restoration duration in the proposed strategy is 93.0 s, which is 29.5 s faster than in the conventional strategy. Furthermore, the harvested mechanical input power during 100.0 s in the proposed strategy is 3.58 MWh, which is 0.07 MWh greater than in the conventional strategy. Simulation results of two cases clearly represents that the proposed strategy can provide approximate performance of the system frequency nadir with less released rotating kinetic energy from a DFIG under different wind speeds; particularly, after supporting the frequency nadir, the proposed strategy releases rotating kinetic energy significantly less than in the conventional strategy. The proposed strategy accelerates the restoration of the rotor speed when it results in the same second frequency deviation compared to the conventional method during STFS. Moreover, the proposed restoration