## 5 Simulation and Experiment  
### Simulation Analysis  
In this paper, a back-stepping SSO suppression strategy based on an adaptive quasi-resonant controller is proposed. The performance of the RSC current controller had to be simulated and analyzed. Assuming that the initial speed of the DFIG is 900 r/min, the expected value of DFIG output active power will be 4000 W at this time, while the expected value of the DFIG output reactive power will always be 0 Var. The values of the power  
Figure 8: Frequency response of RSC \(H_{1}(s)\) based on resonant control: (**a**) frequency response of \(H_{1}(s)\) when \(K_{\text{R}}\) changes; (**b**) frequency response of \(H_{1}(s)\) when \(\omega_{\text{c}}\) changes. Figure 7: Frequency response of RSC \(F_{1}(s)\) based on resonant control. output of the DFIG with the improved controller and the PI controller were compared through a simulation. The simulation results are shown in Figure 9.  
In order to simulate the unpredictable noise signal during the motor control, a set of random numbers were added to the rotor d and q currents, respectively, and the amplitude was limited to within 5% of the actual current component. It can be seen from Figure 9 that both the improved controller and the PI controller could control the DFIG output power and make it reach the desired value. However, due to the interference of the noise signal, the DFIG power controlled by the PI controller exhibited an overshoot and oscillation phenomenon, and it took a period of time to stabilize the DFIG output at the desired value. However, there was no integral link in the back-stepping controller, so it was not necessary to consider the problem of integral saturation. The outputs of the DFIG controlled by the two controllers were smooth; less affected by small disturbances, such as noise signals; and could converge to the target value quickly. Figure 10 shows the improved controller's tracking of changes in power. The simulation condition is that, at 0.5 s, the expected value of the DFIG output active power changed from 4000 W to 4500 W. It can be seen from the simulation results that, when the expected value of the active power changed suddenly, the DFIG active power controlled by the back-stepping controller changed to the expected value, which was reached after 0.1 s-0.2 s. In this process, the output reactive power of the DFIG is still 0 VAR, which verifies that the RSC controlled by the improved controller could realize power decoupling control of the DFIG. Next, the oscillation suppression effect of the back-stepping SSO suppression strategy based on the adaptive quasi-resonant controller was verified at different SSO frequencies. Figure 11 compares the adaptive quasi-resonant controller with the quasi-resonant controller, verifying that the adaptive quasi-resonant controller could still achieve the control target when the SSO frequency changed. The adaptive quasi-resonant controller was used with an oscillation frequency of 10 Hz, while that of the resonant controller was 30 Hz. Figure 11 shows that, with an oscillation frequency of 10 Hz, since the control frequency of the quasi-resonant controller was fixed at 30 Hz, the oscillation frequency deviated significantly from the control range of the controller, so the quasi-resonant controller no  
Figure 10: DFIG output power at rotor speed jump. Figure 9: DFIG output power using different controllers. longer exerted a suppression effect on the sub-synchronous current. When the adaptive quasi-resonant controller was used, the control frequency of the controller changed with the oscillation frequency, so the frequency change in the sub-synchronous current did not affect the performance of the adaptive quasi-resonant controller. Finally, the DFIG stator power and capacitance voltage waveforms before and after SSO inhibition were observed.