## 5 Simulation Results and Discussion
### Simulations and Analysis Under Different Circumstances
#### 5.3.4. DFIG's Shaft Dynamic after Additional Control  
The above comparison shows that the active power additional damping control has a better suppression effect on inter-area oscillation of a system. As the additional active damping controller increases the damping signal gain, the suppression effect is pronounced. As the gain of the damping signal increases, the unbalanced torque excites the torsional oscillation mode of the shafting, and the amplitude of the torsional oscillation of the wind turbine increases. The amplitude of the inherent torsional oscillation frequency of the DFIG's shaft system is increased to an extent.  
Figure 12 shows the dynamic response of the shaft torque of the DFIG. An inherent wind turbine shaft oscillation mode exists in the DFIG. Evidently, the active power modulation exacerbates the amplitude of the oscillations. Figure 13 shows the dynamic response of the electromagnetic torque of the DFIG. As shown in Figure 13, the fluctuation of the torsional oscillation affects the electromagnetic torque fluctuation through the shafting, which in turn causes the fluctuation of the active output amplitude of the DFIG to increase. The active power output of DFIG is plotted in Figure 14. When the output power of the doubly-fed wind turbine is injected into the power grid, an oscillation component of about 1.82 Hz appears in the output power of the wind farm because of the unstable shaft speed oscillation. As the penetration rate of wind energy continues to increase, the fluctuation of the active output of the wind turbine adversely interacts with the power system and threatens the stability of the power system.  
Figure 11: (**a**) Rotor speed of Generator 3 at Case A; (**b**) Rotor speed of Generator 3 at Case B.  
Figure 12: \(T_{s}\) of DFIG at Case A.  
The design of DCPM can flexibly and feasibly allocate the damping control burden between active and reactive power channels of DFIG. The results show that the dual-channel additional damping control can better balance the fluctuations of the shafting torque and also has a good performance in suppressing the inter-area oscillation.  
The test system shown in Figure 5 has a higher order and analytical mathematical modeling is challenging. This paper uses MATLAB's Prony Toolbox to solve the system eigenvalues, including the wind turbine torsional mode, to confirm the above analysis. The damping of the inter-area oscillation mode and the torsional oscillation mode under different operating states according to the eigenvalue analysis is shown in Table 2.  
As shown in the above table, the hybrid dual-channel modulation has better ability to suppress electromechanical oscillation than the reactive modulation. Compared with the active additional modulation, in the case of similar suppression of electromechanical oscillation capability, the torsional dynamic of the shaft can be considered, and it can simultaneously minimize the adverse effects on torsional damping  
Figure 14: Active power output of DFIG at Case A.  
Figure 13: \(T_{e}\) of DFIG at Case A.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control Mode.** & \begin{tabular}{c} **Inter-area Oscillation** \\ **Frequency/Hz** \\ \end{tabular} & \begin{tabular}{c} **Damping (\%)** \\ **Pamping (\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Shaft Oscillation** \\ **Frequency/Hz** \\ \end{tabular} &
\begin{tabular}{c} **Damping (\%)** \\ \end{tabular} \\ \hline No & 0.65 & 1.21 & 1.82 & 7.21 \\ DCPM & 0.65 & 8.05 & 1.82 & 6.52 \\ APM & 0.64 & 8.11 & 1.82 & 4.13 \\ RCM & 0.65 & 5.21 & 1.82 & 7.23 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Inter-area damping and torsional damping under various operating states and modulation methods.