## 5 Simulation Results  
In order to verify the MRSMC strategy for a DFIG system, a simulation model of a 2 MW DFIG wind power system is built on Matlab/Simulink. The system is rated at 2 MW with its parameters given in Table 1. The power system is modeled by a grid impedance and a voltage source, see in Figure 1. The grid impedance in the model is \(L_{\mathrm{grid}}=0.004\) H, which is related to the short-circuit ratio of power system. The distorted grid voltage of the following figs all contains 5% 5 th harmonics and 5% 7 th harmonics. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rated Power** & **2 MW** & \(\mathbf{U_{\mathrm{ab}}}\) **(rms)** & **690 V** & \(\mathbf{f_{\mathrm{s}}}\) & **50 Hz** \\ \hline \(L_{\mathrm{ls}}\) & 77.29 \(\mathrm{\mu H}\) & \(L_{\mathrm{tr}}\) & 83.35 \(\mathrm{\mu H}\) & \(R_{\mathrm{r}}\) & 0.0029 \(\Omega\) \\ \(L_{\mathrm{m}}\) & 2.5 \(\mathrm{mH}\) & \(R_{\mathrm{s}}\) & 0.0025 \(\Omega\) & \(f_{\mathrm{sample}}\) & 10 kHz \\ \(C\) & 8800 \(\mathrm{\mu F}\) & \(U_{\mathrm{dc}}\) & 1200 V & \(f_{\mathrm{switch}}\) & 2.5 kHz \\ stator/rotor & 0.33 & \(L_{\mathrm{g}}\) & 250 \(\mathrm{\mu H}\) & pole pairs & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of The Simulation Model. Figure 6: Schematic diagram of MRSMC for a DFIG system. Figure 7: Experimental results of the \(T_{1}/4\) delay technique. Comparative tests between the conventional ISMC and the MRSMC strategies for the DFIG system with distorted grid voltage were shown in Figure 8. The GSC reactive power command was set to 0.0 pu; the commands of stator's active and reactive power were 1.0 pu and 0 pu. Table 2 shows the system total current harmonics in Figure 8, from which, it can be seen, when conventional ISMC is adopted, the total currents would contain 6.53% 5 th and 6.50% 7 th harmonics, and total harmonic distortion (THD) of total currents was 9.71%; while the proposed MRSMC is adopted, the THD of total currents was reduced to 3.14%, and the 5 th and 7 th harmonic of total current was reduced to 0.65% and 0.64% respectively. It can be validated that due to the introduction of multi-resonant items in the sliding surface, the tracking behave of the MRSMC is more accurate than ISMC, and the better suppression of current harmonics can be guaranteed. Figure 9 shows the simulation results of the MRSMC strategy for a DFIG wind power system. In this fig, the grid voltage was ideal before 0.1 s and distorted after 0.1 s. It can be seen that, when the grid voltage harmonics appeared suddenly, the system achieved steady status quickly. \begin{table}
\begin{tabular}{c c c} \hline
**FFT Result** & **ISMC** & **MRSMC** \\ \hline THD of \(i_{\text{tabcbc}}\) & 9.71\% & 3.14\% \\
5 th harmonics of \(i_{\text{tabcbc}}\) & 6.53\% & 0.65\% \\
7 th harmonics of \(i_{\text{tabcbc}}\) & 6.50\% & 0.64\% \\ \hline \end{tabular}
\end{table} 
Table 2: Fast Fourier transform (FFT) of currents in Figure 8. ISMC: integral sliding mode control; MRSMC: multi-resonant-based sliding mode control. Figure 8: Simulation results of the MRSMC and ISMC for a DFIG system under distorted grid voltage. Figure 10 show the simulation results of the MRSMC strategy with power command change suddenly. In Figure the stator active power command was changed from 1 pu to 0.0 pu at 0.05 s, and from 0.0 pu to 1 pu at 0.1 s; the reactive power command was changed from 0 pu to 0.5 pu at 0.15 s, and from \(-0.5\) pu to 0.5 pu at 0.15 s. In the fig, the total currents were sinusoidal, even at the moment of power setting change. The active power or the reactive power followed their command within 0.02 s. It can be validated that, the dynamic of the proposed MRSMC. Figure 11 shows the simulation results of the MRSMC strategy with rotor speed variation. It can be seen that the system maintains superb performance under this condition, which validated the good dynamic response of the proposed MRSMC. Figure 10: Simulation results of the MRSMC with power command change. Figure 9: Simulation results of the MRSMC for a DFIG system.