## 4 Simulation
### Start-Up  
Firstly, at t = 0 s, the onshore MMC starts charging the submodule capacitors and establishes a DC link current. At t = 0.05, the DC current reaches 1.5 kA, as shown in Figure 7b, and the DC voltage is nearly 0, as shown in Figure 7a. Then, at t = 0.2 s, the first wind turbine string starts up, as shown in Figure 8. The wind turbine gradually outputs active power P1, charging the DC capacitor in the MVDR, the submodule capacitor in the MMC, and the DC output port capacitor in the HVDR to establish the DC voltage vout1 and vdc1 in the parallel wind farm string. At t = 0.8 s, the active power of the wind farm string is 100 MW, the DC voltage of MVDR reaches its rated value of 160 kV, the submodule capacitor voltage of MMC v1 reaches 2.5 kV, and the HVDC output voltage is 100 kV. As  
\begin{table}
\begin{tabular}{l l l} \hline \hline
**Onshorc MMC** & \begin{tabular}{l} Rated power \\ DC voltage \\ DC current \\ Onshore grid voltage \\ \end{tabular} & \begin{tabular}{l} 1000 MW \\ \(\pm\)320 kV \\ 1.6 kA \\ 400 kV \\ \end{tabular} \\ \cline{2-3}  & \begin{tabular}{l} Rated power of PMSG \\ The output voltage of the \\ AC/DC rectifier \\ The output voltage of the MVDR \\ 250 Hz, \\ Isolation transformer \\ \end{tabular} & \begin{tabular}{l} 25 MW \\ 6 kV \\ The output voltage of the MVDR \\ 250 Hz, \\ Y/\(\Delta\), 3.3/66, \\ leakage inductance, 1\% \\ \end{tabular} \\ \cline{2-3}  & \
\begin{tabular}{l} Rated power \\ The output voltage of HVDR converter \\ 250 Hz, \\ Isolation transformer \\ \end{tabular} &
\begin{tabular}{l} 250 MW \\ 160 kV \\ 250 Hz, \\ Y/\(\Delta\), 70/120, \\ leakage inductance, 1\% \\ \end{tabular} \\ \hline Onshore grid & AC voltage & 330 kV \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the system.  
the active power output of the wind turbine increases, according to Equation (6), with the increase of active power, at t = 2 s, the active power of the wind turbine reaches its maximum value of 250 MW, and the DC voltage of HVDR reaches its rated value of 160 kV. The first string of wind turbines has started and is being completed. Subsequently, the other strings are started in sequence, as shown in Figure 9. At t = 3 s, the second string of wind turbines starts at t = 4.5 s. The third string of wind turbines starts at t = 6 s and completes the start-up at t = 7.5 s. The fourth string of wind turbines starts at t = 9 s and completes the start-up at t = 10.5 s. Figure 9 shows no fluctuation in the capacitor voltage in the MMC submodule during the start-up process. It can be concluded that the parallel-series topology is decoupled from other branches during start-up. As shown in Figure 10a, as the wind turbine series gradually starts, the DC voltage in the HVDC line gradually increases to 640 kV. The DC current in the HVDC line does not change during the start-up process, as shown in Figure 10b.  
Figure 8: The waveforms for the wind strings. (**a**) Active power of wind turbine; (**b**) Output voltage of MVDR; (**c**) Average capacitor voltage of MMC; (**d**) Output voltage of HVDC.  
Figure 7: The waveforms for the HVDC link. (**a**) The DC voltage of HVDC link; (**b**) The DC current of HVDC link.  
Figure 9: The waveforms for offshore wind strings. (**a**) Active power of wind turbine; (**b**) Output voltage of MVDR; (**c**) Average capacitor voltage of MMC; (**d**) Output voltage of HVDC.