## 4 Simulation Verification
### Verification of Power Coordinated Control
While the power changes, the input stage exhibits certain inertia and damping characteristics under the control strategy of VSM, which enhances the friendliness to the upper grid. In addition, \(Q\) becomes negative after \(t=5\) s, indicating that PET delivers reactive power to the upper grid and provides reactive power support. Figure 11b illustrates the virtual potential response of VSM. Before \(t=5\) s, the input stage absorbs active power and the reactive power setpoint is zero. At this point, the virtual potential is slightly lower than the voltage amplitude of the upper grid voltage of 28.6 kV, and slight fluctuations occur when the active power changes. After \(t=5\) s, the virtual potential becomes larger than the upper grid voltage because PET delivers reactive power to the upper grid. The grid-side current transient response, steady-state response and total harmonic distortion (THD) of the input stage MMC are shown in Figure 12. In order to analyze the transient response characteristics of the current when the output power changes abruptly, we select the current variation at the third power change for analysis randomly. It can be seen from Figure 12a that the current changes are relatively smooth under the control strategy of VSM. Since the VSM control strategy causes the input stage to have certain inertia and damping characteristics, the dynamic corresponding time is about 0.55 s. Figure 12b shows the steady-state response of the current. It can be seen that the quality of the grid-side current waveform is good at steady state. Figure 12c displays the THD of the grid-side current which takes the first 31 harmonics into account. It can be seen that the current remains at a relatively low THD of about 2.3% during the steady-state operation and the THD becomes higher when the power changes because the frequency of the output current deviates from the rated frequency at that time. It can be summarized that the control strategy of VSM can make the grid-side current of  
Figure 11: Output characteristics of the input stage: (**a**) Active and reactive power between PET and the upper grid; (**b**) Virtual potential of VSM. the input stage have a relatively low THD and ensure the power quality, which can effectively reduce the harmonic pollution caused by PET and reduce its adverse impact on the grid. Figure 13 presents the transient and steady-state response of the current and the THD taking the first 31 harmonics into account of the AC output port. We select the current variation around 4 s to analyze the transient response characteristics. As shown in Figure 13a, the output current responds quickly when the output power changes and reaches a steady state after a small overshoot under the P/Q control. Figure 13b indicates that the quality of the current waveform is good at steady state. Figure 13c shows that the current remains at a relatively low THD of about 1.9% during the steady-state operation except when the output power changes that causing higher THD. Figure 12: Grid-side current characteristics of the input stage MMC: (**a**) Transient response (**b**) Steady-state response (**c**) Total Harmonic Distortion (THD). Figure 14 shows the current waveform of the DC output port. It can be seen that the DC output current remains stable at steady state and the ripple coefficient is approximately 2%. When the power changes, the current responds rapidly and reaches a new steady state after a short period of fluctuation. This is because the DC output port does not control the power directly and the power is determined by the input DC voltages of the isolation stage as analyzed previously. Figure 13: Current characteristics of the AC output port: (**a**) Transient response, (**b**) Steady-state response, (**c**) THD. Figure 15a,b shows the steady-state capacitor voltage waveforms of the MMC sub-modules of the input stage and AC output port, respectively. Due to the large amount of sub-modules, we select the sub-modules in the upper arm of phase A for analysis.