## 4 Simulation Verification and Analysis
### Simulation Verification of Inertia Coordination Response Control Strategy  
To validate the effectiveness of the coordinated control strategy, the frequency of the receiving power grid was adjusted from 50 Hz to 49.5 Hz at the 4 s mark. The results of the system in different control strategies were analyzed. Figure 10: Simulated waveforms of the system under protection control (**a**) voltage on the AC side of the GSMMC; (**b**) current on the AC side of the GSMMC; (**c**) DC voltage of the MMC-HVDC system; (**d**) the output power of the MMC-HVDC system and the output power of the wind turbines. Based on Figure 11, it is evident that the frequency of the AC-side voltage outputted by the WFMMC promptly reacted to variations in the AC grid frequency on the GSMMC side. The WFMMC received the DC voltage modified by the DC voltage-frequency mapping control of the GSMMC and adjusted its frequency accordingly through the frequency variation control. In this way, the wind turbine could perceive frequency changes in the AC connection line and adaptively provide frequency support to the grid. This proves that the proposed communication-free frequency information transmission method is feasible. Figure 12 demonstrates the inertial response simulation waveforms under different control strategies. The green curve represents the simulation results under the conventional grid-following control described in Section 2. The yellow curve corresponds to the scenario with only wind farm inertial response control designed. The red curve illustrates the case where only the MMC-HVDC system employed inertial response control. The blue curve denotes the proposed coordinated inertial response control strategy presented in this paper. Here is our analysis of the simulated waveform:  
(1) Rapid Initial Power Support:  
When a sudden frequency drop occurs in the grid, the inertia response should activate instantly to provide additional power support and slow down the rate of frequency decline. The faster the response, the smaller the frequency deviation, reducing the reliance on secondary frequency regulation. The proposed strategy (blue) showed a rapid increase in active power at the moment of disturbance (around 4 s), significantly quicker than the other strategies. The wind farm inertia-only control (yellow) responded more slowly, with a lower power increase, only reaching approximately 310 MW. The grid-following control (green) showed almost no change in power, indicating insufficient inertia response capability. Figure 11: Frequency simulation results of WFMMC and power grid. Figure 12: Simulated waveform plots under four control strategies. (2) Sufficient Inertial Power Support:  
During a frequency drop, sufficient inertia power support should be provided to maintain system stability and prevent excessive frequency deviations that could trigger load shedding or protection mechanisms. The proposed strategy (blue) delivered the highest inertia support, with a peak power of around 360 MW, significantly higher than the wind-farm-only control (orange) and MMC-HYDC-only control (red). Wind-farm-only control (orange) and MMC-HYDC-only control (red) provided limited power support, indicating that relying solely on either source is insufficient. Grid-following control (green) provided almost no additional power support, failing to meet the inertia response requirement. (3) Oscillation Damping Capability  
After inertia response activation, the power output should converge quickly to reduce system oscillations and improve damping characteristics, preventing additional dynamic stress on the grid. The proposed strategy (blue) rapidly decreased after providing peak support and stabilized at steady-state levels around 4.8 s, without significant secondary dips. MMC-HYDC-only inertia control (red) exhibited prolonged oscillations between 4.2 s and 4.4 s, indicating weaker dynamic recovery capabilities.