## 5 Conclusions  
Ensuring the stability of MMC-HYDC systems for offshore wind farm transmission presents significant challenges, particularly in handling AC-side faults and the lack of inertia in power-electronics-based wind farms. In this work, a grid-forming coordinated inertia support strategy was proposed to enhance frequency stability and response efficiency.  
In terms of information transmission, the DC voltage-frequency-mapping-based method avoids the inertia response delay of the wind farms caused by communication-based transmission methods. This means that the wind farms can quickly receive the frequency information and respond in time. Meanwhile, based on the three key requirements of inertia response (rapid response, sufficient power support, and oscillation damping), the proposed coordinated inertia control strategy outperforms other strategies in the following ways: it has a faster initial inertia response; higher inertia support, significantly improving system inertia and frequency stability; and the strongest oscillation suppression. Thus, the proposed strategy effectively meets the inertia response requirements and offers high practical value for renewable-energy-integrated power systems.  
Furthermore, the fault characteristics of wind farms interconnected with MMC-HYDC systems during AC-side faults were examined. Understanding these transient behaviors provides valuable insights for designing more effective fault protection and control strategies, offering a foundation for future research on enhancing system stability and resilience. Due to the decoupling effect, wind farms continue injecting power during faults, leading to DC overvoltage and potential converter shutdown. To mitigate this, braking resistors (BRs) were tested as a protection measure, and the simulation results confirm that BRs effectively suppress DC overvoltage, preventing excessive power curtailment of wind farms without modifying their control strategy.  
However, this study assumed ideal conditions and did not account for communication delays or renewable generation forecast errors, which could affect real-world performance. Moreover, the offline simulation environment (PSCAD/EMTDC) limits the direct applicability of the findings to practical engineering systems. Future research endeavors should prioritize real-time digital simulation validation to comprehensively evaluate the practical feasibility of the proposed strategy in offshore wind power applications.  
Conceptualization, methodology, software, writing--original draft preparation, and writing--review and editing, J.Z., L.X. and P.F.; supervision, project administration, and funding acquisition, C.L., Z.T. and M.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the technology project of state grid Sichuan electric power Co., Ltd., China (No. 521997230009).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
Authors [PERSON] and [PERSON] were employed by the company Electric Power Research Institute of State Grid Sichuan Electric Power Co., Ltd. The funders participated in the design of the study, as well as in the analyses and interpretation of data, the writing of this article or the decision to submit it for publication.