## 6 Conclusions  
A field-circuit coupling analysis method for overcurrent research in MMC valves is proposed in this paper. The method integrated the electric field characteristics of the MMC valve with the analysis of the MMC-HVDC system. Given the limited overcurrent capability of semiconductor devices in MMC valves and the significant impact of overcurrent  
Figure 16: MMC overcurrent after using current suppression strategy.  
phenomena on the safe operation and system parameter design, accurate calculation of overcurrent in MMC valves is essential and complex.  
Firstly, the method investigates the characteristics and influencing factors of fault currents in valves. Control and protection strategies, protection settings, and post-fault circuit characteristics all contribute to variations in fault currents.  
Additionally, transient parameter changes in nonlinear components, stray parameters of the valve, and electric field distribution can influence the fault loop under transient conditions. Subsequently, a field-circuit coupling model and an electric field calculation model for valves were established, with the system's instantaneous voltage serving as the input for electric field calculation and surge arrester transients. The electric field strength and capacitance values obtained from the electric field calculation were used as inputs for \(C_{\text{g}}\) and \(R_{\text{g}}\) in the field-circuit coupling model. Through this model, the operational circuit characteristics of the system were combined with the electric field characteristics of the valve, enabling precise calculation of overcurrent and the accurate design of suppression strategies. Finally, the method proposed in this paper was applied to the \(\pm\)500 kV offshore MMC-HVDC system for overcurrent analysis and suppression strategy design.  
Simulation experiments were conducted, and the numerical results demonstrate the effectiveness and correctness of the method presented in this paper. This research provides a solid basis for the accurate calculation of overcurrent protection strategies and settings and for improving the utilization rate of power devices in offshore MMC-HVDC valves.  
In the future, a substantial amount of electrical data from system operations can be utilized for model verification. By incorporating measured values such as leakage current of bushings, insulation monitoring quantities of surge arresters, and leakage current of insulators in high-voltage equipment into the field-circuit coupling model proposed in this paper, preemptive risk assessment and rational suppression measures can be developed for system operation. Additionally, the method demonstrated in this paper can be utilized to guide the design of new MMC-HVDC transmission systems.  
Conceptualization, J.Z., S.W., Y.H. and R.T.; methodology, J.Z. and S.W.; software, J.Z.; validation, J.Z.; formal analysis, J.Z.; investigation, J.Z.; resources, J.Z.; data curation, J.Z.; writing--original draft preparation, J.Z.; writing--review and editing, J.Z.; visualization, J.Z. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the State Key Laboratory of Electrical Insulation and Power Equipment (No. EIPE22120).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
The authors declare no conflict of interest.