## 4 Simulation Verification of MMC Overcurrent Calculation
\begin{table}
\begin{tabular}{c c} \hline
**Parameters of System** & **Value** \\ \hline DC voltage \(U\)dc & \(\pm\)500 kV \\ DC transmission power \(P\)dc & 2000 MW \\ Sub-module topological & half-bridge \\ Connection configuration & symmetrical monopolar \\ Number of sub-modules per arm \(N\) & 500 \\ Capacitance of sub-module & 10.5 mF \\ Rated voltage of sub-module & 2.0 kV \\ Rated voltage of offshore AC system & 66 kV \\ Rated voltage of onshore AC system & 500 kV \\ \hline \end{tabular}
\end{table} 
Table 1: Main parameters of offshore MMC-HVDC system. Figure 10: Voltage of offshore MMC (**a**) and voltage of positive valve (**b**) to ground during fault. When a severe fault occurs within the offshore converter station, the electric field distribution when the converter valve voltage reaches its maximum increase is shown in Figure 11.  
As shown in Figure 11, during a fault in the system, the electric field distribution characteristics and stray capacitance under the fault impulse excitation are calculated. Through the electric field calculation, the maximum electric field strength at the end of the MMC valve reaches 2.2 kV/mm under the voltage peak condition. The maximum electric field strength is lower than the air breakdown field strength of 3.0 kV/mm. Therefore, the resistance \(R_{\mathrm{g}}\) is infinite. By the electric field calculation, the capacitance between the valve terminal and ground is approximately 108 pF. The calculated stray capacitance and the results of the electric field analysis are input in real-time into the offshore MMC-HVDC system model, as shown in Figure 9. The MOV arrester current and absorbed energy in the CF model are shown in Figure 12.  
Figure 11: Electrical field distribution of MMC valve during fault. Figure 12: Energy and current of arrester during fault. As shown in Figure 12, the results of the field-circuit coupled model demonstrate that the occurrence of significant overvoltage during the fault event leads to the activation of the surge arrester. As stated in Equation (3), the passage of large currents through the metal oxide varistor (MOV) results in the manifestation of a low-impedance characteristic of the MOV within the CF model, as shown in Figure 6. This low-impedance state allows the MOV to effectively divert fault currents, thereby protecting the system from overvoltage damage. The current of the MMC valve during the fault, analyzed using the field-circuit coupled model of the \(\pm\)500 kV MMC-HVDC transmission system, is shown in Figure 13.  
As shown in Figure 13, the establishment of the CF model in the system fault analysis takes into account the stray capacitance of the MMC valve. The electric field and MOV nonlinear parameters are also applied to the establishment of the CF model. The current through the MMC valve becomes distorted before the system is locked out, with its peak significantly exceeding 4000 A. This may lead to the damage of IGBT. To compare the advantages of the method proposed in this paper, the overcurrent in the MMC valve is investigated using conventional analysis methods without the field-circuit coupling model. Under identical simulation conditions, when a valve bottom ground fault occurs at the offshore station, the current of the MMC valve analyzed using conventional analysis methods is shown in Figure 14.  
Figure 10:0 Overcurrent waveform of offshore MMC during fault. The conventional analysis presented in Figure 14 does not account for the influence of stray parameters. As a result, the current peak in Figure 14 is reduced compared to that in Figure 10:1 Despite the consistency of the main circuit parameters and system parameters, the overcurrent anomaly still occurred in Figure 10:2  
As shown in Figure 14, after the current anomaly occurs, the cause cannot be determined due to the absence of the field-circuit coupling model described in this paper. Under identical simulation conditions, simulations of the overcurrent in the MMC valve were performed using two different analysis methods.