## 4 Simulation Verification of MMC Overcurrent Calculation  
The system simulation model in this paper is built in the PSCAD/EMTDC. The model is constructed based on actual primary parameters and control protection systems. The electromagnetic field calculations for the field-circuit coupling module and the stray parameter calculations for the MMC valves are performed using a finite element computation program, which is interfaced with PSCAD/EMTDC. Based on the aforementioned discussion, a field-circuit coupling model was integrated into the offshore wind power MMC-HVDC transmission system model, as shown in Figure 9 [18; 19; 20]. Figure 9 illustrates a \(\pm\)500 kV, 2000 MW offshore wind power MMC-HVDC transmission system that represents an actual offshore engineering project. The project is currently in the process of technical justification and construction. The content studied in this paper is all related to the technical evaluation phase of the project. As shown in Figure 9, a \(\pm\)500 kV, 2000 MW offshore wind power MMC-HVDC transmission system model incorporating field-circuit coupled models (CFAV, CFBV, CFCV, CFAU, CFAD, CFBU, CFBD, CFCU, CFCD, CFDP, and CFDN) was established. This integration allows for a more comprehensive analysis of the system behavior under various operating conditions, particularly during transient events. The main parameters of the \(\pm\)500 kV, 2000 MW offshore wind power MMC-HVDC transmission system are shown in Table 1.  
Figure 9: Offshore wind MMC-HVDC system with field–circuit coupling model. The parameter table presented herein represents the critical parameters of the system during the system validation process, which were derived through the following formulas and corroborated with the simulation checks. The design of the sub-module capacitor is illustrated as follows [14]:  
\[ \begin{cases}\text{Csm}=\frac{1}{3}\frac{S}{mu^{2}_{\text{max}}{}^{2}N\omega}\\ |\varepsilon_{\text{max}}|\leq 20\%\end{cases}  \tag{10}\]  
In Equation (10), \(C_{\text{sm}}\) is the sub-module capacitance value, \(m\) is the MMC voltage modulation ratio, \(\varepsilon\) is the sub-module voltage ripple, \(\varepsilon_{\text{max}}\) is the maximum sub-module voltage ripple, \(u_{\text{smd}}\) is the sub-module rated voltage, S is the MMC rated capacity, \(N\) is the number of rated sub-modules per arm, and \(\omega\) is the AC side angular frequency. The calculated value was then validated through system simulations to obtain the theoretical capacitance value presented in Table 1.  
Concurrently, an electric field calculation model for the MMC valve was developed. The voltages at critical locations within the system serve as input conditions for the electric field model calculations. The voltage-current (V-I) characteristics' model of the MOV at these locations is also integrated into the field-circuit coupled models. The electric field strength, stray parameter values calculated by the electric field model, and the instantaneous system voltages are then input into the corresponding field-circuit coupled model at each location. When a valve bottom ground fault occurs at the offshore station, the voltage waveform at the MMC and the voltage between the positive valve terminal and the ground are shown in Figure 10.  
As shown in Figure 10, after a ground fault occurs at the valve bottom of the system, the control and protection system detects the fault and performs a lockout and shutdown protection action. During the fault process, severe overvoltage is generated in the system. The voltage values are then input into the electric field calculation model of the MMC valve.