## 2 Influencing Factors of MMC Valve Overcurrent  
The offshore wind power MMC-HVDC transmission system is the primary method for delivering electrical energy from large-scale, deep-sea wind farms. Currently, several offshore wind power MMC-HVDC transmission projects have already been implemented [13]. The schematic diagram of the offshore wind power MM-HVDC transmission system is shown in Figure 1.  
As shown in Figure 1, the offshore wind power MMC-HVDC transmission system consists of the offshore wind farm, the AC collection system, the offshore converter station, the DC submarine cable, the onshore converter station, and the DC energy dissipation device. In the offshore wind power MMC-HVDC system, half-bridge sub-modules are utilized to construct the MMC. The offshore converter station is arranged in the form of an offshore platform located in deep-sea areas, designed to withstand harsh marine environments while ensuring reliable power conversion and transmission. Overcurrent phenomena in the MMC valves of the offshore MMC-HVDC system are typically caused by severe faults occurring in the converter station area or within the DC transmission lines. These faults can lead to significant transient currents that may exceed the rated capacity of the valves, posing risks to the safe and stable operation of the system. The principle of overcurrent caused by faults in the valve hall area of the offshore converter station is illustrated in Figure 2.  
As shown in Figure 2, the offshore wind power MMC-HVDC system employs a monopolar connection configuration. Each converter station consists of six bridge arms. Each bridge arm is composed of a series connection of N half-bridge sub-modules. During operation, power transmission is achieved by controlling the switching of sub-modules. Figure 1: System of MMC-HVDC transmission connected for offshore wind power. When a fault occurs within the offshore converter platform, whether it is a short-circuit fault, a ground fault, or an open-circuit fault, the physical characteristics of the power transmission system are altered. Due to the change in the circuit, the impedance characteristics of the MMC system are also affected. The relationship between the bridge arm current and voltage during operation is defined as follows:  
\[ \begin{cases}u_{\text{armup}\text{C}}=-u_{\text{Cn}}+\frac{U_{\text{dc}}}{2}\\ u_{\text{armdown}\text{C}}=u_{\text{Cn}}+\frac{U_{\text{dc}}}{2}\\ i_{\text{arm}}=f(u_{\text{arm}})=\frac{P_{\text{dc}}}{3U_{\text{dc}}}+\frac{ \sqrt{P_{\text{dc}}{2}^{2}+Q^{2}}}{6u_{\text{Cn}}}\end{cases}  \tag{1}\]  
In Equation (1), \(i_{\text{arm}}\) is the bridge arm current of MMC, \(u_{\text{Cn}}\) is the voltage to ground on the valve side, \(U_{\text{dc}}\) is the DC voltage of the MMC, \(u_{\text{armupC}}\) and \(u_{\text{armdownC}}\) are the voltages of the upper and lower bridge arms, and \(P_{\text{dc}}\) and \(Q\) are the active power and reactive power of MMC. As shown in Figure 2, during the transient process following a fault, the expression for the bridge arm current is defined as follows:  
\[ \begin{cases}u_{\text{armup}}=i_{\text{arm}}Z_{\text{arm}}(\text{t})\\ Z_{\text{arm}}(\text{t})=Z_{\text{on}}N_{1}+Z_{\text{off}}(N-N_{1})+Z_{\text{F}} +Z_{\text{g}}\end{cases}  \tag{2}\]  
In Equation (2), \(Z_{\text{arm}}\) is the equivalent impedance of the bridge arm, \(Z_{\text{on}}\) and \(Z_{\text{off}}\) are the impedances of the sub-modules in the on-state and off-state, \(N\) and \(N_{1}\) are the total  
Figure 2: Equivalent circuit of MMC overcurrent fault. number of modules in the bridge arm and the number of sub-modules in the on-state, \(i_{arm}\) is the bridge arm current of MMC, \(Z_{\text{F}}\) is the impedance in the fault loop, and \(Z_{\text{g}}\) is the impedance resulting from MMC valve stray parameters. According to Equation (2), it can be seen that during steady-state operation, \(Z_{\text{F}}\) is zero, and the effect of \(Z_{\text{g}}\) can be neglected. In this case, the current through the valve can be indirectly controlled based on power.