## 2 Influencing Factors of MMC Valve Overcurrent
Therefore, the peak current Ipeak during a fault must be less than twice the rated current of IGBT to ensure device safety [15; 16; 17]. During time intervals S1 and S2, the development of the fault current is closely related to the characteristics of the fault loop. The time interval S2 is determined by the hardware of the control and protection system. Unreasonable design of the main circuit parameters and stray parameters of the equipment can cause current distortion and a rapid increase, leading to device damage under certain operating conditions. As shown in (2), the fault-induced changes in impedance characteristics lead to overcurrent, especially under impulse excitation, where the effect of \(Z_{\text{g}}\) becomes more pronounced. Because of the different positions and geometric dimensions of the metal components, a large number of stray parameters exist in the MMC valve, especially stray capacitances. The impact of stray capacitance in the MMC valve on the current is shown in Figure 4.  
As shown in Figure 4, \(L_{\text{arm}}\) is the bridge arm inductance, \(C_{\text{SV}}\) is the stray capacitance between the terminal of the MMC valve and ground, \(U_{\text{C}}\) is the voltage to ground at the terminal of the MMC valve, \(C_{\text{m}}\) and \(R_{m}\) are the equivalent capacitance and equivalent resistance of the MMC, \(I_{1}\) is the bridge arm current, and \(I_{\text{G2}}\) is the current in the MMC. The presence of stray capacitance may lead to changes in the bridge arm current. The impact of stray capacitance on the bridge arm current is defined as follows:  
\[ \begin{cases}I_{\text{c1}}=\omega C_{\text{sV}}U_{\text{c}}\\ Z_{\text{m}}=R_{m}-j\frac{1}{\omega C_{\text{m}}}\end{cases}  \tag{4}\]  
Figure 4: Impact of stray capacitance in MMC valve on current. In Equation (4), \(I_{\rm cl}\) is the current generated by stray capacitance, \(U_{\rm C}\) is the voltage to ground at the terminal of the MMC valve, \(C_{\rm m}\) and \(R_{m}\) are the equivalent capacitance and equivalent resistance of the MMC, and \(\omega\) is angular frequency of voltage or current. Stray capacitance can cause changes in the bridge arm current. The impact factor of stray capacitance on the bridge arm current is defined as follows:  
\[ \begin{cases}f_{CI}(\omega)=\frac{I_{\rm cl}}{I_{\rm cl}}=\frac{C_{\rm v}V}{C_ {\rm m}}+j\omega C_{\rm s}VR_{m}\\ f_{CI}=|f_{CI}(\omega)|\end{cases}  \tag{5}\]  
In Equation (5), \(f_{CI}\) is the impact factor of stray capacitance on the bridge arm current. The magnitude of this impact factor is related to the frequency of the current. The impact factor \(f_{CI}\) of stray capacitance on the bridge arm current at different frequencies is shown in Figure 5.  
As shown in Figure 5, the impact of stray capacitance on the bridge arm current is very small at low frequencies. Specifically, higher frequencies tend to result in a more pronounced effect due to the capacitive reactance characteristics. At lower frequencies, the impact factor is relatively small, while at higher frequencies, it can significantly alter the current waveform. When the frequency is below 50 th order, the impact factor \(f_{CI}\) is essentially zero. At a frequency of the 150 th order, the impact factor is only 0.01%. When the frequency reaches the 1000 th order, the impact factor increases to 0.1%, and the influence begins to become more pronounced. When the frequency reaches the 10,000 th order (500 kHz), the impact factor \(f_{CI}\) increases to 1%, and the impact of stray capacitance becomes very significant. In the offshore wind power MMC-HVDC transmission system, MMC valve overcurrent caused by severe station faults is typically in the form of impulses. The rise time of the MMC valve voltage and current waveforms is very short, resulting in the presence of high-frequency components in the waveforms. Therefore, the impact of stray capacitance in the MMC valve must be considered in the analysis of overcurrent.