## 2 Influencing Factors of MMC Valve Overcurrent
In the overcurrent protection of the MMC valve, the instantaneous current value is detected by the bridge arm current transformer. When the peak current of the bridge arm reaches the protection setting \(I_{\text{set}}\) or other conditions, the MMC current protection signal is triggered. Following the protection action, the bridge arm current is reduced. The development process of the bridge arm fault current in MMC is shown in Figure 3.  
Figure 3 presents a schematic diagram constructed based on the development process of arm current during the overcurrent blocking protection in an actual MMC-HVDC system. This diagram is used to analyze the influencing factors of overcurrent in the MMC valve. As shown in Figure 3, when a severe fault occurs in the station at time t\({}_{1}\), the bridge arm current to increases rapidly. When the current \(i_{\text{arm}}\) reaches the protection setting \(I_{\text{set}}\), the protection is triggered, and the system is blocked. After the protection chain delay (S\({}_{2}\)), the blocking is completed, and the MMC valve current reaches its peak value \(I_{\text{peak}}\). When a severe fault occurs in the system, as shown in Figure 2, the operating circuit of the bridge arm will change, and the electrical energy cannot be transferred to the DC side. The electrical energy from the AC side power source is directly released to the ground through the bridge arm, forming a short-circuit current in the bridge arm. The rate of rise in the fault current is closely related to the impedance characteristics of the fault loop. Within the control period following the fault, the increment of the current can be used to represent the rate of current rise. The increase in current within the control period is given as follows [14]:  
\[\Delta i_{\text{arm}}=\frac{\omega U_{\text{armm}}}{\sqrt{R_{\text{d}}^{2}+( \omega L_{\text{armd}})^{2}}}T_{control} \tag{3}\]  
In Equation (3), \(U_{\text{armm}}\) is the maximum arm voltage at the moment of fault occurrence, m is the MMC voltage modulation ratio, \(\omega\) is the AC side angular frequency, \(T_{control}\) is the control period, \(R_{\text{d}}\) is the equivalent resistance in the fault current loop, and \(L_{\text{armd}}\) is the inductive reactance in the fault current loop. As shown in Equation (3), the on-state resistance of the diodes and IGBTs in the sub-module, as well as the number of modules, affect the rise rate of the MMC overcurrent. However, the bridge arm reactor is the most significant factor influencing the current rise rate. Figure 3: Development process of MMC overcurrent during faults. In practical design, the bridge arm reactor is primarily used to suppress the rise rate of the fault current. The sub-module balancing resistor is not involved in the fault loop before the module is blocked. Only after the MMC is blocked does this resistor come into the fault loop. Therefore, the sub-module balancing resistor does not influence the rate of rise in the fault current. The stray capacitances, typically at the pF level and not in the series path of the fault current, have a negligible effect on the current rise rate. The insulation resistance represents the equivalent of the electric field characteristics at the valve terminal. When the transient electric field strength is less than the air breakdown field strength at the position, the insulation resistance does not affect the rate of rise in the fault current. Conversely, when the transient electric field reaches the air breakdown field strength, the resistance value becomes a relatively small value, approximately 1 to 5 ohm or even lower. The insulation resistance significantly influences the rate of rise in the fault current, which potentially causes damage to the equipment. In practical engineering applications of HVDC transmission, the rated gate-emitter voltage for IGBT drivers is typically around 15 V. Additionally, the maximum safe turn-off current of IGBT is generally about twice the rated current.