## 5 Transient Performance of the System in DC Faults
#### 5.1.1 Transient Current and Voltage of the AC System  
Figure 11 shows the AC side current and voltage waveforms for Case-1. Figure 11a presents the AC side current graph. It shows that the peak current approaches 2 kA just after 0.2 s, i.e., before fault interruption. After 0.4 s, i.e., during reclosing, the AC current exceeds its steady-state value before reaching the steady state in 50 ms. A voltage transient with a peak of up to 90 kV can be observed during the reclosing operation, as shown in Figure 11b.  
Figure 10: Comparison of energy dissipation on the circuit breaker (CB). Case-1 is an HCB; Case-2 is an RCB.  
Figure 12 shows the AC-side current and voltage waveforms for Case-2 during interruption and reclosing operations. It can be seen in Figure 12a that there is no current overshoot during fault inception due to the instant blocking of IGBTs. During reclosing, the maximum current does not exceed \(-1.02\) kA, which is \(0.4\) kA higher than that of Case-1.  
Figure 12b shows that an overvoltage of \(120\) kV occurs during the converter blocking at the time of fault. An overvoltage of up to \(100\) kV occurs during the reclosing process, followed by a return to the steady state in \(10\) s.  
As a result, although the magnitude of the current and the voltage are not much different on the AC side, the current magnitude in the reclosing and the overvoltage magnitude in the interruption process are relatively high, and the time to achieve the steady-state voltage after the reclosing process is very long. Therefore, Case-1 would have advantages in terms of the stability of the AC system and lower stress on the insulation.  
1.2 The Analysis of the DC Current and Voltage Waveform Across the HCB and RCB in the Transient State  
Figure 13 is a graph showing the DC current flowing through the circuit breaker and the voltage across the circuit breaker during the fault and reclosing process. As shown in Figure 13a, in Case-1, the maximum fault current is limited to \(3.3\) kA due to the quick HCB operation.  
Figure 11: The transient waveforms of the AC system in Case-1: (**a**) current waveform; (**b**) voltage waveform.  
Figure 12: The current and voltage waveform at the AC side of Case-2 in interruption and reclosing operations: (**a**) current waveform; (**b**) voltage waveform.  
In Case-2, however, due to the fault handling capability of the FB-MMC, it is confirmed that the fault current rapidly increases to about 15.5 kA and then rapidly decreases.  
In the reclosing operation, Case-1 has a maximum fault current magnitude of 0.8 kA, and it is confirmed that it achieves a steady state in 100 ms. Case-2 showed high di/dt as well as the peak magnitude, which is about 2 kA--more than twice the value of that in Case-1.  
Considering the insulation design of the system and device, Case-2 with a high current magnitude and high di/dt slope would be detrimental to the power system components.  
The voltage waveform across the circuit breaker is presented in Figure 13b. In Case-1 and Case 2, the voltage across the circuit breaker increased suddenly after 0.2 s. In the reclosing process, the recovery voltage across the HCB decreases within 50 ms.