## 2 DC Fault Current Analysis
### Protection Demand  
The MMC-HVDC system focuses on the protection and healthy part safety of the converter station. Specifically, the IGBTs are regarded as important components in the converter station given their high cost but low electrical withstanding ability. IGBTs and freewheeling diodes are destroyed due to overheating under extremely high arm current. Another point in protection relaying is that the DCCB occupies a large portion of the cost in the HVDC project considering its high interruption capacity. Therefore, the arm and DC line currents under a fault must be investigated, and the limitation of fault current methods is required to satisfy protection demands. In accordance with the fault current analysis discussed in Section 2, the anti-parallel diodes in removed SMs and IGBTs in inserted SMs experience a dramatic overcurrent before blocking IGBTs. Moreover, the diode \(D_{2}\) in inserted SMs can withstand the peak value of the discharging current when the IGBTs \(T_{1}\) are blocked; this issue is considered an essential challenge to the DC fault protection of the MMC-HVDC system [4]. Considering the action of blocking IGBTs, the arm current under the DC pole-to-pole fault has been simulated (Figure 10). Using Equations (16) and (28), the DC current reaches 30 kA when the \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**System Parameters**} \\ \hline DC voltage & \(\pm\)420 kV & SM number (2 N) & 60 \\ Rated power & 1250 MW & Arm inductance & 140 mH \\ Short-circuit ratio & 20 & Internal grounding & Yg \\ AC voltage & 450 kV & AC line length & 10 km \\ Frequency & 50 Hz & Line resistance & 12.73 m\(\Omega\)/km \\ Transformer voltage & 525 kV/450 kV & Line inductance & 0.9937 mH \\ Transformer grounding & Yn/yn & Line capacitance & 12.74 nF/km \\ Smoothing inductance & 20 mH & DC line length & 200 km \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the modular multilevel converter-based high-voltage direct current system’s simulation model. Figure 8: Simulation and calculation values of the DC line current. Figure 9: Simulation and calculation values of the arm current (Phase-A upper arm). IGBT is blocked beyond the maximum interruption capacity of 16 kA [33]. When a fault occurs, the arm current mainly consists of the capacitor discharging and AC feeding currents in the initial stage. Specifically, the SM capacitor begins to discharge the current through arms and DC loops, and the IGBTs are blocked with a triggering signal while the arm current reaches the threshold value. The IGBT blocking time is set to 1.205 s, that is, 5 ms after fault occurrence to provide a distinguishable vision on the current development; this timeframe is slightly longer than that in the real project (2-3 ms). In addition, the AC side begins to feed current into the fault current circuit while a fault occurs because the rated AC line voltage is set to more than half of the DC voltage (\(V_{AC\_line}=450\) kV, \(V_{DC}=\pm 420\) kV). However, if \(V_{AC\_line}<V_{DC}=0.5U_{DC}\), then the AC feeding current will appear as \(V_{AC\_line}>V_{DC}\) given the SM capacitor's discharging effect. In Figure 10, the AC feed current (red line) in the three-phase uncontrolled rectifier bridge, and the energy stored in the arm reactors begin to freewheel decayed current (blue line) through anti-parallel diodes because the IGBTs are blocked. The AC circuit breaker (ACCB) is triggered to isolate the fault section after a fault is detected. The delay in the ACCB is normally 4-5 cycles. Thus, the triggering time point is set to 100 ms after the fault occurrence. Figure 10 demonstrates that the arm current reaches approximately 10 kA while the IGBT blocks and decays slowly with the AC feeding component. The limitation of the fault current is essential to realize protection considering the limitation in the DCCB capability. The AC feeding current can be restrained using a parallel-connected thyristor in previous works [18; 19; 20; 21].