# Optimal Design Parameters for Hybrid DC Circuit Breakers Using a Multi-Objective Genetic Algorithm
## 4 Simulation Results
### Results and Analysis
#### 4.2.2 Comparison of Using the Initial and Optimized Parameters of the HCB  
The performance of the HCB using the optimized parameters and the initial parameters is compared. Figures 6-10 show the simulation results of the current and voltage waveforms of the branches in the HCB. Figure 6 depicts the total current \(\mathrm{I_{cb}}\) of the component currents in the HCB branches. Figure 5: Convergence curve of: (**a**) multi-objective value, (**b**) value of objective 1, (**c**) value of objective 2, (**d**) value of objective 3. Figure 6: Current waveform of \(\mathrm{I_{cb}}\) of the HCB. Under normal operation (before 0.04 s), the capacitor C is precharged to \(-100\) kV, and the system current flows through switch S\({}_{1}\) in branch 1 with a nominal current of 1 kA, as shown in Figures 6 and 7. Figure 8: Current waveform of I\({}_{\rm inj}\) in branch 2 of the HCB. Figure 10: Voltage waveform of C in branch 2 of the HCB. Figure 7: Current waveform of I\({}_{\rm nom}\) in branch 1 of the HCB. Figure 9: Voltage waveform of MS in branch 1 of the HCB. When a fault occurs on the load side at 0.04 s, the system current increases rapidly. When the system current reaches the 3 kA threshold, an open signal is sent to switch S1, and its contacts generate an arc. After a 2 ms delay, thyristors T1a and T1b are turned on, and the inverse current Iinj generated by the LpCp resonant circuit in branch 2 is injected to oppose the arc current. As a result, the current Inom in branch 1 decreases to zero and the arc extinguishes at 0.04315 s for both cases, using the optimized and initial parameters, as shown in Figure 7. The fault current is commutated into branch 2. The voltages across the MS Vms and the capacitor Vc increase rapidly at the same time, as shown in Figures 9 and 10. When the increasing Vms equals the system voltage, the peak fault current is 7.56 kA for the initial parameters and 6.75 kA for the optimized parameters. Continuously, the increasing Vms exceeds the turn-on voltage of the MOV at 0.044 s for the initial parameters and at 0.04323 s for the optimized parameters, and the fault current is commutated to the MOV in branch 3. The MOV absorbs the remaining fault energy in the system until the fault current is reduced to zero at 0.04743 s for the initial parameters and at 0.04645 s for the optimized parameters, as shown in Figure 8. It is obvious that the total time of fault current interruption from fault inception to fault clearing is 7.43 ms (from 0.04 ms to 0.04743 ms) for the initial parameters and 6.45 ms (from 0.04 ms to 0.04645 ms) for the optimized parameters. After the fault current interruption is completed, switch S2 is fully opened after 20 ms at 0.06743 s for the initial parameters and at 0.06645 s for the optimized parameters, as shown in Figure 10. The HCB is isolated from the rest of the system. To resume operation, the HCB must recover from the overvoltage on the capacitor element. This process begins with the discharge of the capacitor overvoltage to the system voltage. This process takes 0.54 ms with initial parameters and 0.056 ms with optimized parameters, as shown in Figure 10. Furthermore, the polarity of the capacitor is reversed in comparison to the normal condition, so the capacitor polarity is changed. In this study, the process takes 1.984 ms with the initial parameters and 0.275 ms with the optimized parameters. The recovery time to the normal condition of the capacitor after the discharging and reversing operations is 2.52 ms for the initial parameters and 0.37 ms for the optimized parameters. Clearly, the performance of the HCB with optimal parameters exceeds that of the HCB model in [21], as shown in Figure 6:0 Using the optimal parameters, the peak value of the fault current is reduced by 5.66% (from 7.56 kA to 6.75 kA), the interruption time is reduced by 7.06% (from 7.43 ms to 6.45 ms), and the recovery time of discharging and reversing the capacitor is reduced by 74.39% (from 2.52 ms to 0.37 ms).