## 6 Simulation and Analysis
### Verifying the Correctness of IHCDP  
3.1 Case 1: Asymmetrical Short-Circuit Faults with 0.1 \(\Omega\) Fault Resistance Occur at \(f_{1}\)  
At 0.3 s, set single-phase-to-ground (A-G) faults, two-phase-to-ground (AB-G) faults, and phase-to-phase (A-B) faults with 0.1 \(\Omega\) fault resistance occur at \(f_{1}\), respectively. After detecting faults, IBDG1 and IBDG2 inject CHCs into the distribution network according to the injection strategy. The distortion rates of NSCCHCs on both sides of protected feeder B1B2 after faults are shown in Figure 14.  
In Figure 14, \(DR_{\text{/}B1}\) and \(DR_{\text{/}B2}\) represent the distortion rates of NSCCHCs on the GRID and IBDG sides of protected feeder B1B2, respectively. The action threshold of NSCCHCs differential protection criterion is set to 2%. From Figure 14,  
Figure 14: Distortion rate records of asymmetric faults with 0.1 \(\Omega\) fault resistance. (**a**) A–G fault, (**b**) AB-G fault, and (**c**) A–B fault. Figure 12: Distortion rate of A-phase CHC at the outlet of IBDG1 before and after the fault. Figure 13: The amplitude of A-phase CHC and the waveforms of characteristic harmonic signals under the fault. A-B faults occur at \(f_{1}\), the distortion rate difference values of NSCCHCs on both sides of feeder B1B2 are about 0.45, 0.06, and 0.06 after one cycle. It can be seen that the IHCDP can sensitively trip under various asymmetric faults, especially under single-phase-to-ground faults. 3.2 Case 2: Symmetrical Short-Circuit Faults with 0.1 \(\Omega\) Fault Resistance Occur at \(f_{1}\)  
On the basis of Case 1, the fault types at point \(f_{1}\) are changed to three-phase faults with 0.1\(\Omega\) fault resistance. Distortion rates of A-phase CHCs on both sides of feeder B1B2 after the fault are shown in Figure 15.  
In Figure 15, \(DR_{AB1}\) and \(DR_{AB2}\) represent the distortion rates of A-phase CHCs on the GRID and IBDG sides, respectively. The action threshold of the A-phase CHC differential protection criterion is set to 2%. From Figure 15, when a three-phase fault occurs at \(f_{1}\), the distortion rate difference value of A-phase CHCs on both sides of feeder B1B2 is about 0.04 after stabilization, which is greater than the action threshold. The above simulation results are consistent with the theoretical analysis in Section 5, and IHCDP can reliably trip under symmetrical short-circuit faults. 3.3 Case 3: Asymmetrical Short-Circuit Faults with 20 \(\Omega\) Fault Resistance Occur at \(f_{1}\)  
On the basis of Case 1, the fault resistance at point \(f_{1}\) is changed to 20 \(\Omega\). Distortion rates of NSCCHCs on both sides of feeder B1B2 after faults are shown in Figure 16.  
From Figure 16, when the A-G, AB-G, and A-B faults occur at \(f_{1}\), the distortion rate difference values of NSCCHCs on both sides of feeder B1B2 are about 1.58, 1.00, and 0.45 after one cycle. The distortion rate difference values under high-resistance asymmetric faults are much larger than the action threshold. Due to the large fault resistance leading to a small NSCFFC, the distortion rate of NSCCHC on the IBDG side is larger. In conclusion, the IHCDP, under various asymmetric faults with high fault resistance, can reliably trip with high sensitivity. Figure 16: Distortion rate records of asymmetric faults with 20 \(\Omega\) fault resistance. (**a**) A–G fault, (**b**) AB–G fault, and (**c**) A–B fault. Figure 15: Distortion rates of the A-phase CHCs under the three-phase fault with 0.1 \(\Omega\). .3.4 Case 4: Symmetrical Short-Circuit Faults with 20 \(\Omega\) Fault Resistance Occur at \(f_{1}\)  
On the basis of Case 2, the fault resistance at point \(f_{1}\) is changed to 20 \(\Omega\). The distortion rates of A-phase CHCs on both sides of feeder B1B2 after the fault are shown in Figure 17.  
From Figure 17, the difference value of the A-phase CHC distortion rates on both sides is about 3.8% after stabilization, slightly lower than 4%.