**5. Simulation and Discussion**

A two-terminal MMC-HVDC system is modeled on the PSCAD platform, and the topology is as shown in Figure 1. The overhead transmission line model in PSCAD is applied. The line model is shown in Appendix A. The system parameters are show in Table 1.

**Table 1.** The parameters of the system.


This section simulates PPF, PGF, LF, FD, SMF, and AG-AC, with different parameters. The locations of those faults are demonstrated in Figure 1. Among them, the ground resistors are from 0.001 to 50 Ω. The distance to the fault location is from 0 to 200 km. The number of short-circuit modules of the SMF varies from 1 to 12. When the LF occurs, the lightning current amplitude ranges from 25 to 50 kA. When the LD occurs, the lightning current amplitude ranges from 5 to 30 kA. The details of simulation parameters are listed in Table 2.




**Table 2.** *Cont.*

#### *5.1. Protection Operation Results of Different Faults*

Using the simulated MMC-based transmission model and simulated faults with parameters in Table 2, the protection operations of the proposed method are tested with different types of faults. The protection operation results are shown in Table 3.


**Table 3.** Results for different fault types with wavelet entropy.

As shown in Table 3, the proposed protection method can effectively discriminate internal and external faults, and it can also recognize the internal transient type. No misoperations are generated by the wavelet entropy-based method. This method is effective in protecting non-faulted parts and finding faulted ones.

#### *5.2. Effect of Number of Faulted SMs*

The number of faulted SMs will affect the value and change of the short circuit current in DC transmission lines. It is necessary to study the effect of the number of fault SMs. Here, the performance of the proposed protection method is discussed as the number of fault SMs ranges from 1 to 12. The 5th level wavelet entropy W5 of fault current *Idc* is always 0, which is obviously different from the case of an internal fault. It meets the internal and external fault criterion and is judged to be an external fault. As shown in Figure 16, the accuracy of the protection actions of different kinds of faults are all 100%, no matter how many SMs are faulted. Here, AP, AN, BP, BN, CP, and CN represent the upper (positive) and lower (negative) bridge arms of the ABC three-phase in the MMC converter, respectively. The change in the number of fault SMs will not affect the action of the protection criterion.

**Figure 16.** The influence of number of faulted SMs on the action accuracy.
