*4.1. Impacts of Faulty Events on the Performance of Hybrid Grid and Requirement of Protection Schemes*

To investigate the impacts of faulty events on the performance of hybrid grid, root mean square (RMS) voltage at the node 650, frequency, power injected by solar PV system and wind power plant into the hybrid grid during the event of PG (phase A) fault at node 646 at 6th cycle are illustrated in Figure 4a–d, respectively. It is observed from Figure 4a that RMS voltage decreases during faulty event whereas small deviations are observed in the frequency for short duration at the time of fault incidence as depicted in Figure 4b. Power supplied by the solar PV and wind generators reduced as depicted in Figure 4c,d, respectively. Hence, performance of the hybrid grid will be affected adversely, if faulty events persist. Therefore, suitable protection scheme needs to be investigated and designed to isolate the faulty section of the hybrid grid.

**Figure 4.** Phase to ground fault at the node 646 of hybrid power system network (**a**) root mean square voltage (**b**) frequency (**c**) power injected by solar PV system into the hybrid grid (**d**) power injected by wind power plant into the hybrid grid.

#### *4.2. Phase to Ground Fault*

The phase to ground (PG) fault is simulated on phase A at 0.1 s at node 646. Current and voltage signals captured at node 650 for the period of 0.2 s (12 cycles) are detailed in Figure 5a,b, respectively. Current signals are processed using Wigner distribution function (WDF) and WD-index is computed, which is described in Figure 5c. It is observed that WD-index corresponding to phase A has a high magnitude after incidence of PG fault. However, this index, corresponding to phases B and C, has values comparable to the pre-fault values. The ALN-index is computed from the voltage signals and described in Figure 5d. It is concluded that the ALN-index corresponding to all phases sharply increases just after the incidence of PG fault.

Figure 5e describes the FI corresponding to all the phases during the event of PG fault. It can be inferred that FI corresponding to the faulty phase (phase A) has a higher magnitude compared to TM after the incidence of PG fault. However, this FI corresponding to healthy phases (phases B and C) has a lower magnitude compared to TM. Hence, the algorithm is found to be effective for the identification of PG fault, discriminating the healthy and faulty phases. High resolution of FI is illustrated in Figure 5f. It is observed that FI corresponding to phase A rises and crosses the TM after 6 × <sup>10</sup>−<sup>4</sup> *<sup>s</sup>*, whereas the FI corresponding to healthy phases B and C remains below the threshold. Hence, the PG fault was detected effectively in time duration, equal to 3.6% of the total time of the cycle.

**Figure 5.** Recognition of PG fault incident at the node 646 of hybrid test system (**a**) current waveform (**b**) voltage waveform (**c**) WD-index (**d**) ALN-index (**e**) FI (f) plot to compute fault recognition time.

#### *4.3. Double Phase Fault*

The double phase (2P) fault is simulated on phases A and B at 0.1 s at node 646. Current and voltage signals recorded at node 650 for the period of 0.2 s (12 cycles) are illustrated in Figure 6a,b respectively. Current signals are processed using WDF and WD-index is computed which is detailed in Figure 6c. It is observed that WD-index corresponding to phases A and B has a high magnitude after incidence of 2P fault. However, this index corresponding to the phase C has values comparable to the pre-fault values. The ALN-index is computed from the voltage signals and detailed in Figure 6d. It is inferred that ALN-index corresponding to all the phases sharply increases just after the incidence of 2P fault.

Figure 6e details the FI corresponding to all phases during the event of 2P fault. It is seen that FI corresponding to faulty phases (phases A and B) has a higher magnitude compared to TM, after the incidence of 2P fault. However, FI corresponding to healthy phase (phase C) has a lower magnitude as compared to TM. Hence, the algorithm is found to be effective for the identification of 2P fault and the discrimination of healthy and faulty phases. High resolution of FI is illustrated in Figure 6f. It is observed that FI corresponding to phases A and B rises and cross the TM after 7 × <sup>10</sup>−<sup>5</sup> s and <sup>4</sup> × <sup>10</sup>−<sup>5</sup> s, respectively, which are equal to 0.42% and 0.24% of the total time of a cycle in the same order. FI corresponding to healthy phase C remains below the threshold. Hence, the 2P fault was detected effectively in time duration equal to 0.42% of the total time of a cycle.

**Figure 6.** Recognition of 2P fault incident at node 646 of hybrid test system (**a**) current waveform (**b**) voltage waveform (**c**) WD-index (**d**) ALN-index (**e**) FI (f) plot to compute fault recognition time.
