*4.5. Three Phase to Ground Fault*

The three phase to ground (3PG) fault is simulated 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 described in Figure 8a,b, respectively. Current signals are processed using Wigner distribution function (WDF) and WD-index is computed which is detailed in Figure 8c. It is observed that WD-index corresponding to all phases has a high magnitude after the incidence of 3PG fault. The ALN-index is computed from the voltage signals and detailed in Figure 8d. It is concluded that ALN-index corresponding to all phases sharply increases just after incidence of 3PG fault.

Figure 8e details the FI corresponding to all the phases during the event of 3PG fault. It is seen that FI corresponding to all the phases has a higher magnitude compared to TM after the incidence of 3PG fault, which indicates that all the phases are faulty in nature. Hence, the algorithm is found to be effective for the identification of 3PG fault. High resolution of FI is illustrated in Figure 8f. This is observed that FI corresponding to phases A, B, and C rises and cross the TM after 1.7 × <sup>10</sup>−<sup>4</sup> s, <sup>3</sup> × <sup>10</sup>−<sup>5</sup> s and 7 × 105 s, respectively, which are equal to 1.02%, 0.18% and 0.42% of the total time of a cycle in same order. Hence, the 3PG fault was detected effectively in a time duration equal to 1.02% of the total time of a cycle.

**Figure 8.** Recognition of 3PG 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.

Therefore, it is established that all types of faults including PG, 2P, 2PG, and 3PG in the network of the hybrid grid incorporated with RE were identified effectively by using proposed algorithm, within time duration of (1/10)th of a cycle.

## **5. Fault Classification**

Type of fault incident on the hybrid power grid in the presence of RE generation were identified using the algorithm illustrated in Figure 3. The PG fault and 3PG fault were identified based on the number of faulty phases, which are 1 and 3, respectively for the PG and 3PG faults. 2P and 2PG faults are included in the same group using the number of faulty phases, identified based on the proposed FI. These faults were classified using the proposed ground fault index as detailed in Figure 9. It is observed that the magnitude of GFI is higher compared to the TMGFI (2000) for the 2PG fault event. However, during the event of 2P fault, the GFI has values lower than the TMGFI. Hence, all the faults were identified effectively using the proposed algorithm

**Figure 9.** Ground fault index for classification of 2P and 2PG faults.
