## 3 Results
### Voltage Sag Matrix
#### 3.1.2 Two-Phase-to-Ground Fault  
The research is continued with asymmetrical short-circuits, starting from a two-phase-to-ground fault. As has been mentioned before, the investigation of asymmetrical faults has not been found in the literature, where the voltage sag matrix has been applied only in the case of three-phase faults. The asymmetrical case is different: voltages must be analyzed separately with two interdependent voltage sag matrixes--phase-to-phase (Table 4) and phase-to-ground (Table 5). The fault occurs between phase A, phase B, and the ground. In this paper, the cells of asymmetrical fault matrixes are filled in the following order (red, yellow, blue curves): phase-to-phase--AB, AC, BC, phase-to-ground--A, B, C.  
Analogously to the previous case, the short-circuit at the generator's terminals (Scenario No. 1) spreads out to all nodes. In Scenario No. 2, the fault has no impact on the voltage level of the generator's busbar and the right branch, but dist  
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Let us begin with the upstream propagation. The following principle is observed in the case of both of the severest faults (Tables 1-5): if the fault location is not transformer's secondary (tertiary) winding, it does not propagate upwards (to the primary winding), and the maximal effect is within the boundaries of RVC (except Scenario No. 4 in Table 5, when the depth of phase-to-ground voltage sag at M2 is slightly larger--up to 20%). However, in the case of the two-phase-to-ground fault, in spite of the green-colored cells, voltage unbalances (both phase-to-phase and phase-to-ground) are observed at these nodes. For example: (1) when the fault occurs at M6 (Scenario No. 7), the unbalance is seen at M5 (Figure 28a); (2) when the fault occurs at M7 (Scenario No. 9), the unbalance is seen at M6 (Figure 28b). In the case of Scenario No. 4, when the fault occurs at M4 (55 km from the autotransformer), the unbalance is felt not only at the primary winding of the autotransformer, but also at the secondary (Figure 29) and tertiary windings (Figure 30). Figure 28: (**a**) Scenario No. 7, two-phase-to-ground fault, phase-to-phase voltage of M5; (**b**) Scenario No. 9, two-phase-to-ground fault, phase-to-phase voltage of M6. Figure 27: Scenario No. 2, two-phase-to-ground fault. (**a**) Phase-to-phase voltage of M1; (**b**) Phase-to-ground voltage of M1. Considering the above, the interconnection of two-phase-to-ground short-circuits with the unbalance seems to be a promising basis for the voltage sag identification task (see Section 1). Moreover, downstream sags could be identified only with protective relays (and smart meters--to determine whether the negative sequence unbalance is caused by consumers), i.e., without PQ monitors; however, currently, the interconnection patterns of symmetrical components have not been comprehensively examined. Scenario No. 4 patterns (Table 6) can be given as an example. The fault at the end of the 110 kV line (M4) affects not only the autotransformer's 110 kV winding (M3), but also the rest of the windings--the 330 kV (M2) and the 10 kV (M2a): for example, a 6.2% negative sequence phase-to-phase unbalance is observed at M2. Symmetrical component propagation from M4 (the fault node) along the 110 kV line to M3 is given in Figure 31. Please note that this research of symmetrical components is beyond the scope of EN 50160:2010 (because it regulates only negative sequence magnitude). Figure 30: Scenario No. 4, two-phase-to-ground fault. (**a**) Phase-to-phase voltage of M2a; (**b**) Phase-to-ground voltage of M2a. Figure 29: Scenario No. 4, two-phase-to-ground fault. (**a**) Phase-to-phase voltage of M3; (**b**) Phase-to-ground voltage of M3. Next, contrary to the symmetrical case, non-identical propagation patterns are seen in Tables 4 and 5--the rotation is observed among the interruption, sag, swell, and RVC events in both directions.