## 3 Results
### Voltage Sag Matrix
#### 3.1.3 Two-Phase Fault  
Another type of asymmetrical fault is the two-phase short-circuit. The fault occurs between phase A and phase B. Voltage sag matrixes are given in Tables 8 and 9. The comparison of Tables 8 and 9 with two-phase-to-ground matrixes (Tables 4 and 5) reveals that the residual voltages of two-phase faults are higher, and voltage swells are not observed since there is no (direct) contact with the ground. Contrary to the two-phase-to-ground case (Table 7), two-phase fault patterns almost do not depend on the short-circuit location (Table 10). On the other hand, a high degree of similarity can be noticed in the downstream propagations, for example, comparing voltages at M2 (Figures 4  
When a two-phase fault occurs at HV level (Scenarios No. 1, No. 2, and No. 4), the impact on two phase-to-ground voltages of both the 10 kV and 0.4 kV grid (Figure 42) is within the limits of RVC, which means that the majority of single-phase equipment will not be affected. Meanwhile, voltage sag patterns in the 330 kV, 110 kV, and 35 kV grids are similar to those of the fault node (Table 10). The same effect on the LV grid is observed in Scenario No. 6. Conversely, when a fault occurs at the transformer's tertiary winding (Scenarios No. 3 and No. 5), patterns rotate (i.e., patterns are similar to, for example, the voltages of both M3 and M4 in the case of Scenarios No. 1 and No. 2, or M5 in the case of Scenarios No. 1, No. 2, and No. 4): two phase-to-ground voltage sags are caused, while the third phase remain healthy (Figure 43). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Fault Location** & \multicolumn{2}{c}{**Phase-to-Phase Voltage**} & \multicolumn{2}{c}{**Phase-to-Ground Voltage**} \\ \hline Generator’s busbar & **Hour.** & 10\% & 10\% & 50\% & 50\% \\ HV grid & **Hour.** & 20\% & 20\% & 50\% & 50\% \\ MV and LV grid & **Hour.** & 10\% & 10\% & \(\leq\)40\% & \(\leq\)40\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Voltage sag depth dependence on two-phase fault location. Figure 41: Scenario No. 1, two-phase-to-ground fault. (**a**) Phase-to-phase voltage of M2; (**b**) Phase-to-ground voltage of M2. Upward propagation mechanisms of two-phase and two-phase-to-ground faults have many similarities. For example, similar to the two-phase-to-ground case, when a two-phase short-circuit occurs at M4 (Scenario No. 4), the voltage unbalance is observed at M2 (Figure 44), also at M2a, M2b, and M3a. If a fault occurs at the primary winding of the 35/10 kV transformer (Scenario No. 6), it affects the 110/35/10 kV transformer's tertiary winding (Figure 45). If a two-phase short-circuit occurs at the end of the 10 kV 10 km line (Scenario No. 7), voltage sags are observed at the beginning of the line (Figure 46), but only a negative sequence unbalance is observed at the 35/10 kV transformer's primary winding (Figure 47). A short-circuit at the secondary winding of the 10/0.4 kV transformer (Scenario No. 8) is fully felt by both M6 and M7a (Figure 48). Conversely, if the distance from the secondary winding is increased by 1 km (Scenario No. 9), only the voltage unbalance is observed at both M6 and M7a (Figure 49). Figure 42: Scenario No. 2, two-phase fault. **(a)** Phase-to-phase voltage of M7; **(b)** Phase-to-ground-voltage of M7. Figure 43: Scenario No. 3, two-phase fault. **(a)** Phase-to-phase voltage of M5; **(b)** Phase-to-ground-voltage of M5. Figure 46: Scenario No. 7, two-phase fault. (**a**) Phase-to-phase voltage at the beginning of the 10 kV line of M6; (**b**) Phase-to-ground-voltage at the beginning of the 10 kV line of M6. Figure 44: Scenario No. 4, two-phase fault. (**a**) Phase-to-phase voltage of M2; (**b**) Phase-to-ground-voltage of M2. Figure 45: Scenario No. 6, two-phase fault. (**a**) Phase-to-phase voltage of M5c; (**b**) Phase-to-ground-voltage of M5c. Figure 47: Scenario No. 7, two-phase fault. (**a**) Phase-to-phase voltage of M5; (**b**) Phase-to-ground-voltage of M5. Figure 48: Scenario No. 8, two-phase fault.