## 3 Results
### Voltage Sag Matrix
#### 3.1.2 Two-Phase-to-Ground Fault
The example of the dependence of upward voltage patterns on winding configuration is given in Figure 32: when a two-phase-to-ground fault occurs at the end of the 35 kV line (Scenario No. 6), the voltage at M5a is similar in all cases (Figure 33), but the voltage at M5c is not (Figures 34 and 35). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Monitor**} & \multicolumn{3}{c}{**Phase-to-Phase Voltage, kV 1**} & \multicolumn{3}{c}{**Phase-to-Ground Voltage, kV**} \\ \cline{2-9}  & **Initial 2** & **U\({}^{\star}\)** & **U\({}^{\star}\)** & **U\({}^{\star}\)** & **U\({}^{\star}\)** & **Initial 2** & **U\({}^{\star}\)** & **U\({}^{\star}\)** & **U\({}^{\star}\)** & **U\({}^{\star}\)** \\ \hline
**2** & 456.1\(\angle\)28\({}^{\circ}\) & 422.4\(\angle\)27\({}^{\circ}\) & 26.2\(\angle\)–141\({}^{\circ}\) & - & 263.3\(\angle\)\(-\)2\({}^{\circ}\) & 243.9\(\angle\)–2\({}^{\circ}\) & 15.2\(\angle\)–111\({}^{\circ}\) & 25.9\(\angle\)–122\({}^{\circ}\) \\
**2a** & 14.5\(\angle\)–2\({}^{\circ}\) & 13.4\(\angle\)–2\({}^{\circ}\) & 0.8\(\angle\)–109\({}^{\circ}\) & - & 8.4\(\angle\)–33\({}^{\circ}\) & 7.8\(\angle\)–33\({}^{\circ}\) & 0.5\(\angle\)–79\({}^{\circ}\) & - \\
**3** & 158.7\(\angle\)28\({}^{\circ}\) & 146.2\(\angle\)28\({}^{\circ}\) & 9.6\(\angle\)–146\({}^{\circ}\) & - & 91.6\(\angle\)–2\({}^{\circ}\) & 84.4\(\angle\)–2\({}^{\circ}\) & 5.6\(\angle\)–116\({}^{\circ}\) & 26.3\(\angle\)122\({}^{\circ}\) \\
**4** & 151.8\(\angle\)29\({}^{\circ}\) & 66.2\(\angle\)28\({}^{\circ}\) & 66.2\(\angle\)–151\({}^{\circ}\) & - & 87.6\(\angle\)0\({}^{\circ}\) & 38.2\(\angle\)0\({}^{\circ}\) & 38.2\(\angle\)–121\({}^{\circ}\) & 38.2\(\angle\)119\({}^{\circ}\) \\ \hline \hline \end{tabular}  
* Voltages are given in polar form—magnitude and angle. 2 Initial (pre-fault) voltage contains only the positive sequence component.  
\end{table} 
Table 6: Symmetrical components of both voltages of M4 and the rest of the upward monitors, after the two-phase-to-ground fault at M4 (Scenario No. 4). Figure 31: Scenario No. 4, two-phase-to-ground fault. (**a**) Symmetrical magnitudes of phase-to-phase voltage of M4; (**b**) Symmetrical magnitudes of the phase-to-ground voltage of M4; (**c**) Symmetrical magnitudes of the phase-to-phase voltage of M3; (**d**) Symmetrical magnitudes of phase-to-ground voltage of M3. Figure 34: Scenario No. 6, two-phase-to-ground fault. (**a**) Phase-to-phase voltage of M5c, when the winding configuration is \(Y_{0}/Y/\Delta\)-0-11; (**b**) Phase-to-ground voltage of M5c, when the winding configuration is \(Y_{0}/Y/\Delta\)-0-11. Figure 32: Three-winding transformer configuration influence on upward voltage patterns (voltage sag depth at M5a and M5c), after the two-phase-to-ground fault at M5 (Scenario No. 6). In the case of the LV grid, the upward propagation mechanism is as follows: (1) if a fault occurs at the secondary winding of the 10/0.4 kV transformer (Scenario No. 8), voltage sags are observed in both the 10 kV and 35 kV grids (Figure 36a), and also (obviously) in the neighboring 0.4 kV line; (2) if the distance between the fault and the secondary winding is, for example, 1 km (Scenario No. 9), only a voltage unbalance is caused in both the 10 kV busbar (Figure 28b) and the neighboring 0.4 kV line (Figure 36b), i.e., voltage sag does not propagate upwards. Non-uniform patterns are also noticed in the downstream propagation path. In the case of Scenario No. 1, transition M5-M6 (Figures 37 and 38) can be given as an example. Another example can be related to downward propagation through the autotransformer--path M2-M2a-M3 in the case of either Scenario No. 1 or No. 2. The patterns do not coincide (correlate) with the upward propagation path, in particular, through the three-winding transformer (e.g., the case in Figure 32): for example, compare voltage at M2 in the case of Scenarios Nos. 1-3, or M5 in the case of Scenarios No. 4 and No. 5. Figure 36: (**a**) Scenario No. 8, two-phase-to-ground fault, phase-to-phase voltage of M6; (**b**) Scenario No.