## 3 Results
### Voltage Sag Matrix
#### 3.1.1 Three-Phase Fault
Let us investigate the topological changes of the HV grid and begin with power-flow directions (Figure 15). The green arrows indicate the directions of power-flow in normal operation mode, and the directions remain the same in all three possible configurations (i.e., when either both circuit-breakers are closed or any one of them is closed). In fault mode, power always flows towards the short-circuit location. In Figure 15, the red arrows point in the direction of power-flow during Scenario No. 10, when both circuit-breakers are closed. When the directions of power-flow are known, the analysis of voltage sags propagation becomes easier. In the case of Scenario No. 2, when the voltage of M3 remains equal to zero, the circuit-breakers have the following influence:  
1. When the circuit-breaker between M3b and M4 is closed, the power-flow from the right branch supports the busbar of M4, thus the voltage in the 110 kV busbar of M4 is  
Figure 11: Scenario No. 3, three-phase fault. (**a**) Phase-to-phase voltage of M2; (**b**) Phase-to-ground-voltage of M2. Figure 10: Scenario No. 2, single-phase fault. The dependence between the length of the 330 kV line and the phase-to-ground residual voltage of the faulted phase of M1. equal to 0.4 p.u. (Figure 16a). Since the line is sufficiently long (60 km), only transients without sags are observed on the right side (similar to the radial grid case). 2. If both circuit-breakers are closed, the interruption at the 110 kV busbar of M4 is also avoided and the voltage is even higher (0.5 p.u. ); however, in contrast to the previous configuration, the sag is also felt by M4a (Figure 16b). In the opposite case, when the short-circuit occurs at M4a (Scenario No. 10), the circuit-breakers have the following influence:  
1. When both circuit-breakers are closed, the voltage of the dependent M4 is equal to 0.7 p.u. (Figure 17a), while the voltage of M4a is obviously equal to 0. 2. When the (direct) circuit-breaker between M4 and M4a is closed, the voltage of M4 is lower and equal to 0.5 p.u., due to the absence of direct support from the right side (see power-flow direction in Figure 15). 3. When the direct circuit-breaker is open, the electrical distance between the busbars is sufficiently increased, the circuit-breaker between M3b and M4 does not affect the situation (Figure 17b). Figure 12: Scenario No. 3, three-phase fault. (**a**) Phase-to-phase voltage of M1; (**b**) Phase-to-phase-voltage of M4a. Figure 13: Modification of scenario No. 3, three-phase fault. (**a**) Phase-to-phase voltage of M2a, when the distance to the fault is 1 km; (**b**) Phase-to-phase-voltage of M2a, when the distance to the fault is 0.5 km. To sum up, in a general case, ring formations are useful for line current reduction (according to [PERSON]'s current law), and, in a specific case--for voltage sag mitigation (interruption avoidance) in some nodes. On the other hand, circuit-breakers reduce electrical length between busbars, and hence the interdependence and vulnerability of these connected busbars is increased. The solution, i.e., acceptable configuration, depends on the specific circumstances, for example, the criticality (or vulnerability) of end-user equipment or the presence of generators. However, the preferred configuration can be determined only in particular cases, since the optimization of an entire transmission grid is hardly expected due to the large variety of possible configurations. Noteworthy, the topological  
Figure 6:0 Scenario No. 4, three-phase fault. (**a**) Phase-to-phase voltage of M3; (**b**) Phase-to-phase voltage of M2b. Figure 6:1 Power-flow directions in TSO grid when the both circuit-breakers lockout the rings in the case of the normal mode and the fault mode of Scenario No. 10. During the load flow-study, the loads impedances were constant. analysis (at least partial) is rarely found in the PQ literature (even in small test systems), which indicates the poor flexibility of the proposed approaches and algorithms [5]. Let us continue with the faults in the distribution grid.