## 2 Materials and Methods  
### Test Grid  
The voltage sags propagation mechanism will be investigated with simulations in a test grid model created with MATLAB/Simulink. The scheme of the pseudo-realistic test grid is given in Figure 3: the chosen fragment of the Lithuanian power system is slightly (and realistically) expanded for research purposes. The Lithuanian power grid is a part of the post-Soviet BRELL ring where nominal voltage levels are as follows: HV--330 kV and 110 kV; MV--35 kV, 10 kV, and 6 kV; LV--0.4 kV. The test grid contains all possible voltage levels except 6 kV, both the TSO and DSO parts are included. The Lithuanian HV grid's neutral is grounded via a separator (but some separators are disconnected to reduce short-circuit current ratios), the MV grid operates in isolated (or compensated) neutral mode, the LV grid's neutral is grounded. The test grid contains the following oil-filled power transformers:  
* Four 200 MVA 330/110 kV autotransformers. The common winding of an autotransformer is connected in wye with neutral point (\(Y_{0}\)) [58]. The tertiary 10 kV winding supplies substation auxiliary transformer(s) and, in addition, some customers. Power rating of the tertiary winding is 40% (of 200 MVA), a delta configuration (\(\Delta\)) is used in anticipation of zero sequence current harmonics [58; 59];
* One 25 MVA 110/35/10 kV three-winding transformer. Power ratings of all windings are 100%. Noteworthily, in some cases, the rating of the secondary and (or) tertiary winding can be 67% [58]. Winding configuration can be either Y\({}_{0}\)/\(\Delta\)/\(\Delta\)-0-11, Y\({}_{0}\)/\(\Delta\)/\(\Delta\)-11-1, Y\({}_{0}\)/Y/\(\Delta\)-0-11, or Y\({}_{0}\)/\(\Delta\)/Y-11-0, etc. ;
* One 16 MVA 110/35/10 kV three-winding transformer. Power ratings of all windings are 100% [58];
* Two 10 MVA 110/10 kV transformers. Winding configuration is Y\({}_{0}\)/\(\Delta\)-11;
* One 1.6 MVA 35/10 kV transformer. Winding configuration is Y/\(\Delta\)-11;
* Two 0.4 MVA 10/0.4 kV transformers. Winding configuration is Y/\(Y_{0}\)-0. Figure 2: Proposed interconnection model between power system reliability and power quality. The parameters of the power transformers are given in Appendix A: a part of them is given by the manufacturer, the rest must be calculated according to the described methodology. The values of those parameters are required for the equivalent circuits. Two-winding transformers are modeled with a T-type equivalent circuit where the magnetizing branch is connected in series. Noteworthily, the real physical behavior of a transformer can be represented better with the magnetizing branch being connected in parallel, however, it is more convenient to use the T-type model [58]. The task becomes more complicated in the case of the presence of both a three-winding transformer and an autotransformer. For power transmission line modeling, either the nominal \(\Pi\)-model or the distributed-element model can be used. See Appendix A for a detailed description. The lengths of the longest lines in the test scheme are specified in Figure 3. The longest length is 100 km. The test scheme contains only one power source. The commutators of other 330 kV power supply lines in the TSO grid are switched off. Initial topology of the grid is radial: some TSO circuit-breakers are switched off, thus the rings are not formed. Distributed generation is not included. In the normal grid operation mode, the loading of a transformer is equal to 30-50%. In emergency mode, a 140% temporary overload is allowed [58; 59]. Power consumption of auxiliary equipment in the substations is relatively small and equal to 50-500 kW [60]. In normal mode, it is realistically assumed that the average power factor is greater than 0.90, and the load imbalance is 0%. Voltage unbalance (imbalance) is assessed as the ratio of the negative sequence magnitude to the positive sequence, i.e., according to the definition given by EN 50160:2010 and IEEE Std 1159-2019.