## 3 Results
### Voltage Sag Matrix  
The idea of a voltage sag matrix has been inherited from [15; 37; 38; 40]; however, only the case of a symmetrical fault has been found. In this paper, a voltage sag matrix will be introduced for asymmetrical faults too, i.e., two-phase-to-ground (Section 3.1.2), two-phase (Section 3.1.3), and single-phase (Section 3.1.4). For these cases, the following modifications must be applied: the cells of the matrix must be a row vector with three entries, and phase-to-phase and phase-to-ground sags must be analyzed with separate matrixes.  
The terminology used for voltage sag characterization usually is confusing [1]. At present, assessment methods of many PQ events lack a universally unified (agreed) approach [5]. Short-duration RMS variation is not an exception: the reference voltage for the assessment of both voltage sags and swells remains an open question. The following options are available: (1) nominal grid voltage, (2) nominal voltage of transformer windings, (3) pre-fault voltage (Figure 5), and (4) residual voltage. The choice depends on the objective: for example, impact on grid equipment, impact on end-user equipment, legal disputes, determination of settings for relay protection and automation, database for machine learning, classification and situation assessment, etc.  
Figure 5: Pre-fault voltages (p.u.) of the test grid in normal operation mode. During the load-flow study, the loads impedances were constant.  
In this paper, voltage sag matrixes are filled in with residual voltage values expressed in per-unit system (when the reference is the nominal grid voltage). In addition, the following color-coding is used for the analysis from another angle: the dark green color denotes that a fault has no impact on voltage level (when the reference is pre-fault voltage); light green--the impact is not higher than \(-10\%\) (i.e., within the boundaries of rapid voltage change (RVC), when the reference is pre-fault voltage); red--residual voltage is equal to 0.1 p.u. (the reference is the nominal grid voltage); orange--a case of severe voltage sag when residual voltage is 0.2-0.4 p.u. (the threshold is set according to the sag classification table given in EN 50160:2010, the reference is the nominal grid voltage); yellow--the rest of voltage sags whose depth is approximately equal to 20-60% (when the reference is pre-fault voltage); white (no color)--voltage swell (including the boundaries of RVC, when the reference is pre-fault voltage). In the case of voltage swells, the color-coding has not been applied because a sag and a swell of the same percentage will have different effects on grid equipment. Nominal grid voltages are given in Figure 3, nominal voltages of transformer windings in Appendix A. Pre-fault voltage values in normal operation mode are given in Figure 5. Please note that tap changers are used for voltage regulation (nominal voltages of transformer windings are given in Appendix A), but reactive power compensators are not included, hence a voltage drop in some nodes is higher than 10-15%. The issue will not affect the results of this research, but it must be considered for error elimination during the estimation of the level of short-duration RMS variations.  
In all scenarios, the simulation sampling time is \(10^{-6}\) s, stop time is 0.16 s, faults occur at 0.06 s after the start of the simulation. Besides, in MATLAB/Simulink, computational time also depends on the quantity of scopes. The simulation of each scenario took up to 5 min (the base frequency of the 4-core processor is 2.30 GHz, RAM--6.00 GB).