## Appendix A  
The parameters of power transformers included in the test grid are given in Tables A1 and A2. In these tables, all known (determined) significant digits are provided. The parameters and their calculation methods are provided in the literature [58; 59]. In the case of a two-winding transformer, the following equations are used:  
\[R_{SC}=\frac{\Delta{P_{SC}}\cdot{U_{b}}^{2}}{{S_{R}}^{2}},\] (A1)  
\[Z_{SC}=\frac{{U_{SC}}[\%]\cdot{U_{b}}^{2}}{100\;{S_{R}}},\] (A2)  
\[X_{SC}=\sqrt{{Z_{SC}}^{2}-{R_{SC}}^{2}},\] (A3)  
\[\Delta{Q_{OC}}=\frac{{I_{OC}}[\%]}{100}\cdot{S_{R}},\] (A4)  
\[B_{OC}=\frac{\Delta{Q_{OC}}}{{U_{b}}^{2}},\] (A5)  
\[{G_{OC}}=\frac{\Delta{P_{OC}}}{{U_{b}}^{2}},\] (A6)  
\[Z_{OC}=\frac{1}{{G_{OC}}}+j\frac{1}{{B_{OC}}},\] (A7)  
where: \(R_{SC}\)--the short-circuit test resistance, \(\Omega\); \(X_{SC}\)--the short-circuit test reactance, \(\Omega\); \(Z_{SC}\)--the short-circuit test impedance, \(\Omega\); \(U_{SC}\)--the short-circuit test voltage, \(\
u\); \(\Delta{P_{SC}}\)--the full-load copper loss, \(\
u\); \(G_{OC}\)--exciting conductance, \(S\); \(B_{OC}\)--exciting susceptance, \(S\); \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Power 1** & **U1** & **U2** & **U3** & **USC12** & **USC13** & **USC23** & **\(\Delta{P_{SC}}\)** & **\(\Delta{P_{OC}}\)** & **IOC** \\ \hline
200 MVA & 330 kV & 115 kV & 10.5 kV & 10\% & 34\% & 22.5\% & 600 kW 2 & 180 kW & 0.5\% \\
25 MVA & 115 kV & 38.5 kV & 11 kV & 10.5\% & 17\% & 6\% & 145 kV 3 & 36 kW & 1.00\% \\
16 MVA & 115 kV & 38.8 kV & 11 kV & 10.5\% & 17\% & 6\% & 105 kW 3 & 26 kW & 1.05\% \\
10 MVA & 115 kV & 11 kV & - & 10.5\% & - & - & 60 kW & 14 kW & 0.90\% \\
1.6 MVA & 35 kV & 11 kV & - & 6.5\% & - & - & 17.25 kW & 3.65 kW & 1.40\% \\
0.4 MVA & 10 kV & 0.63 kV & - & 4.5\% & - & - & \(\pm\)5.7 kW & \(\pm\)1.00 kW & 2.1–3.0\% \\ \hline \hline \end{tabular}  
* Nomenclature: U1, U2 and U3—nominal voltage of primary, secondary, and tertiary windings, USc12, USc13, and USc23—short-circuit test voltage of each pair of windings; \(\Delta{P_{SC}}\)—copper loss; \(\Delta{P_{OC}}\)—from loss of active power, Iocc—no-load current. 2 Only \(\Delta{P_{SC12}}\) is given. 3 The value of the worst-case is given when power does not flow through the tertiary winding.  
\end{table} 
Table 1: Technical passport parameters of power transformers provided by the manufacturer. \(Z_{OC}\)--exciting impedance, \(\Omega\); \(I_{OC}\)--no-load current, A; \(\Delta P_{OC}\)--the active component of open-circuit iron loss (consisting of hysteresis and eddy current loss), W; \(\Delta Q_{OC}\)--the reactive component of open-circuit iron loss (consisting of hysteresis and eddy current loss), VAr; \(S_{R}\)--the rated power, VA; \(U_{b}\)--base voltage, \(V\); \(j\)--an imaginary unit. Unknown copper losses of an autotransformer can be calculated by combining Equation (A1) with the following system of equations:  
\[\left\{ \begin{array}{l}\Delta P_{\text{SC1}}=\frac{\Delta P_{\text{SC12}}+ \Delta P_{\text{SC13}}-\Delta P_{\text{SC23}}}{2},\\ \Delta P_{\text{SC2}}=\frac{\Delta P_{\text{SC12}}+\Delta P_{\text{SC23}}- \Delta P_{\text{SC13}}}{2}.\end{array} \right. \tag{10}\]  
Sometimes, since \(X\gg R\), resistance can be neglected. Then, the reactance of both autotransformer and three-winding transformer can be calculated by Equation (A2). Analogously to Equation (10), unknown short-circuit test voltage can be found as follows:  
\[U_{\text{SC1}}=\frac{U_{\text{SC12}}+U_{\text{SC13}}-U_{\text{SC23}}}{2}. \tag{11}\]  
Equivalent circuit of a two-winding transformer (Figure A1) can be regarded as a passive quadripole. The horizontal branch of the circuit represents copper loss. The vertical branch represents the ferromagnetic core: physical behavior is more precisely represented when the magnetizing branch is connected in parallel, however, connection in series is usually preferred in order to simplify calculations [58].