## 3 Simulation Results  
The simulation of the analyzed phenomenon was performed with MATLAB R2021b version. The code for determining the transmitted overvoltages was written in C language using the Math Script RT module [37]. The real parameters of the power transformer are as follows:  
- \(\Pi\) winding resistance: \(R_{\text{IT}}=0.5\ [\Omega]\). - MT winding resistance: \(R_{\text{MT}}=0.00787\ [\Omega]\). - T winding resistance: \(R_{\text{T}}=0.0163\ [\ \Omega]\). - \(\Pi\) winding inductance: \(L_{\text{IT}}=0.108268241\ [H]\). - MT winding inductance: \(L_{\text{MT}}=0.002013252\ [H]\). - the inductance of the T winding: \(L_{\text{T}}=0.001175828\ [H]\). - T winding-MT winding capacitance: \(C_{\text{MT}-T}=3.72621\!\cdot\!10^{-9}\ [F]\). - MT winding-IT winding capacitance: \(C_{\text{IT}-MT}=2.10827\!\cdot\!10^{-9}\ [F]\). - Serial capacitance of MT winding: \(C_{\text{sMT}}=2.4988\!\cdot\!10^{-9}\ [F]\). - Capacitance of MT winding to ground: \(C_{\text{MT}-m}=3.748\!\cdot\!10^{-9}\ [F]\). For both the simulation and testing, the value of the pulse that was applied to the transformer was set to 292.4 V, while the value of the voltage pulse that was applied in the laboratory tests was gradually increased according to current standards (see Figure 6). The maximum value of the voltage that was transmitted by electromagnetic induction, \(U_{\text{in}MT}\), was 29.154 V (see Figure 7). The transmission of the lightning impulse energizing the high-voltage winding to the medium-voltage winding through the existing capacitance chain is explained in the Figure 8.  
The lightning voltage division factor is given by the following relation (42):  
\[k_{\text{division}}=\frac{C_{\text{IT}-MT}}{C_{\text{sMT}}+C_{\text{IT}-MT}+C _{\text{e}-m}} \tag{42}\]  
Figure 5: Configuration of the analyzed circuit for the calculation of the voltage that is transmitted to the tertiary winding. where \(C_{e-m}\) is the equivalent capacity of the medium-voltage winding to earth (ground). The equivalent capacity of the medium-voltage winding with respect to earth is determined on the basis of the following relation (43):  
\[C_{e-m}=C_{MT-m}+C_{MT-T} \tag{43}\]  
Figure 8: The capacity chain. Figure 6: Waveform of the applied pulse. Figure 7: Overvoltage transmitted by electromagnetic induction to the medium-voltage winding. The relation describing the time evolution of the oscillating voltage caused by energizing the medium-voltage winding with a pulse wave that has been reduced in amplitude by the factor \(k_{division}\) is determined by the following relation:  
\[u_{oscMT}=k_{division}\cdot U_{0}\cdot\left(e^{-\kappa_{1}\cdot t}-e^{-\kappa_{2 }\cdot t}\right)\cdot e^{-\delta\cdot t}\cdot sin(\omega\cdot t) \tag{44}\]  
The graphical representation of the oscillating voltage variation as a function of time is given in Figure 9.  
The maximum value of the oscillating voltage caused by energizing the medium-voltage winding, \(U_{oscMT}\), is 7.2783 V.  
The voltage transmitted from the high-voltage winding to the medium-voltage winding is the sum of the inductively and capacitively transmitted voltages (see Figures 7 and 9). Overvoltage transmitted from high voltage to medium voltage winding, is depicted in Figure 10.  
The maximum value of the overvoltage that is transmitted from the IT winding to the MT winding is the result of the superposition of the inductive and capacitive propagated overvoltages and has a value of 36.4323 V.  
The MT winding behaves as a screen that prevents the capacitive transmission of the voltage from the IT (energized winding) to the T winding. As a result, the transmission of the overvoltage is inductively proportional to the number of turns between the MT and T windings. \[k_{\text{division}}=\frac{C_{\text{IT}-MT}}{C_{\text{sMT}}+C_{\text{IT}-MT}+C _{\text{e}-m}} \tag{42}\]0 Overvoltage transmitted from high-voltage to medium-voltage winding.