## 3 Voltage Transformer Model
The voltage \(u_{\mathrm{u}21}\), representing the electromotive force (induced voltage) in the primary secondary circuits, forms a voltage equation of the form with the other voltage drops:  
\[u_{\mathrm{u}21}=u_{L21}+u_{\mathrm{R}21}+u_{\mathrm{RB}21} \tag{19}\]  
Knowing that \(u_{\mathrm{u}21}\) is equal to the following:  
\[u_{\mathrm{u}21}=\frac{u_{\mathrm{u}1}}{\theta_{1-21}} \tag{20}\]  
The voltage Equation (19) can be developed into an equation based on the equivalent diagram from Figure 3:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]0  
After substituting Relation (20) into Equation (21) and performing the transformation, the following equation was obtained:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]1  
By performing a further transformation of Equation (22), a first-order differential equation of the form was obtained:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]2  
According to [PERSON]'s law, the voltage drop \(u_{R_{B21}(L1)}\) across the load resistance \(R_{B21}\) in phase L1 is as follows:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]3  
According to the electrical equivalent circuit diagram in Figure 3, the secondary circuit, connected in an open triangle arrangement, forms a series connection of all three secondary winding leads of the auxiliary windings together with the series connected load resistance. This circuit can be described by a voltage equation of the following form:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]4Equation (25) can be developed and transformed to the following form:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]5  
After further transformations, Equation (26) takes the form (27), which is a first-order differential equation. \[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]6  
According to [PERSON]'s law, the voltage drop \(u_{R_{822}}\) across the load resistance \(R_{\mathrm{B22}}\) is as follows:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]7  
The voltage \(u_{R_{822}}\) is equal in value to the tripled secondary voltage of the zero order. The voltage drops across the transverse elements visible in the primary winding circuit in Figure 3--the voltage drop across the non-linear coil, the voltage drop across the non-linear resistance and the voltage drop across the primary winding of an air-perfect transformer--are equal to each other, as expressed in the following equation:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]8  
After appropriate substitutions and transformations, Equation (29) can be developed into an equation of the following form:  
\[i_{1}=i_{\text{\mu}}+i_{2}=(i_{\Psi}(\Psi)+i_{\text{Fe}})+i_{2} \tag{14}\]9  
The above Equation (30) is a non-linear differential equation of the first order. The function describing the non-linear ferromagnetic core coil is expressed in terms of an incomplete power polynomial to approximate the magnetisation curve of the modelled voltage transformer. The function describing the non-linear coil takes the form of the following equation:  
\[i_{2}=\frac{i_{21}}{\theta_{1-21}}+\frac{i_{22}}{\theta_{1-22}} \tag{15}\]0  
The values of the coefficients of the incomplete power polynomial appearing in Equation (31) are taken in turn:  
\[ \begin{array}{l}a_{1}=6\cdot 10^{-4}\\ a_{5}=1.5\cdot 10^{-8}\\ a_{7}=3\cdot 10^{-12}\end{array}