## 2 Materials and Methods  
In order to determine the influence of the neutral point grounding impedance of the MV network on the value of voltage asymmetry factors, an equivalent model of the electric power network was made, as shown in Figure 1.  
Using the nodal potential method, the developed model can be described by the following equations:  
\[\left\{ \begin{array}{l}V_{0}\Big{(}\frac{1}{Z_{0}}+\frac{1}{Z_{ TA}}+\frac{1}{Z_{TB}}+\frac{1}{Z_{TC}}\Big{)}-V_{A1}\frac{1}{Z_{TA}}-V_{B1} \frac{1}{Z_{TB}}-V_{C1}\frac{1}{Z_{TC}}=-E_{A}\cdot\frac{1}{Z_{TA}}-E_{B}\cdot \frac{1}{Z_{TB}}-E_{C}\cdot\frac{1}{Z_{TC}}\\ -V_{0}\cdot\frac{1}{Z_{TA}}+V_{A1}\Big{(}\frac{1}{Z_{TA}}+\frac{1}{Z_{ RABI}}+\frac{1}{Z_{RAC1}}+\frac{1}{Z_{LAI}}+j\omega C_{A1}\Big{)}-V_{B1}\cdot \frac{1}{Z_{RABI}}-V_{C1}\cdot\frac{1}{Z_{RAC1}}-V_{A2}\cdot\frac{1}{Z_{LAI}}= E_{A}\cdot\frac{1}{Z_{TA}}\\ -V_{0}\cdot\frac{1}{Z_{TB}}-V_{A1}\cdot\frac{1}{Z_{RAB}}+V_{B1}\Big{(}\frac{1} {Z_{TB}}+\frac{1}{Z_{RAB1}}+\frac{1}{Z_{RBC1}}+\frac{1}{Z_{B1}}+j\omega C_{B1} \Big{)}-V_{C1}\cdot\frac{1}{Z_{RBC1}}-V_{B2}\cdot\frac{1}{Z_{LB1}}=E_{B}\cdot \frac{1}{Z_{TB}}\\ -V_{0}\cdot\frac{1}{Z_{TC}}-V_{A1}\cdot\frac{1}{Z_{RAC1}}-V_{B1}\cdot\frac{1}{ Z_{RBC1}}+V_{C1}\Big{(}\frac{1}{Z_{TC}}+\frac{1}{Z_{RAC1}}+\frac{1}{Z_{RBC1}}+ \frac{1}{Z_{LC1}}+i\omega C_{C1}\Big{)}-V_{C2}\cdot\frac{1}{Z_{LC1}}=E_{C}\cdot \frac{1}{Z_{TC}}\\ -V_{A1}\cdot\frac{1}{Z_{LAI}}+V_{A2}\Big{(}\frac{1}{Z_{LAI}}+\frac{1}{Z_{RAB}} +\frac{1}{Z_{RAC2}}+\frac{1}{Z_{LAI}}+j\omega C_{A2}\Big{)}-V_{B2}\cdot\frac{1} {Z_{RABI}}-V_{C2}\cdot\frac{1}{Z_{RAC2}}-V_{A3}\cdot\frac{1}{Z_{LA2}}=0\\ -V_{B1}\cdot\frac{1}{Z_{LB1}}-V_{A2}\cdot\frac{1}{Z_{RAB2}}+V_{B2}\Big{(}\frac {1}{Z_{LB1}}+\frac{1}{Z_{RAB2}}+\frac{1}{Z_{RBC2}}+\frac{1}{Z_{RB2}}+\frac{1} {Z_{RB2}}+\mu\omega E_{B2}\Big{)}-V_{C2}\cdot\frac{1}{Z_{RAC2}}-V_{B3}\cdot \frac{1}{Z_{RB2}}=0\\ -V_{C1}\cdot\frac{1}{Z_{LC1}}-V_{A2}\cdot\frac{1}{Z_{RAC2}}-V_{B2}\cdot\frac{1} {Z_{RBC2}}+V_{C2}\Big{(}\frac{1}{Z_{LC1}}+\frac{1}{Z_{RAC2}}+\frac{1}{Z_{RBC2}} +\frac{1}{Z_{LC2}}+\frac{1}{Z_{LC2}}+\mu\omega C_{C2}\Big{)}-V_{C3}\cdot \frac{1}{Z_{LC2}}=0\\ -V_{A2}\cdot\frac{1}{Z_{L2G}}+V_{A3}\Big{(}\frac{1}{Z_{LA2}}+\frac{1}{Z_{RAB3} }+\frac{1}{Z_{RAC3}}+j\omega C_{A3}\Big{)}-V_{B3}\cdot\frac{1}{Z_{RAB3}}-V_{C3 }\cdot\frac{1}{Z_{RAC3}}=0\\ -V_{B2}\cdot\frac{1}{Z_{LB2}}-V_{A3}\cdot\frac{1}{Z_{RAB3}}+V_{B3}\Big{(}\frac {1}{Z_{LB2}}+\frac{1}{Z_{RAB3}}+\frac{1}{Z_{RBC3}}+j\omega C_{B3}\Big{)}-V_{C3 }\cdot\frac{1}{Z_{RBC3}}=0\\ -V_{C2}\cdot\frac{1}{Z_{LC2}}-V_{A3}\cdot\frac{1}{Z_{RAC3}}-V_{B3}\cdot\frac{1} {Z_{RBC3}}+V_{C3}\Big{(}\frac{1}{Z_{LC2}}+\frac{1}{Z_{RAC3}}+\frac{1}{Z_{RBC3} }+j\omega C_{C3}\Big{)}=0\\ \end{array} \right. \tag{1}\]  
When transformed to matrix form, Equation (1) will be of the form  
Figure 1: Equivalent model of MV electric power network with neutral point earthed by a reactor (earth fault compensation). Z\({}_{0}\)—earthing impedance of the MV network neutral point; E\({}_{A}\), E\({}_{B}\), E\({}_{C}\)—electromotive force induced in the HV/MV transformer windings; Z\({}_{TA}\), Z\({}_{TB}\), Z\({}_{TC}\)—impedances of the HV/MV transformer; C\({}_{A1}\), C\({}_{B1}\), C\({}_{C1}\), C\({}_{A2}\), C\({}_{B2}\), C\({}_{C2}\), C\({}_{A3}\), C\({}_{B3}\), C\({}_{C3}\)—ground capacitances of the MV overhead line at the beginning, middle and end of the line; Z\({}_{RAB1}\), Z\({}_{RBC1}\), Z\({}_{RAC1}\), Z\({}_{RAB2}\), Z\({}_{RBC2}\), Z\({}_{RAC2}\), Z\({}_{RAB3}\), Z\({}_{RBC3}\)—load impedance at the beginning, middle and end of the line; Z\({}_{LA1}\), Z\({}_{L1B1}\), Z\({}_{LC1}\), Z\({}_{LA2}\), Z\({}_{LB2}\), Z\({}_{LC2}\)—equivalent impedance of individual MV line sections. \[