## 2 Materials and Methods
Analysing the curves shown in Figures 2-4, one can first of all find an analogy of their shape, with the curves available in the literature [35; 36; 37; 38], which show the dependence of the voltage U\({}_{0}\) depending on the earth fault compensation detuning. An example of the variation in the zero-sequence voltage according to [PERSON] et al. [36] is shown in Figure 5. The highest value of the zero-sequence voltage asymmetry factor \(\alpha_{\text{U}0}\) occurs at resonance (detuning factor s = 0%) and reaches 80-200%. It can be seen that the smaller the cross-section of the line conductors, the higher the value of the asymmetry factor. Increasing the value of the detuning factor to 10% reduces the value of the zero-sequence asymmetry factor \(\alpha_{\text{U}0}\) to 3-8%. This means that keeping the inductance of the Petersen coil close to the line capacitance results in a high zero-sequence voltage asymmetry in the network, which can lead to unnecessary tripping of the protections [39]. It is also worth noting that the value of factor \(\alpha_{\text{U}0}\) also changes with distance from the substation, with the value increasing as the length of the MV line increases. Figure 4: Graph of the relationship \(\alpha_{U0}=f(s)\) for an MV line with a 70 mm\({}^{2}\) conductor cross-section for the analytical model. Figure 3: Graph of the relationship \(\alpha_{U0}=f(s)\) for an MV line with a 50 mm\({}^{2}\) conductor cross-section for the analytical model. An analysis of the curves shown in Figures 6-8 indicates that the negative-sequence voltage asymmetry factor \(\alpha_{U2}\) does not depend on the detuning factor s. Only in the vicinity of the resonance values (s = 0%) are there small changes not exceeding 0.1%. Furthermore, the values of the negative-sequence voltage asymmetry factor \(\alpha_{U2}\), for any value of the detuning factor s, are significantly smaller than the values of the zero-sequence voltage asymmetry factor \(\alpha_{UD}\), and do not exceed 0.4% for the cases analysed. Analogously, as before, the values of the negative-sequence voltage asymmetry factor increase with increasing distance from the substation and decrease with increasing conductor cross-section. In order to verify the correctness of the calculation of voltage asymmetry factors from the equations (1 \(\div\) 20), for the same grid parameters, a computer model of a section of the electric power network was made using PowerFactory software. Analogous to the analytical model, the modelled network is supplied from a 110/15 kV transformer with a rated power of 16 MVA. Connected to the transformer station are three 15 kV overhead lines with bare aluminium-steel conductors of 35, 50 and 70 mm\({}^{2}\), each 20 km long. Each  
Figure 5: Graph of the relationship zero-sequence voltage U\({}^{0}\) depending on the earth fault compensation detuning factor determined by [PERSON] et al. [38]. Figure 6: Graph of the relationship \(\alpha_{UD}\) = \(f\)(s) for an MV line with a 35 mm\({}^{2}\) conductor cross-section for the analytical model. line is loaded every 1 km with a 100 kW transformer station (total of 2 MW in each line) with a power factor \(\cos\varphi=0.95\) of inductive character. A schematic of this model is shown in Figure 9.  
As for the analytical model, simulation calculations were performed for different values of the detuning factor s from \(-100\%\) to \(100\%\). Graphs of the dependence of the zero-sequence voltage asymmetry factor \(\alpha_{\text{U0}}\) as a function of the earth fault compensation detuning factor s are shown in Figures 10-12, while the dependence of the negative-sequence voltage asymmetry factor \(\alpha_{\text{U2}}\) as a function of factor s is shown in Figures 13-15. By analysing the curves shown in Figures 10-12, it can be seen that they are analogous to the analytical calculations. Also, the obtained values of the voltage asymmetry factors remain approximately the same.