## 1 Introduction  
The energy transformation that has been taking place in recent years is also affecting distribution networks. The rapid increase in the capacity of photovoltaic installations, wind power plants and electric vehicle charging stations poses challenges to the existing network infrastructure [1, 2]. In power grids, there are both differences in loads and in the generation of energy in the individual phases [3, 4]. This is the main cause of voltage asymmetry in power grids [5]. Additional factors influencing the asymmetry of voltage levels in individual phases are unequal ground capacitances in medium-voltage lines (especially overhead lines) and incorrect tuning of the earth fault compensating reactor [6]. In addition, photovoltaic [7, 8] and wind power plants [9] affect power quality parameters, including the value of voltage asymmetry [10]. Electric car charging stations [11, 12] and energy storage [13] can also cause voltage asymmetry. In summary, voltage asymmetry in power grids can have very different causes. The most important ones may include the following:  
* Unbalanced loading on individual phases of a three-phase circuit, which is more often the case on low-voltage networks;* Unbalanced generation from single-phase sources, especially small wind and photovoltaic power plants in low-voltage networks;
* The asymmetrical construction of power lines, consisting mainly of asymmetrical earth capacities, particularly in the case of medium-voltage overhead lines;
* The method and parameters for earthing the neutral point of the medium-voltage grid. The value of the grid voltage can be regulated by controlling the active or reactive power produced by photovoltaic power plants [14; 15]. The efficiency of these methods depends on the structure of the grid, bearing in mind that the transmission of reactive power causes additional power losses in electric power equipment [16]. Another method of voltage control is shunt connection to the energy storage network, where the active and reactive components of the current are regulated [17]. Additional methods to mitigate voltage asymmetry are based on increasing the cross-section of cables used, installing voltage stabilisers and implementing asymmetry compensation techniques in PV inverters [18]. In many cases, voltage asymmetry is due to asymmetrical loading but mainly in low-voltage grids. Unbalanced currents lead to a reduction in the actual load capacity of power cables and transformers [19]. In addition, load asymmetry significantly affects the differences between actual and estimated values of power quality indicators [20]. The stability of the power system depends primarily on the way the neutral point operates, which can be isolated, earthed directly, through a resistor or a compensation reactor (Petersen coil) [21]. The method of earthing is driven by the requirements for the value of currents and ground overvoltages, so different solutions can be found in different countries [22]. In networks with an isolated neutral point, the zero-sequence component circuit is closed by existing capacitances and leakage in the power network [23]. The capacitive earth fault current can be compensated by an inductive current [24]. For this purpose, an additional earthing transformer is installed in the medium-voltage switchgear, the neutral point of which is earthed by a Petersen coil [25]. Earthing the neutral point of the network through a resistor reduces overvoltages occurring during earth faults. The resistance value of this resistor should allow earth fault currents to flow with a value that ensures the correct operation of the earth fault protection devices installed in the network [26]. Phenomena related to voltage asymmetry are particularly evident in networks earned through a Petersen coil and must be taken into account, among other things, when determining the operating conditions of earth fault protections [27; 28].