Settings of protection are essential to ensure the sensitivity and selectivity needed to detect defects. Making the correct settings requires the calculation of the fault currents with as little error as possible. Fault currents are influenced by the parameters of the electrical networks, including the state of the insulation and the Petersen coil, which changes during their operation electrical networks. This paper analyzes how the insulation parameters of medium voltage power lines, the parameters of the Petersen coil used to treat the neutral of the medium voltage electrical network and the value of the resistance at the fault location influence the fault current in the case of a single-phase fault. The large number of single-phase faults that occur in medium voltage electrical networks justifies this analysis. The symmetrical components method was used to calculate the fault current. The results obtained by calculation were verified experimentally by causing a single-phase-to-ground fault in a real medium voltage network. The paper presents the situations in which the analytical calculation of the single-phase-to-ground fault current can lead to inadmissibly large errors, even over 50%, but also the situations in which the errors fall below 3%.

One important problem in the operation of medium voltage networks is the detection of a single-line-to-ground fault in its incipient state, when the fault resistance values are very high. In a medium voltage (MV) distribution network with a neutral grounding resistor (NGR), one of the methods employed to discriminate a single line-to-ground fault is the use of an overcurrent relay with an operating characteristic adjusted according to the effective value of the current flowing through the limiting resistor. In case of a single line-to-ground fault with a high fault resistance value, the correct tripping settings of the protective relay require the precise computation of this current. In comparison to the assumptions made by the models from the literature—the three-phase voltage system of the medium voltage busbars is symmetrical and there are no active power losses in the network insulation—the model proposed in this paper considers the pre-fault zero-sequence voltage of the medium voltage busbars and the active power losses in the network insulation, which is necessary in certain fault conditions where the use of the former leads to unacceptable errors.

The paper analyses how the characteristics of the medium-voltage network with insulated neutral and the conditions under which the single line-to-ground fault occurs (insulation condition and value of the fault resistance) influence the zero-sequence components of the voltage of the transformer station medium-voltage bus bar, the fault current, the currents of the faulted line and the currents of the other non-faulted power lines connected to the transformer station bus bars. Assuming the waveform of the medium voltage bus voltages in the transformer station is known, the influence of the fault resistance on the total distortion coefficient of the fault current is analysed. This establishes the conditions under which a single line-to-ground fault can be detected by controlling the total distortion coefficient of the fault current and the currents of the fault-free lines. It also examines the conditions under which a single line-to-ground fault can be selectively detected by checking the effective value and direction of flow of the zero-sequence currents of the medium-voltage lines during the fault. The results obtained by the calculation were verified experimentally in the medium voltage network considered in the study. The acceptable differences, considering the degree of accuracy with which the parameters of a medium voltage network are known, between the results obtained by calculation and those obtained experimentally show that the simplifying assumptions accepted for the mathematical models used in the calculation are correct.

The increasing complexity of electrical power installations requires more and more sophisticated mathematical models for the analysis of their operating regimes in relation to transient regimes. This requirement can be solved by using numerical mathematical models implemented in professional programming environments. MATLAB/Simulink is such a programming environment that allows for the analysis of transient regimes caused by faults occurring in electrical power installations. In this paper, the transient regime caused by the phase-to-ground fault is analyzed using a numerical model of a 20 kV nominal voltage power network, implemented in the MATLAB/Simulink programming environment. The numerical model was validated by comparing the obtained results with those experimentally determined in a real 20 kV network. Using the numerical model, we can analyze how the zero-sequence voltage of the 20 kV bus bars and the fault current in the 20 kV network, which are neutrally treated with a Petersen coil, are influenced by the following parameters: the initial phase of the voltage at the fault location; the regime in which the medium voltage network operates (resonance, under-compensated, or over-compensated); the insulation state (value of the electrical resistance of the insulation); and the value of the resistance at the fault location. The differences between the experimentally obtained results and those obtained using the numerical model are as follows: for the fault current, 6.67% if R_t = 8 Ω and 4.94% if R_t = 268 Ω; for the zero-sequence voltage, 3.21% if R_t = 8 Ω and 6.19% if R_t = 268 Ω.