Numerical Mathematical Model for the Analysis of the Transient Regime Caused by a Phase-to-Earth Fault

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 Rt = 8 Ω and 4.94% if Rt = 268 Ω; for the zero-sequence voltage, 3.21% if Rt = 8 Ω and 6.19% if Rt = 268 Ω.