Resumen
The mathematical model of the frequency converter cable branch as a part of the mine section power network with a single phase-to-ground fault is clarified. The model takes into account a discrete nature of the output voltage and power switches commutation inertia of a voltage inverter as a part of the converter. A technique is proposed for the formation of a mathematical model of a cable line with distributed parameters as a set of differential equations of state and algebraic coupling equations in matrix form. In this case, the cable is divided into three-phase elementary sections, for a set of typical equivalent circuits of which a graph is built, the matrix of the main sections and the matrix coefficients of the equations are calculated. The latter are solved by numerical methods. This allows to take into account the wave processes in the cable for a high-frequency pulse-width modulated output voltage of the frequency converter. Also the asymmetry of the insulation ground resistance, accompanying a ground fault, is taken into account. The matrix-topological approach allows to avoid operations with partial derivatives with respect to geometric coordinates of the cable. The relevance of the research resulted from the neglect of significant factors in known models, which reduces the accuracy of the analysis. In particular, the influence of the discrete nature of the output voltage of the frequency converter, the distributed nature of the cable line insulation parameters and the transverse asymmetry in emergency mode on the instantaneous values of the ground fault current are not taken into account. As a result of numerical simulation for the network of specific configuration, it was found that the occurrence of ground fault through a human body in the cable branch of the frequency converter is characterized by an unacceptably high probability of fatal electrocution. The monitoring method of the insulation resistance of the power network branch, equipped with the semiconductor frequency converter, is proved. The implementation of the method will improve the electrical safety of underground electrical networks due to the timely detection of insulation damage of the frequency converter cable branch and the transmission of a signal to turn off the supply voltage.