Solution of the System of State Equations of an Electrical Network With an Insulation Defect or With a Single-Phase Ground Fault

Abstract

A method for solving the system of equations of the state of an electric network with an isolated neutral is proposed, which is created based on the results of measuring the current vectors of the load connection phases and the phase voltages in relation to the ground, which allows to determine the occurrence of insulation defects, including single-phase short circuits to the ground, and also to determine distance to the single-phase ground fault location. In the well-known system of equations of the state of the electrical network, the parameters of the longitudinal resistance of the line phases are additionally taken into account, which consist of the resistance to the shorting point and the resistance beyond the point of shorting the phase to the ground. Due to simplification, the replacement circuit with additional line phase resistances turns into exactly the same circuit as the circuit without taking into account the line phase resistances, due to which the determination of the line resistance to the closing point is performed using a known algorithm. The accuracy of determining the distance to the closing point was evaluated on the mathematical model of the network node. It was established that the main factors affecting accuracy include the ratio of the capacitance values of the line and the network, the distance to the shorting point, as well as the resistance at the shorting point. When using automatic correction, the error in determining the distance to the shorting point with a resistance of 0.1 Ohm does not exceed 0.9% over almost the entire length of the line. Analytical expressions for determining insulation conductivity and the distance to a local insulation defect are proposed. The elements of the algorithm for determining the distance to the location of a local insulation defect and the results of the accuracy assessment of the method for the specific case of a phase-to-ground fault, in which the transient resistance at the fault location is not taken into account, are given. Automatic selection of circuits with low resistance at the point of the circuit is ensured by checking the value of the determined active resistance, as well as checking the voltage of the damaged phase in relation to the ground.