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Abstract. A mathematical model of steady-state radial medium voltage electrical network with earthed neutral via arc-suppression coils has been carried out. A detailed equivalent circuit of the examined network using the completed equivalent circuit of phase coordinates methods and Kirchhoff's laws has been developed. The system of mathematical models equations has been completed. The advantage of the created mathematical model is the ability to increase the accuracy of the simulation by a detailed account of features of a network with arc-suppression coils. The mathematical model considers the load currents, the non-linear nature of consumers, the impact of the power lines asymmetry. Using the developed mathematical model there are presented results of the carried out researches of three power lines with different cross sections with neutral grounding via arc-suppression coils. The analysis of asymmetry parameters impact of power lines on the value of the neutral displacement voltage and on the voltage value at the end of the lines at different values of the reactor inductance has been completed. The conclusion about the model possibility to perform validation of the reactor tuning, to evaluate voltage quality parameters, to carry out the formation of reliable initial conditions for calculating the overload in the single-phase earth faults. In conclusion the model performs validation of the reactor tuning and it evaluates voltage quality parameters in order to carry out the formation of reliable initial conditions. It also calculates the overload in the single-phase earth faults.

Abstract. One can offer based on the solution of the heat equation and the heat balance equation a mathematical model of steady thermal regime of the conductor, which allows to determine the temperature of bare and insulationcovered conductors of overhead power lines, considering weather conditions, as well as to perform the calculation of electricity losses with conductors temperature. The expressions are for the gradient of temperature distribution in the current-carrying conductor, as well as conductor insulation with and without dielectric losses. The accuracy of the created model is checked when compared with the methods of CIGRE, IEEE and the Finite Element Method. High precision of matching results is achieved.

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