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This paper presents the calculation of non-stationary non-sinusoidal mode of the power supply system (PSS) under the condition of current resonance (parallel resonance). Evaluation of the need for higher harmonics (HH) filtering was carried out. To achieve this, measurements of the actual level of HH and other unified power quality indexes were conducted, and oscillograms of the network mode parameters and HH spectrum were constructed. The measurement of unified power quality indexes was carried out with certified and calibrated power quality analyzers Metrel 2792A. These instruments satisfy the effective world standards on power quality and other reference documentation. Resonance frequencies where resonance modes emergence is possible were determined by calculation. Maximum overvoltage ratios for different points of the examined PSS were also determined.

To improve the efficiency of existing networks, special mathematical models for assessing the losses and temperature of conductors in real time can be used, with the climatic factors being taken into account. The approximate analytical solution of the nonlinear differential equation of heating and cooling of the insulated conductor with numerical method simulation of heat transfer is proposed comparison in this work. The solution is based on lowering the degree of temperature of the conductor using the least squares method in the integral form. A positive feature of the proposed solution is its universality. It allows the analysis of overhead conductors both with and without insulation. The developed method is almost as accurate as the calculation of the conductor temperature by numerical methods. The reliability of the heat balance equation of overhead power lines at non-stationary thermal mode developed by this method is confirmed by comparison with the results obtained by the finite elements method.

Electrical energy losses increase in modern grids. The losses are connected with an increase in consumption. Existing models of electric power losses estimation considering climatic factors do not allow estimating the cable temperature in real time. Considering weather and mode factors in real time allows to meet effectively and safely the consumer's needs to minimize energy losses during transmission, to use electric power equipment effectively. These factors increase an interest in the evaluation of the dynamic thermal mode of overhead transmission lines conductors. The article discusses an approximate analytic solution of the heat balance equation in the transient operation mode of overhead lines based on the least squares method. The accuracy of the results obtained is comparable with the results of solving the heat balance equation of transient thermal mode with the Runge-Kutt method. The analysis of mode and climatic factors effect on the cable temperature in a dynamic thermal mode is presented. The calculation of the maximum permissible current for variation of weather conditions is made. The average electric energy losses during the transient process are calculated with the change of wind, air temperature and solar radiation. The parameters having the greatest effect on the transmission capacity are identified.