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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.

To provide the accurate thermal rating of overhead power lines is required to consider the conductor temperature depending on a variety of weather factors. New types of conductors, such as overhead insulation-covered conductors are widely used in electrical networks. Wellknown IEEE 738 and CIGRE standards calculate the bare overhead conductors only and are not applicable for thermal rating of overhead insulation-covered conductors. Numerical methods are able to calculate the insulated conductors, but have many drawbacks, such as the difficulty of modeling and low computation speed. The authors propose an analytical mathematical model to determine the thermal rating both overhead insulation-covered and bare conductors. Results of temperature calculation and active power losses calculation for overhead insulation-covered and bare conductors with the same cross section at selected weather conditions and changes in load current have been presented. Neglect of insulation can lead to errors in calculating of temperature up to 30%.  Index Terms-insulation-covered conductors; bare conductors; overhead lines; conductor temperature; thermal rating; active power losses; weather conditions Vladimir N. Goryunov received the D.Sc. degree in electrical engineering from Moscow Power Engineering Institute, Moscow, Russia in 1992. Currently, he is a Professor and Head of

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