Comparison approximate analytical solution of the nonlinear differential equation of heating with numerical

Abstract

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.

Influence degree of skin-effect for overhead line conductors

“…The finite element method is well known and widely used in engineering practice [11,13,18]. So we used the open-source finite element method program FreeFem++ v4.8 [19].…”

“…The clear way of this problem is numerical methods such as the finite element method (FEM). But researchers ignore this way for unknown reasons [11][12][13][14] [15][16][17], but these papers are written in Chinese for one conductor, and, even worse, are not available.…”