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

• Published in: Journal of physics. Conference series 2019-08, Vol.1260 (5), p.52006
• Main Authors: Girshin, S S, Ya Bigun, A, Kropotin, O V, Shepelev, A O, Tkachenko, V A, Petrova, E V, Goryunov, V N
• Format: Article
• Language: English
• Subjects: Conductors; Differential thermal analysis; Exact solutions; Finite element method; Heat balance; heat balance equation; Heating; Insulation; Least squares method; Mathematical analysis; Nonlinear differential equations; Numerical analysis; Numerical methods; overhead power lines; Physics; Power lines; power losses; temperature dependence of resistance; the conductor temperature; transient thermal modes
• ISSN: 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/1260/5/052006

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.