Overhead power line heating dynamic processes calculation based on the heat transfer quadratic model

A new approach to the non-stationary thermal processes calculation in the overhead power lines was developed. Using the developed approach we can solve the current problem of increasing the grids with overhead lines efficiency. An approximate analytical solution of the wire heating nonlinear differential equation was developed. The solution is based on the wires temperature exponent lowering using the least squares method. Ratio to calculate power losses and the average temperature in the overhead lines wires for an arbitrary time period are offered. Unlike the numerical methods for solving nonlinear differential equations of heating an analytical approach improves analysis and the results generalization. Along with the calculation simplification high accuracy simulating of dynamic thermal processes in the overhead power lines was developed. The developed approach accuracy evaluation was carried out on the base of a comparison with the results obtained with the numerical Runge-Kutta method of the fourth order. We determined that the discrepancy between the temperature calculation results at any given time does not exceed a few hundredths of a degree.