Application of least square method for heat balance equation solving of overhead line conductors in case of natural convection

The paper provides an approach to the solution of the heat balance of overhead power lines based on the least squares method. The equations for determining temperature and active power losses of both insulated and bare conductors are determined. The advantages of these ratios are correct account of resistances depending on the temperature and analytic form of equations. A quadratic form of the heat balance equation for the case of natural convection is offered. The advantage of the equation is convenience of the analysis considering the conductor temperature, wind speed, current load and solar radiation. The accuracy of the developed approach is compared with the calculation results obtained with the same formulas used with the CIGRE method. Satisfactory results are obtained when calculating the temperature and power loss of bare conductor.