Numerical approximation of heat run test results of transformers by means of double exponential and power functions

Two methods of estimating the average oil temperature rise inside a winding are presented. The first method is based on a differential equation of the nonlinear cooling of a uniform body. The second method is a modification of a graphical method given in IEC Publication 76-2 (1976). The first method assures excellent agreement with measurements in the case of OD cooling. The accuracy of the modified graphical method is also quite good. The verification carried out is not sufficient to state whether the methods can be applied to ON cooling. Numerical calculation based on an optimisation method of Fletcher-Powell-Dawidon with golden cut is incorporated. Newton´s method is used to calculate the coefficients of approximation functions of a top oil temperature rise and an average winding temperature rise after shutdown