Heat Flux Analysis in Electrical Transformers through Integral Operators of Mechanics

Francisco Bulnes, Alejandro R. Tello, Máximo Livera

Federal Highway Mexico-Cuautla “La Candelaria”, Chalco, Mexico.
Headquarters of Computational Systems Engineering, TESCHA, Federal Highway Mexico-Cuautla “La Candelaria”, Chalco, Mexico.
Research Department of Mathematics and Engineering, TESCHA, Federal Highway Mexico-Cuautla “La Candelaria”, Chalco, Mexico.

DOI: 10.4236/mme.2014.42009                

Abstract

Considering the continuous functioning of a power transformer under charge of high capacity of 50 MVA, predicted studies are proposed to be performed of their thermal behavior under perma nent and variable regimens of flow of charge, using noninvasive methods based in integral trans forms that measure and determine parameters of geometrical, analytical and physical type of the transformer. In before works, we have studied a basic geometry of a winding composed of high and low voltage sections with a uniform heat generation and heat convection boundary conditions. The heat conduction equation representing the phenomena of heat generation in a cylindrical structure was solved by using an integral transform. In this sense, this new study considers the basic geometry composed of a three cylindrical windings (high and low voltage turns) and a rec tangular core. Thus it is proposed to solve magnetic flow equations using integral transforms (Han kel transforms and Bessel integrals) in order to obtain the heat source distribution in the core due to the magnetization currents which are developed in function of the magnetic field flow equations. Based on this, it is proposed as a second step to use this heat source distribution to obtain the corresponding temperature distribution in the core by solving the cylindrical heat conduction equation for the core (cylindrical). Bearing this in mind, it is proposed finally to solve the 3D cylindrical heat conduction equation for the one winding using the calculated heat convection coefficients, the conductivity of the winding, behavior of the mineral oil and the non uniform winding heat generation predicted in recent researches. This equation will be solved by using integral methods (Radon, Hankel and Fourier transforms). This methodology will be useful to establish a new design of a power transformer based on the values of their integrals and the results that throw the inverse methods for this case. Finally if possible we will use the programs of Fluent and/or Phoenics for the validation of functional proposed models of prediction and prevention of heat flow and charge based on the obtained results.

 

Keywords

Power Transformer, Thermal Model, Critical Temperature Points, Integral Transforms to Heat Flux, Magnetic Flux

Conflicts of Interest

The authors declare no conflicts of interest.

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