MME  Vol.4 No.2 , May 2014
Heat Flux Analysis in Electrical Transformers through Integral Operators of Mechanics
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.  
Cite this paper: Bulnes, F. , Tello, A. and Livera, M. (2014) Heat Flux Analysis in Electrical Transformers through Integral Operators of Mechanics. Modern Mechanical Engineering, 4, 84-107. doi: 10.4236/mme.2014.42009.

[1]   Pierce, L.W. and Holifield, T. (1999) A Thermal Model for Optimized Distribution and Small Power Transformer Design. IEEE Transactions on Power Systems, 2, 925-929.

[2]   (1996) ANSI/IEEE Loading Guide for Mineral oil Immersed Transformer. C57.91-1995.

[3]   Tello, A. (2009) Modelo Térmico de Transformador Eléctrico. Tesis de Doctorado, Escuela Superior de Ingeniería Mecánica (ESIME), Instituto Politécnico Nacional, Ciudad de México.

[4]   Susa, D., Lethonen, M. and Nordman, H. (2005) Dynamic Thermal Modeling of Power Transformers. IEEE Transactions on Power Delivery, 20, 197-204.

[5]   Nordman, H. (2004) Average Oil Temperature Rise in Distribution Transformers without External Oil Circulation. Technical Memorandum, 2004-03-15.

[6]   Montsinger, V.M. (1951) Thermal Characteristics of Transformer. In: Blume, L.F., et al., Eds., Transformers Engineering: A Treatise on the Theory, Operation and Application of Transformers, Wiley, New York.

[7]   Pradhan, M.K. and Ramu, T.S. (2003) Prediction of Hottest Spot Temperature (HST) in Power and Station Transformers. IEEE Transactions Power Delivery, 18, 1275-1283.

[8]   (2005) Market and Technology Assessment. Prentice Hall, Upper Saddle River.

[9]   Bulnes, F. (1998) Treatise of Advanced Mathematics: Analysis of Signals and Systems. Faculty of Science, National Autonomous University of Mexico, Mexico City.

[10]   Bulnes, F. (2008) Analysis of Prospective and Development of Effective Technologies through Integral Synergic Operators of the Mechanics. In: 14th Scientific Convention of Engineering and Arquitecture: Proceedings of the 5th Cuban Congress of Mechanical Engineering, ISPJAE and Superior Education Ministry of Cuba, Eds., 2-5 December 2008, Havana.

[11]   Feynman, R., Leighton, R. and Sands, M. (1964) Electromagnetism and Matter. Addison-Wesley, Boston.

[12]   Bulnes, F. and Maya, J. (2009) Synergic Integral Operators and Thompson Effect to the Evaluating to Temperature Electrical Conductors. CIM2009, Electrical Engineering, Instituto Tecnológico de Orizaba, Veracruz, 328-335.

[13]   Bulnes, F. and Tello, A. (2010) Thermal Modeled of Electric Transformers through Their Evaluating by Integral Operators of the Mechanics (II). Proc. 15a CCIA-SIDEGI, CUJAE, Ministerio de Educación Superior de Cuba, Habana, 273-279.

[14]   Pierce, L.W. (1994) Hottest Spot Temperatures in Ventilated Dry Type Transformers. IEEE Transactions on Power Delivery, 9, 257-264.

[15]   Alegi, G.L. and Black, W.Z. (1990) Real Time Thermal Model for an Oil-Immersed Forced Air Power Transformer. IEEE Transactions on Power Delivery, 5, 991-999.

[16]   Ramaswamy, B. and Jue, T.C. (1992) Some Recent Trends and Development in Finite Element Analysis for Incompressible Flows. International Journal for Numerical Methods in Engineering, 35, 671-707.

[17]   Patankar, S.V. (1980) Numerical Heat Transfer and Fluid Flow. Hemisphere, New York.