Numerical calculation of magnetic dissipation and forces on coil in power transformers

Abstract

Numerical methods of determining the magnetic dissipation and forces for different positions and shapes of windings and magnetic core are more and more used by the constructors in the transformers manufacture. Special attention during the calculation and analysis of the magnetic dissipation has to be dedicated to the non-linearity of the transformer magnetic circle (µ=3Df(B)). Before, these weaknesses, exercised at resolving the Poisson's differential equation by analytical methods, were avoided by utilization of the graphical methods based on the orthogonal characteristics of lines of field and lines of the constant potentials. Numerical calculation of the transformer magnetic field was done by using the method of finite elements. This method enables determination of allocation of static or time changing field in linear or nonlinear, isotropic or anti-isotropic type of material with electric current or permanent magnetic stimulus. The finite elements analysis is divided on pre-processing, resolution and post-processing phases. A result accuracy of magnetic field depends on modeling and discretization of the problem, determined edge conditions and parameters of the materials used. It is hard to find general methodology for discretization and determining the edge conditions. With the application of the finite elements method, the field function, described by differential equation, can not be directly determined from the differential equation, but it provides data on minimization of an appropriate function. From the numerical calculation of magnetic field, the dissipation inductivity is determined by the application of the energy method and linked fluxes method. For calculation of electromagnetic forces the energetic method was used, by which, basing on small shifts of body on which the forces exercise along directions of coordinate axes, the appropriate increase of magnetic energy or co-energy of nonlinear magnetic system is calculated.