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Eigenfunction expansion of the stray field of large power transformers

The paper presents an analytic method for the stray field calculation of the windings of large power transformers which takes into account for the detailed configuration of both low and high voltage windings as well as tapping windings. The algorithm solves for the 3D Laplacian equation of the 3D magnetic vector potential by using series expansions according to the orthogonal Eigenfunctions of the related Eigenvalue problem. In order to fulfil the appropriate boundary conditions at the boundaries of the high permeable laminated iron core, fictious surface currents at the iron core boundaries are introduced. In summary, the gauged 3D magnetic vector potential will be obtained from one main part generated by the currents of the windings and another main part produced from the surface currents representing the iron core boundaries. Thus, a very fast evaluation of the stray field is achieved which can be included in the initial design of large power transformers within an industrial environment.