Solution of Eddy Current Problems Using Three Dimensional Finite Element Complex Magnetic Vector Potential

The three dimensional finite element formulation of eddy current problems with ac sinusoidally time varying excitations is given using magnetic vector potential and complex phasor representation. First order tetrahedral elements are utilized. In this formulation, magnetic saturation is neglected. Three values of magnetic reluctivity, vx, vy and vz, are defined within each tetrahedral element, while it is assumed that in tetrahedrals laying in conducting material one value of electrical conductivity,σ, is valied in the x, y and z directions. The method was applied to the calculation of the eddy current losses at 60 Hz in a finite length aluminum bar of square cross-section, which was excited by a surrounding coil with considerable three dimensional end effects. These losses under identical conditions were determined in the laboratory, and the results of calculation and measurement are in substantial agreement. This confirms the validity of use of this method for more complex applications including calculation of induced eddy current losses in metalic structures surrounded by three dimensional fields, such as in structures near power transformer windings, and similar situations