Nonlinear Vector Potential Formulation and Experimental Verification of Newton-Raphson Solution of Three Dimensional Magnetostatic Fields in Electrical Devices

An iterative technique, based on magnetic vector potential formulation and the Newton-Raphson method, for the determination of the three dimensional magnetostatic field distributions in electrical devices is given. The proper degrees of magnetic saturation in the various materials within a given volume under consideration are obtained by repeated evaluation of the reluctivities in that volume, using a cubic spline representation of the B-H magnetization characteristics of composite materials (laminations). The formulation has been applied to a practical example of determining the field in and around a shell type 1.5 kva single phase transformer. The convergence and implementation characteristics of the developed method are given in this paper which show a saving of about 34% in CPU solution time in comparison with previously published methods. Experimental verification is given in terms of a comparison between computed and experimentally obtained values of flux densities surrounding the transformer core and winding, under heavily saturated conditions. Excellent agreement between test and calculated flux densities was achieved. This method is thus quite applicable to the solution of a wide class of three dimensional magnetostatic field problems associated with electrical apparatus.