Combined Analytical-Numerical Approach for the Modeling and Analysis of Threephase Transformers

This paper deals with a combined analytical-numerical approach for the study of the steady-state and transient behaviour of three-phase transformers. This approach based on magnetic equivalent circuits, takes into account the nonlinear B-H curve. The nonlinear B-H curve is constituted by a set of measurement data and can be represented by a Fourier series or by a polynomial representation. For the numerical simulations, two methods have been developed, by considering the total magnetic fluxes respectively the currents as state variables. Analytical expressions of all the self and mutual inductances are expressed in function of the magnetic reluctances of the cores. The approach has been verified on small and large distribution transformers for different steady-state cases of no-load, symmetrical and unsymmetrical loads as well as no-load switching. Numerical results compared with test results and with 2D FEM computations confirm the validity of the present approach. The present approach has been developed and applied on ten vector groups for three-limb core ('core-type') 3-phase transformers