This paper is the completion of a previous work, published recently, on transformer modeling where the magnetic core topology is taken into account. A new circuit, that represents the magnetic core, is proposed, more easily handled mathematically in antithesis to the conventional magnetic circuit that is used in the literature. The proposed circuit has the same topology with the nonlinear magnetic circuit of the core and, in each time interval of a dynamic simulation, it is considered as linear circuit. Its excitations and responses are the time derivatives of both the magnetomotive forces and the magnetic fluxes, respectively. This modeling approach helps power engineers to construct easily a nonlinear transformer model. Applying any method of circuit analysis on the proposed circuit, one can directly write linear differential equations, in each time interval Δt, for the magnetic core and the state equations of the electrical part are written in standard form. ©2010 IEEE.