In this paper, a three-phase transformer model is developed to be suitable for slow transient and power-quality studies. The proposed model takes into account the eddy currents, the magnetic core topology, and the nonlinear characteristics of the core material. In order to model the eddy currents effects in the magnetic core, Bertotti’s work for the eddy currents is used and nonlinear resistors dependent on the magnetic core topology are proposed. A systematic procedure is developed for the determination of the incremental self and mutual inductances of the windings. The nonlinear characteristics of the core material are represented either by a magnetization curve or by a hysteresis loop. The hysteresis loop is introduced either by the mathematical model proposed by Tellinen or by the macroscopic model presented by Jiles-Atherton. Simulations results are compared to published measurements in order to verify the proposed model. © 2009 IEEE.