In this work, a novel three-phase transformer non-linear model is developed. The proposed model takes into account the magnetic core topology and the windings connections. The non-linear characteristic curve of the core material is introduced by its magnetization curve or by its hysteresis loop using the mathematical hysteresis model proposed by Tellinen or the macroscopic hysteresis model proposed by Jiles-Atherton. The eddy currents effects are included through non-linear resistors using Bertotti’s work. The proposed model presents several advantages. An incremental linear circuit, having the same topology with the magnetic circuit of the core, is used in order to directly write the differential equations of the magnetic part of the transformer. The matrix Ld that describes the coupling between the windings of the transformer is systematically derived. The electrical equations of the transformer can be easily written for any possible connection of the primary and secondary windings using the unconnected windings equations and transformation matrices. The proposed methods for the calculation of the coupling between the windings, the representation of the eddy currents and the inclusion of the core material characteristic curve can be used to develop a transformer model appropriate for the EMTP/ATP-type programs. Copyright © 2009 John Wiley & Sons, Ltd.