This paper deals with to elaborate a model of single-phase core type transformer. The model uses the principle of duality based on corrections made to the Π-model. First, we will highlight modifications to already existing models, and a comparison between the Modified Π-model with the T and Π-models and experimentation will be made. The main interest of this model is to introduce of hysteresis loop instead of an anhystretic curve in both T and especially in the Π-model that seeks to improve. The hysteresis loop can have an important role in the simulation of the transient phenomena, such as ferroresonance. Also, for the correction of the Π-model and T-model, we include the hysteresis reactor in the elements of the transformer core to model the non-linear effects of hysteresis, and saturation.