This paper presents a new dynamical model of superconducting magnetic energy storage systems (SMESs). The dynamical model is developed based on the equivalent circuit diagram of an SMES which is connected to the power grid through a converter. The switching actions of the converter are also considered within the proposed model. The power balance at the input and output of the converter is taken into account in order to complete the model. The proposed model is suitable for the implementation of model-based control techniques which cannot be done with instantaneous models. The model is transformed into dq-frame in order to facilitate the implementation of model-based control techniques. Finally, the usefulness of the proposed model is discussed and a nonlinear feedback linearizing controller is designed to regulate the current injection into the power grid.