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We present a model suitable for use in a vector control algorithm for synchronous reluctance machines with solid conducting rotors. The model takes the rotor flux dynamics into consideration. It is similar to an induction machine model, yet includes a magnetic saliency of the rotor. Here, we discuss techniques for parameter extraction and suggest a modification of the model to incorporate the nonlinear magnetic phenomena. We also investigate the influence of nonlinear magnetics on the model-based controller. Our model yields improved performance for a fast-changing torque command compared to the conventional model when utilized in a current regulator. Experimental results on a 120 kW, 55thinspace 000 rpm machine in a flywheel energy storage system validate the performance of the proposed model .