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This paper presents a systematic approach for coupling the space-vector model of a synchronous machine with the static field equations and solve the whole system of equations with the finite element method. The aim of the approach is to reduce the computation time without losing the accuracy. The methodology is validated on a permanent magnet synchronous machine and then applied to a bearingless synchronous reluctance machine. Comparison of the results with the measurements and the time stepping finite element analysis shows that the method has great potential in reducing the computation time and reproducing accurate results.Index Terms--bearingless synchronous reluctance machine, computational electromagnetics, electromagnetic fields, finite element analysis, machine control, permanent magnet machine. VII. BIOGRAPHIESAnouar Belahcen (M'13-SM'15) received M.Sc. (Tech.) and Doctor (Tech.) degrees from Helsinki University of Technology, Finland, in 1998, and 2004, respectively. Since 2011 he is Professor of electrical machines at Tallinn University of Technology, Estonia and since 2013 he is Professor of Energy and Power at Aalto University. His research interest are numerical modeling of electrical machines, especially magnetic material modeling, coupled magnetic and mechanical problems, magnetic forces, and magnetostriction. . His research interests deal with numerical modeling of electrical machines as well as power losses and magnetomechanical effects in soft magnetic materials. Marko Hinkkanen (M'06-SM'13) received the M.Sc. (Eng.) and D.Sc. (Tech.) degrees from Helsinki University of Technology, Espoo, Finland, in 2000 and 2004, respectively. Since 2000, he has been with Helsinki University of Technology (part of Aalto University, since 2010). He is currently an Assistant Professor with the School of Electrical Engineering, Aalto University. His current research interests include power-electronic converters, electric machines, and electric drives.

In the control of electric drives, inaccurate estimation of the motor parameters affects the robustness of the control. This effect is observed particularly when the linear lumped parameter-based models are employed to represent a machine composed of nonlinear magnetic materials. Finite element (FE) models consider the material nonlinearity accurately. However, implementing these models in a real-time system is challenging due to the computational burden. In this paper, we propose a fastdynamic model, based on a model order reduction method, to control a permanent magnet synchronous machine in a wide range of speed. The stator currents in the rotor frame of reference are given as inputs to a reduced FE model, which computes the nodal values of the magnetic vector potential and thereafter the flux linkages. A discrete-time model is used to control the rotor speed and the stator current components. Experiments on a 2.2 kW interior permanent magnet synchronous machine verify the viability of the proposed model. Index Terms-Electrical machine, interior permanent magnet, model order reduction, orthogonal interpolation method, real-time control, rotor frame of reference, singular value decomposition.