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A coupled finite element phase-domain model for superconducting synchronous machine is presented. It allows fast and accurate prediction of the transient and steady-state behavior of grid-connected machines. On the one hand, the machine self and mutual inductances as function of rotor angle are obtained from static finite element analysis. On the other hand, the machine is represented by a lumped-parameter phase-domain model. This approach offers two main advantages. Firstly, as opposed to the classical qd model, the phase-domain model takes into account inductance space harmonics. Secondly, it allows easy and efficient simulation of machine transients with the same accuracy as the one that could be obtained with a computationally expensive full finite element model. To show the flexibility of the proposed method, it is applied to an air-cored high temperature superconducting 10 MW class wind turbine generator with double layer distributed three-phase armature windings connected to the grid through an AC/DC/AC converter.