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The structure and the operation of the model for the brushless excitation system for a synchronous machine are presented. The nonlinear model including the excitation machine, the AC-AC converter supplying the excitation machine and the rectifier diode bridge, mounted on the rotor, is based on a state machine. The states are defined by current commutation in the power electric devices. The operation of the excitation system model is verified by measurements with a slip-ring machine imitating the excitation machine. The excitation system model is integrated and simulated as a part of a synchronous machine simulator.