This paper presents a suitable method for time-domain identification of synchronous machine parameters from the hybrid state model recently introduced by the authors in a compact matrix form. The saturated version of this model is developed in terms of generator equivalent-circuit parameters. The load rejection test of a combined resistive/inductive load is performed for the parameter identification while the online symmetrical three-phase short-circuit test is carried out for the model cross-validation. For weak power factor initial loads connected to the generator, the rotor speed is quite constant during the full load rejection test. Thus, the mechanical transients do not have any influence on estimated electrical parameters since they are decoupled from the electrical model of the machine. The method is successfully applied for the parameter identification of 380 V, 3 kV.A, four-pole, 50 Hz saturated synchronous generator.