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The paper details a method by which the equations describing a 3-phase synchronous machine may be transformed into the frequency domain to provide a means of digitally simulating faults at the generator terminals. Evaluation of the Fourier integrals involved in determining the machine response is achieved by means of the fast-Fourier-transform algorithm, and numerical results are presented together with the criteria necessary to achieve an accuracy comparable with that attainable using direct-phase quantities. The methods provide a basis for combining synchronous sources with transmission lines having frequency-variant parameters, and which are not therefore amenable to simulation using other than frequency-domain techniques. Studies using the new method indicate that, when predetermining the armature currents of a faulted machine, considerable economies in computing time may be effected, and the possibility of improving the simulation to simulate more accurately rotor eddycurrent effects by utilising the direct- and quadrature-axis frequency response emerges.