A comprehensive model of a salient-pole synchronous machine is developed for a real-time environment. By obtaining the effective specific permeance of the machine from simple experimental measurements and the exact geometry of the rotor pole arc, a model is developed that includes the exact distribution of windings and operating-point-dependent saturation. This model offers a superior simulated response of the machine for fault transients, as well as for steady-state harmonic behavior, and is suitable for the closed-loop testing of relays and controls. The inductances of the machine are computed using the modified winding function approach and validated using finite-element analysis. Finally, the performance of the model is validated under healthy and faulted conditions by comparison with tests on an actual machine.