A new synchronous machine model is presented which is readily implemented in either circuit-based or differential-equation-based simulation programs. This model is well suited for the simulation and analysis of synchronous machine - converter systems, It is based upon standard representations and no approximations are made in its derivation, However, the numerical implementation is shown to be significantly more efficient. An example is provided which demonstrates a 1700% increase in simulation speed with no observable loss in accuracy. The model includes provisions for an arbitrary number of damper or rotor windings and may be easily modified to represent synchronous or induction machines with an arbitrary number of stator phases.