An improved technique for incorporating saturation into the q-d sris model (Park＇s model) of a synchronous machine is proposed. By choosing magnetizing flux linkage as a state variable, iterative procedures required by traditional methods are avoided. The saturation function is represented by an arctangent function which has some distinct advantages over polynomial representations and look-up tables. In particular, the parameters of the proposed function all have physical significance and the proposed function is defined over an infinite range of flux linkage. The model is verified for steady-state and transient conditions using a laboratory synchronous machine - rectifier system similar to those commonly used for Naval and aerospace power generation.