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A synchronous machine model with saturation and cross saturation and an arbitrary rotor network representation that uses a voltage-behind-reactance representation for both the stator windings and the field winding of the machine is proposed. This allows the stator windings and the field winding to be represented as branches in a circuit solver, permitting straightforward simulation with connected circuitry. In particular, the model can be simulated with rectifier loads or with rectifier sources applied to the field winding. The model is validated against experimental data, and its utility is demonstrated in an excitation failure case study.