The paper describes a general model of a hybrid-excited synchronous machine with multiple voltage levels each generated by a 3-phase stator system in a voltage-behind-reactance formulation. The different voltage level of each 3-phase stator system is realized in the same machine design. The rotor is excited through an excitation winding and a permanent magnet. The model incorporates magnetic saturation of the main inductance, magnetic and electric coupling between all phases, and the field winding and a mechanical displacement angle. The cross coupling between q and d axes of the main inductances is included as a constant saliency factor a for all saturation levels. The turn ratio of each 3-phase stator winding system to another 3-phase system is also modeled as a constant value. Each 3-phase system saturates the iron core with a different weighting represented by the number of turns relative to the reference stator system. The proposed model is included in a field-oriented control scheme. Simulations are carried out with requested I-q,I-d and field winding currents to demonstrate model's dynamics, and the results are verified with measurements on a test bench.