Abstract: This paper discusses the general methods to saturation
in the steady-state, two axis (d & q) frame models of synchronous
machines. In particular, the important role of the magnetic coupling
between the d-q axes (cross-magnetizing phenomenon), is
demonstrated. For that purpose, distinct methods of saturation
modeling of dumper synchronous machine with cross-saturation are
identified, and detailed models synthesis in d-q axes. A number of
models are given in the final developed form. The procedure and the
novel models are verified by a critical application to prove the
validity of the method and the equivalence between all developed
models is reported. Advantages of some of the models over the
existing ones and their applicability are discussed.