Commonly, the Park model is used to calculate transients or steady-state operations of synchronous machines. The expanded Park theory derives the Park equations from the phase-domain model of the synchronous machine by the use of transformations. Thereby, several hypothesis are made, which are under investigation in this article in respect to the main inductances of two different types of synchronous machines. It is shown, that the derivation of the Park equations from the phase-domain model does not lead to constant inductances, as it is usually assumed for these equations. Nevertheless the Park model is the most common analytic model of synchronous machines. Therefore, in the second part of this article a method using the evolution strategy is shown to obtain the parameters of the Park model.