Discrepancies of the expanded park equations and parameter identification with evolution strategy

The Park equations are a well known analytic model for describing synchronous machines. Over the years they were consistently extended, like the additional Canay leakage inductance in the rotor circuit. Although, there are newer and more accurate analytic models, the Park equations are still applied by all manufacturers and grid operators. The expanded Park theory [1] derives these equations from the phase-domain model. In this paper at hand, it is shown that this derivation is based on false assumptions for calculating the inductances. Therefore the transformation of the phase-domain parameter does not lead to a decoupled system as it should in the expanded Park theory. It is shown that the new system is more complex and the parameter of this system could not be derived from the phase-domain model. Two different synchronous machines, one with a salient pole rotor and one with a round rotor, are modeled by a finite-element-method (FEM) software and all stator self and mutual inductances are calculated. The model of the round rotor machine is verified by measurements. Due to common application of the Park equations a new method to determine the parameter is also presented. The results of a three-phase sudden short circuit are used in combination with the evolutionary algorithm to derive the Park parameters. All optimized parameters are totally detached from the physics. The found parameters are verified by measurements of other transients, like the twophase short circuit.