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Investigation of the stator inductances of the expanded Park model and an approach on parameter identification using the evolution strategy

Schmuelling Ch., Kreischer Ch., Gołebiowski M.

Archives of Electrical Engineering

2016

Vol. 65, nr 3

585--599

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.

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

Schmuelling Ch., Kreischer Ch., Gołȩbiowski M.

Maszyny Elektryczne : zeszyty problemowe

2015

Nr 3 (107)

81--87

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.