Abstract
This article presents a comparison between integer and non-integer order modelling of a synchronous generator, in the frequency domain as well as in the time domain. The classical integer order model was compared to one containing half-order systems. The half-order systems are represented in a Park d-q axis equivalent circuit as impedances modelled by half-order transmittances. Using a direct method based on the approximation of the half-order derivatives by the Grünwald–Letnikov definition, a state-space equation system was solved. For both models, a computational program written in Matlab® software was used. For the purpose of time domain simulation, the machine models were connected to an electric load composed of an RL circuit. To validate and compare both models, simulation results of a three-phase short-circuit and a no-load voltage recovery were compared with corresponding measurements performed on a solid salient-pole synchronous generator of 125 kVA.
Highlights
Non-integer order modelling is generally used to model devices where diffusion phenomena are present and influence their functionality
The comparative study was based on measurement data performed on a 125 kVA synchronous generator
Non-integer order derivatives are mathematical tools that have risen in popularity over the last few decades
Summary
Non-integer order modelling is generally used to model devices where diffusion phenomena are present and influence their functionality These can be, for example, diffusions of temperature, electric field or gases. In theory, to better represent the diffusion effect, which is a distributed phenomenon described by partial differential equations, one has to integrate into equivalent circuits an infinite number of such ladders This number is a chosen finite to meet the desired accuracy over a studied frequency range [13]. For electrical machine models represented by equivalent circuits with non-integer order systems, the structure and circuit parameters have been directly derived from Maxwell equations [14]. This compactness feature is most pronounced in the frequency domain.
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