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2018 | OriginalPaper | Buchkapitel

29. Dynamics in Vector Control and Field Orientation

verfasst von : Jan A Melkebeek

Erschienen in: Electrical Machines and Drives

Verlag: Springer International Publishing

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Abstract

In Chap. 17 of Part III, vector control and field orientation have already been presented. However, the dynamics have not been analysed. In this chapter we discuss vector control and field orientation more thoroughly, including an analysis of their dynamic behaviour.

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Vorheriges Kapitel Modelling and Dynamic Behaviour of Synchronous Machines

Nächstes Kapitel Transient Phenomena in Electrical Machines

The term brushless AC machine is used when the field profile in space is sinusoidal; for trapezoidal or rectangular field profiles the term brushless DC machine is normally used.

Note that this superposition of mmfs also seems more correct than the traditional one with superposition of emfs, which is not allowed in case of saturation; the air-gap emf is also representative of the main field saturation level in a synchronous machine.

This circuit may also be derived as the solution of the vectorial equation \(\underline{I}_{s}=\underline{I}_{s\phi }+\underline{I}_{s\tau }\) where the two components are orthogonal, with \(\underline{I}_{s\tau }\)in phase with the emf \(\underline{E}_{r}\).

It is slow, because it is bound by physical laws prohibiting any sudden flux changes.

Except for machines with closed rotor slots where the rotor leakage flux may vary considerably.

Keep in mind that this is not the rotor flux angle but the mechanical rotor angle.

The compensation can also be regarded as an integration constant: the switching angle of the inverter has to change from \(\gamma _{1}+(\omega _{s1}+\omega _{r})t\) to \(\gamma _{2}+(\omega _{s2}+\omega _{r})t\) and not to \(\gamma _{1}+(\omega _{s2}+\omega _{r})t\).

Prove this using the flux definitions \(\underline{\varPsi }_{s}=L_{s}\underline{I}_{s}+L_{m}\underline{I}_{r}\), \(\underline{\varPsi }_{r}=L_{m}\underline{I}_{s}+L_{r}\underline{I}_{r}\), \(\underline{\varPsi }_{m}=L_{m}(\underline{I}_{s}+\underline{I}_{r})\) (where the turns ratio has been supposed as equal to 1).

Prove this, introducing the leakages with \(L_{s}=L_{s\sigma }+L_{m}\), \(L_{r}=L_{r\sigma }+L_{m}\).

Titel: Dynamics in Vector Control and Field Orientation
verfasst von: Jan A Melkebeek
Verlag: Springer International Publishing
Buch: Electrical Machines and Drives
Print ISBN: 978-3-319-72729-5

Electronic ISBN: 978-3-319-72730-1

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-72730-1_29