A Geometric Interpretation of Reference Frames and Transformations: dq0, Clarke, and Park
Name
Final_Submission__Open_Access.pdf
Size
4.26 MB
Format
Adobe PDF
Checksum (MD5)
5763c89b8dc74d4a6fdd0f6b073aff5e
Author(s)
O'Rourke, Colm Joseph
Qasim, Mohammad Mowafaq
Overlin, Matthew R
Kirtley Jr, James L
Date Issued
December 2019
Journal
IEEE Transactions on Energy Conversion
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
O'Rourke, Colm J. et al. "A Geometric Interpretation of Reference Frames and Transformations: dq0, Clarke, and Park." IEEE Transactions on Energy Conversion 34, 4 (December 2019): 2070 - 2083 © 2019 IEEE
Version
Author's final manuscript
Abstract
Transformations between abc, stationary dq0 (αβ0) and rotating dq0 reference-frames are used extensively in the analysis and control of three-phase technologies such as machines and inverters. Previous work on deriving the matrices describing these transformations follows one of two approaches. The first approach derives Clarke's matrix by modifying symmetrical components. Park's matrix can be subsequently found from a rotation matrix. The second approach derives Park's matrix using trigonometric projection by interpreting the transformation as a rotation in the plane of the cross-section of a machine. Then, Clarke's matrix can be found trivially using a reference angle of zero in Park's matrix. This paper presents a third approach to deriving the Clarke and Park transformation matrices: a geometric interpretation. The approach exploits properties of the linear transformation using the Cartesian representation. We introduce the locus diagram of a three-phase quantity and show how these diagrams have applications in power quality. We show that, unlike a phasor diagram, a single locus diagram can fully represent a three-phase system with harmonics.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
http://dx.doi.org/10.1109/tec.2019.2941175
