 Dqo transformation

"Odq" redirects here. For the professional association, see ODQ.
Additional information needed In electrical engineering, direct–quadrature–zero (or dq0 or dqo) transformation or zero–direct–quadrature (or 0dq or odq) transformation is a mathematical transformation used to simplify the analysis of threephase circuits. In the case of balanced threephase circuits, application of the dqo transform reduces the three AC quantities to two DC quantities. Simplified calculations can then be carried out on these imaginary DC quantities before performing the inverse transform to recover the actual threephase AC results. It is often used in order to simplify the analysis of threephase synchronous machines or to simplify calculations for the control of threephase inverters. The dqo transform presented here is exceedingly similar to the transform first proposed in 1929 by R.H. Park.^{[1]} In fact, the dqo transform is often referred to as Park’s transformation.
Contents
Definition
The dqo transform applied to threephase currents is shown below in matrix form:^{[2]}
The inverse transform is:
Geometric Interpretation
The dqo transformation can be thought of in geometric terms as the projection of the three separate sinusoidal phase quantities onto two axes rotating with the same angular velocity as the sinusoidal phase quantities. The two axes are called the direct, or d, axis and the quadrature, or q, axis. Not surprisingly the qaxis is at an angle of 90 degrees to (in quadrature with) the direct axis.
Comparison With Other Transforms
Park's Transformation
The transformation originally proposed by Park differs slightly from the one given above. Park's transformation is:
and
Although useful, Park's transformation is not power invariant whereas the dqo transformation defined above is^{[citation needed]}. Park's transformation gives the same zero component as the method of symmetrical components. The dqo transform shown above gives a zero component which is larger than that of Park or symmetrical components by a factor of .
αβγ transform
The dqo transform is conceptually similar to the αβγ transform. Whereas the dqo transform is the projection of the phase quantities onto a rotating twoaxis reference frame, the αβγ transform can be thought of as the projection of the phase quantities onto a stationary twoaxis reference frame.
References
 Inline references
 ^ R.H. Park Two Reaction Theory of Synchronous Machines AIEE Transactions 48:716730 (1929).
 ^ P.M. Anderson and A.A. Fouad Power System Control and Stability Iowa State University Press, Iowa (1977). ISBN 0813812453
 General references
 J. Lewis Blackburn Symmetrical Components for Power Systems Engineering, Marcel Dekker, New York (1993). ISBN 0824787676
 Zhang et al. A threephase inverter with a neutral leg with space vector modulation IEEE APEC '97 Conference Proceedings (1997).
See also
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Alpha–beta transformation — In electrical engineering, the αβγ transformation (also known as the Clarke transformation) is a mathematical transformation employed to simplify the analysis of three phase circuits. Conceptually it is similar to the dqo transformation. One very … Wikipedia