Hi,
For balanced three-phase electrical signals, the Clarke transform is a well-proven technique for dimensional reduction. Indeed, this transform can project the information from a 3D space to a 2D space without any loss of information. For sinusoidal balanced signal, the projected signal describes a circle in the projected plane (see the first attached image). This simplifies the frequency estimation since the circle simply corresponds to the analytic signal.
Conference Paper Maximum likelihood frequency estimation in smart grid applications
Now, for unbalanced system, the use of the Clarke preprocessing is quite questioning. Indeed, for unbalanced sinusoidal signals, the signal describes a circle in a particular plane (which is not the same that the one obtained for balanced systems). By using the Clarke transform, the projected signal describes an ellipse instead of a circle (see the second attached image) and the projection will inevitably loss some kind of information. This makes the frequency estimators suboptimal regarding the information contained in the three phases. From my point of view, this makes the Clarke transform inappropriate for the analysis of unbalanced three-phase signals.
In this context, I don’t know why many papers still use the Clarke transform for dimensional reduction in unbalanced three-phase systems ?
References:
Article Maximum Likelihood Parameter Estimation of Unbalanced Three-...
Article A Clarke Transformation-based DFT Phsor and Frequency Algori...
Article Adaptive Frequency Estimation in Smart Grid Applications: Ex...
Article Three-Phase Adaptive Frequency Measurement Based on Clarke's...
Conference Paper An adaptive Clarke transform based estimator for the frequen...
There are two main reasons:
1. less calculation because of omitting an equation
2. zero sequence parameters could be find out by equations in alpha-beta-zero frame (there are many articles about this topic, take a look)
Reduces the number of parameters for calculation and converts the quantities into space vectors of stationary reference frame in order to overcome phase difference
Thank you for your answer. So the main answers seem to justify the use of the Clarke transform for dimensional reduction reasons.
From a statistical sense, i think that the use of other linear preprocessing techniques seems to be more adequate. In particular, a Principal Component Analysis can reduce the signal dimension without sacrificing too much information.
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