  Affordable and reliable electric power is fundamental to modern society and
economy, with the Smart Grid becoming an increasingly important factor in power
generation and distribution. In order to fully exploit it advantages, the
analysis of modern Smart Grid requires close collaboration and convergence
between power engineers and signal processing and machine learning experts.
Current analysis techniques are typically derived from a Circuit Theory
perspective; such an approach is adequate for only fully balanced systems
operating at nominal conditions and non-obvious for data scientists - this is
prohibitive for the analysis of dynamically unbalanced smart grids, where Data
Analytics is not only well suited but also necessary. A common language that
bridges the gap between Circuit Theory and Data Analytics, and the respective
community of experts, would be a natural step forward. To this end, we revisit
the Clarke and related transforms from a subspace, latent component, and
spatial frequency analysis frameworks, to establish fundamental relationships
between the standard three-phase transforms and modern Data Analytics. We show
that the Clarke transform admits a physical interpretation as a "spatial
dimensionality" reduction technique which is equivalent to Principal Component
Analysis (PCA) for balanced systems, but is sub-optimal for dynamically
unbalanced systems, such as the Smart Grid, while the related Park transform
performs further "temporal" dimensionality reduction. Such a perspective opens
numerous new avenues for the use Signal Processing and Machine Learning in
power grid research, and paves the way for innovative optimisation,
transformation, and analysis techniques that are not accessible to arrive at
from the standard Circuit Theory principles, as demonstrated in this work
through the possibility of simultaneous frequency estimation and fault
detection.
