A Data Analytics Perspective of the Clarke and Related Transforms in Power Grid Analysis Teaching Old Power Systems New Tricks Danilo P. Mandic, Sithan Kanna, Yili Xia, Ahmad Moniri, and Anthony G. Constantinides 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 conver- gence 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 Com- ponent 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 via adaptive Clarke and Park transforms. In addition, the introduced seamless transition between the Circuit Theory concepts and Data Analytics ideas promises to provide a straightforward and unifying platform for further the understanding of sources of imbalance in modern power grids, together with an avenue for learning strategies, optimal parameter selection, and enhanced interpre- tation of Smart Grid problems and new avenues for the mitigation of these issues. In addition, the material may be useful in lecture courses in multidisciplinary research from Smart Grid to Big Data, or indeed, as interesting reading for the intellectually curious and generally knowledgeable reader. Tribute to Edith Clarke, a pioneer of power grid analysis Edith Clarke (1883-1959) is a true pioneer in the application of circuit theory and mathematical techniques to electrical power systems. She was the first woman to obtain an M.S. in Electrical Engineering from MIT, in 1919, and the first female professor of Electrical Engineering in the USA, having been appointed at the University of Texas at Austin, in 1947. Her pivotal contribu- tions were concerned with the development of algorithms for the simplification of the laborious computations involved in the design and operation of electrical power systems [1]. One of her early inventions was the Clarke calculator (1921), a graphical device that solved power system equations 10 times faster than a human computer [2]. The Clarke transform, also known as the αβ transform, was introduced by Edith Clarke in 1943, and has since been established as a fun- damental and indispensable tool for the analysis of three–phase power systems. With the advent of Smart Grid, the Clarke transform represents an underpinning technology for signal processing, control and machine learning applications related state estimation, frequency tracking, and fault detection [3–5], the most important aspects in the development of the future Smart Grid. 1 arXiv:1807.08720v1 [eess.SP] 23 Jul 2018