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Tensor decomposition plays a key role in identifying common features across acollection of matrices in many areas of science. A fundamental need in big dataresearch is to process data tabulated as large-scale matrices usingeigenvectors. A higher order generalized singular value decomposition techniquesuccessfully captures the common features of the same organ from multipleanimals in genomic signal processing. A recent semidefinite programmingapproach to solve an AC optimal power flow was accompanied by the problemformulation in the Cartesian coordinate system. The collection of nodalKirchhoff laws introduces a 3D tensor with a common feature of individualmatrices to maintain local power balance. In this paper, the mathematicalprocess is established and the common feature is identified. The common featureis a key element to a fully decentralized and therefore scalable algorithm tosolve AC optimal power flow.

Tensors in Power System Computation I: Distributed Computation for Optimal Power Flow, DC OPF