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

Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors. A higher order generalized singular value decomposition technique successfully captures the common features of the same organ from multiple animals in genomic signal processing. A recent semidefinite programming approach to solve an AC optimal power flow was accompanied by the problem formulation in the Cartesian coordinate system. The collection of nodal Kirchhoff laws introduces a 3D tensor with a common feature of individual matrices to maintain local power balance. In this paper, the mathematical process is established and the common feature is identified. The common feature is a key element to a fully decentralized and therefore scalable algorithm to solve AC optimal power flow.