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

TL;DR

This paper introduces a tensor-based mathematical framework for decentralized computation of AC optimal power flow, leveraging tensor decomposition to identify common features across matrices for scalable power system optimization.

Contribution

It develops a novel tensor decomposition approach to facilitate fully decentralized algorithms for AC optimal power flow in power systems.

Findings

Tensor decomposition captures common features in power system matrices.

The method enables scalable, decentralized AC optimal power flow solutions.

Mathematical process for tensor-based power flow computation is established.

Abstract

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.