Hypermatrix Representation of Unbalanced Power Distribution Systems

TL;DR

This paper introduces a tensor-based representation for unbalanced power distribution systems, simplifying calculations, reducing storage, and enhancing computational efficiency, with a fixed point algorithm demonstrated through simulations.

Contribution

It presents a novel tensor representation for unbalanced power systems and a fixed point algorithm, improving computational efficiency and simplifying system analysis.

Findings

Tensor representation simplifies calculations in unbalanced grids.

Reduces storage requirements for system data.

Demonstrates improved computation speed in simulations.

Abstract

Tensor analysis has been a widely studied in physics applications including circuit theory and electric machines. This paper reviews some of the main features of this type of representation for unbalanced power distribution systems and discusses its implementation in modern programming languages. A tensor representation simplifies the nomenclature and calculations in three phase unbalanced grids, reduces the storage requirement and improves the computation speed. A fixed point algorithm is proposed for the power flow solution showing the flexibility of the tensor approach. Simulations in Matlab/Octave demonstrate the advantages of this representation.