Putting Tensors Back in Power Systems Analysis

Tensor analysis and multi-dimensional arrays have been a widely studied in all kind of physical 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 sparse storage of the tensor is proposed showing high efficiency. However, the main advantage of the tensor approach lies in the simplification of the nomenclature for three phase applications. A fixed point algorithm is also presented for the power flow calculation using tensor representation. Simulations in Matlab/Octave demonstrate the advantages of this representation.