Revisiting symmetrical components with the modern linear algebra framework
Circulant Matrix, Circular convolution, Symectrical-Components
As Fortescue developed the symmetrical components method, modern linear algebra was in its early days and restricted to mathematical circles. Since then, Fortescue's method has become the standard way to analyse power systems with symmetry. However, publications about the theme show that current symmetrical components method formulation doesn’t benefit from the modern linear algebra framework. We intend to fulfill this gap, relating Fortescue's method with the diagonalization of a circulant matrix, leading to the Discrete Fourier Transform (DFT). We then underline the fact that the DFT is a unitary transformation, from what we get interestings results that aren’t easy to see from the original formulation.