Corrected transformation matrices from Clarke's matrix - asymmetrical three-phase lines applications

Clarke's matrix is an eigenvector matrix for transposed three-phase transmission lines and its application as a phase-mode transformation matrix for untransposed three-phase transmission lines has been studied using error and frequency scan analyses. Considering untransposed asymmetrical three-phase transmission lines, a correction procedure is applied searching for better results from the Clarke's matrix use as a phase-mode transformation matrix. The error analyses are carried out using Clarke's matrix and the new transformation matrices obtained from the correction procedure. Using the Clarke's matrix, the relative errors of the eigenvalue matrix elements can be considered negligible and the relative values of the off-diagonal elements are significant. Applying the corrected transformation matrices, the relative values of the off-diagonal elements are decreased. The comparisons among the results of these analyses show that the homopolar mode is more sensitive to the frequency influence than the two other modes related to three-phase lines.