Single real transformation matrix application for asymmetrical three-phase line transient analyses

Single real transformation matrices can change the Z and Y matrices into diagonal ones for transposed three-phase lines. Considering non-transposed non-symmetrical three-phase lines, the errors between the Clarke’s matrix application results (called quasi-modes) and the eigenvectors are negligible. In this text, some other analyses are performed for two line designs. So, the arithmetic media among error curves tends to zero for every design. The non-diagonal elements of the quasi-mode matrix are compared to the correspondent eigenvalues. There are non-diagonal elements that present significant relative values when compared to the eigenvalues. Using all these analyses, it is suggested the hypothesis that the interactions among the Clarke’s matrix application, the non-symmetrical line characteristics and propagated signal spectrum can be maximizing the error of the proposed single real transformation matrix application. Because of this, in future development, correction procedures should be applied to Clarke’s matrix searching for minimizing the non-diagonal elements of the quasi-mode matrices.