Asymmetric transmission line analyses based on a constant transformation matrix

The application of modal transformation models for transmission lines have been analyzed extensively because in mode domain there are facilities in representation of frequency dependent line parameters. Because the determination of exact modal transformation matrices for general cases is not a simple task, simplifications about these applications can be considered. Using non-transposed three-phase transmission line samples and Clarke’s matrix, the errors of the single real transformation matrix in this line type are analyzed, appointing the main influences of this simplification on the calculation of electrical variable values such as impedances, admittances, characteristic impedances and propagation constants. The application of Clarke’s matrix to balanced and unbalanced phase voltage vectors is also analyzed. With these analyses, it is determined which of the studied variables is the most sensitive to the Clarke’s matrix application, searching for strategies that decrease the errors of the proposed transformation matrix.