A Method for the Calculation of Frequency-Dependent Transmission Line Transformation Matrices

A stable and efficient method for evaluating the transformation matrices of both overhead transmission lines and underground cables as smooth functions of frequency is presented. The proposed method is based on the postprocessing of the eigenvectors obtained by the conventional methods where optimization is employed to maximize the smoothness of the transformation matrices. Even in the case of the underground cable systems composed of several identical single core coaxial cables, where some of the eigenvalues become arbitrarily close at high frequencies, it is capable of producing smooth transformation matrices that can be accurately fitted with rational functions.