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

Modeling of transmission lines for the analysis of electromagnetic transient behavior requires the calculation of a modal transformation matrix in a wide range of frequencies. In this paper, a comprehensive framework for smooth calculating the transformed matrix is ​​presented. Accordingly, at each frequency, a general set for eigen vectors corresponding to each eigen value is computed. Then, on the basis of a smoothing criterion and an optimization algorithm, at each frequency the set of eigen vectors are chosen arbitrarily, avoiding sudden mutations and smoothing the fitted function for different elements The conversion matrix is​​guaranteed. The proposed algorithm is implemented on an underground cable 3 phases system and overhead line in order to obtain a transformation matrix. The simulation results indicate the effectiveness of the algorithm used to calculate the transformation matrix in a very smooth and precise manner. Also, this algorithm will continue to show significant accuracy in a situation where the frequency sampling rate is reduced, so that it exhibits acceptable tracking capability at low sampling rates.