Modal Transformation Analyses for Double Three-Phase Transmission Lines

• Published in: IEEE transactions on power delivery Vol. 22; no. 3; pp. 1926 - 1936
• Main Authors: do Prado, A.J., Filho, J.P., Kurokawa, S., Bovolato, L.F.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Admittance; Applied sciences; Clarke's matrix; Convolution; eigenvalue; Eigenvalues; Eigenvalues and eigenfunctions; eigenvector; Eigenvectors; Electric potential; Electric power generation; Electrical engineering. Electrical power engineering; Electrical power engineering; Electromagnetic modeling; Error analysis; Exact sciences and technology; frequency; Frequency dependence; Impedance; Miscellaneous; mode domain; Power networks and lines; Time domain analysis; transformation matrix; Transformations; Transmission line matrix methods; Transmission lines; Voltage; Electric energy transportation; Modal analysis; mode domain; Three phase line; Eigenvector; Eigenvalue; transmission lines; frequency; Phase transformation; Convolution; Transmission line; transformation matrix; S matrix; Clarke's matrix; Facility; TLM method; Power transmission line
• ISSN: 0885-8977; 1937-4208
• DOI: 10.1109/TPWRD.2007.899769

Eigenvector and eigenvalue analyses are carried out for double three-phase transmission lines, studying the application of a constant and real phase-mode transformation matrix and the errors of this application to mode line models. Employing some line transposition types, exact results are obtained with a single real transformation matrix based on Clarke's matrix and line geometrical characteristics. It is shown that the proposed technique leads to insignificant errors when a nontransposed case is considered. For both cases, transposed and nontransposed, the access to the electrical values (voltage and current, for example) is provided through a simple matrix multiplication without convolution methods. Using this facility, an interesting model for transmission line analysis is obtained even though the nontransposed case errors are not eliminated. The main advantages of the model are related to the transformation matrix: single, real, frequency independent, and identical for voltage and current.