Phase-domain transmission line models considering frequency-dependent transformation matrices

• Published in: IEEE transactions on power delivery Vol. 19; no. 2; pp. 708 - 714
• Main Authors: Fernandes, A.B., Neves, W.L.A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2004; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Brazil Council; Conductors; Discontinuity; Eigenvalues; Eigenvalues and eigenfunctions; Eigenvectors; EMTP; Frequency dependence; Mathematical analysis; Mathematical models; Matrices; Matrix methods; Power transmission lines; Symmetric matrices; Transformations; Transmission line matrix methods; Transmission line theory; Transmission lines
• ISSN: 0885-8977; 1937-4208
• DOI: 10.1109/TPWRD.2003.822536

When modeling overhead multiphase transmission lines in modal or phase domain, transformation matrices derived from eigenvalue/eigenvector theory are needed to obtain the characteristic admittance Y/sub c/(/spl omega/) and the propagation function A(/spl omega/). Although these matrices are complex and frequency-dependent, electromagnetic transients programs (EMTP) assume them to be real and constant, and for their computation shunt conductances are usually neglected. Also, the transformation matrix elements do not always behave smoothly due to eigenvector switchovers. In this paper: 1) shunt conductances are included in eigenvalue/eigenvector calculations; 2) transformation matrices are considered to be complex and frequency dependent; and 3) a procedure to avoid eigenvector switchovers is used. Y/sub c/(/spl omega/) and A(/spl omega/) are calculated considering the transformation matrices to be real-constant, complex-constant, and complex-frequency-dependent. It is shown that discontinuities due to eigenvector switchovers may produce discontinuities in Y/sub c/(/spl omega/) and that accuracy is improved if the transformation matrices are considered to be complex and frequency dependent.