Frequency-dependent transformation matrices for phase-domain transmission line models

When modelling overhead multi-phase 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 not taken into account. Also, the transformation matrix elements do not always behave smoothly due to eigenvector switchovers. In this paper: (a) shunt conductances are included in eigenvalue/eigenvector calculations; (b) transformation matrices are considered to be complex and frequency-dependent; (c) a procedure to avoid eigenvector switchovers is used; and (d) 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.