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

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_c(ω) and the propagation function A(ω). 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_c(ω) and A(ω) 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_c(ω) and that accuracy is improved if the transformation matrices are considered to be complex and frequency dependent.