Phase-domain multiphase transmission line models

Abstract

In general, multiphase transmission line and cable models for transient programs, such as the EMTP, base their solutions on transformations between the phase and modal domains. The main difficulty with these models is the synthesis of the frequency dependent transformation matrices. This paper presents two line models that circumvent this problem by writing the propagation functions directly in the phase domain and thus avoid the use of modal transformation matrices. The first model (developed in connection with our work on corona modelling) avoids the use of modal transformation matrices by separating the ideal-line travelling effect from the loss effects (resistance and internal inductance). The second proposed model is a full frequency dependent distributed parameter model based on idempotent decomposition. By using idempotents instead of eigenvectors as the basis for modal decomposition, the problems associated with the indeterminacy of the frequency dependent eigenvector functions are eliminated.