TABLE OF CONTENTS Approximate nominal PI section models are often used for short transmission lines (of the order of 15 km), where the travel time is less than the solution time-step, but such models are unsuitable for transmission distances. Instead, travelling wave theory is used in the development of more realistic models.
A simple and elegant travelling wave model of the lossless transmission line has already been described in Chapter 4 in the form of a dual Norton equivalent. The model is equally applicable to overhead lines and cables; the main differences arise from the procedures used in the calculation of the electrical parameters from their respective physical geometries. Carson's solution [1] forms the basis of the overhead line parameter calculation, either as a numerical integration of Carson's equation, the use of a series approximation or in the form of a complex depth of penetration. Underground cable parameters, on the other hand, are calculated using Pollack's equations [2], [3].
Multiconductor lines have been traditionally accommodated in the EMTP by a transformation to natural modes to diagonalise the matrices involved. Original stability problems were thought to be caused by inaccuracies in the modal domain representation, and thus much of the effort went into the development of more accurate fitting techniques. More recently, Gustavsen and Semlyen [4] have shown that, although the phase domain is inherently stable, its associated modal domain may be inherently unstable regardless of the fitting. This revelation has encouraged a return to the direct modelling of lines in the...
