Phase domain transmission line modelling for EMTP-type studies with application to real-time digital simulation
This research project is primarily concerned with the development of a new generation of power transmission lines for both non-real-time and real-time electromagnetic transient studies. The method proposed is entirely formulated in phase co-ordinates, avoiding the use of modal transformation matrices at every stage in the analysis. In comparison, the phase domain models presented thus far in the open literature have all incorporated the concept of modal decomposition in the initial frequency domain formulation of the problem. Only the time domain analysis is conducted in the phase domain. These models can therefore be regarded as a hybrid between the phase and modal methodologies. Algorithms are presented which allow accurate and efficient determination of the characteristic admittance matrix, Yc(), and wave propagation matrix, H(), directly in phase co-ordinates. A Padé iteration scheme is used for evaluating the characteristic admittance matrix, derived by exploiting a relationship between the matrix sign function and the matrix square root. Padé techniques have also been used to approximate the matrix exponential in order to evaluate the wave propagation function. By evaluating Yc() and H() directly in phase co-ordinates, any imbalances naturally present in the line will intrinsically be taken into account in these functions. Both methods have been extensively tested using line configurations of different size and complexity and both algorithms are shown to be very robust, accurate and efficient in all cases. One of the main difficulties in formulating the analysis entirely in phase co-ordinates for multiconductor systems concerns the unwinding of the wave propagation matrix. This is addressed in this research by evaluating a matrix phase shift function in phase co-ordinates. Since the method inherently takes into account the coupled time delays of the line, the elements of H() can be successfully unwound, irrespective of the configuration of the line, e.g. single-circuit, multi-circuit or asymmetrical.