The modelling of wave propagation in multiconductor transmission line involves
full matrices for the wave propagation and characteristic impedances functions. Modal
decomposition, as in the fdLine model in the EMTP, leads to an elegant and numerically
efficient solution, even in the presence of frequency dependent parameters.
The advantages of modal decomposition are lost, however, when the
transformation matrix relating modal and phase quantities cannot be assumed constant
and real but is complex and changes with frequency. This is the case, for instance, when
there is strong conductor asymmetry in multicircuit transmission lines and cable systems.
A number of alternatives have been proposed to solve the problem of frequency
dependent transformation matrices: from frequency synthesis of the transformation
matrices to working directly in the phase domain. Both of these approaches, however,
have drawbacks. Direct synthesis of the transformation matrices with stable rational
functions is difficult because the eigenvectors that make up the columns of these matrices
are not uniquely defined at each frequency point. Direct phase-domain modelling is also
difficult because an N-phase transmission line has N propagation modes and N time
delays and the N2 elements of [Aphase] are a combinations of these basic travelling times
and modes.
The idempotent Line Model (idLine) expresses the line propagation function as a
matrix directly in phase coordinates [Aphase] (thus avoiding modal transformation
matrices), but the expression is in terms of the N natural propagation modes (thus
avoiding mixed-up travelling times). With idempotent decomposition, the line
propagation matrix can be written as a combination of the modal propagation functions
with the idempotent matrices as weighting factors. As opposed to the eigenvectors, which
are defined only up to an arbitrary complex constant, the idempotent coefficient matrices
are uniquely defined at each frequency point.
In the idempotent line model, each scalar modal propagation function is
synthesised in the frequency domain using a rational function approximation for the wave
shaping and the mode's travelling time for the wave delay. The elements of the
idempotent matrices are relatively simple functions of frequency that can also be
synthesised using rational function approximations.
The proposed model is very accurate and numerically stable. A number of
simulations are presented and comparisons are made between the new model, the
traditional fdLine model, and the "exact" solution obtained with the frequency domain
program FDTP. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/6015 |
| Date | 11 1900 |
| Creators | Marcano, Fernando JoseĢ |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Format | 2286686 bytes, application/pdf |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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