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UBC Theses and Dissertations

Full frequency-dependent phase-domain modelling of transmission lines and corona phenomena Castellanos, Fernando


This thesis presents two main developments in the modelling of power transmission lines for the simulation of electric networks. The first one is a wide bandwidth circuit corona model and the second a phase-domain multiphase full frequency-dependent line model. The latter can be easily used in connection with the former. Both models have been developed for implementation in time domain simulation computer programs, such as the ElectroMagnetic Transients Program (EMTP). Corona in overhead transmission lines is a highly nonlinear and non-deterministic phenomenon. Circuit models have been developed in the past to represent its behaviour, but the response of these models is usually limited to a narrow band of frequencies. The corona model presented in this thesis overcomes this problem by: 1) matching closely the topology of the circuit to the topology of the physical system, and 2) duplicating the high-order dynamic response of the phenomenon with a high-order transient circuit response. The resulting model is valid for a wide range of frequencies and is able to represent waveshapes from switching to lightning surges. A unique set of model parameters can be obtained directly from test-cage measurements, and the same set can be used directly for an arbitrary overhead line configuration. The model uses only standard EMTP circuit elements and requires no iterations. Simulations of corona charge-voltage (q-v) curves and of travelling surges were performed and compared to existing field test measurements. The proposed new transmission line model (z-line) can be used for the representation of multicircuit transmission lines in time-domain transient solutions. The model includes a full representation of the frequency-dependent line parameters and is formulated directly in phase coordinates. The solution in phase coordinates, as opposed to modal coordinates, avoids the problems associated with the representation of the frequency-dependent transformation matrices that relate the two domains. The main obstacle in phase-domain modelling, which is the mixing or superposition of propagation modes with different travelling times in the elements of the phase-domain propagation matrix [e ⁻ƴ⁽ω⁾ ̽] is effectively circumvented by discretizing in space rather than in time. In simple terms, instead of synthesizing the elements of [e ⁻ƴ⁽ω⁾ ̽] by rational functions as in the traditional approach ("time discretization"), propagation on a discrete-length segment of line can be represented as propagation on a discretized segment of ideal line (which has an exact solution) plus wave shaping by the line losses. The losses are represented by a frequencydependent impedance matrix [Zloss(ω)] which is synthesized directly in the phase-domain by rational function approximations. A new coordinated-fitting procedure is introduced to ensure numerically stable fitting functions. An additional advantage of space discretization is that it allows the interface of transversal line phenomena between sections (such as corona models, tower models, grounding connections, etc.). The z-line model is accurate, efficient, and numerically stable, and is specially suited for strongly asymmetrical line configurations where conventional models can give inaccurate results. A number of simulations were performed for highly asymmetrical line configurations and system conditions and the results compared against other time domain and frequency-domain models. The new z-line model was combined with the proposed corona circuit model in the simulation of a field test measurement of travelling-wave propagation under corona conditions.

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