A general analytical method to derive the distributed circuit parameters and mode propagation constants for an n-conductor transmission line is developed. The analysis uses electromagnetic field concepts and the results are interpreted in terms of distributed circuit parameters. The procedure involves transforming the problem of the n-conductor line above a ground with finite conductivity into that of an n-conductor above a ground with infinite conductivity. Correction factors are added to account for the finite conductivity of the ground. The distributed circuit parameters thus calculated are used to calculate the mode propagation constants over a frequency range from 10 Hz to 1 MHz for values of ground conductivity varying between 1 mho/m and 10⁻⁵ mho/m and relative permittivity varying between 10 and 50. Numerical results for the distributed circuit parameters and mode propagation constants for a typical 500 kV single circuit transmission line and various ground conditions are given. The results show that one mode has a higher attenuation and a lower velocity than either of the other two modes, suggesting the zero sequence mode for a completely balanced system. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The Location of a fault in a power cable is by no means a simple task and the techniques used at present warrant further improvement. Many methods of fault location have been devised but each has its particular limitations. Some of these methods include D.C. and A.C. bridge methods, echo-ranging methods, and high-frequency methods. The limitations and impracticability of these various techniques has been the main reason for this research. In this thesis, a review of the high-frequency method has been made, resulting in the development of a method of locating high-resistance faults. Expressions, permiting the use of this improved method in instances where cable potheads are relatively inaccessible have also been developed and checked experimentally. Briefly, the method consists of determining the input impedance of the cable with its remote end terminated in its surge impedance. This is done by simultaneously measuring the voltage drops across a standard resistor and across the cable. The ratio of these drops is an indication of the cable impedance at that frequency. Observations are taken on a band of frequencies on a faulted cable and on a good cable, both terminated in the characteristic impedance. The difference of these two effects is attributed to the reflections from the fault. From the plot of the impedance as a function of the frequency, by a short graphical computation, the distance to the fault may be obtained. Faults as high as twenty times the surge impedance have been successfully located on relatively short lengths of cable. The distance to the fault has been estimated well within [page missing] / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

In this thesis some numerical techniques for obtaining the time optimal control of a class of time delay systems are studied and compared. The delays may be fixed or time varying. The delay systems considered, which need not be linear or time invariant, are those for which the time optimal control is bang-bang. The optimal control is found by carrying out a search in switching interval space. The method of Rosenbrock⁽²’³⁾ is used to find the switching intervals which maximize a performance index of the final states and terminal time. Kelly's⁽²¹⁾ method of gradients is shown to be applicable to systems with time varying time delays by using the costate equations of ref. [10]. The perturbations in the control are chosen in such a way that the descent in function space is changed to a steepest descent in switching interval space. In a third approach, a technique similar to that of Bryson and Denham⁽¹⁹⁾ is used to account for the terminal conditions directly. All the methods are illustrated by examples. The advantages of the direct search based on Rosenbrock's method are a) ease of programming and b) rapid convergence close to the optimum. However, initial convergence is slow when compared to that of either gradient method. Of the two gradient methods, that based on a penalty function approach was superior in ease of programming and convergence close to the optimum to that based on a descent to the final target set. Neither gradient scheme could match the rapid convergence of the Rosenbrock method close to the optimum / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis describes numerical methods for the evaluation of the series impedance matrix and shunt admittance matrix of underground cable systems. In the series impedance matrix, the terms most difficult to compute are the internal impedances of tubular conductors and the earth return impedance. The various formulae for the internal impedance of tubular conductors and for the earth return impedance are, therefore, investigated in detail. Also, a more accurate way of evaluating the elements of the admittance matrix with frequency dependence of the complex permittivity is proposed. Various formulae have been developed for the earth return impedance of buried cables. Using the Pollaczek's formulae as the standard for comparison, the formula of Ametani and approximations proposed by other authors are studied. Mutual impedance between an underground cable and an overhead conductor is studied as well. The internal impedance of a laminated tubular conductor is different from that of a homogeneous tubular conductor. Equations have been derived to evaluate the internal impedances of such laminated tubular conductors. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis presents a new model to simulate the behaviour of underground cable systems under transient conditions. The new cable model belongs to the class of time-domain, frequency-dependent models, and it is directly compatible with the solution algorithm of the EMTP (Electromagnetic Transients Program). The most important feature of the new model is that it takes into account the frequency dependence of the modal transformation matrices and cable parameters, thus overcoming the main limitation of currently-used transmission line and cable models, which assume that the modal transformation matrices are constant Conceptually, the new model is relatively simple. The system parameters which define the behaviour of an underground cable (namely the modal characteristic admittance matrix, the modal propagation matrix, and the modal transformation matrix), are expressed in closed form by approximating them with rational functions in the frequency domain. Therefore, in the time domain, all numerical convolutions can be expressed recursively. The host transients program (to which the model is interfaced) sees the new model as a constant, real admittance matrix, in parallel with a continuously-updated vector current source. The accurate approximation by rational functions of the modal transformation matrix is possible when its elements are continuous and smooth functions of frequency. Standard eigenvalue/eigenvector algorithms are not well suited for this purpose. Therefore, a new procedure to generate eigenvalues and eigenvectors has been developed. This procedure is based on the Jacobi method, and it produces the desired smooth functions of frequency. This manuscript presents a number of simulations where the performance of the new cable model is compared with exact analytical solutions. These simulations show an excellent agreement between analytical and numerical answers. The effects of not taking into account the frequency dependence of the modal transformation matrices is illustrated with the simulation of a line-to-ground fault on a three-phase cable. The response of the new cable model is also compared with results measured in a field test The new cable model is numerically stable. Its computational speed is comparable to that of frequency-dependent line models with constant transformation matrices. The new cable model is general. Its extension to the simulation of multiple-circuit overhead transmission lines should also be of considerable practical importance. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The propagation of the switching surge wave front on multiphase power lines was investigated by modal analysis and conventional Fourier Transformation. A 500 kV untransposed, three-phase transmission line, for which field test results were available, was chosen as a test case. Phase A of this test line was excited from a double exponential voltage source and the voltage response at the receiving end was calculated and measured in all three phases. The calculated voltage arrival time matched closely the measured value, and was very close to the time taken by electromagnetic waves in air at a speed of 0.3 km/μs. The calculated voltage response curves also came close to the measured results (errors within 8%). / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

This thesis discusses elliptic geometry including the order and incidence properties, projective properties and congruence properties.

The Gemini Near Infrared Spectrograph - Distant Quasar Survey (GNIRS-DQS) is the largest uniform, homogeneous survey of its kind, covering 260 quasars at 1.5 ≤ z ≤ 3.5. This unique survey, coupled with data from the Sloan Digital Sky Survey (SDSS), enables new investigations into redshifts, supermassive black hole masses (MBH), and accretion rates at high redshift through spectroscopic coverage of important rest-frame UV-optical emission lines. The importance of this survey is highlighted in the fact that the optical emission lines provide more reliable measurements of these quasar parameters than their UV counterpart. With such a unique sample compiled here, I construct prescriptions to calibrate these quasar parameters derived from rest-frame UV emission lines to those derived from rest-frame optical emission lines. These prescriptions provide important insight into how these parameters depend on redshift and are potentially biased as we look out further into the universe. Additionally, all the work completed with this sample will help shape our understanding of how these quasars and their host galaxies co-evolve over cosmic time.

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