This thesis presents the modeling of general medium constitutive relationships in the Transmission Line Matrix (TLM) method. The technique is shown for two- and three-dimensional cases. The procedure consists of decoupling the impulse scattering at the nodes from equations describing the medium. This is achieved by using nodal sources connected to the TLM node. The nodal sources are implemented with the state-variable description of the constitutive relationships. The technique requires only few modifications to the TLM algorithm. The procedure is validated for frequency-dependent, nonlinear, anisotropic and gyromagnetic media. This thesis also presents a dispersion analysis of TLM with frequency-dependent dielectrics. This study is performed in two- and three-dimensions by solving the dispersion relationship of TLM with nodal sources. The sources are used to model the frequency dependent dielectric. The study shows that the nodal source and stub-loaded models are equivalent for frequency independent dielectrics. The accuracy bounds of the TLM frequency-dependent dielectric model are presented. This thesis also investigates the physical origin of the coarseness and dispersion errors influencing two-dimensional TLM solutions of Maxwell's equations. The study is performed by solving the difference equations of the numerical method analytically. The results confirm a reduction of the accuracy of the discrete solution near field singularities. The solution of a partially filled waveguide is also investigated. The results show that TLM can have positive or negative frequency shifts, depending on the dielectric filling, excited mode and geometry. These results are also valid for the finite difference time domain method (FDTD). / Graduate

Problems concerning transmission lines have been solved in the past by treating the line in terms of lumped parameters. Pioneering work was done by L. V. Bewley and S. Hayashi in the application of matrix theory to solve polyphase multiconductor distributed parameter transmission system problems. The availability of digital computers and the increasing complexity of power systems has renewed the interest in this field. With this in mind, a systematic procedure for handling complex transmission systems was evolved. Underlying the procedure is the significant concept of a complete system which defines how the parametric inductance, capacitance, leakance and resistance matrices must be formed and used. Also of significance is the use of connection matrices for handling transpositions and bonding, together with development of the manipulation of these matrices and the complex (Z) and (T) matrices. In the numerical procedure, methods were found to transform complex matrices into real matrices of twice the order and to determine the coefficients in the general solution systematically. The procedure was used to deal with phase asymmetry and mixed end boundary conditions. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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

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

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A dissertation submitted to the Faculty of Engineering, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering Degree awarded with distinction on 8 December I998 Johannesburg, 1998 / This report discusses high phase order (HPO) technology, i.e. the use of more than the conventional 3 phases for transmission of electric power, its use in the compaction of lines, and power density maximization over existing servitudes. It is structured in four parts. The first part introduces the concepts, establishes the need, and lists the advantages ofHPO. The second part deals with the technology itself and shows that it is possible to analyze HPO systems using symmetrical component analysis, lists common transformer configurations, covers protection, and so on. The third part analyses 5 case studies, the first 3 being analytical, and the last 2 being the first experimental test line, and the world's :first utility application ofHPO lines. The fmal section is a South African case study and compares an HPO line to an existing 400 kV 3-phase line and shows that the former is 87.5% more expensive to implement than the latter. Comparing the 3-phase and 6-phase lines on a more even basis, yielded a breakeven distance of225.86 km, above which the 6-phase option becomes more economical. These results are then explained and discussed in the conclusions section.