Prepared in association with Electric Power Systems Engineering Laboratory and Dept. of Civil Engineering, M.I.T

Thesis (M.S.)--Rochester Institute of Technology, 1993. / Typescript. Includes bibliographical references (leaves 152-153).

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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

Thesis (Masters Diploma(Technology) - Cape Technikon, Cape Town, 1996 / ESKOM control a massive power grid in a vast geographical area in the R.S.A.. This power originates at the power stations, from where it is distributed to the users. All the power generated is pumped into a National Power Grid. The backbone of the network consists of the following supply voltages: • 765 kV • 400 kV • 132 kV These voltages are stepped down locally at substations to lower voltages for the customers. Bigger customers (e.g. Municipalities, Mines, etc.) are bulk users and use high voltages. Lower voltages range from 220V up to 66kV. In order to ensure a good service to all power user customers ESKOM must be able to identify power failures and other abnormal conditions as quickly as possible and react fast to restore power again. When supervising a power grid good communication systems are essential. Communications systems serve as links between the following functional systems: • Contacting personnel with radio (Mobile or Handheld) • Contacting personnel \\ith pagers (Digital or Analogue) • Receiving up to date information on the SCADA network • Protection on power lines and transformers (Fault conditions) Without good telecommunication ESKOM will not be able to control the national grid efficiently. The Telecommunication Department fulfil a vital role ensuring that the National Grid functions at its optimum. It is normally impossible to do an accurate measurement of the power level in dBm or dBv on a communication line while an RTU is communicating to the MASTER. This is mainly because the duration of the data burst on the communication line is less than the sample time required by the level meters available. The time duration on a TELKOR PUTU general poll is 250ms. With the available digital meters (e.g. W & G SPM33A) it is totally impossible to get a power level reading because the sampling time of the instrument is I second. With the analogue meters available (e.g. W&G SPM09, SPM31) it is possible to get a reading, but this normally between 2 dBm and 4 dBm Iow, because of the dynamic behaviour of the moving coil. Thus before the pointer of the meter has reached the correct level, the burst of data has stopped This is characterised by three quantities: 1. The inertia (1) of the moving coil about its axis of rotation. 2. The opposing torque (S) developed by the coil suspension 3. The damping constant (D) A solution is to sample the receive and transmit levels during polling with an electronic circuit and feed it into an ADC connected to a Microcontroller (e.g. 8031 family). The Microcontroller will do all the converting and mathematical functions and will output a value through a DAC. This output value will be a current (mA) value directly proportional to the input level (e.g. -20dBm to OdBm = 0 to 5mA). These RX and IX level values can be fed into analogue inputs of the RTU. This realtime measurement of the levels on communication lines will be available at the SCADA master. These values can then be trended and if a downward trend is observed, maintenance can be done on the line before a failure. This should result in higher availability of the SCADA network.

M.Ing. / Open-wire telecommunications were developed in the 19th and early 20th centuries without any consideration of the deleterious effects of power lines; compatibility problems were later caused by the proximity of power lines and telephone lines. The coexistence of such systems requires careful planning in terms of energy coupled to the telephone lines; this induction can cause interference, as well as dangerous overvoltages in telephone circuits, and requires detailed studies of the effects of coupling between high voltage lines and telephone systems to be done. In terms of inductive co-ordination in South Africa, the minimum separation distances between high voltage power lines and communication systems are calculated only for power frequency and lower order harmonics (up to the 13th). The aim of the study was to explore the agreement between theory and measurement for frequencies from 50 Hz to the high order harmonic range of 4 kHz; this makes it possible to extend existing methods for predicting compatible separations to cases where high order harmonics (up to the 73rd) are present (balanced and unbalanced) on a 132 kV power line feeding a large aluminium smelter plant.

M.Ing. / Please refer to full text to view abstract

This thesis describes the development of an accurate method of fault location in transmission lines and cables. While the presence of a high frequency transient superimposed on the 50 Hz f a u l t voltage and current waveforms must be removed for most of the transmission line protection methods, the method presented in this thesis, which draws from travelling wave principles, locates the fault position using recordings from the fault waveform independent of the frequency components present. Using the telegraph equations as a line model, voltage and current samples taken at one end of a line within the first 5 ms of fault inception were used to generate instantaneous voltage and current profiles for the rest of the transmission line. The voltage and current estimation were based on the solution of the equations of the line model by the method of characteristics. Different criteria functions, involving the computed variables were applied to determine the fault positions. The basic functions involve any one of the square of the voltage, the square of the current or the product of the two. Fault position is determined by the turning or inflexionary point in the functions. In a further development the variation of the tangent to the functions described was considered and the fault position was found to be indicated by the peak of the scatter diagram produced. This latter function finds special application for resistive faults and faults in teed networks where the turning point given by the earlier functions are not usually well defined. The algorithm has been tested both with laboratory simulations and digital computer simulated data on typical 33 kV, 132 kV and 400 kV systems. Fault location accuracies of between 0.1% to 3.3% were achieved. Following the success with laboratory tests on models, a proposal has been put forward for an on-line fault locator.

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