From the early days of HVDC system applications, the importance of mathematical modelling of the dynamics of Line Commutated Converter (LCC) HVDC systems has been appreciated. There are essentially two methodologies used to develop mathematical models of dynamic systems. One methodology is to define the properties of the system by the “laws of nature” and other well-established relationships. Basic techniques of this methodology involve describing the system’s processes using differential equations. This methodology is called “Deductive Modelling”. The other methodology used to derive mathematical models of a dynamic system is based on experimentation. Input and output signals from the original system are recorded to infer a mathematical model of the system. This methodology is known as “Inductive Modelling”. A review of the current state of the art of modelling LCC HVDC systems indicates that majority of the techniques utilized to develop mathematical models of LCC HVDC systems have used the “Deductive Modelling” approach. This methodology requires accurate knowledge of the ac systems and the dc system and involves complicated mathematics. In practice, it is nearly impossible to obtain accurate knowledge of the ac systems connected to LCC HVDC systems. The main aim of this thesis is to present an “Inductive Modelling” methodology to calculate the plant transfer functions of LCC HVDC systems. Due to the uncertain nature of the effective short circuit ratio of rectifier and inverter converter stations, generic ranges of parametric uncertainties of the developed plant transfer functions were determined. Based on the determined range of HVDC plant parametric uncertainty, Quantitative Feedback Theory (QFT) methodology was used to design the parameters of the LCC HVDC control system. The stability of the start-up and step responses for varying ac system conditions validated the “Inductive Modelling” technique and the QFT design methodology. The thesis presents the following, which are considered to be scientific advancements and contributions to the body of knowledge: · Novel LCC HVDC Step Response (HSR) equations were developed using an “Inductive Modeling” technique. · The range of parametric variations of the LCC HSR equations were determined for various rectifier and inverter ac system effective short circuit ratios. · The LCC HSR equations were used to develop the LCC HVDC plant transfer functions for various rectifier and inverter effective short circuit ratios. · The LCC HVDC plant transfer functions were utilized to design an LCC HVDC control system for varying ac system conditions using Quantitative Feedback Theory (QFT) methodology. The main contributions of this thesis relate to LCC HVDC systems. This thesis does not attempt to advance control theory however this thesis does apply existing classical control theory to LCC HVDC control systems. Index Terms: Line Commutated Converter, HVDC, inductive modelling, power system, transient analysis. / Thesis (Ph.D.)-University of KwaZlu-Natal, Durban, 2011.

The development of a simple efficient Pulse Width Modulation (PWM) modulator has been a goal for many research workers. In general three techniques have been used, namely; the analogue triangular wave technique; the use of look-up tables, and the use of Analogue to Digital converters together with analogue circuitry. The modulator described in this thesis is based on an iterative numerical algorithm, and is thus fundamentally different from all previous techniques. The algorithm is limited only by the speed and precision of the associated digital circuitry and can achieve higher modulating frequencies with greater accuracy than can be realised using any of the methods that have previously been investigated. The use of high switching frequencies simplifies the design of filters to reduce both unwanted harmonics and acoustic noise. In this thesis, an equation of a multiphase digital oscillator is derived which is simple to implement and will operate over a wide range of frequencies. The conditions for stable oscillation are derived, and two classes of oscillator are developed. It is shown how the frequency and amplitude of oscillations can be independently and continuously varied. The errors in computing the amplitude and frequency are analysed, and are shown to be cyclic. Upper bounds for the amplitude errors are derived. Single and three phase PWM modulators are described and the implementation procedures for their practical realisation are developed. Two specific implementations of the algorithm are investigated and experimental results confirm theoretical analyses. The algorithm can be incorporated in the Space Vector Modulation (SVM) method of PWM, to improve the resolution at low speeds and to enable the SVM technique to be applied at high gear ratios. A 3-phase 16-bit PWM modulator was built and operated satisfactorily with a pulse switching frequency of 20 kHz and an output frequency range of 1000:1. / Thesis (Ph.D.)-University of Natal, Durban, 1989.

Subsynchronous Resonance (SSR) is a condition which occurs when turbogenerators are connected to series capacitively compensated transmission systems and it can cause large scale damage to the turbogenerators. The accuracy of predictions of this phenomenon are limited by the accuracy of the mathematical models used for the various system elements. The modal method of modelling a turbogenerator shaft, in which parameters are associated with each natural torsional mode of the shaft, is investigated in detail and the sensitivity of SSR predictions (both small signal and transient) to uncertainties in the mode parameters is evaluated. The modal model is then used to obtain reduced order shaft models and the accuracy of these reduced order modal models in SSR predictions is ascertained. The determination of mode parameters from generator transient response waveforms is investigated. A continuing problem in this field is the separation of damping values obtained from measurements on a synchronized generator, into their mechanical and electrical components. A method is proposed in this thesis which uses eigenvalue scanning techniques together with FFT analysis to achieve this separation. The SSR stability of, and the torsional interaction between two adjacent generators at a power station is studied. The analysis covers identical generators, nominally identical generators with small differences between their mode parameters and different generators with a coincident torsional mode. In addition, the torsional interaction between generators at different power stations which are remote from each other is investigated. This entire analysis is greatly assisted by modelling the turbogenerator shafts in modal form. Finally the damping of SSR oscillations in two non-identical adjacent turbogenerators with a single controlled shunt reactor, which uses the sum of the generator speed signals as an input to the controller, is investigated. / Thesis (Ph.D.)-University of Natal, Durban, 1987.

The quantitative feedback theory (QFT) of Horowitz is theoretically well developed for multivariable systems but there is not sufficient knowledge on its application to practical problems. A "flying machine" consisting of an airframe with two independently controlled sets of wings has been designed and constructed as a 2-input 2-output control problem. The airframe is constrained to move vertically on guide wires and to rotate about a pivot. Air flow over the wings is provided by two 7.SkW fans operated without any attempt at providing non-turbulent flow. The arrangement of the wings is such that in open loop, the dynamic behaviour of the airframe from the rear set of wings to the height is non-minimum phase. Additionally, the airframe is unstable for some flight conditions. This uncertain, non-linear and highly disturbed plant provides an ideal practical environment in which to test controller design theory. The construction, modelling, parameter estimation and simulation of the flying machine is described. Three different controller structures are disGussed, with actual controller designs arrived at from QFT understanding. The controller designs for the flying machine take into account parameter uncertainty and trade off disturbance attenuation against rate and amplitude saturation at the wing angle inputs. / Thesis (Ph.D.)-University of Natal, Durban, 1989.

The work presented in this thesis focuses on the problem of reconstructing threedimensional models of fire from real images. The intended application of the reconstructions is for use in research into the phenomenon of fire-induced high voltage flashover, which, while a common problem, is not fully understood. As such the reconstruction must estimate not only the geometry of the flame but also the internal density structure, using only a set of a few synchronised images. Current flame reconstruction techniques are investigated, revealing that relatively little work has been done on the subject, and that most techniques follow either an exclusively geometric or tomographic direction. A novel method, termed the 3D Fuzzy Hull method, is proposed, incorporating aspects of tomography, statistical image segmentation and traditional object reconstruction techniques. By using physically based principles the flame images are related to the relative flame density, allowing the problem to be tackled from a tomographic perspective. A variation of algebraic tomography is then used to estimate the internal density field of the flame. This is done within a geometric framework by integrating the fuzzy c-means image segmentation technique and the visual hull concept into the process. Results are presented using synthetic and real flame image sets. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, 2007.

The main objective of this research was to study DC conductor corona loss (CL) and audible noise (AN) in the context of local climatic conditions, through corona cage measurements, and do a comparative analysis of the measured data with results available in literature and EPRI TLW software simulation results. The ultimate aim was to assess the applicability of the software to our local conditions and hence determine, if necessary, appropriate correction factors for application in HYDC transmission line designs. For this study, short term measurements of corona AN and currents were carried out in an indoor meshed cylindrical corona cage, under DC and AC voltages. The cage was later converted into a short test line and some of the measurements repeated. The DC supply was obtained from a two stage ±500 kV Walton-Cockroft generator. The AC voltages were obtained from a 2x 100 kV, 50 Hz, AC test transformer set. The tests were performed using single solid and stranded aluminum conductors with three different diameters (1.6 cm, 2.8 cm, and 3.5 cm). All the measurements were carried out at low altitude. A CoroCAM I camera was used to determine the corona inception gradients and to observe the corona activity at different surface gradients and under different voltages and polarities. AN measurements at different conductor surface gradients were done using the Rohde&Schwarz and the Bruel&Kjaer sound level meters. To obtain the frequency spectra, a Bruel&Kjaer octave-band filter set attached to the sound level meter was used. The measured data was corrected for both height and length effects, and then compared with simulations from the EPRI-TLW software through curve fitting. A digital micro-ammeter connected to the centre of the cage through a 560 .Q measuring resistor was used to measure the corona current. Current pulses were viewed using a digital storage oscilloscope. To verify the corona current results obtained from the cage measurements, current measurements were also done for a point-plane spark gap. The corona current data was, later on, used to evaluate the total corona power loss for DC. The results obtained from test line measurements were used to compare the CL and AN for different configurations. The effect of the space charge under DC voltages was assessed through current measurements. The measurements were done with the cage covered with an aluminum foil to trap the charge and then repeated with the cage uncovered. On the test line, the space charge effect was investigated using a high power fan blowing along the conductor, to simulate the wind factor. The results of this study have shown the characteristics of corona discharges under different system voltages. The results also give an understanding of how factors such as conductor surface conditions and size, polarity and system voltage affect CL and AN. Both CL and AN were found to increase with conductor size for the same conductor surface gradient and to be higher for stranded conductors. Positive polarity DC and AC noise levels were higher than the negative polarity levels. CL under positive polarity DC was lower than the negative polarity loss. The effects of space of space charge were noted to some extend. The comparison of test line results and cage results showed that CL depends more on the gap size and the shorter the gap the higher the loss. Hence CL results were not compared with the software simulations. The comparison between the corrected AN results and the software simulations showed a very good agreement. The comparison was done for the 3.5 cm and the 2.8 cm diameter conductors under both positive and negative polarities. The trends compared through curve fitting were quite similar and the trend line equations were of the same order of magnitude. The magnitudes of the corrected noise levels were higher than the CRIEPI and BPA predictions but closer to the EPRl prediction. Generally there is a very good and encouraging agreement between the available literature, simulation results and the results obtained from the laboratory measurements. It is proposed, as part of further studies, to extend this work to high altitude regions and use bundled conductors as well. Consideration of different and larger test configurations will provide an understanding of the effects of geometry on corona discharges. Space charge analysis will also assist in determining the effect of space charge on different configurations. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2007.

Bringing broadband access to rural and remote communities has been a very difficult task due to the high cost of installation and complete lack of infrastructure in certain areas. Options currently under serious consideration to enable this access have included GSM, CDMA, Power line telecommunications, and DSL technologies. However, with the addition of the IEEE 802.16 standard - commonly referred to as WiMAX - with its various advantages, another serious option is now being considered. WiMAX is standard developed to provide wireless broadband access to metropolitan area networks. It is capable of providing LOS and NLOS coverage in the range of 350 km with data rates up to 75 Mbps. This research therefore looks at the WiMAX standard MAC and PHY layers with special focus on the PHY layer properties enabling provision ofNLOS coverage (WirelessMAN OFDM PHY). The research evaluates the performance of WiMAX in a rural environment in terms of coverage and traffic analysis. Other aspects include multipath fading and channel estimation. The traffic analysis is carried out using traffic projection formulated over a period often years for Nkandla, a typical rural area in South Africa. This is done to evaluate the sustainability of the designed base stations over the ten-year period with the growing traffic. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2006.

The majority of Eskom's 22kV lines use wood as the support structure material. The economics of wood pole cross arms and their flashover withstand capabilities outweigh those of steel cross arms. However, wood pole structures are vulnerable to what is known as a Pole Top Fire. When insulators and wood cross arms become polluted, small and sustained leakage currents flow along the surface of the insulator and thereafter into the wood itself. This eventually leads to burning of the wood. Many of the 22kV lines traverse vast rural lands, going over people's path ways. If this fire is not discovered timeously, it can cause breakage of the relevant cross arm or the pole itself. A broken cross arm usually causes the outer phase conductor to hang between one and two meters above ground. When it's dark, rural inhabitants cannot see clearly and walk directly into these low lying energized conductors which cause severe injuries and often fatalities. Low hanging conductors cannot be detected electrically and are potentially hazardous to humans and animals. Safety is currently one of the highest priorities for Eskom Distribution and hence there is a dire need to mitigate Pole Top Fires. The researcher hypothesizes that the implemented mitigating technique of bonding does not eliminate Pole Top Fires. In this study accurate statistics on Pole Top Fires in KwaZulu - Natal are provided and causes of fires investigated to provide an understanding thereof. Two basic mechanisms of burning have been identified and explained. These are surface tracking and sparking, and internal sparking. This has helped to explain what mitigation techniques will be effective. A critical analysis on the performance of recommended mitigation techniques is conducted. This study therefore aims to conclude on the effectiveness of implemented techniques to mitigate Pole Top Fires. By comprehensive and critical analysis of a complex operational and safety related problem technical options for mitigating or eliminating the fires are identified, critically analyzed and only those options that are really technically feasible are proposed. This has not been properly done in Eskom before. It is within this context that this research has been undertaken. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2007.

Rain affects the design of any communication system that relies on the propagation of electromagnetic waves. Above a certain threshold of frequency, the attenuation due to rain becomes one of the most important limits to the performance of terrestrial line-of-sight (LOS) microwave links. Rain attenuation which is the dominant fading mechanism at these frequencies is based on nature which can vary from location-to-Iocation and from year-to year. In this dissertation, the ITU-R global prediction techniques for predicting the cumulative distribution of rain attenuation on terrestrial links are studied using a five-year rain rate data for twelve different geographical locations in the Republic of South Africa. The specific attenuation rR (dB/km) for both horizontal and vertical polarization is determined. The path attenuation (dB) exceeded for 0.01% of the time is estimated using the available existing models for the twelve different geographical locations on a I-minute integration time rain rate at 0.01% exceedance of the time averaged over a period of 5 years. A comparison study is done on these available rain attenuation mode'ls; The ITU-R model, Crane Global model, and the Moupfouma models at different frequencies and propagation path lengths based on the actual I-minute integration time rain rate exceeded at 0.01% of the time averaged over a period of 5 years for each geographical locations. Finally, from the actual signal attenuation measurements recorded in Durban over a period of 1 year at 19.5 GHz and a propagation path length of 6.73 km, a logarithmic attenuation model and power attenuation model is proposed for Durban, South Africa. Recommendation for future work is given in the concluding chapter for future improvement on this study. Radio communication designers will find the results obtain in the report useful. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2006.

Analog-to-digital converters (ADCs) are required in almost all signal processing and communication systems. They are often the most critical components, since they tend to determine the overall system performance. Hence, it is important to determine their performance limitations and develop improved realizations. One of the most challenging tasks for realizing software defined radio (SDR) is to move ND conversion as close to the antenna as possible, this implies that the ADC has to sample the incoming signal with a very high sample rate (over 100 MSample/s) and with a very high resolution (14 -to -16 bits). To design and implement AID converters with such high performance, it is necessary to investigate new designing techniques. The focus in this work is on a particular type of potentially high-performance (high-resolution and highspeed) analog-to-digital conversion technique, utilizing filter banks, where two or more ADCs are used in the converter array in parallel together with asymmetric filter banks. The hybrid filter bank analog-todigital converter (HFB ADC) utilizes analog filters (analysis filters) to allocate a frequency band to each ADC in a converter array and digital synthesis filters to reconstruct the digitized signal. The HFB improves the speed and resolution of the conversion, in comparison to the standard time-interleaving technique by attenuating the effect of gain and phase mismatches between the ADCs. Many of the designs available in the literature are compromising between some metrics: design complexity, order of the filter bank (computation time) and the sharpness of the frequency response rolloff (the transition from the pass band to the stop band). In this dissertation, five different classes of near perfect magnitude reconstruction (NPMR) continuoustime hybrid filter banks (CT HFBs) are proposed. In each of the five cases, two filter banks are designed; analysis filter bank and synthesis filter bank. Since the systems are hybrid, continuous time IlR filter are used to implement the analysis filter bank and digital filters are used for the synthesis filter bank. To optimize the system, we used a new technique, known in the literature as frequency response masking (FRM), to design the synthesis filter bank. In this technique, the sharp roll-off characteristics can be achieved while keeping the complexity of the filter within practical range, this is done by splitting the filter into two filters in cascade; model filter with relaxed roll-off characteristics followed by a masking filter. One of the main factors controlling the overall complexity of the filter is the way of designing the model filter and that of designing the masking filter. The dissertation proposes three combinations: use of HR model filter and IlR masking filter, HR model filter/FIR masking filter and FIR model filter/FIR masking filter. To show the advantages of our designs, we considered the cases of designing the synthesis filter as one filter, either FIR or IlR. These two filters are used as base for comparison with our proposed designs (the use of masking response filter). The results showed the following: 1. Asymmetric hybrid filter banks alone are not sufficient for filters with sharp frequency response roll-off especially for HR/FIR class. 2. All classes that utilize FRM in their synthesis filter banks gave a good performance in general in comparison to conventional classes, such as the reduction of the order of filters 3. HR/HR FRM gave better performance than HR/FIR FRM. 4. Comparing HR/HR FRM using FIR masking filters and HR/IIR FRM using IIR masking filters, the latter gave better performance (the performance is generally measured in terms of reduced filter order). 5. All classes that use the FRM approach have a very low complexity, in terms of reduced filter order. Our target was to design a system with the following overall characteristics: pass band ripple of -0.01 dB, stop band minimum attenuation of - 40 dB and of response roll-off of 0.002. Our calculations showed that the order of the conventional IIR/FIR filter that achieves such characteristics is aboutN =2000. Using the FRM technique, the order N reduced to aboutN = 244, N = 179 for IIRJFIR and IIR/IIR classes, respectively. This shows that the technique is very effective in reducing the filter complexity. 6. The magnitude distortion and the aliasing noise are calculated for each design proposal and compared with the theoretical values. The comparisons show that all our proposals result in approximately perfect magnitude reconstruction (NPMR). In conclusion, our proposal of using frequency-response masking technique to design the synthesis filter bank can, to large extent, reduce the complexity of the system. The design of the system as a whole is simplified by designing the synthesis filter bank separately from the design of the analysis filter bank. In this case each bank is optimized separately. This implies that for SDR applications we are proposing the use of the continuous-time HFB ADC (CT HFB ADC) structure utilizing FRM for digital filters. / Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.