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A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science in Engineering Date submitted: 28 August 2015 / Many generator transformers were installed many years ago during the initial commissioning of Eskom’s power stations. Many of these transformers have started showing signs of significant ageing of the paper insulation and hence require regular monitoring. There are two methods that are currently being employed to assess the degree of ageing of the paper insulation in a generator transformer, which are paper sampling and furan level measurement. This dissertation investigates an alternative method of predicting the degree of ageing of the paper insulation instead of what is used currently. This method uses the Arrhenius equation that relates time and temperature to determine the degree of degradation of organic materials. The reliability of the Arrhenius estimation method is assessed by comparing the predicted DP (Degree of polymerisation) values with the measured DP values of the same transformer paper insulation. The results obtained showed that there is reasonable correlation between the DP values estimated from the Arrhenius equation and the DP values estimated from the measured furan levels. The accuracy of the prediction method is reduced when the oil temperature greatly differs from the paper insulation temperature. The application of the Arrhenius equation to estimate the ageing of paper insulation is a great milestone in the quest to predict the remaining life of a transformer. It is the only method available to do this prediction and using online temperature measurement on transformers makes the method more reliable. / MT 2017

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2009. / ENGLISH ABSTRACT: From a systems operation and design perspective, it is important to understand the behaviour of HVDC system insulation when presented with high voltage transients, such as induced by lightning and switching operations. Therefore, this thesis investigates the design, operation and performance of a circuit arrangement that can be used in high voltage laboratories to generate impulse voltage waveforms superimposed on a dc bias voltage. The circuit arrangement consists of an impulse generator and a dc source that supplies continuous dc voltage to stress the test object, which can be any type of insulator, i.e. composite, porcelain, glass, gap arrangements, etc. The composite waveform obtained from the test arrangement is used experimentally to investigate the impulse flashover of insulators. For modelling and analysis purposes, the test circuit was transformed to a Laplace equivalent in order to derive the applicable nodal voltage equations. After substitution of circuit parameter values, the voltage equations are then transformed to time domain equations that predict the time-domain behaviour of the circuit. To validate this mathematical approach, the voltage waveforms obtained with this mathematical model is compared with the waveforms measured under laboratory conditions and also with waveforms simulated with HSPICE software. These comparisons are performed using graphical representations. Good correlation was obtained and the results are presented in this thesis. The final stage of this thesis discusses the application of the designed test arrangement for flashover and withstands tests on a silicon rubber insulator. The determination of the flashover values is done by using the existing statistical methods. The insulator was tested under dry conditions and also under polluted wet conditions for both positive and negative impulses compared to the DC bias voltage polarity. The results show that the dc bias voltage does not affect the total voltage flashover of the insulator significantly. It was also observed that wetting affects the flashover for negative impulse more severely, while the influence of wetting is minimal with positive impulse voltages / AFRIKAANSE OPSOMMING: Vanuit ‘n stelselbedryf en ontwerp perspektief, is dit is belangrik om die gedrag van HSGS stelsels te verstaan wanneer dit onderwerp word aan hoogspanning oorgangsverskynsels soos veroorsaak deur weerlig en skakeloperasies. Daarom ondersoek hierdie tesis die ontwerp, werking en werkverrigting van ‘n stroombaanopstelling wat gebruik kan word in hoogspanningslaboratoriums om impulsspannings gesuperponeer op gelykspanning voorspannings op te wek. Die stroombaan bestaan uit ’n impulsgenerator en ‘n gs-bron wat die langdurige gs-spanning voorsien aan die toetsvoorwerp, wat enige tipe isolator kan wees. bv. porselein, glas, gapings, ens. Die saamgestelde golfvorm wat met die toetsopstelling verkry word, is eksperimenteel gebruik om die impulsoorvonking van isolators te ondersoek. Vir die doel van modellering and analise, is die stroombaan na ‘n Laplace ekwivalent getransformeer om die toepaslike knooppunt spanningsvergelykings af te lei. Na substitusie van die stroombaan parameter waardes, word die spanningsvergelykings getransformeer na die tydgebied vergelykings wat die tydgebied gedrag van die stroombaan voorspel. Om die wiskundige benadering te toets, word die spanningsgolfvorms wat met die wiskundige model voorspel word, vergelyk met golfvorms wat onder laboratorium toestande gemeet is en ook met golfvorms wat met HSPICE programmatuur gesimuleer is. Hierdie vergelykings word gedoen met behulp van grafiese voorstellings. Goeie korrelasie is verkry en die resultate word in die tesis gegee. Die finale stadium van hierdie tesis bespreek die toepassing van die ontwerpte toetsopstelling vir oorvonk- en weerstaantoetse op ‘n silikonrubber isolator. Die bepaling van die oorvonkwaardes word gedoen deur bestaande statistiese metodes te gebruik. Die isolator is onder droë en nat besoedelde toestande gedoen, vir beide positiewe sowel as negatiewe impulse met verwysing na die GS voorspan spanning. Die resultate toon dat die gsvoorspanning nie die oorvonkspanning van die isolator beïnvloed nie. Dit is ook waargeneem dat die benatting die oorvonking neer beïnvloed met ‘n negatiewe impuls terwyl die invloed minimaal is met positiewe impulsspannings.

Over the last 20 years "composite" insulators have been increasingly used in high voltage applications as an alternative traditional materials. More recently, polydimethylsiloxane (PDMS) have been used as weather sheds on these composite insulators. The main attraction with PDMS is that the surface hydrophobicity can be recovered following pollution or surface discharges. Among the possible mechanisms for recovery the most likely is the migration of low molecular weight silicone oil (LMWS) from the bulk to the surface encapsulating pollutant particles. Although it is widely recognised that the migration of LMWS is the cause of this recovery of hydrophobicity, the mechanism of what actually occurs is not well understood. It is also not known for how long this process will continue. The main objective of this study program was to gain improved understanding of the surface hydrophobic recovery process that is unique to polydimethlysiloxane high-voltage insulators. Fundamental knowledge of this mechanism has been increased through the development of the Contact Angle DRIFT Electrostatic Deposition (CADED) novel analytical technique. This technique enabled study of the degradation of silicone elastomers subjected to high voltage environments by closely following LMWS migration from the bulk material to the surface and linking it to the contact angle measurements. The migration rate data showed that the aged material recovered faster that the virgin material. Differences in the rate and maximum surface levels of silicone were seen between materials from different manufacturers. This has significant implications for the life-time of these materials A model system has been developed to examine LMWS diffusion through the bulk material and into the interface of surface and pollutant. This was achieved by examining theoretical and empirically derived equations and using existing experimental data to better understand the mechanism of recovery. This diffusion was Fickian in the initial stages of recovery. X-ray photoelectron spectroscopy (XPS) and contact angle measurements were used to substantiate the degree of degradation in in-field silicone insulators by quantifying the levels of the major degradation products: silica and silica-like material and alumina.

abstract: This thesis concerns the flashover issue of the substation insulators operating in a polluted environment. The outdoor insulation equipment used in the power delivery infrastructure encounter different types of pollutants due to varied environmental conditions. Various methods have been developed by manufacturers and researchers to mitigate the flashover problem. The application of Room Temperature Vulcanized (RTV) silicone rubber is one such favorable method as it can be applied over the already installed units. Field experience has already showed that the RTV silicone rubber coated insulators have a lower flashover probability than the uncoated insulators. The scope of this research is to quantify the improvement in the flashover performance. Artificial contamination tests were carried on station post insulators for assessing their performance. A factorial experiment design was used to model the flashover performance. The formulation included the severity of contamination and leakage distance of the insulator samples. Regression analysis was used to develop a mathematical model from the data obtained from the experiments. The main conclusion drawn from the study is that the RTV coated insulators withstood much higher levels of contamination even when the coating had lost its hydrophobicity. This improvement in flashover performance was found to be in the range of 20-40%. A much better flashover performance was observed when the coating recovered its hydrophobicity. It was also seen that the adhesion of coating was excellent even after many tests which involved substantial discharge activity. / Dissertation/Thesis / M.S. Electrical Engineering 2013

Topological phases of matter represent a new phase which cannot be understood in terms of Landau’s theory of symmetry breaking and are characterized by non-local topological properties emerging from purely local (microscopic) degrees of freedom. It is the non-trivial topology of the bulk band structure that gives rise to topological phases in condensed matter systems. Quantum Hall systems are prominent examples of such topological phases. Different quantum Hall states cannot be distinguished by a local order parameter. Instead, non-local measurements are required, such as the Hall conductance, to differentiate between various quantum Hall states. A signature of a topological phase is the existence of robust properties that do not depend on microscopic details and are insensitive to local perturbations which respect appropriate symmetries. Examples of such properties are the presence of protected gapless edge states at the boundary of the system for topological insulators and the remarkably precise quantization of the Hall conductance for quantum Hall states. The robustness of these properties can be under-stood through the existence of a topological invariant, such as the Chern number for quantum Hall states which is quantized to integer values and can only be changed by closing the bulk gap. Two other examples of topological phases of matter are topological superconductors and Weyl semimetals. The study of transport in various kinds of junctions of these topological materials is highly interesting for their applications in modern electronics and quantum computing. Another intriguing area to study is how to generate new kind of gapless edge modes in topological systems. In this thesis I have studied various aspects of topological phases of matter, such as electronic transport in junctions of topological insulators and topological superconductors, the generation of new kinds of boundary modes in the presence of granularity, and the effects of periodic driving in topological systems. We have studied the following topics. 1. transport across a line junction of two three-dimensional topological insulators, 2. transport across a junction of topological insulators and a superconductor, 3. surface and edge states of a topological insulator starting from a lattice model, 4. effects of granularity in topological insulators, 5. Majorana modes and conductance in systems with junctions of topological superconducting wires and normal metals, and 6. generation of new surface states in a Weyl semimetal in the presence of periodic driving by the application of electromagnetic radiation. A detailed description of each chapter is given below. • In the first chapter we introduce a number of concepts which are used in the rest of the thesis. We will discuss the ideas of topological phases of matter (for example, topological insulators, topological superconductors and Majorana modes, and Weyl semimetals), the renormalization group theory for weak interactions, and Floquet theory for periodically driven systems. • In the second chapter we study transport across a line junction which separates the surfaces of two three-dimensional topological insulators. The velocities of the Dirac electrons on the two surfaces may be unequal and may even have opposite signs. For a time-reversal invariant system, we show that the line junction is characterized by an arbitrary real parameter α; this determines the scattering amplitudes (reflection and transmission) from the junction. The physical origin of α is a potential barrier that may be present at the junction. If the surface velocities have the same sign, edge states exist that propagate along the line junction with a velocity and orientation of the spin which depend on α and the ratio of the velocities. Next, we study what happens if the two surfaces are at an angle φ with respect to each other. We study the scattering and differential conductance across the line junction as functions of φ and α. We also show that there are edge states which propagate along the line junction with a velocity and spin orientation which depend on φ. Finally, if the surface velocities have opposite signs, we find that the electrons must necessarily transmit into the two-dimensional interface separating the two topological insulators. • In the third chapter we discuss transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. This junction is more complicated than the line junction discussed in the previous chapter because of the presence of the superconductor. In a topological insulator spin-up and spin-down electrons get coupled while in a superconductor electrons and holes get coupled. Hence we have to use a four-component spinor formalism to describe both spin and particle-hole degrees of freedom. The junction can have three time-reversal invariant barriers on the three sides. We compute the subgap charge conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters which characterize the barriers. We find that the presence of topological insulators and a superconductor leads to both Dirac and Schrodinger-like features in the charge conductances. We discuss the effects of bound states on the superconducting side on the conductance; in particular, we show that for triplet p-wave superconductors such a junction may be used to determine the spin state of its Cooper pairs. • In the fourth chapter we derive the surface Hamiltonians of a three-dimensional topological insulator starting from a microscopic model. (This description was not discussed in the previous chapters where we directly started from the surface Hamiltonians without deriving them form a bulk Hamiltonian). Here we begin from the bulk Hamiltonian of a three-dimensional topological insulator Bi2Se3. Using this we derive the surface Hamiltonians on various surfaces of the topological insulator, and we find the states which appear on the different surfaces and along the edge between pairs of surfaces. The surface Hamiltonians depend on the orientation of the surfaces and are therefore quite different from the previous chapters. We use both analytical methods based on the surface Hamiltonians (which are derived from the bulk Hamiltonian) and numerical methods based directly on a lattice discretization of the bulk Hamiltonian in order to find surface and edge states. We find that the application of a potential barrier along an edge can give rise to states localized at that edge. These states have an unusual energy-momentum dispersion which can be controlled by applying a potential along the edge; in particular, the velocity of these states can be tuned to zero. The scattering and conductance across the edge are studied as a function of the edge potential. We show that a magnetic field applied in a particular direction can also give rise to zero energy states on certain edges. We point out possible experimental ways of looking for the various edge states. • In the fifth chapter we study a system made of topological insulator (TI) nanocrystals which are coupled to each other. Our theoretical studies are motivated by the following experimental observations. Electrical transport measurements were carried out on thin films of nanocrystals of Bi2Se3 which is a TI. The measurements reveal that the entire system behaves like a single TI with two topological surface states at the two ends of the system. The two surface states are found to be coupled if the film thickness is small and decoupled above a certain film thickness. The surface state penetration depth is found to be unusually large and it decreases with increasing temperature. To explain all these experimental results we propose a theoretical model for this granular system. This consists of multiple grains of Bi2Se3 stacked next to each other in a regular array along the z-direction (the c-axis of Bi2Se3 nanocrystals). We assume translational invariance along the x and y directions. Each grain has top and bottom surfaces on which the electrons are described by Hamiltonians of the Dirac form which can be derived from the bulk Hamiltonian known for this material. We introduce intra-grain tunneling couplings t1 between the opposite surfaces of a single grain and inter-grain couplings t2 between nearby surfaces of two neighboring grains. We show that when t1 < t2 the entire system behaves like a single topological insulator whose outermost surfaces have gapless spectra described by Dirac Hamiltonians. We find a relation between t1, t2 and the surface state penetration depth λ which explains the properties of λ that are seen experimentally. We also present an expression for the surface state Berry phase as a function of the hybridization between the surface states and a Zeeman magnetic field that may be present in the system. At the end we theoretically studied the surface states on one of the side surfaces of the granular system and showed that many pairs of surface states can exist on the side surfaces depending on the length of the unit cell of the granular system. • In the sixth chapter we present our work on junctions of p-wave superconductors (SC) and normal metals (NM) in one dimension. We first study transport in a system where a SC wire is sandwiched between two NM wires. For such a system it is known that there is a Majorana mode at the junction between the SC and each NM lead. If the p-wave pairing changes sign at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the subgap conductance between the leads and the SC. We derive an analytical expression as a function of and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the energies oscillate and decay exponentially as L is increased. The energies exactly match the locations of the peaks in the conductance. We find that the subgap conductances do not change noticeably with the sign of . So there is no effect of the extra Majorana modes which appear inside the SC (due to changes in the signs of Δ) on the subgap conductance. Next we study junctions of three p-wave SC wires which are connected to the NM leads. Such a junction is of interest as it is the simplest system where braiding of Majorana modes is possible. Another motivation for studying this system is to see if the subgap transport is affected by changes in the signs of . For sufficiently long SCs, there are zero energy Majorana modes at the junctions between the SCs and the leads. In addition, depending on the signs of the Δ’s in the three SCs, there can also be one or three Majorana modes at the junction of the three SCs. We show that the various subgap conductances have peaks occurring at the energies of all these modes; we therefore get a rich pattern of conductance peaks. Next we study the effects of interactions between electrons (in the NM leads) on the transport. We use a renormalization group approach to study the effect of interactions on the conductance at energies far from the SC gap. Hence the earlier part of this chapter where we studied the transport at an energy E inside the SC gap (so that − < E < Δ) differs from this part where we discuss conductance at an energy E where |E| ≫ . For the latter part we assume the region of three SC wires to be a single region whose only role is to give rise to a scattering matrix for the NM wires; this scattering matrix has both normal and Andreev elements (namely, an electron can be reflected or transmitted as either an electron or a hole). We derive a renormalization group equation for the elements of the scattering matrix by assuming the interaction to be sufficiently weak. The fixed points of the renormalization group flow and their stabilities are studied; we find that the scattering matrix at the stable fixed point is highly symmetric even when the microscopic scattering matrix and the interaction strengths are not symmetric. Using the stability analysis we discuss the dependence of the conductances on the various length scales of the problem. Finally we propose an experimental realization of this system which can produce different signs of the p-wave pairings in the different SCs. • In the seventh chapter we show that the application of circularly polarized electro-magnetic radiation on the surface of a Weyl semimetal can generate states at that surface. The surface states can be characterized by their momenta due to translation invariance. The Floquet eigenvalues of these states come in complex conjugate pairs rather than being equal to ±1. If the amplitude of the radiation is small, we find some unusual bulk-boundary relations: the Floquet eigenvalues of the surface states lie at the extrema of the Floquet eigenvalues of the bulk system when the latter are plotted as a function of the momentum perpendicular to the surface, and the peaks of the Fourier transforms of the surface state wave functions lie at the momenta where the bulk Floquet eigenvalues have extrema. For the case of zero surface momentum, we can analytically derive interesting scaling relations between the decay lengths of the surface states and the amplitude and penetration depth of the radiation. For topological insulators, we again find that circularly polarized radiation can generate states on the surfaces; these states have much larger decay lengths (which can be tuned by the radiation amplitude) than the topological surface states which are present even in the absence of radiation. Finally, we show that radiation can generate surface states even for trivial insulators.

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Thesis (MSc)--Stellenbosch University, 2004. / ENGLISH ABSTRACT: Polydimethylsiloxane (PDMS) compounds are utilized in outdoor high voltage insulation due to their low weight, vandalism resistance, better anti-contamination performance and their superior hydrophobic nature. Under severe environmental conditions and over prolonged service time, however, the hydrophobic surface can gradually become hydrophilic and then recover with adequate resting period. In this study, room temperature vulcanized (RTV) PDMS samples were prepared with different formulations and then exposed to corona discharge to evaluate its effect. The influence of different additives, such as different types and amount of fillers and additionally added low molar mass silicone oils, on the hydrophobicity recovery of the material was investigated. The effects of two types of corona treatment were also evaluated. Hydrophobicity recovery of corona and UV-C aged PDMS samples was evaluated by means of static contact angle measurements. Positron annihilation spectroscopy (PAS) gave important information on the micro structural change after corona treatment of RTV PDMS as well as naturally aged high temperature vulcanized (HTV) PDMS samples. The different formulations of the RTV PDMS samples and the effect of the additives were studied with this technique. The formation of a thin, highly crosslinked inorganic silica-like (SiOx) layer was confirmed even at the early stage of degradation. It was also possible to estimate the thickness of the silica-like layer formed during corona exposure that is responsible for the loss and recovery of hydrophobicity. The surface hardness and hydrophilicity change of PDMS samples due to corona treatment were studied simultaneously with force distance measurements by atomic force microscopy (AFM). The adhesive force calculated from the pull-off force-distance curves showed that the adhesive force between the probe and the sample decreased with increasing corona treatment time, indicating hydrophobicity recovery. In addition to this, the increase in hardness after corona exposure provides indirect evidence of the formation of a silica-like layer. In all cases the hydrophilicity and the surface hardness of the PDMS samples increased directly after corona treatment and recovered with time. Two types of FTIR spectroscopy were used to analyse the surface of the polymer. / AFRIKAANSE OPSOMMINGS: Polidimetielsiloksaan (PDMS) word in buitelug hoogspanninginsulasie gebruik as gevolg van sy lae massa, weerstand teen vandalisme, verbeterde anti-kontaminasie werkverrigting en superieure hidrofobiese karakter. Die hidrofobiese oppervlakte kan egter gelydelik hidrofillies word onder uiterste omgewingsomstandighede en oor langdurige dienstyd. PDMS materiaal herstel egter nadat dit genoeg rustyd toegelaat is. Kamertemperatuur-gevulkaniseerde (KTV) PDMS met verskillende formulasies is in hierdie studie voorberei, aan korona ontlading blootgestel, geëvalueer en vergelyk. Die invloed van bymiddels soos verskillende tipes en hoeveelhede vuiler, asook addisionele lae molekulêre massa silikoonolie, op die herstel van hidrofobisiteit van die materiaal is ondersoek. Twee verskillende metodes van korona behandeling is ook geëvalueer. Die herstel van hidrofobisiteit van korona en UV-C verouderde PDMS monsters is met statiese kontakhoekmeting geëvalueer. Positronvernietigingspektroskopie (PVS) is 'n kragtige tegniek wat belangrike inligting oor die mikrostrukturele verandering van korona behandelde van KTV PDMS sowel as natuurlik-verouderde hoë temperatuur gevulkaniseerde (HTV) PDMS monsters gee. Die verskillende formulasies van die KTV PDMS monsters, sowel as die effek van die vullers, is met behulp van hierdie tegniek ondersoek. Die vorming van 'n dun, hoogskruisgebinde, anorganiese silika-agtige (SiOx) laag op die PDMS oppervlak, selfs tydens die vroeë stadium van degradasie, is bevestig. Dit was ook moontlik om die dikte van die silika-agtige laag wat gedurende die korona blootstelling gevorm het, en wat verantwoordelik is vir die verlies aan hidrofobisiteit, te bepaal. Die oppervlakhardheid en hidrofilisiteit verandering van PDMS monsters as gevolg van korona behandeling, was gelyktydig met krag-afstand metings deur middel van atoomkragmikroskopie (AKM) bestudeer. Die kleefkrag, soos bereken van aftrek kragafstandkurwes, dui daarop dat kleefkragte tussen die taster en die monster afneem met toenemende korona behandelingstyd, wat beduidend is op die herstel van hidrofobisiteit. Daarbenewens is die toename van oppervlakhardheid na korona blootstelling "n indirekte bewys van die formasie van 'n silika-agtige laag. In alle gevalle het die hidrofilisiteit en die oppervlakhardheid van die PDMS monsters toegeneem direk na afloop van korona behandeling en gevolglik herstel met tyd. Twee tipes IR spektroskopie metodes is gebruik vir die chemiese-oppervlak analises

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2005. / The cause of the largest number of faults on the Eskom main transmission system is unknown. It is believed that a non-uniform pollution layer along an insulator string is the reason for these anomalous flashovers. This non-uniform pollution layer results in the highest electric field strength, and thus the highest voltage, across the cleanest and driest discs. There thus exists a strong possibility that the anomalous flashover phenomenon is caused by a combination of mechanisms involving the pollution and air breakdown flashover mechanisms. This research project attempted to prove that flashover of the insulators is possible in accordance with the above model. Various experiments were set up in the high voltage laboratory and at a natural test site with a low source impedance supply attempting to simulate the conditions that lead to flashover in accordance with the hypothesis. All the tests done have not proven the non-uniform light pollution flashover mechanism successfully. However, future research has proposed an air breakdown flashover mechanism in light pollution conditions where the polluted part of the insulator string has a specific non-uniform distribution. Full scale testing in conditions similar to the normal operating conditions is proposed to prove the validity of this new hypothesis.