Call number: LD2668 .T4 1964 C15 / Master of Science

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

An important aspect for precision guidance, navigation, and control for lunar operations is environmental modeling. In particular, consider gravity field modeling. Available gravity field models for the Moon reach degree and order 165 requiring the use and storage of approximately 26,000 spherical harmonic coefficients. Although the high degree and order provide a means by which to accurately predict trajectories within the influence of the Moon's gravitational field, the size of these models makes using them computationally expensive and restricts their use in design environments with limited computer memory and storage. It is desirable to determine reduced complexity realizations of the gravitational models to lower the computational burden while retaining the structure of the original gravitational field for use in rapid design environments. The extended Kalman filter and the unscented Kalman filter are used to create reduced order models and are compared against a simple truncation based reduction method. Both variations of the Kalman filter out perform the truncation based method as a means by which to reduce the complexity of the gravitational field. The extended Kalman filter and unscented Kalman filter were able to achieve good estimates of position while reducing the number of spherical harmonic coefficients used in gravitational acceleration calculations by approximately 5,400, greatly increasing the speed of the calculations while reducing the required computer allocation. / text

Harmonic domain models have been developed for Thyristor Controller Reactors (TCR) and other power electronic devices. Recently, these models have been extended to describe not just the steady-state harmonic interactions but harmonic transients as well. However, these dynamic models consistently do not incorporate models for controls. On the other hand, for the TCR as a FACTS Controller, dynamic models are available in which only the fundamental frequency component of the Controller is included; excluding harmonic interactions presumes that these do not affect the dynamics of the Controller. This thesis describes the development of a Harmonic State Space (HSS) model of a three phase TCR. As an extended state space description, this model describes the dynamics of the Controller while capturing harmonic interactions. It also includes the effect of switching instant variation which significantly improves the effectiveness of the model and allows the controller feedback characteristics to be included. The result of this model was validated with a purely time-domain simulation in PSCAD/EMTDC. Using the HSS to model a power system with TCR, it is illustrated that harmonic interactions play a significant role in the dynamics of the system. It is observed that for the specific system analysed, the least-damped pole-pair which dominates the dynamics of the system is associated with the 5th harmonic. Failure to include interactions with this specific harmonic produces an inaccurate dynamic description. Preliminary to the development of HSS model, a linearised harmonic domain model of a TCR which establishes the harmonic interactions across the device is also developed. Results of this model are validated with a time-domain simulation. This characterisation paves the way for a reduced harmonic state space model that is used in the HSS model. The principles and procedures established in this thesis can be applied to the development of models for other FACTS Controllers or HVDC links.

Frequency domain models for power electronic circuits are either based on iterative techniques such as Newton's method or linearised around an operating point. Iterative frequency domain models provide great accuracy as they are capable of calculating the exact switching instants of the device. On the other hand, the accuracy of a linearised frequency domain model relies on the magnitude of input waveform to be small so that the circuit's operating point does not vary or varies very little. However, an important advantage of a linearised model is its ability to provide insight into waveform distortion interaction, more specifically, the frequency cross-coupling around a power electronic circuit. In general, a linearised model for harmonic analysis would not normally include the description of feedback control. Likewise a linearised model for control analysis would usually disregard frequency interactions above the fundamental (or the most significant component); that is assuming the cross-coupling between harmonic frequencies does not affect the dynamics of control. However, this thesis proposes that a linearised model for control analysis shall also include the complete description of frequency cross-coupling between harmonics to produce the correct dynamic response. This thesis presents a harmonic state-space (HSS) model of an HVdc converter that incorporates the full effect of varying switching instants, both through control and commutation period dynamics, while remaining within the constraints of a linear time-invariant (LTI) system. An example is given using the HSS model to explain how a close to fifth harmonic resonance contributes to the dominant system response through the frequency cross-coupling of the converter and the controller feedback loop. The response of the system is validated against a time domain model built in PSCAD/EMTDC, and more importantly, the correct response cannot be produced without including the harmonic interactions beyond the fundamental frequency component.

The present power system is loaded with sophisticated energy conversion technologies like solid state converters. With the rapid advance in semiconductor technology, power electronics have provided new devices that are highly efficient and reliable. These devices are inherently non-linear, which causes the current to deviate from sinusoidal conditions. This phenomenon is known as harmonic current distortion. Multiple consumers are connected to the utility at the point of common coupling. Harmonic currents are then transmitted into the distribution system by various solid state users and this could lead to voltage distortion. Harmonic distortion is just one of the power quality fields and is not desirable in a power system. Distortion levels could cause multiple problems in the form of additional heating, increased power losses and even failing of sensitive equipment. Utility companies like Eskom have power quality monitors on various points in their distribution system. Data measurements are taken at a single point of delivery during certain time intervals and stored on a database. Multiple harmonic measurements will not be able to describe distortion patterns of the whole distribution system. Analysis must be done on this information to translate it to useful managerial information. The aim of this project is to develop a benchmarking methodology that could aid the supply industry with useful information to effectively manage harmonic distortion in a distribution system. The methodology will implement distortion indexes set forth by the Electrical Power Research Institute [3], which will describe distortion levels in a qualitative and quantitative way. Harmonic measurements of the past two years will be used to test the methodology. The information is obtained from Eskom’s database and will benchmark the North-West Province distribution network [40]. This proposed methodology will aim to aid institutions like NERSA to establish a reliable power quality management system. / Thesis (M.Ing. (Nuclear Engineering))--North-West University, Potchefstroom Campus, 2012

A significant component of recent space exploration has been unmanned mission to comets and asteroids. The increase in interest for these bodies necessitates an increase in demand for higher fidelity trajectory simulations in order to assure mission success. Most available methods for simulating trajectories about asymmetric bodies assume they are of uniform density. This thesis examines a hybrid method that merges a mass concentration ("mascon") model and a spherical harmonic model using the "Brillouin sphere" as the interface. This joint model will be used for simulating trajectories about variable density bodies and, in particular, contact binary asteroids and comets. The scope of this thesis is confined to the analysis and characterization of the spherical harmonic modeling method in which three bodies of increasing asymmetrical severity are used as test cases: Earth, asteroid 101955 Bennu, and asteroid 25143 Itokawa. Since the zonal harmonics are well defined for Earth, it is used as the initial baseline for the method. Trajectories in the equatorial plane and inclined to this plane are simulated to analyze the dynamical behavior of the environment around each of the three bodies. There are multiple degrees of freedom in the spherical harmonic modeling method which are characterized as follows: (1) The radius of the Brillouin sphere is varied as a function of the altitude of the simulated orbit, (2) The truncation degree of the series is chosen based upon the error incurred in the acceleration field on the chosen Brillouin sphere, and (3) The gravitational potential and acceleration field are calculated using the determined radial location of the Brillouin sphere and the truncation degree. An ideal Brillouin sphere radius and truncation degree are able to be determined as a function of a given orbit where the error in the acceleration field is locally minimized. The dual-density model for a contact binary is found to more accurately describe the dynamical environment around Asteroid 25143 Itokawa compared to the single density model.

M.Ing. / The study looks into the impact of harmonic distortion on power-plant equipment in general, and then focuses on the impact it has on power transformers operating near the thermal limit. The feasibility of the study is firstly evaluated and then the theory on harmonics and transformer losses is analysed. The study had been narrowed down to power transformers due to the high numbers of failures nationally and internationally attributed to unknown causes. A transformer model is then developed through theoretical considerations. Finally, a case study is done on the capability of a fully loaded transformer under harmonics conditions evaluated through transformer capability calculations and the proposed transformer model. Thereafter the transformer model developed is verified with measured results. The main impact of harmonic current distortion on power transformers is an increase in the rated power losses that results in a temperature rise inside the power transformer. The heat build-up can lead to degradation of insulation, which can shorten the transformer’s life and lead to eventual breakdown. The harmonic current distortion impacts transformer losses – namely, ohmic losses, the winding eddy current losses and other stray losses. All of these harmonic effects on transformer losses are verified theoretically, mathematically and practically. The harmonic impact on the transformer capability is then evaluated through a numerical example of a transformer feeding a harmonic load. The transformer capability is determined via two methods – namely, harmonic capability calculations in the standard “IEEE Recommended Practice for Establishing Transformer Capability when Supplying Nonsinusoidal Load Currents”, [11] and a proposed transformer model derived from theoretical and mathematical analysis. The results show that an increase in the winding eddy current losses can decrease the maximum permissible nonsinusoidal load current substantially. If the load current of the transformer is derated accordingly it translates into a loss of the output power capacity of the power transformer. The standard recommended capability calculations for winding eddy current losses are conservative and not satisfactorily accurate. This results in a large loss of power capacity. The proposed transformer model includes a parameter that estimates the winding eddy current loss in the transformer that results in a smaller loss in power capacity. Furthermore, it was shown that the harmonic current distortion levels could exceed the permissible levels although the harmonic voltage distortion levels are within acceptable levels. The proposed transformer equivalent model is thereafter practically verified with experimental results of papers published by M.A.S. Masoum, E.F. Fuchs and D.J. Roesler, [19], [20] and [29].

M.Ing. / With the increased use of nonlinear loads such as variable speed motor drives and rectifiers, the voltages and currents on the power system grid are no longer sinusoidal. These non-sinusoidal waveforms cannot be analyzed by conventional power theories and the usual recourse is to decompose the nonlinear waveform into a set of harmonics. Harmonic voltage and current components are detrimental to the power system and may cause additional losses, or premature failure of equipment, and as such they have a definite influence on the quality of supply. This thesis shows the limitations and potential pitfalls of harmonic decomposition and other power theories, and examines various methods used for identifying, quantifying and modelling nonlinear loads. The aim of the thesis is to evaluate methods for attaching a specific disturbance or non-linearity on the voltage waveform to a specific load connected at the point of common coupling. The power theories examined include the total complex power, the IEEE working group definitions of apparent power, true power factor and harmonic adjusted power factor. Some new techniques for estimating the degree to which a load is disturbing the voltage at the point of common coupling is introduced, including the calculation of correlation indices, and the the use of wavelets.

Avec les progrès de la technologie, la densité de puissance des appareils électriques augmente, ce qui conduit à une augmentation des interférences électromagnétiques entre deux systèmes d’électroniques de puissance. Ces interférences peuvent engendrer un dysfonctionnement des appareillages. Afin d’éviter de tels problèmes, une grande quantité de vérifications expérimentaux sont nécessaires après le développement d’un prototype, ce qui conduira à un surcoût important dans son cycle industriel. Cette thèse a pour objectif de prendre en compte des problèmes de compatibilité électromagnétique en champ proche dès la phase de conception d’un produit. Ceci est basé sur le développement en harmoniques sphériques du rayonnement parasite engendré par les dispositifs ou les composants d’un dispositif. Les coefficients harmoniques d’un dispositif permettent non seulement de modéliser ses champs proches par une source ponctuelle, mais également de déterminer le couplage inductif avec les autres. Dans ce contexte, la méthode du développement multipolaire est étudiée théoriquement, numériquement (par le logiciel Flux3D) et expérimentalement dans ce travail. Dans ce document, le nouveau système de mesure automatisé est présenté et différentes approches liées à la solution de ce problème sont étudiées, tels que le choix optimal d’origine du développement, la compensation d’erreurs des mesures dues aux sources secondaires, l’étude de propagation d’incertitude dans le problème inverse et prise en compte d’informations a priori, etc. / With the advances in technology, the power density of electrical equipment is increasing, which leads to an increase in electromagnetic interference between two power electronic systems. This interference may cause the electronic equipment to malfunction. In order to avoid such problems, a large number of experimental verifications are necessary after the development of a prototype, which leads to a significant additional cost in its industrial cycle. This thesis aims at taking into account the problems of near-field electromagnetic compatibility in the design phase of a product. The method is based on the development in spherical harmonics of the parasitic radiation generated by the devices or the components of the device. The harmonic coefficients of a device make it possible not only to model its near field by a punctual source, but also to determine the inductive coupling with the others. In this context, the multipole expansion method is studied theoretically, numerically (by the software Flux3D) and experimentally in this work. In this document, the new automated measuring system is presented and different approaches related to the solution of this problem are then studied, such as the optimal choice of the development origin, the error compensation of the measurements due to the secondary sources, the study of the propagation of uncertainty in the inverse problem and how to take into account the a priori information, etc.