Utfört examensarbete undersöker vinkelfelet i mätkretsen för riktade jordfelsskydd och hur det påverkar dess felbortkoppling. Uppkomna vinkelfel i mätkretsen kan påverka det riktade jordfelsskyddet så att verklig felström och uppmätt felström inte stämmer överens, vilket kan leda till uteblivna eller obefogade felbortkopplingar. Vattenfall ställer krav på att vinkelfelet får uppgå till max ±2 grader för mätkretsen. Eftersom vinkelfelet i många fall har en hög påverkan på jordfelsskyddets noggrannhet undersöks vad Vattenfalls vinkelkrav egentligen innebär. Största orsaken till vinkelfelet uppstår oftast i strömtransformatorn och därför undersöks hur mycket två strömtransformatorer med olika klassificeringar som är vanliga i elnätet påverkar vinkelfelet i mätkretsen. Jordfel är det vanligast uppkomna felet i mellanspänningsnät och dess storlek beror till stor del på hur mycket kapacitivt bidrag som finns på linjerna samt värdet på nollpunktsresistorn. Det kapacitiva bidraget från linjen kompenseras centralt i fördelningsstationen och ibland lokalt ute på ledningen. Den högst tillåtna centralt kompenserade delen av en linje får vara 30 A, vid reservdrift av en linje kan denna del uppgå till 60 A. Vinkelfelet har en högre påverkan vid stora kapacitiva bidrag och vid låga värden på nollpunktsresistorn. I många fall sitter det flera riktade jordfelsskydd på samma linje där selektivitet alltid eftersträvas. Vinkelfelet kan ha en negativ påverkan på denna selektivitet. Genom beräkningar, simuleringar och provningar har ett antal slutsatser dragits. Vattenfalls vinkelkrav ger en otydlig bild angående tillåten påverkan på jordfelsskyddet. Med rätt val av strömtransformator påvisas att det troligtvis är möjligt att skärpa vinkelkravet. För att minska vinkelfelets påverkan kan den högst tillåtna centralt kompenserade delen minskas och/eller öka värdet på nollpunktsresistorn. En beloppsselektivitet på 1000 Ω kan inte alltid tillämpas då vissa fall kräver en beloppsselektivitet på 2000 Ω. Genom att sätta nollpunktsspänningen som utlösningsvillkor och nollpunktsströmmen som frigivningsvillkor kan enligt studien troligen ett noggrannare jordfelsskydd uppnås. / This bachelor's thesis examines the angular error in the measurement circuit for directional earth-fault protection and how this error affects the fault disconnection. Angular errors in the measurement circuit can affect the directional earth-fault protection in such a way that the real fault current and the measured fault current do not match. This can lead to missed or unwarranted fault disconnections. Vattenfall has a requirement which states that the angular error must not exceed ±2 degrees for the measurement circuit. Since the angular error in many cases has a high impact on the earth-fault accuracy, an investigation concerning what Vattenfalls angle requirement really means. The main cause of the angular error usually occurs in the current transformers and therefore two commonly used current transformers in the grid with different classifications and their impact on the angular error in the measurement circuit are examined. Ground fault is the most common fault which occurs in a distribution network, its size depends largely on the amount of capacitive current which the grid contributes with as well as the size of the neutral grounding resistor. The capacitive contribution of the grid compensates centrally in the distribution station and sometimes locally on the line. The maximum permitted centrally compensated part of a line is limited to 30 A, this central part can go up to 60 A in case the line needs to be fed from a second distribution station. The angular error has a higher impact if the capacitive contribution is high and for low values of the neutral grounding resistor. In many cases more than one earth-fault protection are found on the same line, in these cases selectivity is always pursued. The angular error may have a negative effect on the selectivity. By calculations, simulations and tests a number of conclusions can be drawn. Vattenfalls angle requirement gives an unclear picture concerning the permitted impact on the earthfault protection. Moreover selecting the correct current transformer demonstrates that the angular requirement can probably be sharpened. To reduce the influence of the angular error the maximum permitted centrally compensated part be reduced and/or the value of the neutral grounding resistor can be increased. A selectivity of 1000 Ω can not always be applied since certain cases require a selectivity of 2000 Ω. By setting the zero sequence voltage as the trigger condition and the zero sequence current as the realese condition, according to this study it may be possible to achieve a more accurate earth-fault protection.

No / This paper investigates the effect of channel bandwidth on the accuracy of AOA estimation algorithms based on the detection of the direct path. The accurate detection of the Line of Sight (LOS) signal in a multipath environment is crucial for reliable direction finding. In this work, the estimation algorithms are applied to the LOS component in the time domain channel impulse response which is acquired by applying the inverse Fourier transform to the simulated channel transfer function in the desired bandwidth. Different channel bandwidths as well as two AOA estimation methods have been considered in the modelling to investigate the performance of the standard deviation of angle estimation error. It has been shown that increasing the bandwidth in all simulated channel scenarios improves the estimation accuracy. / Seven Technologies Group, KTP project grant No. 008734.

O desempenho metrológico de uma Máquina de Medir a Três Coordenadas (MM3C) está relacionado com a sua capacidade de medir peças com a precisão requerida ou desejada. No entanto, como todo instrumento de medição, essas máquinas possuem erros que afetam as medições gerando o que se convencionou chamar de erros volumétricos. Tais erros podem ser obtidos através de modelos matemáticos que descrevem como os erros individuais de todos os componentes da MM3C se combinam por todo o volume de trabalho. Atualmente, no modelamento dos erros, adota-se a independência entre os erros individuais, entretanto, se analisada a geometria estrutural da máquina, verifica-se que existe dependência entre os erros de retilineidade e os erros angulares. O objetivo deste trabalho é expressar o erro angular em função do erro de retilineidade, possibilitando assim minimizar o número de calibrações necessárias e, consequentemente, o tempo de máquina parada requerido para o levantamento do seu comportamento metrológico. Para que se pudesse atingir o objetivo proposto, foram levantados os erros de retilineidade e os angulares de uma Máquina de Medir a Três Coordenadas da marca Brown & Sharp do tipo Ponte Móvel. Com esses dados e o conhecimento da geometria da máquina, os erros angulares foram equacionados, calculados e comparados com os obtidos experimentalmente. / The metrological performance of a Three Coordinate Measuring Machines (CMM) is related to the capacity of measuring workpieces with a required precision. As every measurement instrument, these machines undergo the effects of internal and external factors that affect the measurement, generating what has been denominated as volumetric errors. Such errors can be obtained through a mathematical model that simulates how the individual errors of the CMM are combined and propagated to any point within the machine working volume. Usually, the independence among the individual errors is adopted when the machine error model is built. However, if the machine geometry is analyzed, the dependence between the straightness error and the angular error can be noted. The objective of this work is to express the angular error as a function of the straightness error. The formulation proposed in this work to express this correlation minimizes the number of calibrations necessary to evaluate the machine behavior. A Brown & Sharp Moving Bridge Coordinate Measuring Machine was used for the experimental evaluation. With this data set and knowing the machine geometry, a mathematical expression relating straightness and angular error was obtained. The calculated error values were then compared with the errors experimentally measured.

O desempenho metrológico de uma Máquina de Medir a Três Coordenadas (MM3C) está relacionado com a sua capacidade de medir peças com a precisão requerida ou desejada. No entanto, como todo instrumento de medição, essas máquinas possuem erros que afetam as medições gerando o que se convencionou chamar de erros volumétricos. Tais erros podem ser obtidos através de modelos matemáticos que descrevem como os erros individuais de todos os componentes da MM3C se combinam por todo o volume de trabalho. Atualmente, no modelamento dos erros, adota-se a independência entre os erros individuais, entretanto, se analisada a geometria estrutural da máquina, verifica-se que existe dependência entre os erros de retilineidade e os erros angulares. O objetivo deste trabalho é expressar o erro angular em função do erro de retilineidade, possibilitando assim minimizar o número de calibrações necessárias e, consequentemente, o tempo de máquina parada requerido para o levantamento do seu comportamento metrológico. Para que se pudesse atingir o objetivo proposto, foram levantados os erros de retilineidade e os angulares de uma Máquina de Medir a Três Coordenadas da marca Brown & Sharp do tipo Ponte Móvel. Com esses dados e o conhecimento da geometria da máquina, os erros angulares foram equacionados, calculados e comparados com os obtidos experimentalmente. / The metrological performance of a Three Coordinate Measuring Machines (CMM) is related to the capacity of measuring workpieces with a required precision. As every measurement instrument, these machines undergo the effects of internal and external factors that affect the measurement, generating what has been denominated as volumetric errors. Such errors can be obtained through a mathematical model that simulates how the individual errors of the CMM are combined and propagated to any point within the machine working volume. Usually, the independence among the individual errors is adopted when the machine error model is built. However, if the machine geometry is analyzed, the dependence between the straightness error and the angular error can be noted. The objective of this work is to express the angular error as a function of the straightness error. The formulation proposed in this work to express this correlation minimizes the number of calibrations necessary to evaluate the machine behavior. A Brown & Sharp Moving Bridge Coordinate Measuring Machine was used for the experimental evaluation. With this data set and knowing the machine geometry, a mathematical expression relating straightness and angular error was obtained. The calculated error values were then compared with the errors experimentally measured.

Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2011. / ENGLISH ABSTRACT: The In the Physiotherapy Division of the Faculty of Health Sciences on the Tygerberg Hospital Campus of the University of Stellenbosch, the challenge arose to develop a portable, affordable and yet accurate 3D measurement machine for the assessment of posture in school children in their classroom environment. Currently Division already uses a state-of-the-art VICON commercial medical measuring machine to measure human posture in 3D in their physiotherapy clinic, but the system is not portable and is too expensive to cart around to different places for testing. To respond to this challenge, this Master’s thesis designed and analyzed a machine and its supporting system through both research on stereo-vision methodologies and empirical appraisal in the field. In the development process, the research was required to overcome the limitations posed by small image resolutions and lens distortions that are typical of cheap cameras. The academic challenge lay in the development of an error prediction model through Jacobian derivation and Error Propagation Law, to predict uncertainties of angular measurement calculated by the system. The research culminated in a system that is comparable in accuracy to the VICON within 3mm, and that has 1.5mm absolute accuracy within its own system for a measurement volume radius of 2.5 m. As such, the developed error model is an exact predictor of the angular error to within 0.02° of arc. These results, for both system accuracy and the error model, exceed the expectations on the basis of the initial challenge of the system. The development of the machine was successful in providing a prototype tool that is suitable for commercial development for use by physiotherapists in human posture measurement and assessment. In its current incarnation, the machine will also serve the Engineering Faculty as the most fundamental form of a three-dimensional measuring apparatus using only basic theories and algorithms of stereo-vision, thereby providing a basic experimental platform from which further scientific research on the theory and application of computer vision can be conducted. / AFRIKAANSE OPSOMMING: Die Fisioterapie Afdeling van die Fakulteit Gesondheidswetenskappe op die Tygerberg kampus van die Universiteit van Stellenbosch gebruik ’n allernuutste VICON kommersiële mediese meettoestel om menslike postuur in drie dimensies te meet. Vanuit hierdie Afdeling het die uitdaging ontstaan om ’n draagbare, bekostigbare, maar tog akkurate, drie-dimensionele meetapparaat geskik vir die meet van die postuur van skoolkinders in die klaskamer te ontwikkel. In aanvaarding van hierdie uitdaging, het hierdie Magistertesis ’n toestel en ondersteuningstels ontwerp en ontleed deur beide navorsing in stereo-visie metodiek en terplaatse beoordeling. In die ontwikkelingsproses moes die navorsing die beperkings wat deur klein-beeld resolusie en lens-distorsie (tipies van goedkoop kameras) meegebring word, oorkom. Die akademiese uitdaging lê in die ontwikkeling van ’n voorspellende foutmodel deur van die Jacobianse-afleiding en die Fout Propageringswet gebruik te maak om onsekerheid van hoeksberekening deur die stelsel te voorspel. Die navorsing het gelei tot ’n stelsel wat binne 3mm vergelykbaar is in akkuraatheid met dié van die VICON en ook 1.5mm absolute interne akkuraatheid het in ’n meet-volume radius van 2.5m radius. Die ontwikkelde foutmodel is dus ’n presiese voorspeller van hoekfout tot binne 0.02° van boog. Die resultate met betrekking tot beide die akkuraatheid en die foutmodel het die oorspronklike verwagtinge van die uitdaging oortref. Die ontwikkeling was suksesvol in die skep van ’n prototipe-toestel geskik vir kommersiële ontwikkeling, vir gebruik deur fisioterapeute in die meting en evaluering van menslike postuur. Die stelsel is in sy fundamentele vorm, deur die gebruik van slegs basiese teorieë en algoritmes van stereo-visie, funksioneer as ’n drie-dimensionele meetapparaat. In die fundamentele vorm sal die stelsel die Ingenieursfakulteit dien as ’n basiese eksperimentele platform waarop verdere wetenskaplike navorsing in die teorie en toepassing van rekenaar-visie gedoen kan word.