There are several approaches for creating double-ended heaps from the single-ended heaps. We build on one of them, the leaf correspondence heap, to create a generic double ended heap scheme called L-correspondence heap. This will broaden the class of eligible base single-ended heaps (e.g. by Fibonacci heap, Rank-pairing heap) and make the operations Decrease and Increase possible. We show this approach on specific examples for three different single-ended base heaps and give time complexity bounds for all operations. Another result is that for these three examples, the expected amortized time for Decrease and Increase operations in the L-correspondence heap is bounded by a constant.

Fault location within electric power systems is an important topic that helps reduce outage duration and increases reliability of the system. This paper explores the topic of fault location using traveling waves generated by fault conditions and the discrete wavelet transform used for time-frequency analysis. The single-ended and double-ended traveling wave methods are presented and evaluated on a single circuit and double circuit 500kV system modeled using MATLAB SIMULINK. Results are compared on the basis of wavelet used for analysis, sampling rate, and fault resistance.

No description available.

This master thesis presents the development of an auxiliary power supply to provide energy to sensors, gate drivers, instrumentation circuits and control of a three-stage Solid State Transformer (SST). These devices require an insulated power supply of ±15V and 5V. For reason of reliability and modularity, a distributed auxiliary source is proposed. Thus, it is necessary a power supply to provide energy to the low voltage (LV) side and another to the medium voltage (MV) side. With this proposal, the auxiliary power supply does not need to have the same galvanic insulation of the SST, 25kV. However, a local power supply must operate at high voltage levels and, consequently, contain a high step-down voltage gain. Relative to LV side, the most generally used topologies as an auxiliary power supply are discussed. However, these topologies cannot be used at the MV converters, due to the high voltage stress levels involved. A study of topologies used on medium and high voltage and which enable to reach a high step-down voltage gain is realized, and two interesting topologies for this application were found. One of them uses a Flying capacitor converter connected in cascade with a Double-Ended Flyback converter. The Flying capacitor converter lowers the DC bus voltage in a controlled manner to low voltage levels. So the Double-ended Flyback converter operates in LV and provides the insulated outputs to command circuits of SST. The other topology is a unidirectional four-level NPC converter operating as Double-ended Flyback converter. For this case, a modulation strategy that allows the converter to reach a high step-down voltage gain was also proposed. These topologies were evaluated and the one which showed the best result was the four-level Double-ended Flyback converter. This converter was implemented and the experimental results prove to be effective. For the LV side, a Half-bridge LLC resonant converter as auxiliary power supply was used. This converter operates in ZVS and performs the output voltage regulation through the operating frequency variation. The experimental results of this converter are also presented. / Este trabalho de mestrado apresenta o desenvolvimento de fontes auxiliares para alimentar sensores, circuitos de comando, instrumentação e o controle de um Transformador de Estado Sólido (SST) de três estágios. Estes dispositivos necessitam de alimentação isolada com tensões de ±15V e 5V e por questões de confiabilidade e modularidade, propõe-se a utilização de fontes auxiliares distribuídas. Assim, emprega-se uma fonte auxiliar para alimentar o lado de média tensão (MT) e outra para alimentar o lado de baixa tensão (BT). Com essa proposta, as fontes auxiliares não necessitam ter a mesma isolação galvânica do SST, 25kV. Entretanto, uma das fontes locais deve operar em níveis de tensão elevados e, por consequência, apresentar baixo ganho estático. No lado de BT, as principais topologias normalmente utilizadas como fonte auxiliar são discutidas. No entanto, devido aos altos níveis de tensão envolvidos, estas topologias não podem ser aplicadas ao conversor que opera em MT. Um estudo sobre topologias aplicadas a média tensão e que possibilitam alcançar um baixo ganho estático é realizado, sendo que duas topologias se mostram interessantes para esta aplicação. Uma consiste na utilização de um conversor de capacitores flutuantes conectado em cascata com um conversor Double-Ended Flyback. O conversor de capacitores flutuantes rebaixa a tensão do barramento CC, de forma controlada, para baixa tensão. Assim o Double-Ended Flyback opera em BT e fornece as saídas isoladas para alimentar os circuitos de comando do SST. A outra topologia trata-se de um conversor NPC de quatro níveis unidirecional operando como conversor Double-Ended Flyback. Para este caso, também foi proposta uma estratégia de modulação que permite o conversor alcançar o baixo ganho estático. Essas topologias foram avaliadas, apresentando melhor resultado a esta aplicação o conversor Double-ended Flyback de quatro níveis, conforme será demonstrado neste trabalho. Esse conversor foi implementado e os resultados experimentais comprovam o seu funcionamento. Para a fonte do lado de BT utilizou-se um conversor Half-Bridge LLC ressonante que opera em ZVS e realiza a regulação da tensão de saída pela variação da frequência de operação. Os resultados experimentais deste conversor também são apresentados.

In vorliegender Arbeit werden Aufbau und Charakterisierung des beidseitig antastenden Interferometers vorgestellt, mit dem die absolute Länge prismatischer Körper ohne Anschub an eine Referenzplatte gemessen werden kann, was Verformungen durch Wechselwirkungen von Endmaßen mit angeschobenen Platten verhindern kann. Die Messunsicherheit im Vergleich zum Prototypen konnte aufgrund eines verbesserten Temperaturmesssystems, eines temperaturstabilisierten Vakuumkessels, Optiken mit besserer Ebenheit und Kameras größerer Auflösung deutlich reduziert werden. Das entwickelte Justageverfahren mit Autokollimationsscan und die Korrektur von Wellenfrontaberrationen tragen ebenso zu einer reduzierten Messunsicherheit bei, wie der durch optimale Ausrichtung der keilförmigen Strahlteilerplatten reduzierte Einfluss von Störinterferenzen. Vergleichsmessungen eines Stahl- und eines Filterglasendmaßes mit einseitig antastenden Interferometern zeigten mit Differenzen im Bereich von 0,4 bis 2,6 nm im Rahmen der Unsicherheiten konsistente Probenlängen, was die gute Eignung des beidseitig antastenden Interferometers für absolute Längenmessungen zeigt. Vergleichsmessungen an Silizium ergaben für die beidseitig antastend gemessenen Längen gegenüber im einseitig antastenden Interferometer gemessenen Längen deutlich geringere Werte und eine reproduzierbare Differenz zwischen den mit 532 und 633 nm gemessenen Längen von etwa 4 nm. Diese Effekte sind vermutlich auf die sich beim beidseitig antastenden Verfahren deutlich stärker auswirkenden Material- und Oberflächeneigenschaften zurückzuführen. Das volle Potential des beidseitig antastenden Interferometers entfaltet sich aufgrund des großen Messunsicherheitsbeitrages der Rauheit und des Phasensprungs bei der Reflexion vor allem bei der Messung von Längenänderungen, wie der thermischen Ausdehnung oder der Langzeitstabilität verschiedener Materialien, für die die Effekte der Rauheit und des Phasensprungs eine vernachlässigbare Rolle spielen. / The present thesis adresses the setup and characterization of PTB´s double-ended interferometer, which allows for absolute length measurement of prismatic bodies without the need for wringing to a platen, which prevents deformation caused by their interaction. In comparison with PTB´s prototype, the measurement uncertainty has been substantially reduced due to an improved temperature measurement system, a temperature stabilized vacuum chamber, optics of better flatness and cameras with higher resolution. Further reduction of the measurement uncertainty has been achieved by the developed adjustment procedure including an autocollimation scanning and a correction of the influence of wavefront aberrations. Multiple configurations of orientation of the beamsplitter plate wedges were tested to minimize the influence of parasitic interferences. Comparison measurements against single-ended interferometers on a steel and a filter glas gauge block resulted in deviations of the measured length in the range of 0.4 to 2.6 nm, which is in good agreement with measurement uncertainties. This proves the capability of absolute length measurement of the double-ended interferometer. Comparison measurements on silicon gauge blocks resulted in significantly shorter lengths than those measured in single-ended interferometers with a reproducible length difference of 4 nm for the different used wavelengths of 532 and 633nm. Those effects are presumably based on material and surface characteristics which seem to have a much stronger impact on the measured length when the sample is not wrung to a platen. Due to the large contribution of the roughness and the phase change on reflection to the measurement uncertainty, the full potential of the double ended interferometer will unfold for measurements on lengths changes, like measurement of the thermal expansion or long term stability of different materials, for which the influence of the roughness and phase change on reflection can be neglected.