<p>Disturbances in power systems are common and they result in electromechanical oscillations called power swing. The power swings could be severe and it may lead to loss of synchronism among the interconnected generators. This is referred to as out-of-step condition. The voltage and current swings during an out-of-step condition damage power system equipments and also cause unwanted operations of various protective devices. The protection systems require an effective algorithm for fast and accurate detection of out-of-step condition. </p> <p>This research is focused on the development of a simple and effective out-of-step relay capable of detecting out-of-step condition in a complex power system. To achieve this, the research has gone through four distinct stages: development of an algorithm, simulation, hardware implementation and its testing. </p> <p>An out-of-step algorithm is proposed based on equal area criterion in time domain. The equal area criterion in time domain is obtained by modifying the traditional equal area criterion in power angle domain. A single machine infinite bus system, a two machine infinite bus system and a three machine infinite bus system and a 17-bus multiple machines system are used as case studies and are modeled using simulation tool(PSCAD). </p> <p>To test the effectiveness of the proposed algorithm, various out-of-step conditions are simulated by applying disturbances at various locations in the above chosen power system configurations. For hardware implementation and testing of the algorithm, a digital signal processing board (ADSP-BF533 from Analog Devices ) is used. To test the performance of the developed digital relay in a closed loop, real time power system signals are necessary and therefore for this purpose, a Real Time Digital Simulator (RTDS) available in the power research laboratory is used. The RTDS simulator mimics the actual power systems in real time. The signals required by the relays can be tapped from the RTDS and the signals coming from relay can be fed back into the RTDS, which makes the closed loop testing of the digital relay possible. This research has yielded a simple out-of-step algorithm and unlike the other out-of-step detection techniques proposed in the literature does not need offline system studies to arrive at a solution.The developed digital out-of-step relay is capable of making decisions based only on the information available from its point of installation, thus it avoids the communication devices which is advantageous for the out-of-step protection of a complex power system. Finally, the simulation results show that the proposed algorithm can be applied to any power configurations and is faster compared to the conventional concentric rectangle schemes used in the literature.</p>

<p>Disturbances in power systems are common and they result in electromechanical oscillations called power swing. The power swings could be severe and it may lead to loss of synchronism among the interconnected generators. This is referred to as out-of-step condition. The voltage and current swings during an out-of-step condition damage power system equipments and also cause unwanted operations of various protective devices. The protection systems require an effective algorithm for fast and accurate detection of out-of-step condition. </p> <p>This research is focused on the development of a simple and effective out-of-step relay capable of detecting out-of-step condition in a complex power system. To achieve this, the research has gone through four distinct stages: development of an algorithm, simulation, hardware implementation and its testing. </p> <p>An out-of-step algorithm is proposed based on equal area criterion in time domain. The equal area criterion in time domain is obtained by modifying the traditional equal area criterion in power angle domain. A single machine infinite bus system, a two machine infinite bus system and a three machine infinite bus system and a 17-bus multiple machines system are used as case studies and are modeled using simulation tool(PSCAD). </p> <p>To test the effectiveness of the proposed algorithm, various out-of-step conditions are simulated by applying disturbances at various locations in the above chosen power system configurations. For hardware implementation and testing of the algorithm, a digital signal processing board (ADSP-BF533 from Analog Devices ) is used. To test the performance of the developed digital relay in a closed loop, real time power system signals are necessary and therefore for this purpose, a Real Time Digital Simulator (RTDS) available in the power research laboratory is used. The RTDS simulator mimics the actual power systems in real time. The signals required by the relays can be tapped from the RTDS and the signals coming from relay can be fed back into the RTDS, which makes the closed loop testing of the digital relay possible. This research has yielded a simple out-of-step algorithm and unlike the other out-of-step detection techniques proposed in the literature does not need offline system studies to arrive at a solution.The developed digital out-of-step relay is capable of making decisions based only on the information available from its point of installation, thus it avoids the communication devices which is advantageous for the out-of-step protection of a complex power system. Finally, the simulation results show that the proposed algorithm can be applied to any power configurations and is faster compared to the conventional concentric rectangle schemes used in the literature.</p>

Stability analysis methods may be categorized by two major stability analysis methods: small-signal stability and transient stability analyses. Transient stability methods are further categorized into two major categories: numerical methods based on numerical integration, and direct methods. The purpose of this thesis is to study and investigate transient stability analysis using a combination of step-by-step and direct methods using Equal Area Criterion. The proposed method is extended for transient stability analysis of multi machine power systems. The proposed method calculates the potential and kinetic energies for all machines in a power system and then compares the largest group of kinetic energies to the smallest groups of potential energies. A decision based on the comparison can be made to determine stability of the power system. The proposed method is used to simulate the IEEE 39 Bus system to verify its effectiveness by comparison to the results obtained by pure numerical methods.

The rotor shaft of a synchronous machine can experience severe mechanical stress due to torque pulsations during a pole-slip condition. All pole-slip protection relays currently on the market use the impedance pole-slip protection method to detect a pole-slip. No commercial relay currently available can predict accurately when a generator is about to experience a damaging pole-slip. All the relays will only trip a generator after it has pole-slipped one or more times. Severe mechanical damage could be caused to a machine after only one pole-slip. It is therefore essential to enhance pole-slip protection relays to such an extent that it can trip a generator before it pole slips. The proposed pole-slip protection function must predict when a generator will become unstable during a network fault. As soon as instability is predicted, the generator must be tripped before the fault is cleared to avoid damaging post-fault torque effects. Conventional impedance pole-slip protection methods are are also discussed and the shortcomings of impedance pole-slip protection are investigated. The new pole-slip protection function was designed by using PSCAD. Detailed PSCAD simulations on different network configurations proved that the new pole-slip protection function will trip a generator before a damaging pole-slip occurs. The new pole-slip protection function was also implemented on an ABB REM543 multifunctional protection relay and tested on a RTDS. The concept of the new pole-slip function was successfully demonstrated on the protection relay. The operation of conventional impedance scheme relays was compared with the proposed pole-slip function for different fault conditions. Although the new pole-slip protection function is more complex than the existing impedance functions, it was concluded that similar skills are required to test and commission the new protection function. The new pole-slip function outperforms the impedance protection methods, since the new protection function can trip the generator before it pole-slips. / PhD (Electrical Engineering), North-West University, Potchefstroom Campus, 2011

The rotor shaft of a synchronous machine can experience severe mechanical stress due to torque pulsations during a pole-slip condition. All pole-slip protection relays currently on the market use the impedance pole-slip protection method to detect a pole-slip. No commercial relay currently available can predict accurately when a generator is about to experience a damaging pole-slip. All the relays will only trip a generator after it has pole-slipped one or more times. Severe mechanical damage could be caused to a machine after only one pole-slip. It is therefore essential to enhance pole-slip protection relays to such an extent that it can trip a generator before it pole slips. The proposed pole-slip protection function must predict when a generator will become unstable during a network fault. As soon as instability is predicted, the generator must be tripped before the fault is cleared to avoid damaging post-fault torque effects. Conventional impedance pole-slip protection methods are are also discussed and the shortcomings of impedance pole-slip protection are investigated. The new pole-slip protection function was designed by using PSCAD. Detailed PSCAD simulations on different network configurations proved that the new pole-slip protection function will trip a generator before a damaging pole-slip occurs. The new pole-slip protection function was also implemented on an ABB REM543 multifunctional protection relay and tested on a RTDS. The concept of the new pole-slip function was successfully demonstrated on the protection relay. The operation of conventional impedance scheme relays was compared with the proposed pole-slip function for different fault conditions. Although the new pole-slip protection function is more complex than the existing impedance functions, it was concluded that similar skills are required to test and commission the new protection function. The new pole-slip function outperforms the impedance protection methods, since the new protection function can trip the generator before it pole-slips. / PhD (Electrical Engineering), North-West University, Potchefstroom Campus, 2011

In today’s dynamic environment, where product demands are highly volatile and unstable, the ability to design and operate manufacturing facilities that are robust with respect to uncertainty and variability is becoming increasingly important to the success of any manufacturing firm in order to operate effectively in such an environment. Hence manufacturing facilities must be able to exhibit high levels of robustness and stability in order to deal with changing market demands. In general, Facility Layout Problem (FLP) is concerned with the allocation of the departments or machines in a facility with an objective to minimize the total material handling cost (MHC) of moving the required materials between pairs of departments. Most FLP approaches assume the flow between departments is deterministic, certain and constant over the entire time planning horizon. Changes in product demand and product mix in a dynamic environment invalidate these assumptions. Therefore there is a need for stochastic FLP approaches that aim to assess the impact of uncertainty and accommodate any possible changes in future product demands.This research focuses on stochastic FLP with an objective to present a methodology in the form of a framework that allows the layout designer to incorporate uncertainty in product demands into the design of a facility. In order to accomplish this objective, a measure of impact of this uncertainty is required. Two solution methods for single and multi period stochastic FLPs are presented to quantify the impact of product demand uncertainty to facility layout designs in terms of robustness (MHC) and variability (standard deviation). In the first method, a hybrid (simulation) approach which considers the development of a simulation model and integration of this model with the VIPPLANOPT 2006 algorithm is presented. In the second method, mathematical formulations of analytic robust and stable indices are developed along with the use of VIPPLANOPT for solution procedure. Several case studies are developed along with numerical examples and case studies from the literature are used to demonstrate the proposed methodology and the application of the two methods to address different aspects of stochastic FLP both analytically and via the simulation method. Through experimentation, the proposed framework with solution approaches has proven to be effective in evaluating the robustness and stability of facility layout designs with practical assumptions such as deletion and expansion of departments in a stochastic environment and in applying the analysis results of the analytic and simulation indices to reduce the impact of errors and make better decisions

Heterogenität von Umweltbedingungen gilt als einer der wichtigsten Faktoren für die Verteilung von Artenreichtum weltweit. Laut der Habitatheterogenität-Hypothese bieten räumlich heterogenere Gebiete eine höhere Vielfalt an Umweltparametern und weisen mehr Refugien und Möglichkeiten zur Isolation und Radiation auf. Dadurch begünstigen sie Koexistenz, Persistenz und Diversifikation von Arten. Die Erforschung potentieller positiver Effekte von Heterogenität auf Artenreichtum fasziniert Ökologen und Evolutionsbiologen seit Jahrzehnten. Dementsprechend existieren zahlreiche Studien über die Beziehung zwischen Heterogenität und dem Artenreichum verschiedener Taxa unter unterschiedlichsten ökologischen Gegebenheiten. Heterogenität kann sich auf biotische und abiotische Bedingungen beziehen und wurde daher mittels vieler verschiedener Maße quantifiziert. Diese finden zudem auf sehr unterschiedlichen Skalen Anwendung, die von der Architektur einer einzelnen Pflanze über Landschaftsstruktur bis hin zu topographischem Relief reichen. Die Vielfalt der Maße sowie eine oft unbestimmte und inkonsistente Terminologie, die in der Forschung zu Heterogenität-Artenreichtums-Beziehungen verwendet wird, erschweren das Verständnis, den Vergleich und die Synthese der entsprechenden Studien. Desweiteren gibt es große Unterschiede in der Form und Stärke der Beziehungen: während viele Studien einen positiven Zusammenhang zwischen Heterogenität und Artenreichtum nachwiesen, sind auch negative, unimodale und nicht signifikante Zusammenhänge bekannt. Deshalb existiert bisher kein eindeutiger Konsens bezüglich der generellen Heterogenität-Artenreichtums-Beziehung. Im Rahmen der vorliegenden Dissertation fertige ich ein systematisches Literaturreview an, mit dem ich einen Überblick über die verwendeten Maße und Begriffe gebe, die bisher in der Forschung zu Heterogenität-Artenreichtums-Beziehungen Anwendung fanden. Basierend auf 192 Studien identifiziere ich 165 verschiedene Heterogenitätsmaße, die ich bezüglich ihrer Themenfelder und Berechnungsmethoden klassifiziere. Es werden fünf Themenfelder unterschieden, nämlich Landbedeckung und Vegetation als biotische Komponenten, und Klima, Boden und Topographie als abiotische Komponenten von Heterogenität. Desweiteren identifiziere ich achtzehn verschiedene Berechnungsmethoden, wie z.B. Anzahl, Standardabweichung und Variationskoeffizient. Die Höhenspannweite in einem Gebiet erweist sich als das häufigste Heterogenitätsmaß in der Literatur, wohingegen Maße von klimatischer Heterogenität und Bodenheterogenität unterrepräsentiert sind. Weiterhin stelle ich ein deutliches räumliches und taxonomisches Ungleichgewicht in der Forschung fest, wobei ein Großteil der Studien den Einfluss von Heterogenität in der Paläarktis untersucht und sich auf den Artenreichtum von Vertebraten oder Pflanzen konzentriert. Ich kompiliere über 100 verschiedene Begriffe für Heterogenität, wie z.B. Habitatdiversität oder Habitatheterogenität, und weise auf mangelhafte und teilweise sogar widersprüchliche Definitionen hin. Solche Unklarheiten erschweren das Verständnis der Begriffe und Studien, weshalb ich für eindeutige Terminologie plädiere und mich gegen die Verwendung von Synonymen ausspreche. Desweiteren gebe ich einen Überblick über mögliche Mechanismen, die als Grundlage von positiven Zusammenhängen zwischen Heterogenität und Artenreichtum in der Literatur diskutiert werden. Insgesamt identifiziere ich sieben Hauptmechanismen, die mit der Förderung von Koexistenz, Persistenz und Diversifikation von Arten zusammenhängen. Diese Mechanismen stelle ich in Beziehung zu den Themenfeldern der Heterogenitätsmaße, den Taxa und den räumlichen Skalen, die in den jeweiligen Studien behandelt werden. Basierend auf dem gleichen Datensatz von 192 Studien und 1148 Datenpunkten führe ich anschließend eine Meta-Analyse durch, um die generelle Richtung und Stärke des Zusammenhangs zwischen Heterogenität und dem Artenreichtum terrestrischer Pflanzen und Tiere zu untersuchen. Hierbei weise ich quantitativ nach, dass der Zusammenhang von der Landschaftsebene bis zur globalen Skala über Taxa, Habitattypen und räumliche Skalen hinweg generell positiv ist. Während kein signifikanter Unterschied in der Effektgröße zwischen biotischer und abiotischer Heterogenität besteht, weisen Vegetations- und topographische Heterogenität signifikant stärkere Assoziationen mit Artenreichtum auf als klimatische Heterogenität. Durch gemischte Meta-Regressionen identifiziere ich weiterhin Studieneigenschaften, die die Stärke des Zusammenhangs zwischen Heterogenität und Artenreichtum beeinflussen. Räumliche Skalen, insbesondere Flächenkonstanz, räumliche Auflösung und Ausdehnung, stellen sich als besonders wichtige Einflussgrößen für die untersuchte Beziehung zwischen Artenreichtum und auf Landbedeckung und Höhe basierenden Heterogenitätsmaßen heraus. Ausgehend von den Ergebnissen des Literaturreviews untersuche ich schließlich die Ähnlichkeit zwischen einer Reihe von Heterogenitätsmaßen sowie deren differentiellen Einfluss auf den globalen Artenreichtum terrestrischer Säugetiere. Ich berechne systematisch 51 verschiedene Heterogenitätsmaße auf globaler Ebene, die alle fünf Themenfelder von Heterogenität abdecken und neun verschiedene Berechnungsmethoden beinhalten. Ich zeige, dass manche dieser Maße sich deutlich voneinander abheben, während andere stärker kollinear und zum Teil redundant sind. Ich stelle Ähnlichkeiten und Unterschiede zwischen verschiedenen Regionen in Bezug auf räumliche Muster einzelner Heterogenitätsmaße sowie einen multidimensionalen Heterogenitätsraum heraus, der auf einer Hauptkomponentenanalyse beruht. Außerdem untersuche ich den Zusammenhang zwischen jedem einzelnen Heterogenitätsmaß und dem Säugetierreichtum in einfachen und multiplen Regressionsmodellen, welche zusätzlich den Einfluss von Klima, biogeographischer Region und menschlichem Einfluss berücksichtigen. Mit Hilfe von bedingten Inferenzbäumen analysiere ich den Einfluss der verschiedenen Themenfelder und Berechnungsmethoden der Heterogenitätsmaße auf die Modellgüte über drei räumliche Auflösungen hinweg. Die Wahl der Themenfelder stellt sich dabei als wichtigster Einflussfaktor heraus, wobei sich Maße klimatischer und topographischer Heterogenität besonders positiv auf die Modellgüte auswirken. Desweiteren zeichnen sich Modelle mit Anzahl- oder Spannweitemaßen ebenfalls durch hohe Modellgüte aus, wohingegen der Variationskoeffizient und ein Geländeschroffheitsindex mit relativ geringer Modellgüte zusammenhängen. Insgesamt betonen meine Ergebnisse die hohe Bedeutung methodischer Entscheidungen auf die Ergebnisse von Heterogenität-Artenreichtums-Studien. Dies wiederum dokumentiert wie wichtig es ist, sinnvolle, taxon- und skalenabhängige Heterogenitätsmaße zu verwenden, die dem jeweiligen Untersuchungssystem und dem zu untersuchenden Mechanismus entsprechen. Diese Dissertation stellt die bisher umfangreichste Untersuchung der Quantifizierung und Terminologie von Heterogenität über Themenfelder und verschiedene taxonomische Gruppen hinweg dar. Sie belegt erstmals einen generell positiven Zusammenhang zwischen biotischer und abiotischer Heterogenität und dem Artenreichtum terrestrischer Pflanzen und Tiere auf relativ großen räumlichen Skalen. Meine Forschung demonstriert deutlich die enorme Komplexität von Heterogenität als Thema und Forschungsgebiet. Trotz der beachtlichen Fortschritte, die durch diese Arbeit in der Erforschung von Heterogenität-Artenreichtums-Beziehungen gemacht wurden, gilt es noch zahlreiche offene Fragen zu beantworten. Die vorliegende Dissertation soll eine solide Basis schaffen, um diese Herausforderung in Zukunft anzugehen.

This dissertation supplies the methodology of the measure (area) in the Earth model adopted for Geodesy. This model is the ellipsoid of revolution, in which the system of Cartesian coordinates, the curvilinear coordinate system and the polar coordinate system are described. The coordinate nature in the development of the surface measure calculation is discussed. The following demonstrations are illustrated: the ellipse equation, the eccentricity of the ellipse, the meridian section curvature radius equation, the meridian transversal section curvature radius equation and elliptic integral. It define algebraic geodesic line and geometrically. The juridical basis are the article 3º of Brazilian Federal Law 10.267/2001, which modify article 176 of the Brazilian Federal Law 6.015/1973 (Public Record Law) and adds to this article the paragraphs 3º and 4º, the paragraph 3º of article 225 of the Brazilian Law 6.015/1973 and the article 971 of the Código de Processo Civil (CPC), which require the coordinates of the corners of the real property on the Brazilian Geodetic System (SGB). The partitioning of the regular ellipsoid quadrilateral and the partitioning of the irregular ellipsoid quadrilateral located in the real property Pó de Serra is presented. To become this partitioning, it was used surface of the Lambert azimuthal equal-area projection, i. e., the curvilinear geodetic coordinates in plane coordinates has been transformed. The surface partitioning was determined using the method area equation of the Gauss trapezes connected with the equation of the straight line. The direct problem of the Lambert azimuthal equal-area projection and the inverse problem supply the methodology that become feasible the juridical exigence (articles 176 and 225 of Brazilian Federal Law 6.015/1973 and article 971 of the CPC). The methodology to the geodetic coordinates system with the purpose to calculate the partitioned areas of surface on the ellipsoid can be applied. The calculation of surface measure supplies the effective practice of the mencioned juridical basis. / O propósito deste trabalho é fornecer os fundamentos de cálculo de medida de superfície (área) no modelo de Terra adotado pela Geodésia. Esse modelo é o elipsóide de revolução ao qual se vincula o sistema de coordenadas cartesianas, o sistema de coordenadas curvilíneas e o sistema de coordenadas polares. Discute a natureza das coordenadas no desenvolvimento do cálculo da medida de superfície. Efetuam-se as seguintes demonstrações: equação da elipse, equação da excentricidade da elipse, equação do raio de curvatura da seção meridiana, equação do raio de curvatura da seção transversal meridiana e integral elíptica. Define linha geodésica algébrica e geometricamente. Apresentam-se os instrumentos legais que são o artigo 3º da Lei 10.267/2001, o qual altera o artigo 176, inciso II da Lei 6.015/1973 (Lei de Registros Públicos) e acrescenta a este artigo os parágrafos 3º e 4º, o parágrafo 3º do artigo 225 da Lei 6.015/1973 e o artigo 971 do Código de Processo Civil (CPC), os quais vinculam as coordenadas dos vértices do imóvel ao Sistema Geodésico Brasileiro (SGB). Efetuam-se a divisão do quadrilátero elipsóidico regular e também do quadrilátero elipsóidico irregular localizado na gleba Pó de Serra. Para se fazer esta divisão, usou-se a superfície da projeção azimutal equivalente de Lambert, ou seja, as coordenadas elipsóidicas curvilíneas foram transformadas em coordenadas planas desse sistema de projeção. A divisão destas superfícies foi efetuada pelo método da equação da área dos trapézios de Gauss em conjunto com a equação da reta. Os problemas direto e inverso da projeção azimutal equivalente de Lambert fornecem a metodologia que tornam exeqüíveis os dispositivos legais (artigos 176 e 225 da Lei 6.015/1973 e artigo 971 do CPC). A metodologia de cálculo proposto pode ser aplicada ao sistema de coordenadas geodésicas com a finalidade de calcular as áreas de uma divisão de superfície no elipsóide. Os fundamentos do cálculo de medida de superfície instrumentalizam o efetivo cumprimento dos dispositivos legais retrocitados.