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Determinação da posição de bobinas implantáveis via sistema de transferência de energia sem fio / Implantable coil determination position via wireless power transfer systemGarcia, Lucas Ricken 26 September 2016 (has links)
CNPq / Este trabalho apresenta o estudo de um método para a determinação da posição e orientação de uma bobina implantável em relação à bobina transmissora localizada externamente ao paciente. No aspecto elétrico, conhecer a posição e orientação da bobina implantada permite um maior domínio sobre o posicionamento do enlace e, consequentemente, das características de eficiência e potência entregue ao secundário, i.e. ao IMD. Já no aspecto clínico, detectar e determinar a posição da bobina implantável e, se possível, do IMD, pode auxiliar na determinação de possíveis movimentações do dispositivo na região implantada que podem influenciar o seu desempenho. Neste sentido, realizou-se análises teóricas a cerca da indutância mútua, do coeficiente de acoplamento magnético e de sistemas de transferência de energia sem fio (WPT) a duas bobinas. Por meio do modelo matemático implementado no software Matlab e o projeto experimental de sistemas de WPT a duas bobinas, avaliou-se a influência de desalinhamentos laterais e angulares sobre o acoplamento magnético. A partir das características observadas, descreveu-se os procedimentos necessários para estimar a posição e orientação relativa da bobina do dispositivo implantável apenas mensurando os parâmetros elétricos do primário. Em uma avaliação preliminar, por meio de testes virtuais, observou-se um erro médio e incerteza padrão na determinação da posição relativa de 2,4 mm e 1,1 mm, respectivamente, que se comparada às dimensões das bobinas (40 mm de diâmetro para bobina externa e 5,5 mm para a bobina implantável) indicam uma exatidão adequada. Para a determinação do ângulo relativo o método também apresentou resultados promissores, uma vez que o erro médio foi de 7º e a incerteza padrão obtida de 8,2º. Desta forma, o método estudado possibilita o desenvolvimento de equipamentos para determinação da posição e orientação relativa de uma bobina implantável mensurando apenas a corrente no primário, sem a necessidade de circuitos adicionais no IMD ou a utilização de equipamentos de imagem médicos. / This paper presents the study of a method for determining the implanted coil position and orientation relative to the transmitter coil externally located to the patient. In the electrical aspect, knowing the implanted coil position and orientation allows greater control over the placement of the link and thus the efficiency of features and power delivered to the secondary, i.e. the IMD. In the clinical aspect, detect and determine the implantable coil position, if possible, the IMD can assist in determining possible device movements in the implanted area that can influence their performance. In this sense, a theoretical analysis about the mutual inductance, the magnetic coupling coefficient and two coils wireless power transfer (WPT) systems was realized. Through mathematical model implemented in Matlab and experimental design of two coil WPT systems, the influence of lateral and angular misalignment on the magnetic coupling was assessed. From the observed characteristics, was described the necessary procedures to estimate the relative position and orientation of the implantable device coil only measuring the primary electrical parameters. In a preliminary evaluation, through virtual testing, there was an average error and standard deviation in determining the relative position of 2.4 mm and 1.1 mm, respectively, compared to the dimensions of the coils (40 mm diameter to external coil and 5.5 mm for implantable coil) indicate adequate accuracy. To the relative angle the method also yielded promising results, since the average error was 7° and the standard deviation obtained 8.2°. Thus, the method studied enables the development of equipment for determining the implanted coil relative position and orientation measuring only the primary current without the need for additional circuitry in IMD or the use of medical imaging equipment.
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Investigation of the application of IEC61850 standard in distribution busbar protection schemesMnguni, Mkhululi Elvis Siyanda January 2013 (has links)
Thesis submitted in fulfilment of the requirements for the degree
Master of Technology: Electrical Engineering
in the Faculty of Engineering
at the Cape Peninsula University of Technology
Supervisor: Prof. R. Tzoneva
Co-supervisor: Prof. P. Petev
2013 / Busbars are the most important components in the distribution networks. Faults on the busbar are uncommon, however an occurrence of a busbar fault can lead to a major loss of power. Busbars are the areas in a substation where the levels of current are high and therefore the protective relay application is very critical. In order for the protection scheme to be successful it is important to carry out the following specifications: Selectivity, Stability, Sensitivity, and Speed. To meet all of the above requirements protection must be reliable, meaning that the protection scheme must trip when called up to do so (dependability) and it must not trip when it’s not supposed to (security).
The thesis focuses on the reverse blocking busbar protection scheme with aim to improve the speed of its operation and at the same time to increase operational reliability, flexibility and stability of the protection during external and internal faults by implementation of the extended functionality provided by the IEC61850 standard-based protective IEDs. The practical implementation of the scheme by the use of IEC 61850 standard communication protocol is investigated. The research analyzes in detail the reverse blocking busbar protection scheme that is used at the moment in the power systems and it develops an improved IEC 61850 based reverse blocking busbar protection scheme for a distribution network. The proposed scheme is designed for a radial type of a distribution network and is modeled and simulated in the DigSILENT software environment for various faults on the busbar and its outgoing feeders. The results from the simulations are used further for implementation of the designed protection scheme.
A laboratory test bench is build using three compliant with the IEC 61850 standard ABB IEDs 670 series, CMC 356 Omicron test injection device, PC, MOXA switch, and a DC power supplier. Two ways of the reverse blocking signals between the IEDs implementation are considered: hard wired and Ethernet communication by using IEC 61850 standard GOOSE messages.
Comparative experimental study of the operational trip response speed of the two implementation shows that the performance of the protection scheme for the case of Ethernet communication is better
The thesis findings and deliverables will be used for postgraduate studies of other students, research, short courses, and solution of industrial problems.
Keywords: Busbar, Power system, reverse busbar blocking scheme; IEC61850; Distribution, Protection relays, IEDs, GOOSE message, laboratory test bench
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Development of an embedded system actuator node for intergration into an IEC 61850 based substation automation applicationRetonda-Modiya, John-Charly January 2012 (has links)
Thesis submitted in fulfilment of the requirements for the degree
Master of Technology: Electrical Engineering
in the Faculty of Engineering
at the Cape Peninsula University of Technology, 2012 / The introduction of the IEC 61850 standard in substations for communication networks and
systems by the International Electrotechnical Commission (IEC) in 2003 provided the
possibility for communication between devices of different manufacturers. However, the
advent of this standard also brought about many challenges associated with it.
The challenges introduced by this fairly recent standard of communications in Substation
Automation Systems (SAS), and the need for the development of cost effective IEC 61850-
compliant devices, motivated the decision of the Centre for Substation and Energy
Management Systems within the Electrical Engineering Department of the Cape Peninsula
University of Technology to focus on the implementation of the IEC 61850 standard using an
embedded hardware platform.
The development of an IEC 61850 embedded application requires substantial knowledge in
multiple domains such as data networking, software modelling and development of Intelligent
Electronic Devices (IEDs), protection of the electrical system, system simulation and testing
methods, etc. Currently knowledge about the implementation of the IEC 61850 standard
usually resides with vendors and is not in the public domain.
The IEC 61850 standard allows for two groups of communication services between entities
within the substation automation system. One group utilizes a client-server model
accommodating services such as Reporting and Remote Switching. The second group
utilizes a peer-to-peer model for Generic Substation Event (GSE) services associated with
time-critical activities such as fast and reliable communication between Intelligent Electronic
Devices (IEDs) used for protection of the power network.
The messages associated with the GSE services are the Generic Object Oriented Substation
Event (GOOSE) messages. The use of GOOSE messages for protection of the electrical
system is very important in modern substations. Detailed knowledge of the structure of these
messages is important in instances requiring fault diagnosis to determine the cause of mal–
operation or to address interoperability concerns or when developing custom IEC 61850-
compliant devices with limited functionality.
A practical protection application (overcurrent) case study is presented where GOOSE
messages are exchanged between a commercial IED and an IEC 61850-compliant controller
based on an embedded platform. The basic data model and software development of an
actuator node for a circuit breaker is proposed using an IEC 61850 communication stack on
an embedded platform. The performance of the GOOSE messages is confirmed to be as per
the functional behaviour specified, and per the IEC 68150 standard in terms of the temporal
behaviour required.
This thesis document tables the methods, software programs, hardware interfacing and
system integration techniques that allow for the development and implementation of a low
cost IEC 61850-compliant controller unit on an embedded systems platform for the
substation automation system.
The overcurrent case study distributed between a commercial IED (SIEMENS Siprotec
device) and the actuator application developed on an embedded platform for this project
(DK60 board) is in compliance with the IEC 61850 standard and utilizing GOOSE messaging
is successfully completed both in terms of functional and temporal behaviour.
This novel research work contributes not only to the academic community, but to the
international Power Systems community as a whole.
Keywords: IEC 61850 standard, IEDs, GOOSE message, software modelling, software
development, substation automation systems, communication stack, embedded systems,
actuator.
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Utilizando chaves ópticas para controle de qualidade de serviços em redes inteligentes / Using optical switches for quality of service control on smart gridBressam, Wagner Caldas 30 September 2016 (has links)
Redes inteligentes de distribuição de energia fornecem serviços com o potencial de aumentar a eficiência energética e a qualidade de vida da sociedade, mas possuem requisitos severos de tempo de resposta, confiabilidade, escalabilidade e QoS. As chaves ópticas são dispositivos comutadores de caminhos em fibras ópticas popularmente utilizados para trocas físicas de rotas. Neste trabalho sugere-se utilizar estes dispositivos para ativamente reorganizar uma rede com o objetivo de diminuir a latência de comunicação, visando atender aos requisitos de comunicações dos serviços de redes inteligentes. Foram estudadas as características de protocolos de roteamento conhecidos e aplicou-se o algoritmo de Dijkstra na criação de quatro heurísticas de otimização dos caminhos máximos em redes com chaves ópticas. Simulações realizadas mostram que as heurísticas propostas reduzem o número de saltos nos caminhos máximos, levando à redução de latência. É sugerida a continuação deste estudo aperfeiçoando as heurísticas propostas com outros mecanismos de otimização e diferentes métricas, como redução de congestionamento de tráfego e de consumo de energia na rede. / Smart grid networks provide services with the potential to increase energy efficiency and the quality of life of society, but have strict requirements regarding response time, reliability, scalability and QoS. The optical switches are fiber optic switching devices commonly used for physical route changing. In this study, it is suggested to use these devices to actively rearrange a network in order to reduce the communication latency, to meet the communications requirements of smart grid services. The characteristics of known routing protocols have been studied and the Dijkstra algorithm has been applied at the creation of four heuristics that aim to optimize the maximum paths in networks with optical switches. The simulations show that the heuristics reduce the maximum number of hops in the paths, leading to reductions in latency. It is suggested the continuation of this study improving the heuristics with other optimization engines and different metrics, such as reducing traffic congestion and energy.
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Utilizando chaves ópticas para controle de qualidade de serviços em redes inteligentes / Using optical switches for quality of service control on smart gridBressam, Wagner Caldas 30 September 2016 (has links)
Redes inteligentes de distribuição de energia fornecem serviços com o potencial de aumentar a eficiência energética e a qualidade de vida da sociedade, mas possuem requisitos severos de tempo de resposta, confiabilidade, escalabilidade e QoS. As chaves ópticas são dispositivos comutadores de caminhos em fibras ópticas popularmente utilizados para trocas físicas de rotas. Neste trabalho sugere-se utilizar estes dispositivos para ativamente reorganizar uma rede com o objetivo de diminuir a latência de comunicação, visando atender aos requisitos de comunicações dos serviços de redes inteligentes. Foram estudadas as características de protocolos de roteamento conhecidos e aplicou-se o algoritmo de Dijkstra na criação de quatro heurísticas de otimização dos caminhos máximos em redes com chaves ópticas. Simulações realizadas mostram que as heurísticas propostas reduzem o número de saltos nos caminhos máximos, levando à redução de latência. É sugerida a continuação deste estudo aperfeiçoando as heurísticas propostas com outros mecanismos de otimização e diferentes métricas, como redução de congestionamento de tráfego e de consumo de energia na rede. / Smart grid networks provide services with the potential to increase energy efficiency and the quality of life of society, but have strict requirements regarding response time, reliability, scalability and QoS. The optical switches are fiber optic switching devices commonly used for physical route changing. In this study, it is suggested to use these devices to actively rearrange a network in order to reduce the communication latency, to meet the communications requirements of smart grid services. The characteristics of known routing protocols have been studied and the Dijkstra algorithm has been applied at the creation of four heuristics that aim to optimize the maximum paths in networks with optical switches. The simulations show that the heuristics reduce the maximum number of hops in the paths, leading to reductions in latency. It is suggested the continuation of this study improving the heuristics with other optimization engines and different metrics, such as reducing traffic congestion and energy.
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Wind PowerMakhalas, Kharsan Al, Alsehlli, Faisal January 2015 (has links)
This Bachelor thesis has been written at the Blekinge Institute of Technology. This thesis concentrates on the wind power and their components, also the large wind farm is studied. The electrical power is generated by using the power in wind to drive a wind turbine to produce mechanical power. This mechanical power can be converted into electrical power by using electrical induction generators. There are two types of the wind turbines, the horizontal axis and vertical axis wind turbine, where the horizontal axis wind turbine is mostly used and was studied in this thesis. The rotor can be placed in two directions: an upwind rotor where the blade of turbine faces to the wind, so it operates more smoothly and transmit more power. The other type is a downwind rotor which orients itself with respect for the wind direction. Moreover, the tower shadow makes the blade to flex, consequently resulting in fatigue, noise, and reduces output of the power. The modern wind turbine has been built with an odd number of blades which is important for the stability of the turbine. The rotor with an odd number of blades can be considered to be similar to a disc when calculating the dynamic properties of the machine. The main idea of this thesis is to study the wind power in general and large wind parks specifically. The Horns Rev wind park was taken as an example of a wind park in Denmark and the Gotland wind park as an example of a wind park in Sweden too. Into account, the distance between wind turbine in the wind direction cannot be too small. If the wind turbines are located to close to each other, the wind will be more and more turbulent after it passes through each single wind turbine. This would lead to that wind turbines downstream in the wind park, and it might even have to shut down due to that mechanical loading gets to high during strong conditions. This is due to the fact that when wind passes through the rotor of the wind turbine it gets very turbulent and the wind speed is decreased. The minimum length of the rotor should be approximately 5-7 rotor diameters to avoid that issue. Gotland Energy AB (GEAB) considered, that high voltage direct current light would be the only realistic way to solve the technical problems for the high amount of wind power in-feed. One result is that The stability of voltage during transient events, has become much better by using the high voltage direct current light so that the output current stability from the asynchronous generators have been improved, which reduces the stresses on the AC grid and on the mechanical construction of the windmills. / In general the wind turbines with three blades accommodated a thicker root are used. It is obvious that, the less number of blades on the wind turbine, the cost of material and manufacturing will be lower. It is worthy to mentioned that, the modern wind turbine has been built with an odd number of blades. When the length of the blade increases the deflection of blade tip due to axial wind force also increase as well. So without consider the increase in length of blade may lead to dangerous situation of collision of tower and blade. Moreover, by increasing the number of blades cost of the system would increased as well. The limit of transfer for the AC transmission system depends on the distance from shore and is therefore physically limited by this. AC large wind parks that are placed at a long distance from the shore, which means AC long transmission line, and more drop voltage A solution to AC long transmission line, it could be to decrease the offshore frequency and use a low frequency AC networks. There is a suggestion by for instance (Schütte, Gustavsson and Ström 2011). The usages of a low frequency system are in electrified railway systems, where the frequency ranges from 16.67 Hz to 25 Hz. However, the network of a low frequency would allow a simpler design of the offshore WTs and The aerodynamic rotor of a large WT operates at maximum revolutions at 15-20 rpm. The lower frequency would then allow a smaller gear ratio for turbines with a gearbox, or decrease the poles number for WTs with direct driven generators. This would lead to lighter and cheaper turbines. One of the disadvantages by using a low frequency system is the size of transformer would be increased, and hence, the costs of transformer will increased too. The operator of the grid, Gotland Energy AB (GEAB) considered, that HVDC light would be the only realistic way to solve the technical problems for the high amount of wind power in-feed. The experiences have supported expected improvements in the characteristics for example: - Stability in the system arose. - Reactive demands, power flows, as well as voltage level in the harmonic and system were reduced. - Flicker problems were eliminated with the installation of HVDC light and transient phenomena disappeared. Moreover, Overall experiences of Gotland Energy AB (GEAB) are that the control of power flow from the converters makes the AC grid easier to observe than a conventional AC network and the power variations do not stress the AC grid as much as in normal network. Voltage quality has been better with the increased wind power production. A topic to study in the future is the consequences of blackouts in power supply with many wind power farm. / 004676396018
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Prise en compte de l’usure dans la modélisation du comportement sous charge des engrenages roues et vis tangentes / Modelling the loaded behavior of worm gears, taking the wear into accountJbily, Dalia 22 April 2016 (has links)
Les engrenages roues et vis sans fin sont une solution avantageuse pour transmettre le couple entre des axes perpendiculaires non concourants. Ces engrenages offrent une solution simple et efficace en terme de coût dans les applications de transmission de puissance, où un grand rapport de réduction est nécessaire, en comparaison avec les engrenages classiques à axes parallèles qui nécessitent normalement deux ou trois étapes pour obtenir les mêmes réductions avec une augmentation conséquente de complexité et du nombre de pièces. L’usure de surface est un des modes de défaillance observés dans la vie des engrenages roues et vis sans fin qui influe sur la portée de contact, les caractéristiques de transmission et le bruit résultant. La première étape de ces travaux est la mise au point d’un modèle numérique pour étudier le comportement quasi statique des engrenages roues et vis sans fin avec une roue en bronze et une vis en acier. Le modèle est basé sur la résolution des équations de compatibilité des déplacements ainsi que sur la méthode des coefficients d’influence. Les effets globaux de flexion et les effets locaux de contact ont été séparés. Les effets de contact ont été obtenus par la théorie de Boussinesq. Les coefficients de flexion sont estimés par la combinaison d’un calcul Éléments Finis et des fonctions d’interpolation, permettant d’une part de prendre en compte l’environnement de l'engrenage (la géométrie des arbres, des jantes et des voiles, l’emplacement des roulements,...) et d’autre part de réduire significativement les temps de calculs. Dans une seconde étape, une méthodologie est proposée pour modéliser l’usure de la surface de dent de la roue. Le modèle de contact quasi-statique de la répartition des charges est combiné avec un modèle d’usure d’Archard. Ce modèle suppose que la profondeur d’usure est directement proportionnelle à la pression de contact et à la distance de glissement et inversement proportionnelle à la dureté du matériau. Cette loi d’usure est modifiée pour prendre en compte l’influence des conditions de lubrification en utilisant un coefficient d’usure local, dépendant de l’épaisseur du film lubrifiant, rapportée à l’amplitude des rugosités des surfaces. L’enlèvement de matière par l’usure du flanc de la roue influe sur la répartition des pressions et donc les modifications de la géométrie des dents doivent être incluses dans la prédiction de l’usure. Le calcul des pressions de contact est ainsi mis à jour pour tenir compte des changements de géométrie. Enfin, pour valider le modèle développé des comparaisons du modèle avec des résultats expérimentaux issus de la bibliographie ont été effectuées. / Worm gears are one of the technical devices for transmitting torque between spatial crossed axes. They provide a simple and cost effective solution in power transmission applications, where a high reduction ratio is required. Comparable conventional parallel axis gearing would normally require two or three stages to achieve the same reduction, with a consequent increase in complexity and number of parts. Surface wear is one of the failure modes observed in life worm gear sets which affects the contact patterns, the other transmission characteristics and the resultant noise. The first step of this work is the development of a numerical model to study provide the quasi-static behavior of worm gears with bronze wheel and steel worm. The model is based on solving of the equation of displacement compatibility and the influence coefficient method. The global effects of bending and local effects of contact are separated. The contact effects are obtained with the theory of Boussinesq. Bending effects are estimated by the combination of one standard FEM computation and interpolation functions. These methods allow, on the one hand, to take into account the environment of the gear (shaft shape, rim, web, bearing location ...) and on the other to reduce significantly the computation time. In a second step, a methodology is proposed for predicting the wear of the wheel tooth surface. In this process, a quasi-static contact model of the load distribution is combined with Archard's wear model. This model assumes that the wear depth is directly proportional to the contact pressure and sliding distance and inversely proportional to the hardness of the material. The wear law is modified to take into account the influence of the lubrication conditions using a local wear coefficient, depending on the lubricant film thickness, relative to the amplitude of surface roughness. Removal of material by wear on the wheel flank affects the pressure distribution, therefore the changes in teeth must be included in the prediction of wear. The calculation of contact pressures must also be updated to take into account the modification of the gear flank geometry. The last step concerns the validation of the numerical. Comparisons have been carried out between the model results and experimental ones issued from the bibliography.
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Etude de la performance énergetique d’une transmission de puissance haute vitesse / Study of the efficiency of a high-speed mechanical power transmissionNeurouth, Adrien 16 March 2016 (has links)
Une des voies d’amélioration des véhicules hybrides et électriques est l’utilisation de moteurs tournant plus vite, jusqu’à plus de 42.000tr/min. Le but est d’augmenter la densité de puissance et le rendement des groupes motopropulseurs. Pour utiliser ces moteurs de nouveaux réducteurs mécaniques doivent être développés. Cela doit se faire sans générer de surcoût important face aux solutions utilisées à basse vitesse et en assurant un niveau de performance énergétique élevé. Cette thèse se situe en amont de la phase de conception d’un réducteur haute vitesse lubrifié par barbotage. Elle a pour but d’identifier les problèmes d’échauffement et de pertes de puissance ainsi que de proposer des pistes d’amélioration énergétique. Ce travaille propose la modélisation thermomécanique de l’étage grande vitesse (GV) du réducteur, réalisée à l’aide de la méthode des réseaux thermiques. Ce modèle couple les pertes de puissance avec les températures. Une attention particulière est portée sur la modélisation des roulements de l’arbre GV. Un nouveau modèle thermomécanique de roulement est développé. Les pertes par barbotage deviennent importantes à grande vitesse. Une méthode permettant de fortement les réduire est caractérisée. / A way to improve both electric and hybrid vehicles is to use high speed motors, operating over than 42.000rpm. The goal is to increase the power density and the efficiency of powertrains. Using these new motors, new gearboxes should be developed. This must be done without generating significant additional cost regarding already mastered low speed solutions. High energy performance level also has to be maintained. This PhD comes before the design phase of a high-speed oil bath lubricated gearbox. It aims to identify the warm-up and power loss problems, and propose ways to improve efficiency. This work proposes a thermomechanical modelling of the gearbox’s first stage, using the thermal network method. This model links power losses with temperatures. Particular attention is paid to high speed bearing modelling. A new thermomechanical model of rolling element bearing is developed. As churning losses being significant at high speeds, a method to greatly reduce this power loss is characterized.
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Analysis Of SubSynchronous Resonance With Voltage Source Converter Based FACTS And HVDC ControllersNagesh Prabhu, * 09 1900 (has links) (PDF)
No description available.
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Modelo reduzido de linhas de transmissão para transitorios eletromagneticos : aplicação de propriedades complexas / Condensed transmission line model to electromagnetic transient phenomena : use of complex propertiesPaz, Marcos de Araujo 18 November 2005 (has links)
Orientador: Maria Cristina Dias Tavares / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e Computação / Made available in DSpace on 2018-08-07T13:37:43Z (GMT). No. of bitstreams: 1
Paz_MarcosdeAraujo_D.pdf: 6127820 bytes, checksum: 21f6dc485bcf097846769f086c2362ad (MD5)
Previous issue date: 2005 / Resumo: O objetivo deste trabalho é contribuir para o estudo de linhas de transmissão e o desenvolvimento de modelos de linhas voltados a programas do tipo EMTP. O trabalho desenvolvido consiste em aproveitar as propriedades e semelhanças dos modos não homopolares de propagação das linhas de transmissão, sejam elas idealmente transpostas ou que apresentem plano de simetria vertical. Por meio de manipulações da matriz de transformação fase-modo-fase através do uso de vetores ortogonais e elementos complexos no domínio modal, pode-se reduzir a dimensão dos vetores de estado. O procedimento proposto é direcionado às modelagens que utilizam transformação fase-modo-fase na determinação das variáveis de estado (corrente e tensão) nas linhas de transmissão. Os recursos usados levam a uma redução tanto em número de operações por iteração quanto em alocação de estados, otimizando o procedimento de cá1culo e aumentando a velocidade de simulação no processamento. A economia computacional que o procedimento proposto proporciona pode ser usada em ferramentas de simulação em tempo real / Abstract: The research objective is to contribute with the study of the transmission line and the development of line models in EMTP-type programs. The proposed model takes advantage of some similarities between non homopolar modes, applying orthogonal vectors and complex number theory to manipulate the state vectors in modal domain reducing the state vectors dimension. The proposed procedure is aimed to the modelling that use phase-mode-phase transformation in the determination of state variables (current and voltage) in transmission lines. The resources used lead to a reduction both in the number of operations per iteration and state allocation, optimizing the procedure and increasing the processing simulation speed. The computational economy, which the proposed procedure provide, can be applied to real-time simulation tools / Doutorado / Energia Eletrica / Doutor em Engenharia Elétrica
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