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Three-phase high-frequency transformer isolated soft-switching DC-DC resonant convertersAlmardy, Mohamed S. M. 14 October 2011 (has links)
There is an increasing demand for power converters with small size, light weight, high conversion efficiency and higher power density. Also, in many applications, there is a need for dc-to-dc converters to accept dc input voltage and provide regulated and/or isolated dc output voltage at a desired voltage level including telecommunications equipment, process control systems, and in industry applications.
This thesis presents the analysis, design, simulation and experimental results of three-phase high-frequency transformer isolated resonant converters. The first converter presented is a three-phase LCC-type dc-dc resonant converter with capacitor output filter including the effect of the magnetizing inductance of the three-phase HF transformer. The equivalent ac load resistance is derived and the converter is analyzed by using approximation analysis approach. Base on this analysis, design curves have been obtained and a design example is given. Intusoft simulation results for the designed converter are given for various input voltage and for different load conditions. The experimental verification of the designed converter performance was established by building a 300 W rated power converter and the experimental results have been given. It is shown that the converter works in zero-voltage switching (ZVS) at various input voltage and different load conditions.
A three-phase (LC)(L)-type dc-dc series-resonant converter with capacitive output filter has been proposed. Operation of the converter has been presented using the operating waveforms and equivalent circuit diagrams during different intervals. An approximate analysis approach is used to analyze the converter operation, and design procedure is presented with a design example. Intusoft simulation results for the designed converter are given for input voltage and load variations. Experimental results obtained in a 300 W converter are presented. Major advantages of this converter are the leakage and magnetizing inductances of the high-frequency transformer are used as part of resonant circuit and the output rectifier voltage is clamped to the output voltage. The converter operates in soft-switching for the inverter switches for the wide variations in supply voltage and load and it requires narrow switching frequency variation (compared to LCC-type) to regulate the output voltage.
A three-phase high-frequency transformer isolated interleaved (LC)(L)-type dc-dc series-resonant converter with capacitive output filter using fixed frequency control is proposed. The converter operation for different modes is presented using the operating waveforms and equivalent circuit diagrams during different intervals. This converter is modeled and then analyzed using the approximate complex ac circuit analysis approach. Based on the analysis, design curves were obtained and the design procedure is presented with a design example. The designed converter is simulated using PSIM software to predict the performance of the converter for variations in supply voltage and load conditions. The converter operates in ZVS for the inverter switches with minimum input voltage and loses ZVS for two switches in each bridge for higher input voltages. / Graduate
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Μελέτη και κατασκευή ηλεκτροκινητήριου συστήματος υβριδικού οχήματος : σχεδιασμός και κατασκευή ηλεκτρονικού κυκλώματος ελέγχου της υβριδικής κατάστασηςΠατσιάς, Ευστάθιος 25 January 2010 (has links)
Η θεματολογία της εργασίας αυτής περιλαμβάνει την υβριδική τεχνολογία στην αυτοκίνηση. Γίνεται μία εκτεταμένη ανάλυση των υβριδικών οχημάτων, αρχικά κάνοντας αναφορά στην ιστορία των υβριδικών και μη οχημάτων και έπειτα στα περιβαλλοντικά θεμάτα που τα έφεραν στο προσκήνιο. Η ανάλυση περιλαμβάνει επίσης την μελέτη των διαφόρων κατηγοριών υβριδικών οχημάτων, την εξέταση των κατασκευαστικών μερών τους και κλείνει με την παρουσίαση κάποιων χαρακτηριστικών οχημάτων που βγήκαν στην παραγωγή.
Στη συνέχεια, η εργασία περνά στο πειραματικό της στάδιο, που περιλαμβάνει τη μελέτη και κατασκευή ενός ηλεκτροκινητήριου συστήματος για εφαρμογή σε πειραματικό όχημα. Το όχημα μετά τις επεμβάσεις θα είναι υβριδικό, κάνοντας χρήση δύο πηγών ενέργειας, ορυκτά καύσιμα και ηλεκτρισμό. Έγινε η προμήθεια του οχήματος και των απαραίτητων μερών του συστήματος δηλαδή ενός ασύγχρονου ηλεκτροκινητήρα και των μπαταριών, που είναι τύπου οξέος-μολύβδου. Ακολούθησαν μηχανολογικές μετατροπές στο αμάξωμα ώστε να δεχθεί το πρόσθετο σύστημα μετάδοσης κίνησης, οι οποίες και αναλύονται.
Παράλληλα βρίσκονταν σε εξέλιξη οι μετατροπείς ισχύος που απαιτούνται στο σύστημα ηλεκτρικής κίνησης για να προσαρμόσουν τα ηλεκτρικά μεγέθη κατάλληλα ώστε να επιτρέψουν την ροή ισχύος από τις μπαταρίες προς τον κινητήρα, κατά την επιτάχυνση του οχήματος, και την επιστροφή ενέργειας στις μπαταρίες από τη μηχανή, που λειτουργεί ως γεννήτρια λαμβάνοντας ενέργεια από την κινητική του οχήματος.
Οι απαιτούμενοι μετατροπείς είναι ένας αμφικατευθυντήριος μετατροπέας ανύψωσης – υποβιβασμού συνεχούς τάσης σε συνεχή και ένας μετατροπέας συνεχούς τάσης σε τριφασική εναλλασσόμενη, ή πιο απλά τριφασικός αντιστροφέας. Ο δεύτερος μετατροπέας πραγματοποιεί και τον έλεγχο της ροπής που παράγει σε κάθε στιγμή ο κινητήρας μέσω της μεθόδου του Άμεσου Έλεγχου Ροπής (DTC). Περιγράφονται οι μεθοδολογίες ελέγχου των τριφασικών ασύγχρονων κινητήρων και γίνεται λεπτομερής ανάλυση της χρησιμοποιούμενης μεθόδου.
Στο τελευταίο τμήμα περιγράφονται οι πειραματικές μετρήσεις που διεξήχθησαν με το σύστημα που κατασκευάστηκε, στον εργαστηριακό πάγκο και επί του οχήματος της εφαρμογής. Τέλος, γίνεται ανάλυση των αποτελεσμάτων που προέκυψαν. / The subject of this work includes the use of hybrid technology in automotive. An extensive analysis of hybrid vehicles is carried out, referring to the history of hybrid and other vehicles and then to the environmental matters that brought hybrids to the fore. The analysis also includes the study of different types of hybrid vehicles, examining their components and ends with the presentation of some remarkable vehicles that have been produced.
The work then passes into the experimental phase, involving the design and construction of an electric system to be applied in a conventional vehicle. The vehicle is meant to function as a hybrid, using two energy sources, fossil fuels and electricity. For the reason, a vehicle has been supplied along with the necessary parts of the system, which consist of an asynchronous electric motor and lead acid batteries. Mechanical modifications that were made to the chassis to accept the additional drivetrain are discussed in detail.
The construction of the necessary power converters is carried out in parallel. Their purpose is to adjust the electrical values in order to allow the flow of power from the batteries to the engine during acceleration of the vehicle and return energy to the batteries from the electrical machine, which acts as generator powered from the vehicle’s wheels..
The required converters are: a bi-directional buck/boost DC to DC converter and a three-phase DC to AC converter, which is simply described as inverter. The second converter also performs the control of the torque produced at any time from the engine, using Direct Torque Control (DTC). Alternate methodologies are also described, while the used technique is fully analyzed.
The final section describes the experimental procedures performed to the constructed systems. At first they are tested in the laboratory and afterwards they are applied on the vehicle. Finally, an analysis of the results is performed.
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Estimador fuzzy de velocidade para motores de indução trifásicos usando abordagem sensorless / Speed fuzzy estimator for three-phase induction motors using sensorless approachCristiano Minotti 08 July 2008 (has links)
O uso da tecnologia sensorless é uma tendência crescente para acionamentos industriais aplicados em máquinas elétricas. A estimação dos parâmetros elétricos e mecânicos envolvidos com o controle da máquina elétrica são utilizados freqüentemente para se evitar medir todas as variáveis envolvidas no processo. A redução de custos em acionamentos industriais, além do incremento da robustez do sistema, são algumas das vantagens do uso de técnicas sensorless. Este trabalho propõe o uso de lógica fuzzy para estimar a velocidade de rotação de motores de indução trifásicos. Estão presentes resultados de simulações computacionais e comparação com outras técnicas inteligentes para validação da abordagem apresentada. / The use of sensorless technologies is an increasing tendency on industrial drives for electrical machines. The estimation of electrical and mechanical parameters involved with the electric machine control is used very frequently in order to avoid measurement of all variables from this process. The cost reduction may also be considered in industrial drives, besides the increasing robustness of the system, as advantages of the use of sensorless technologies. This work proposes the use of fuzzy logic to estimate the speed in three-phase induction motors. Simulation results are presented to validate the proposed approach and comparative analyses with other intelligent techniques are also outlined.
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Sistemas inteligentes para monitoramento e diagnósticos de falhas em motores de indução trifásicos / Intelligent systems for faults monitoring and diagnosis in three-phase induction motorsMarcelo Suetake 11 April 2012 (has links)
O objetivo desta tese consiste na implementação de sistemas inteligentes para monitoramento e diagnósticos de falhas ocorrentes em motores de indução trifásicos. Para tanto, desenvolveu-se uma bancada de experimentos que visa ensaios de falhas relacionados a curto-circuito entre as bobinas do enrolamento de estator, quebras nas barras da gaiola de esquilo do rotor e, finalmente, rolamentos defeituosos. Mais especificamente, o enfoque principal consiste na proposição de uma abordagem neural de detecção de quebras nas barras de rotores de motores de indução trifásicos mediante a análise do espectro de frequência e aplicação de técnicas de análise das componentes principais. Considerou-se o acionamento do motor de indução tanto pela tensão de alimentação da rede quanto por inversor trifásico em diferentes frequências, operando sob diversas condições de torque de carga para a avaliação da metodologia. / The objective of this thesis consists of the implementation of intelligent systems for three-phase induction motors fault diagnosis and condition monitoring. Therefore, an experimental test stand for stator winding inter-turn short circuit faults, broken rotor bar in squirrel cage and, finally, defective wheel bearing has been designed. The main focus is to propose a neural network approach, which uses spectral frequency analysis and principal component analysis techniques to detect broken rotor bar in squirrel cage induction motor. Induction motor operating at different load torque conditions and supplied with sinusoidal voltage supply and three-phase inverter at different frequency was considered in the experiment for methodology evaluation.
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Avaliação de abordagens de controle preditivo aplicadas em um motor de indução trifásico / Evaluation of predictive control approaches applied to a three phase induction motorCavalca, Eduardo Bonci 12 July 2013 (has links)
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Previous issue date: 2013-07-12 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Model-based predictive control (MPC) approaches has been studied in a wide range of areas, as petrochemical and aerospace, mainly due to its capability of easily deal with physical and operational constraints. Moreover, such approaches can be extended for the application in control loops with nonlinear and time-variant systems. At
this context, the objective of this work is to study some MPC techniques in order to evaluate their applicability to control a three-phase induction motor. More specifically, it was analyzed a Dynamic Matrix Control (DMC) approach, as well as two MPC techniques that uses state space modeling. The control algorithms in question and the nonlinear mathematical model of the motor in study were programmed using the free computing environment Scilab-Xcos®. The models of the threephase motor used in the MPC were obtained by a system identification method (based on the step response of the classical non-linear motor model) and by a phenomenological three-phase modeling approach. Multiple simulations have been performed considering variations in load and speed reference. Besides, some discussions are made related to the influence of the control parameters and about the computational cost. Finally, the results showed that the use of MPC techniques in induction machines has great potential. / Abordagens de controle preditivo baseado em modelo (MPC, do inglês model-based predictive control) têm sido estudadas em diversas áreas, como petroquímica e aeroespacial, principalmente devido à capacidade que apresentam em tratar restrições físicas e operacionais de forma simples. Além disso, tais abordagens podem ser estendidas para aplicação em malhas de controle de sistema não lineares e variantes no tempo. Nesse contexto o objetivo desse trabalho é estudar algumas técnicas de MPC a fim de avaliar sua aplicabilidade no controle de um motor de indução trifásico. Mais especificamente, é analisada a técnica DMC (do inglês Dynamic Matrix Control) bem como duas técnicas de MPC que utilizam modelos no espaço de estados. Os algoritmos de controle em questão e o modelo matemático não linear do motor estudado foram programados utilizando o Scilab-Xcos®, um ambiente de processamento de código livre. Os modelos do motor de indução trifásico utilizados no MPC foram obtidos por meio de um método de identificação de sistemas (baseado na resposta ao degrau do modelo clássico não linear do motor) e por uma abordagem de modelagem fenomenológica trifásica. Múltiplas simulações foram realizadas, considerando variações de carga e referência de velocidade, sendo então apresentadas algumas discussões sobre a influência dos parâmetros de controle e custo computacional. Finalmente, os resultados obtidos demonstraram que a aplicação de técnicas MPC em máquinas de indução apresenta um grande potencial.
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Desenvolvimento e implementação de um sistema de controle de posição e velocidade de uma esteira transportadora usando inversor de frequência e microcontrolador /Raniel, Thiago. January 2011 (has links)
Orientador: Jozué Vieira Filho / Banca: Carlos Antonio Alves / Banca: Tony Inácio da Silva / Resumo: A automação de esteiras rolantes é algo comum e importante em sistemas industriais, mas problemas práticos ainda representam desafios. Um dos desses desafios é manter a precisão em sistemas que exigem paradas sistemáticas, pois folgas mecânicas tendem a provocar variações nas posições de paradas ao longo do tempo. A aplicação de motores de indução têm se tornado comum e soluções eficientes e de baixo custo têm sido pesquisadas. Neste trabalho foi desenvolvido e implementado um sistema de controle de posição e velocidade aplicado em esteiras transportadoras utilizando inversor de frequência, microcontrolador, encoder óptico incremental e sensor indutivo. O movimento da esteira transportadora é efetuado por um motor de indução trifásico, que é acionado pelo conjunto microcontrolador - inversor de frequência. Este conjunto impõe uma frequência no estator do motor através de uma troca de mensagens entre microcontrolador e inversor de frequência (Sistema Mestre-Escravo). Para o envio e recebimento das mensagens, utilizou-se o protocolo de comunicação serial USS® (Universal Serial Interface Protocol) através do padrão RS-485. Os controles de posição e velocidade de rotação do eixo do motor fundamentam-se no sinal gerado pelo encoder óptico incremental, responsável por informar a posição do eixo do motor ao longo da trajetória, e no sensor indutivo que determina uma referência externa importante para a esteira transportadora. Para o funcionamento automático da esteira, elaborou-se um software em linguagem de programação C. Como resultado obteve-se um sistema de controle de posição e velocidade do eixo do motor de indução trifásico que apresenta bons resultados / Abstract: Automated conveyors system have been largely used in industrial applications. However, there are still practical issues to be overcome. One of them is due to the system mechanical limitation which can lead to low accuracy for applications based on "stop-and-go" movements. Induction motors have been largely used in such applications and low costs solutions have been searched. In this work it was developed and implemented a system of positioning and velocity control applied to conveyors which is based on frequency inverter, microcontroller, optical incremental encoder and inductive sensor. The conveyor's movement is made by means of a three-phase induction motor, which is driven by the couple microcontroller-frequency inverter. There are messages exchange between the microcontroller and the frequency inverter (Master - Slave configuration) which is based on the communication serial protocol USS through the RS-485 standard. The position and velocity of the motor spindle are controlled using an optical incremental encoder, which is responsible to provide the position of the trajectory, and an inductive sensor which determines the initial reference to the conveyor. The software used to control the system was developed in C language. The results show a low cost system with good results / Mestre
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Um estudo das características dinâmicas elétrica e mecânica de um gerador de indução duplamente alimentado acoplado à rede elétrica / A study of electrical and mechanical dynamic characteristics of a doubly fed induction generator coupled to the gridRêgo, Saulo Loiola 31 August 2015 (has links)
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Previous issue date: 2015-08-31 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work is carried out a detailed study of the electrical and mechanical behavior of a doubly fed induction machine that operates as wind generator (DFIG), when it is faced with disturbances from both the grid as wind variations. The dynamic analysis becomes closer to the wind turbine connection to a three-phase electrical network containing several bars. The wind turbine has a classical control system, commonly found in the literature, which is to use PI controllers. From the junction of the control system, the power grid model and the turbine model, serial information will be analyzed. The way the system is designed makes possible, simply, changes of parameters and characteristics of the systems, making it possible to perform simulation of many different wind turbines. By the representation adopted of the electrical grid, it was possible to simulate different types of disturbances, enabling a detailed analysis of the system response in front of the disturbances / Nesse trabalho é realizado um estudo detalhado do comportamento elétrico e mecânico de uma máquina de indução duplamente alimentada que opera como gerador eólico (DFIG), quando esta se encontra diante de perturbações provenientes tanto da rede elétrica quanto de variações de vento. A análise da dinâmica torna-se mais detalhada com a conexão do aerogerador a uma rede elétrica trifásica que contem diversas barras. O aerogerador possui um sistema clássico de controle, comumente encontrado na literatura, que é a utilização de controladores do tipo PI. A partir da junção do sistema de controle, do modelo da rede elétrica e do modelo do aerogerador, uma série de dados serão analisados, tais como velocidade de rotação, corrente e potências fornecidas pelo DFIG, tensão elétrica nos barramentos, dentre outros. Ao utilizar uma representação trifásica na rede elétrica, qualquer forma de perturbação elétrica é facilmente implementada e analisada. A forma como o sistema foi elaborado viabiliza, de maneira simples, modificações de parâmetros e características dos sistemas, tornando possível realizar simulação de diversos modelos de aerogeradores. Através da representação adotada na rede elétrica, foi possível simular diferentes tipos de perturbações, viabilizando uma análise detalhada da resposta do sistema diante das mesmas
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Metodologia de análise e caracterização de materiais compósitos magnéticos macios aplicados em atuador planar de induçãoMota Neto, João January 2015 (has links)
O trabalho apresenta o desenvolvimento de uma metodologia denominada modelo de núcleo reduzido, aplicada para avaliar o desempenho de máquinas elétricas no que tange a geometria e materiais empregados na fabricação do núcleo completo. Para fins de validação da metodologia utiliza-se um Atuador Planar de Indução Trifásico com dois graus de liberdade, comparando os resultados numéricos e experimentais. Através desta metodologia, pode-se realizar a análise dos fenômenos eletromagnéticos ocorridos no núcleo completo por meio da avaliação de seu modelo reduzido, composto neste caso por 33% do núcleo completo empregado no Atuador Planar de Indução Trifásico. A comprovação da metodologia do modelo de núcleo reduzido ocorreu através da fabricação de uma bancada de testes, composta por uma célula de carga para realizar aquisição da força de propulsão planar, interface de potência e os núcleos reduzidos com seguintes materiais ferromagnéticos: compósitos SMC 1P Somaloy 500®, Ferro resinado e Aço ABNT 1020. Com auxilio da estrutura de testes, validou-se o modelo numérico dos três núcleos reduzidos quanto a força de propulsão planar. Na análise dos dados experimentais e numéricos, o material Ferro resinado apresentou a diferença 14% referente a força de propulsão planar, sendo a maior diferença entre os materiais estudados. Com a convergência dos resultados experimental e numéricos, realiza-se a comparação numérica entre os núcleos reduzidos e completos utilizando-se os três materiais ferromagnéticos. A análise numérica do núcleo reduzido com o material SMC 1P Somaloy 500® apresentou o fator de relação médio da força de propulsão planar de 2,65 em relação ao núcleo completo. O núcleo completo com Aço ABNT 1020 resultou no consumo médio de 56,7Watts para gerar a força de propulsão planar de 1 Newton. Dessa forma, proporciona-se uma ferramenta de maior rapidez para fabricação e avaliação do desempenho de materiais ferromagnéticos utilizados no núcleo completo da máquina elétrica. / This paper presents the development of a methodology denominated low core model applied to evaluate the performance of electrical machines with respect to geometry and materials used in manufacturing of the complete core. For validation purposes of the methodology is used a Planar Three-phase Induction Actuator with two degrees of freedom, comparing the experimental and numerical results. Through this methodology, it is possible to perform the analysis of electromagnetic phenomena occurring in the complete core based evaluation of the reduced model, made in this case with 33% of the full core employed in the Planar Three-phase Induction Actuator. The verification of the reduced core model methodology occurred through the manufacture of a testing bench, which is composed of a load cell to realize the acquisition of the planar propulsion force, potency interface and reduced cores with the following ferromagnetic materials: SMC 1P Somaloy 500® composites, resinated Iron and Steel ABNT 1020. With the help of the test structure, it was validated the numerical model of the three reduced cores regarding to the planar propulsion force. In the analysis of experimental and numerical data, the resinated Iron material showed a 14% difference concerning the strength of the planar propulsion, which is the biggest difference between the materials studied. With the convergence of the experimental and numerical results, a numerical comparison is performed between the reduced and complete cores using the three ferromagnetic materials. The numerical analysis of the reduced core with the SMC 1P Somaloy 500® material showed the average ratio of the planar factor propulsive force of 2.65 when compared with the complete core. The complete core with ABNT 1020 Steel resulted in an average consumption of 56.7 Watts to generate a planar propulsive force of 1 Newton. Thus, it is provided a faster tool for manufacturing and evaluation of ferromagnetic materials performance used in the complete core of the electric machine.
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Využití židovské hudby v hodinách hudební výchovy / The Use of Jewish Songs in Music ClassesFilipová, Eva January 2018 (has links)
Czech school's curriculum often omits Jewish music. Based on the proposal of concrete music classes, this thesis aims at evolving and enriching this topic. The thesis is divided into two parts. Theoretical part (chapters one and two) begins with description of Jewish culture, history, religion, habits and holidays, including Jewish languages and specifics between Ashkenazi and Sephardic Jews, and follows with description of Jewish music, comprising particular modes and religious and secular music. The objective of this part is to present necessary broader information about Jewish culture for proposed concrete classes. Practical part (third chapter) proposes five thematically divided music classes based on three-phase model. Each music class includes staves extracts and texts; sheet music is annexed. The objective of music classes, which are based on music activities and methods of critical thinking and emphasise creativity of students and cooperation among them, is to build key competences and evolve multicultural behaviour. Nonetheless, this thesis is not a dogmatic proposal of plan of music classes, but primary serves as a source of inspiration for use and further development of concrete musical activities at school. KEY WORDS Jewish culture, Jewish music, music education, three-phase model,...
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Algoritmo de evolução diferencial dedicado ao planejamento de reativos e controle de tensão em sistemas de distribuição de energia elétrica /Serrano, Hugo de Oliveira Motta January 2018 (has links)
Orientador: José Roberto Sanches Mantovani / Resumo: O problema de alocação ótima de banco de capacitores em sistema de distribuição radiais consiste em definir as barras onde devem ser alocados os bancos de capacitores, além de determinar os tipos, potência nominal e em quais fases eles devem ser alocados, atendendo a restrições físicas e operacionais das redes elétricas, juntamente com os padrões da qualidade de fornecimento normatizados pelas agências reguladoras do setor. Também deve-se definir o esquema de controle, ou seja, quando os bancos capacitivos variáveis devem operar em diferentes níveis de carregamentos. A alocação de bancos de capacitores em sistemas de distribuição é um problema de programação não-linear inteiro misto, não convexo, de difícil solução através de técnicas clássicas de otimização, pela sua natureza combinatória, devido o aumento no número de variáveis inteiras envolvidas na solução de problemas de médio e grande porte. Neste trabalho, propõe-se para a sua solução a meta-heurística de Evolução Diferencial (ED), que deve fornecer a localização e dimensionamento dos bancos de capacitores fixos e chaveados ao longo dos alimentadores primários, em sistemas de distribuição radiais trifásicos e desbalanceados. A alocação deve atender aos critérios de mínimo custo de investimento e operação do sistema, dados pela soma do custo de aquisição, instalação e manutenção dos bancos de capacitores, mais o custo de perdas ativas no sistema além de melhorar o fator de potência. São apresentados neste trabalho, resu... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The optimal allocation problem of capacitor bank in radial distribution systems is to define the bus where the capacitor banks must be allocated, furthermore determine the types, nominal power and which phase they must be allocated as they attended the physical and the operational constraints of power systems in conjunction with the supplier quality standards normalized by the sector regulatory agencies. Moreover, you must define the check schema, in the words, when the variable capacitor banks must operate at different load levels. The allocation of capacitor banks in distribution systems it's a not convex mixed integer nonlinear programming problem with a difficult solution through classical optimization techniques due to the increase of integer variables involved in the solution of large and medium-size problems. This works proposes for the solution, a metaheuristic based on Differential Evolution (DE) which provide the location and the sizing of fixed capacitor banks, switched over the primary feeders in unbalanced three-phase radial distribution systems, with the aim of minimizing the total investment and the system operation cost, given by sum of acquisition cost, installation and maintenance of capacitor banks, plus the cost of active losses in the system and to im-prove the power factor. Results for a 135-bus unbalanced three-phase system are presented. / Mestre
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