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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
121

Coordination of reactive power scheduling in a multi-area power system operated by independent utilities

Phulpin, Yannick 13 October 2009 (has links) (PDF)
This thesis addresses the problem of reactive power scheduling in a power system with several areas controlled by independent transmission system operators (TSOs). To design a fair method for optimizing the control settings in the interconnected multi-TSO system, two types of schemes are developed.<br />First, a centralized multi-TSO optimization scheme is introduced, and it is shown that this scheme has some properties of fairness in the economic sense.<br />Second, the problem is addressed through a decentralized optimization scheme with no information exchange between the TSOs. In this framework, each TSO assumes an external network equivalent in place of its neighboring TSOs and optimizes the objective function corresponding to its own control area regardless of the impact that its choice may have on the other TSOs.<br />The thesis presents simulation results obtained with the IEEE 39 bus system and IEEE 118 bus systems partitioned between three TSOs. It also presents some results for a UCTE-like 4141 bus system with seven TSOs. The decentralized control scheme is applied to both time-invariant and time-varying power systems. Nearly optimal performance is obtained in those contexts.
122

Design And Implementation Of A Voltage Source Converter Based Statcom For Reactive Power Compensation And Harmonic Filtering

Cetin, Alper 01 April 2007 (has links) (PDF)
In this thesis, design and implementation of a distribution-type, voltage source converter (VSC) based static synchronous compensator (D-STATCOM) having the simplest converter and coupling transformer topologies have been carried out. The VSC STATCOM is composed of a +/- 750 kVAr full-bridge VSC employing selective harmonic elimination technique, a low-pass input filter, and a &amp / #8710 / /Y connected coupling transformer for connection to medium voltage bus. The power stage of VSC based STATCOM is composed of water-cooled high voltage IGBT modules switched at 850 Hz for the elimination of 5th, 7th, 11th, 13th, 17th, 19th, 23rd,and 25th voltage harmonics. Special care has been taken in the laminated busbar design to minimize stray inductances between power semiconductors and dc link capacitor. Reactive power control is achieved by applying the phase angle control technique. The effect of input filter on total demand distortion has been investigated theoretically by mathematical derivations. The proposed VSC STATCOM has been implemented for reactive power compensation of Coal Preparation System in Kemerk&ouml / y Thermal Power Plant. The field test results have shown the success of the implemented system in view of fast response in reactive power compensation, and minimum input current harmonic content, and compliance with the IEEE Std. 519-1992 even for the weakest power systems. The application of selective harmonic elimination technique and phase angle control to VSC STATCOM has led to optimum switching frequency and device utilization for high voltage IGBTs at the expense of slower response as compared to other PWM techniques.
123

Large Scale Solar Power Integration in Distribution Grids : PV Modelling, Voltage Support and Aggregation Studies

Samadi, Afshin January 2014 (has links)
Long term supporting schemes for photovoltaic (PV) system installation have led to accommodating large numbers of PV systems within load pockets in distribution grids. High penetrations of PV systems can cause new technical challenges, such as voltage rise due to reverse power flow during light load and high PV generation conditions. Therefore, new strategies are required to address the associated challenges. Moreover, due to these changes in distribution grids, a different response behavior of the distribution grid on the transmission side can be expected. Hence, a new equivalent model of distribution grids with high penetration of PV systems is needed to be addressed for future power system studies. The thesis contributions lie in three parts. The first part of the thesis copes with the PV modelling. A non-proprietary PV model of a three-phase, single stage PV system is developed in PSCAD/EMTDC and PowerFactory. Three different reactive power regulation strategies are incorporated into the models and their behavior are investigated in both simulation platforms using a distribution system with PV systems. In the second part of the thesis, the voltage rise problem is remedied by use of reactive power. On the other hand, considering large numbers of PV systems in grids, unnecessary reactive power consumption by PV systems first increases total line losses, and second it may also jeopardize the stability of the network in the case of contingencies in conventional power plants, which supply reactive power. Thus, this thesis investigates and develops the novel schemes to reduce reactive power flows while still keeping voltage within designated limits via three different approaches: decentralized voltage control to the pre-defined set-points developing a coordinated active power dependent (APD) voltage regulation Q(P)using local signals developing a multi-objective coordinated droop-based voltage (DBV) regulation Q(V) using local signals   In the third part of the thesis, furthermore, a gray-box load modeling is used to develop a new static equivalent model of a complex distribution grid with large numbers of PV systems embedded with voltage support schemes. In the proposed model, variations of voltage at the connection point simulate variations of the model’s active and reactive power. This model can simply be integrated intoload-flow programs and replace the complex distribution grid, while still keepingthe overall accuracy high. The thesis results, in conclusion, demonstrate: i) using rms-based simulations in PowerFactory can provide us with quite similar results using the time domain instantaneous values in PSCAD platform; ii) decentralized voltage control to specific set-points through the PV systems in the distribution grid is fundamentally impossible dueto the high level voltage control interaction and directionality among the PV systems; iii) the proposed APD method can regulate the voltage under the steady-state voltagelimit and consume less total reactive power in contrast to the standard characteristicCosφ(P)proposed by German Grid Codes; iv) the proposed optimized DBV method can directly address voltage and successfully regulate it to the upper steady-state voltage limit by causing minimum reactive power consumption as well as line losses; v) it is beneficial to address PV systems as a separate entity in the equivalencing of distribution grids with high density of PV systems. / <p>The Doctoral Degrees issued upon completion of the programme are issued by Comillas Pontifical University, Delft University of Technology and KTH Royal Institute of Technology. The invested degrees are official in Spain, the Netherlands and Sweden, respectively. QC 20141028</p>
124

Δυναμικές επιδράσεις του αιολικού συστήματος στο σύστημα ηλεκτρικής ενέργειας / Dynamic influences of the wind system to power system

Σταματόπουλος, Ευάγγελος, Σαμαράς, Ιωάννης 29 August 2011 (has links)
Η αιολική ενέργεια είναι το κλειδί για να επιτευχθεί ο στόχος της Ε.Ε. για συμμετοχή των Α.Π.Ε. στην παραγωγή ενέργειας σε ποσοστό τουλάχιστον 20% το 2020.Για το λόγο αυτό, αυτή η διπλωματική εργασία έχει σκοπό τη μελέτη των επιπτώσεων του συστήματος αιολικής ενέργειας στο σύστημα ηλεκτρικής ενέργειας.Η έρευνα επικεντρώνεται στο τμήμα των δυναμικών επιπτώσεων, που αφορά κυρίως στις μεταβολές της αέργου ισχύος και των τάσεων στους ζυγούς του συστήματος λόγω μεταβολών διαφόρων παραμέτρων όπως ο άνεμος, οι γραμμές μεταφοράς και διάφορα είδη σφαλμάτων. / The contribution of renewable sources of energy in percent at least 20% is the energy goal of E.U. in 2020.Thus, wind power is considered to be the key to the achievement of this goal.For this reason, this diploma thesis intendsto study the influences of the wind power system to the electrical power system.The research specifies in the section of the dynamic influences, which mostly includes the variations of the voltage and the reactive powe in the systems buses due to variations of variables such as the wind speed, the transmission lines and different types of fault.
125

Mínimo corte de carga em sistemas elétricos de potência sob contingência usando fluxo de potência ótimo reativo com dispositivos SVC

Osorio, Luis Miguel Monroy January 2017 (has links)
Orientador: Prof. Dr. Edmarcio Antonio Belati / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Engenharia Elétrica, 2017. / Esta pesquisa propõe uma metodologia baseada no Fluxo de Potência Ótimo Reativo (FPOR), para a operação dos sistemas de transmissão sob emergência usando o mínimo corte de carga em associação com dispositivos Static VAr Compensator (SVC). O SVC é modelado pelo método da susceptância variável e inserido no problema do FPOR. A função multiobjetivo é formada em três partes, perdas de potência ativa, desvio da tensão e cortes de carga. Propõese um procedimento para calcular os valores dos pesos das funções de perdas e desvio da tensão sendo uma das contribuições deste trabalho. A função de mínimo corte de carga foi associada a uma variável que pode ser contínua ou binária, que corta uma porcentagem (contínua) ou a totalidade (binária) da potência da barra candidata, tratando-se assim como problemas de programação não linear (PNL) ou programação não linear inteira mista (PNLIM) respectivamente. O conjunto de barras candidatas ao corte de carga foi formado pelas barras críticas do sistema para cada situação de contingência e foi definido por meio de uma estratégia proposta neste trabalho para identificar as barras mais susceptíveis ao corte de carga. Para o tratamento das variáveis binárias do problema, foi usado o algoritmo Branch &Bound associado com o FPOR. A metodologia foi testada nos sistemas IEEE de 14 e 118 barras modificados para as diferentes situações de contingência simuladas neste trabalho. / This research proposes a methodology based on the Optimal Reactive Power Flow (ORPF) for the operation of the emergency transmission systems using the minimum load shedding in association with Static VAr Compensator (SVC) devices. The SVC was modeled as a variable susceptance and inserted in the ORPF problem. A multi-objective function was formed by three parts, namely, active power losses, voltage deviation and load shedding was device. Propose a procedure to calculate the values of the weights of the loss functions and the voltage deviation, one of the contributions of this research. The minimum load shedding function uses a variable that can be continuous or binary, which turns off a percentage (continuous) or all (binary) loads of candidate power buses, resulting in a Nonlinear Programming Problems (NLP) or Mixed Integer Nonlinear Programming (MINLP) respectively. The critical buses of the system for each contingency formed the candidate set of buses for the load shedding and was defined by a strategy proposed in this research to identify the bus most susceptible to the load shedding. For the treatment of the binary variables of the problem, a Branch & Bound algorithms associated with the ORPF was used. This methodology was tested in the modified IEEE 14 and 118-bus systems for the different contingency situations simulated in this research.
126

Uma proposta de controle de paralelismo de inversores com a rede elétrica utilizando-se a técnica de realimentação de fase

Paiva, élcio Precioso de 26 May 2006 (has links)
Fundação de Amparo a Pesquisa do Estado de Minas Gerais / The purpose of this work is to present an active and reactive power flow controller applied to inverter paralelism with the stiff AC system. An additional loop is implemented into a conventional control loop based on the characteristic curves of active power versus frequency and reactive power versus voltage. This loop uses the active power variation as feedback to generate the load angle of the voltage reference of the inverter, when it is connected in parallel with the electric network. As a consequence, the active and reactive transitory power oscillations are atenuated, without producing undesirable colateral effects as significative voltage and reactive power variations presented in the utilization of PSS (Power System Stabilizer), another technique used to improve the system damping, [Martins, M. P., 2004]. A dynamic model of the system based on the small signal analysis is presented. The root locus graphics, showing the system poles under parametric variations are also presented, allowing the analysis of the system stability. The simulation results and the experimental ones using a laboratory prototype with and without the additional loop are showed, which validate the obtained small signal model. / Este trabalho apresenta um controlador de fluxos de potência ativa e reativa aplicado ao paralelismo de um inversor com a rede elétrica. Uma malha adicional de controle é inserida a um controlador convencional, o qual é baseado nas curvas características de potência ativa versus freqüência e potência reativa versus tensão. Essa malha utiliza a realimentação da própria variação da potência ativa para a geração do ângulo de carga da tensão de referência do inversor, quando o mesmo é conectado em paralelo com a rede elétrica. Como resultado as oscilações transitórias das potências ativa e reativa são melhor atenuadas, sem produzir efeitos colaterais indesejáveis tais como as variações de tensão e potência reativa presentes na utilização do PSS (Power System Stabilizer Estabilizador de Sistemas de Potência), outra técnica usada para melhorar o amortecimento do sistema, [Martins, M. P., 2004]. Um modelo dinâmico do sistema baseado na análise para pequenos sinais é apresentado. Gráficos do lugar das raízes, mostrando os pólos do sistema diante de variações paramétricas também são apresentados, permitindo a análise de estabilidade do sistema. Resultados de simulação e resultados experimentais utilizando-se um protótipo de laboratório, com e sem a malha de realimentação adicional são mostrados, os quais validam o modelo para pequenos sinais obtido. / Doutor em Ciências
127

Serviços ancilares através da geração distribuíba = reserva de potência ativa e suporte de reativos / Ancillary services provide by distributed generation : active power reserves and reactive support

Moya Chaves, Francisco David 16 August 2018 (has links)
Orientadores: Gilberto de Martino Jannuzzi, Luiz Carlos Pereira da Silva / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-16T17:50:00Z (GMT). No. of bitstreams: 1 MoyaChaves_FranciscoDavid_D.pdf: 2595862 bytes, checksum: b7384c05596f9dc99d6f2e42bbbe231c (MD5) Previous issue date: 2009 / Resumo: Com a finalidade de constituir os princípios para um futuro marco regulatório no Brasil, que contemple a participação da geração distribuída para o fornecimento de serviços ancilares, este trabalho apresenta uma análise desenvolvida em três grandes áreas assim: técnica, econômica e regulatória. Como objetivo específico do projeto, realiza-se uma analise da utilização da GD para o fornecimento de reservas de potência ativa e suporte de reativos. Para atingir os objetivos dessa pesquisa, o trabalho e realizado em três seções complementares. A primeira parte á uma análise técnica, feita mediante a simulação de sistemas elétricos em regime permanente utilizando a analise de fluxos de carga. Apresentam-se algumas das vantagens e limitações técnicas no uso da GD no fornecimento de potencia ativa e reativa. Apresenta-se também, o estudo sobre o fornecimento de reservas operativas com GD, propondo-se uma metodologia para estabelecer o nível máximo de GD que pode ser instalado sem causar impactos negativos sobre a rede. Apresenta-se o desempenho da GD e seus impactos em situações de entrega de reservas operativas, simulando casos diante de possíveis desligamentos de geradores centralizados. Listam-se diversas tecnologias que podem ser utilizadas em aplicações de GD fornecendo serviços ancilares. A segunda seção é uma análise econômica, na qual, e apresentado o despacho adequado de geradores centralizados e descentralizados, realizada mediante a simulação de cenários de sistemas elétricos com fluxos de carga ótimos. Também e feita uma quantificação da contribuição da GD no fornecimento de suporte de reativos. A análise regulatória lista os aspectos a serem considerados num marco regulatório que permita o fornecimento de serviços ancilares através da GD para o futuro mercado de eletricidade no Brasil. Este trabalho, conseqüentemente, conceitua a GD; especifica suas aplicações; evidencia as suas vantagens; lista os segmentos potencialmente geradores e os principais agentes operantes da GD; aponta as tecnologias ora disponíveis e aquelas em processo de desenvolvimento; mostra, generalizadamente, os aspectos legais e institucionais vigentes que influenciam a GD; detalha as principais barreiras a sua inserção como uma alternativa complementar, no fornecimento de servicos ancilares tão necessários nos sistemas elétricos / Abstract: In order to set the principles for a future regulatory framework in Brazil which involves the participation of distributed generation (DG) to provide ancillary services; this work presents an analysis developed in three broad areas, technical, economic and regulatory. A specific objective of the project is to make an analysis of the use of the DG for the supply of active power reserves and reactive support. To achieve the objectives of this research it is necessary to develop three additional sections. The first part is a technical analysis done through the simulation of electrical systems on a permanent regime that uses the analysis of power flows. There are some advantages and technical limitations in the use of DG for the supply of active and reactive power. This part also presents the study on the provision of operating reserves with DG, and proposes a methodology to establish the level of DG, which can be installed without causing negative impacts on the network. In addition to this, this section shows the performance of DG and its impact in case of delivery of operating reserves, simulating some cases before possible disconnections of centralized generators. Finally, it lists different technologies that can be used in applications of DG provided with ancillary services. The second section is an economic analysis which is presented in the appropriate order that centralized and decentralized generators are made by the simulation of scenarios in electrical systems with optimal power flows. It is a quantification of the contribution of DG in the provision of reactive support. The analysis lists the regulatory aspects to be considered in a regulatory framework that enables the provision of ancillary services through the DG for the future market of electricity in Brazil. This work, therefore, conceptualizes a DG; specifies its applications highlighting their advantages, listing segments and potentially generating the key players involved in DG; outlines the technologies now available and those in the development process; shows generally, the legal and institutional force affecting DG; details the key barriers to their inclusion as an additional alternative in the provision of ancillary services as needed in the electrical systems / Doutorado / Engenharia Mecanica / Doutor em Planejamento de Sistemas Energéticos
128

Controle do fluxo de potencia da maquina de indução duplamente alimentada / Control of the power flux of the doubly fed induction machine

Segnini, Helio Henrique de Agostini 17 March 2006 (has links)
Orientador: Edson Bim / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-06T02:49:03Z (GMT). No. of bitstreams: 1 Segnini_HelioHenriquedeAgostini_M.pdf: 1646244 bytes, checksum: d03ec95486ccbccae70ffedf89d964f1 (MD5) Previous issue date: 2006 / Resumo: O objetivo deste trabalho é estudar o modelo da máquina de indução duplamente alimentada no sistema de referência síncrono, bem como controlar seu fluxo de potências através de orientação de fluxo. São analisadas as orientações de fluxo de estator, de entreferro e de rotor em várias operações: compensador de reativos, gerador e motor, com fator de potência indutivo, capacitivo e unitário, nas faixas de velocidade subsíncrona, síncrona e supersíncrona / Abstract: The purpose of this work is to study the Doubly Fed Induction Machine modeling at the synchronous reference frame, as well as to control its power flux by flux oriented control The stator, rotor and air gap flux orientations with the machine operating as reactive compensator, generator and drive, with lag power factor, lead power factor and unity power factor at subsynchronous, synchronous and supersynchronous speeds are analyzed. / Mestrado / Energia Eletrica / Mestre em Engenharia Elétrica
129

Redes neurais artificiais aplicadas a sistemas de potencia / Artificial neural networks for load flow and external equivalents studies

Muller, Heloisa Helena, 1965- 03 December 2008 (has links)
Orientadores: Carlos Alberto de Castro Jr., Marcos Julio Rider Flores / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação / Made available in DSpace on 2018-08-11T05:47:59Z (GMT). No. of bitstreams: 1 Muller_HeloisaHelena_M.pdf: 1272493 bytes, checksum: d78e9e8d9a329ccbf0cc8be6f666af25 (MD5) Previous issue date: 2008 / Resumo: A operação de um sistema de energia elétrica pode ser gerenciada remotamente através dos centros de controle utilizando sistemas de gerenciamento de energia (Energy Management Systems-EMS). Nesses centros de controle são realizadas e executadas freqüentemente muitas funções em tempo real e em modo de estudo. Dentre estas funções têm-se: o controle automático da geração, a estimação de estado, análise de topologia e análise estática de segurança entre tantas outras. A base da resolução destas funções é a execução e testes de um grande número de cálculos de fluxos de potência. A estimativa de estado de um sistema de potência pode ser determinada resolvendo as equações de um fluxo de carga, que matematicamente são representadas por um conjunto de equações algébricas não lineares. Este problema é conhecido como fluxo de potência ou fluxo de carga, e o seu objetivo principal é o cálculo das magnitudes das tensões e seus ângulos de fase, e consequentemente dos fluxos de potência nas linhas de transmissão. O objetivo deste estudo é usar redes neurais artificiais (RNA) na: (a) solução do fluxo de carga (FC); (b) solução do FC considerando controle de limites de tensão nas barras PV; (c) inicialização de um FC para sistema mal condicionados; e (d) cálculo de equivalentes externos estáticos para sistemas de energia elétrica. A idéia é que um fluxo de potência baseado em RNA seja mais rápido que o fluxo de potência convencional baseado no método de Newton-Raphson, particularmente nos casos envolvendo aplicações em tempo rela e em modo de estudo avançadas de fluxos de potência no EMS / Abstract: The operation of electric power systems can be managed remote and automatically from control centers using energy management systems (EMS). In these control centers many on-line and off-line functions are carried out periodically. Among those functions, we can list: the automatic generation control, state estimation, topological analysis, and static security analysis. These functions are based on the calculation of a large number of power flows. The operating state of power systems may be determined by solving power flow equations that are mathematically represented by a set of non-linear algebraic equations. This problem is known as the load flow or power flow problem and its main objective is the calculation of all bus voltage magnitudes and angles, and consequently the power flows through the transmission lines. The goal of this study is to propose an artificial neural networks (ANN) based methodology for (a) solving the basic load flow, (b) solving basic load flow considering reactive power limits of generation (PV) buses, (c) determining a good quality load flow starting point for ill-conditioned systems, and (d) computing static external equivalent circuits. The proposed ANN based power flow solver is intended to be faster than the conventional power flow problem solvers which use Newton-Raphson method, particularly in those cases involving advanced on-line applications of the power flow problem in the EMS / Mestrado / Energia Eletrica / Mestre em Engenharia Elétrica
130

METODOLOGIA DE ANÁLISE PARA UM MERCADO COMPETITIVO DA POTÊNCIA REATIVA / METHODOLOGY OF ANALYSIS FOR A COMPETITIVE MARKET OF REACTIVE POWER

Flores, Marcos Julio Rider 22 February 2002 (has links)
Made available in DSpace on 2016-08-17T14:52:41Z (GMT). No. of bitstreams: 1 Marcos Julio Rider Flores.pdf: 929755 bytes, checksum: 2e82c5bdaf782d2a755462e205cd4c32 (MD5) Previous issue date: 2002-02-22 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / In this work a flexible methodology for computation of active and reactive power marginal costs in competitive electrical markets is proposed. In the formulation is adopted a static model of the synchronous generators which it considers the nonlinearity of the reactive power limits. The total reactive power production cost is considered as a non-linear model that represent the economic loss when an active power is not generated, that cost is referred as the opportunity cost. The reactive power production cost of the static compensators is also included in the formulation. The proposed methodology may calculate the active and reactive power marginal costs, the last ones incentive the agents of the electrical market to participate in a reactive power market. Those marginal costs are computed with a optimal power flow computer program that includes a sequential quadratic programming (SQP) which is a non-linear optimization method that uses na approximation of the Hessian matrix updated in a similar manner to the BGFS (Broyden - Fletcher Goldfarb Shanno) second order optimization method. A computer program, AMDREA, that takes in account the proposed methodology, has been coded in C++ and with object oriented programming techniques. The test systems IEEE 30-bus, IEEE 118-bus and a power system in the southern-south-east Brazilian region has been used to perform several simulations using the proposed methodology. Analysis of the test systems results indicate that the active and reactive power marginal costs supply economic signals that may incentive investments in reactive power by the distributors and big consumers. These results oppose with other results reported in the literature in which is considered that the reactive power productions costs are not relevant. / Neste trabalho é proposta uma metodologia flexível para o cálculo dos custos marginais da potência ativa e reativa em mercados elétricos competitivos. Na formulação adotou-se um modelo estático dos geradores síncronos com considerações não lineares dos limites de potência reativa. O custo total de produção da potência reativa é considerado como um modelo não linear que representa uma perda econômica quando a potência ativa não é gerada, esse custo é denominado custo de oportunidade. O custo de produção de potência reativa dos compensadores estáticos também é incluída na formulação. A metodologia proposta permite determinar custos marginais de potência ativa e reativa sendo que estes últimos tendem a incentivar a participação dos agentes do mercado elétrico no mercado da potência reativa. Os custos marginais da potência ativa e reativa são calculados com um programa computacional de fluxo de potência ótimo que inclui uma técnica de programação quadrática seqüencial (PQS) que é um método de otimização não linear que usa uma aproximação da matriz Hessiana atualizada de maneira similar ao método de otimização BFGS (Broyden - Fletcher Goldfarb - Shanno) de segunda ordem. A metodologia proposta foi implementada num programa computacional interativo e gráfico em ambiente Windows e denominado AMDREA, codificado em linguagem C++ com técnicas de programação orientada a objetos. Os sistemas de teste IEEE de 30 barras, IEEE de 118 barras e mais um sistema elétrico real da região sul-sudeste brasileiro foram utilizados para realizar estudos de simulação aplicando a metodologia proposta. A análise dos resultados obtidos com os sistemas de teste indica que os custos marginais de potência ativa e reativa fornecem sinais econômicos que podem incentivar investimentos de potência reativa por parte dos distribuidores e grandes consumidores. Esses resultados diferem com outros resultados reportados na literatura correspondente em que os custos de produção de potência reativa não são relevantes.

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