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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.
371

Digital Tuft Flow Visualisation of Wind Turbine Blade Stall

Swytink-Binnema, Nigel 20 May 2015 (has links)
Wind turbines installed in the open atmosphere experience much more complex and highly-varying flow than their counterparts in wind tunnels or numerical simulations. In particular, aerodynamic stall—which occurs often on stall-regulated wind turbines in such variable flow conditions—can affect both wind turbine blade lifespan and noise generation. A field test site was therefore installed at the outer limits of the city of Waterloo, Ontario to study a small-scale 30 kW stall-regulated wind turbine. Experimental equipment was installed to monitor parameters such as wind speed and direction, electrical power output, blade pitch angle, rotor rotational speed, and wind turbine yaw orientation. Extensive hardware and software was developed and installed to wirelessly collect data from all instrumentation. Tufts and a remote-operated camera were also installed on one of the two blades of the 10 m diameter horizontal-axis turbine. In a variation on the tuft flow visualisation technique, video files were analysed using a novel digital image processing code. The code was developed in MATLAB to calculate the fraction of the blade which was stalled by determining the position and angle of each tuft in every video frame. The algorithm was able to locate on average 85% of the visible tufts and correctly tagged those which were stalled with a bias of only −5% compared to the typical manual method. When the algorithm was applied to 7 h of tuft video at the outboard 40% of the blade, the total average fraction of stalled tufts varied from 5% at 5 m/s to 40% at 21 m/s. This trend was expected for the stall-regulated design since, as the wind speed is increased, the stall progresses from inboard to outboard regions and from trailing edge to leading edge. The 7 h time period represents at least a two order-of-magnitude increase compared with time periods analysed using previous manual methods. This work has demonstrated a digital implementation of tuft flow visualisation which lends statistical validity (through long-time-period averaging) to a common tool for researching wind turbine stall. The speed and ease with which the tuft method can be implemented, combined with the high cost per energy of small-scale wind turbines, suggest that this digital algorithm is a highly beneficial tool for future studies.
372

Wind-turbine wake flows - Effects of boundary layers and periodic disturbances

Odemark, Ylva January 2014 (has links)
The increased fatigue loads and decreased power output of a wind turbine placed in the wake of another turbine is a well-known problem when building new wind-power farms and a subject of intensive research. These problems are caused by the velocity gradients and high turbulence levels present in the wake of a turbine. In order to better estimate the total power output and life time of a wind-power farm, knowledge about the development and stability of wind-turbine wakes is crucial. In the present thesis, the flow field around small-scale model wind turbines has been investigated experimentally in two wind tunnels. The flow velocity was measured with both hot-wire anemometry and particle image velocimetry. To monitor the turbine performance, the rotational frequency, the power output and the total drag force on the turbine were also measured. The power and thrust coefficients for different tip-speed ratios were calculated and compared to the blade element momentum method, with a reasonable agreement. The same method was also used to design and manufacture new turbine blades, which gave an estimate of the distribution of the lift and drag forces along the blades. The influence of the inlet conditions on the turbine and the wake properties was studied by subjecting the turbine to both uniform in flow and different types of boundary layer in flows. In order to study the stability and development of the tip vortices shed from the turbine blades, a new experimental setup for phase-locked measurements was constructed. The setup made it possible to introduce perturbations of different frequencies and amplitudes, located in the rear part of the nacelle. With a newly developed method, it was possible to characterize the vortices and follow their development downstream, using only the streamwise velocity component. Measurements were also performed on porous discs placed in different configurations. The results highlighted the importance of turbine spacings. Both the measurements on the turbine and the discs were also used to compare with large eddy simulations using the actuator disc method. The simulations managed to predict the mean velocity fairly well in both cases, while larger discrepancies were seen in the turbulence intensity. / <p>QC 20140424</p>
373

Simulation and control of windfarms

Spruce, Christopher John January 1993 (has links)
This thesis examines the design of supervisory controllers for windfarms of pitch-controlled wind turbines. The control objectives are the maximisation of the financial income from the generated electricity and the minimisation of the turbines' fatigue damage. The design exploits the wide variations in the ratio of financial income to fatigue damage which are found both spatially across windfarms and as a function of time. The supervisory control strategy makes use of the ability of pitch-controlled turbines to operate with variable power set points; a capability which is rarely exploited in practice. A windfarm simulation which has been developed for the purposes of testing supervisory controllers is described. It is shown that the simulation is a suitable test-bed for this application. Results are presented which demonstrate how the fatigue damage of a turbine's gearbox and structural components vary as functions of the mean wind-speed, turbulence intensity and power set point, both for isolated turbines and for turbines experiencing wake effects. A lifetime performance function is proposed and 'ideal' power set point curves are evaluated using a genetic search algorithm. It is shown that significant improvements in performance can be achieved if the operation of the turbines is altered to take account of variable electricity tariffs. A windfarm control strategy that splits the turbines into interacting and non-interacting categories is found to give good results. Using data generated by the simulation, it is shown that simple cost functions can be developed for non-interacting turbines which, when used in a controller, give performance that is close to the 'ideal'. A similar cost function is applied to a group of three interacting turbines, and it is found that substantial reductions in all measures of total annual fatigue damage are achieved for a small reduction in total annual financial income. The on-line implementation of windfarm supervisory controllers is discussed and the behaviour of a simple hill-climbing algorithm is examined using a simulated group of three interacting turbines.
374

Constant Voltage, Constant Frequency Operation Of A Self-excited Induction Generator

Caliskan, Ahmet 01 October 2005 (has links) (PDF)
In this thesis, control schemes for the self-excited induction generator are developed with Matlab/Simulink. Self-excited induction generator is considered as a constant voltage-constant frequency supply for an isolated load. A wind turbine is assumed to be the variable-speed drive of the induction generator. Control schemes aim to ensure a constant voltage-constant frequency operation of the induction generator in case of the variations in the wind speed and/or the load. From the general model of the self-excited induction generator, the characteristics of the system and the dynamic responses of the system in case of any disturbance are examined. Next, the control strategies are developed both for the squirrel-cage rotor induction generator and for the wound-rotor induction generator. Two control loops are necessary for constant voltage-constant frequency operation of a variable speed induction generator, one for the voltage regulation and the other for the frequency regulation. After developing the control loops, constant voltage-constant frequency operation of the self-excited induction generator is simulated with a cage type saturation adaptive induction generator, a fixed capacitor with thyristor controlled reactor (TCR) used for frequency regulation and switched external resistors connected to the stator terminals used for voltage regulation.
375

Estudo do fluxo de potência de um gerador de indução de dupla alimentação atuando em um sistema de geração eólio-elétrica / Study of variation of power flow of a doubly-fed induction generator acting on a wind power generation system

Natália Moreira Jacob 03 April 2013 (has links)
A captação de energia eólica tem sido alvo de estudos em todo o mundo nas últimas décadas devido aos incentivos pela busca por geração de energia por meio de fontes alternativas. A configuração mais utilizada atualmente são as turbinas de três pás com eixo horizontal, upwind, operando com velocidade variável com limitação de potência por variação de passo, e utilizando o gerador de indução de dupla alimentação. A operação em velocidade variável com atuação no ângulo de passo permite a máxima captação de energia para as diferentes velocidades de vento, enquanto evita que a turbina ultrapasse o seu valor nominal de potência. O uso de conversores permite o controle das correntes do rotor, variando sua velocidade, e o controle da potência reativa de estator, e a montagem do tipo back-to-back permite que o fluxo de energia do rotor flua para a rede ou da rede. A modelagem matemática do sistema foi toda referenciada no referencial síncrono com notação vetorial e orientação de fluxo de rede, simplificando os modelos matemáticos. Para a montagem dos controladores foi utilizado o método de Controle de Modelo Interno e de Resistência Ativa. A montagem de todo o sistema para simulação foi realizada no Matlab/Simulink, e seu desenvolvimento é mostrado no decorrer do trabalho. Este trabalho analisa o fluxo de energia do sistema, desde a energia captada pelo vento até a energia entregue à rede. Para isso, são feitas análise dos fluxos das potências ativa e reativa do sistema, para fator de potência unitário, indutivo e capacitivo e para os mais recorrentes comportamentos do vento. Também são feitas análises a respeito dos regimes de operação do sistema, definidos a partir da relação entre os fluxos de potência, concluindo que a máquina poderá operar como gerador ou motor, devido principalmente à intensidade da variação do vento. / The use of wind energy has been the subject of studies around the world in recent decades due to the incentives to search for power generation through alternative sources. The most widely used configuration has been the three blades with horizontal axis and upwind turbine, operating in variable speed with power limitation by varying the pitch angle, and using the doubly fed induction generator configuration. The variable speed operation with power limitation enable for maximum energy harvesting for different wind speeds and prevents the turbine exceeds its nominal power. The use of converters allows for control of the rotor currents, varying the speed, and stator reactive power, and assembling type back-to-back allows for the rotor energy flux to flow into and out of the grid. Mathematical modeling of the whole system was referenced in the synchronous reference frame with vector notation and oriented by the grid flux, simplifying the mathematical models. For installation of the drivers, were used the Internal Model Control and Active Damping methods. The assembly of the entire system for simulation was conducted on Matlab / Simulink, and its step to step is shown in this work. This study analyzes the energy flow of the system, from the energy harvest from de wind to the energy delivered to the grid. To reach this, flow analysis of active and reactive power of the system is done, using unity, inductive and capacitive power factor, for the most recurrent wind behaviors. Analysis are made about the operation regimes of the system, defined as the relationship between the power flows, concluding that the machine can operate as a generator or motor, mainly due to the variation of the wind intensity.
376

Emulação dos regimes permante e transitório das turbinas de eixo horizontal incluindo o modelo estático da turbina magnus / Emulation of the static and dynamic characteristics of horizontal axis wind turbines including the steady-state representation of a magnus turbine

Corrêa, Leonardo Candido 24 January 2014 (has links)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The lodgment of wind sites is in a visible growing demand not only in Brazil, but all over the world. The wind energy, even though consolidated, still hosts many scientific researches and industrial development in several areas such as control, power converter topologies and stability of grid connected wind turbines (WT). Due to the remarkable development of this technology in the market and the wind seasonality characteristics, it is difficult to study this power source in its operation field. Thus, a controlled environment for testing is desirable. This dissertation presents a topology of horizontal axis wind turbines (HAWT) emulator using a DC motor to provide an electrical generator the same torque that it would if it was driven by a typical WT. In addition to the static model, represented by the pitch angle and power coefficient, a dynamic model of HAWT is proposed in order to improve the representation of real turbines in the field, which allows characterizing the effect of wind shear, towering shadowing and turbine yaw. Furthermore, it permits emulating large inertia machines through smaller engines, by changing the torque imposed on the generator. The appealing motivation in this thesis is that the Magnus turbine emulation includes a relative new type of wind machine that possesses rotating cylinders instead of the traditional propeller blades in traditional HAWT. It is shown how these cylinders increase the available torque, then producing useful power even at lower wind speeds. Simulated and experimental results to evaluate the performance of the wind turbine emulator are presented. Both turbines are analyzed with and without MPPT. Finally the conclusions of this work are presented as well as new proposals for future works. / A instalação de parques eólicos tem se expandido não só no mundo, mas também no Brasil. A energia eólica, apesar de ser já bastante consolidada, ainda é palco para muitos trabalhos científicos e pesquisas na indústria nas áreas de controle, topologias de conversores de potência e estabilidade na conexão de aerogeradores com a rede. Devido a este fato junto com a sazonalidade do vento, torna-se difícil estudar esse tipo de fonte em seu âmbito de operação, sendo assim desejável um ambiente controlado para testes. Esta dissertação apresenta uma topologia para emulação de turbinas de eixo horizontal (HAWT) utilizando um motor de corrente contínua para acionar geradores com o mesmo torque que haveria caso estivessem acoplados a uma turbina real. Para melhor verossimilhança com as turbinas em campo, além do modelo estático composto pelo ângulo de passo das pás e o coeficiente de potência, propõe-se um modelo dinâmico para representar o efeito cortante do vento, o sombreamento da torre e o direcionamento da turbina em relação ao vento. Além do mais, o modelo proposto permite também a emulação de máquinas de grande inércia usando motores de menor porte, pela simples alteração do torque imposto ao gerador. O diferencial nesta dissertação consiste na possibilidade de emulação da turbina Magnus, que é um aerogerador que possui cilindros girantes no lugar das tradicionais pás presentes nas HAWT, que aumentam o torque disponível. Com isto, pode-se mostrar como a turbina Magnus pode gerar maior potência em baixas velocidades vento. São apresentados então os resultados simulados e experimentais avaliando o comportamento completo do emulador de turbinas eólicas. Ambas as turbinas são analisadas com e sem MPPT. Finalmente, são mostradas as conclusões do trabalho e as propostas para futuros trabalhos.
377

Estudo comparativo de p?s para aerogeradores de grande porte fabricadas em materiais comp?sitos refor?adas com fibra de carbono ou fibra de vidro

Campos, Maxdavid Oliveira 30 December 2013 (has links)
Made available in DSpace on 2014-12-17T14:07:12Z (GMT). No. of bitstreams: 1 MaxdavidOC_DISSERT.pdf: 4786704 bytes, checksum: 3c7952fbe7ed29e1b8d03e70a62dab6c (MD5) Previous issue date: 2013-12-30 / Conselho Nacional de Desenvolvimento Cient?fico e Tecnol?gico / The research and development of wind turbine blades are essential to keep pace with worldwide growth in the renewable energy sector. Although currently blades are typically produced using glass fiber reinforced composite materials, the tendency for larger size blades, particularly for offshore applications, has increased the interest on carbon fiber reinforced composites because of the potential for increased stiffness and weight reduction. In this study a model of blade designed for large generators (5 MW) was studied on a small scale. A numerical simulation was performed to determine the aerodynamic loading using a Computational Fluid Dynamics (CFD) software. Two blades were then designed and manufactured using epoxy matrix composites: one reinforced with glass fibers and the other with carbon fibers. For the structural calculations, maximum stress failure criterion was adopted. The blades were manufactured by Vacuum Assisted Resin Transfer Molding (VARTM), typical for this type of component. A weight comparison of the two blades was performed and the weight of the carbon fiber blade was approximately 45% of the weight of the fiberglass reinforced blade. Static bending tests were carried out on the blades for various percentages of the design load and deflections measurements were compared with the values obtained from finite element simulations. A good agreement was observed between the measured and calculated deflections. In summary, the results of this study confirm that the low density combined with high mechanical properties of carbon fibers are particularly attractive for the production of large size wind turbine blades / A pesquisa e desenvolvimento de p?s de aerogeradores s?o fundamentais para acompanhar o crescimento no setor de energias renov?veis em todo mundo. Apesar das p?s atualmente serem produzidas tipicamente com materiais comp?sitos refor?ados com fibras de vidro, a tend?ncia de aumento no tamanho das p?s, especialmente no setor offshore, cresce tamb?m o interesse por materiais comp?sitos refor?ados com fibras de carbono, devido ?s suas propriedades, como elevado m?dulo de elasticidade combinado com baixa densidade. Nesse trabalho um modelo de p? desenvolvido para geradores de grande porte (5 MW) foi estudado em escala reduzida. Foram realizados estudos num?ricos empregando t?cnicas de Computational Fluid Dynamics (CFD) para determinar o carregamento aerodin?mico na p?. Foram projetadas e fabricadas duas p?s com materiais comp?sitos de matriz ep?xi, sendo uma p? com refor?o de fibras de vidro e outra com fibras de carbono. Para os c?lculos estruturais, foi adotado o crit?rio de falha por tens?o m?xima. As p?s foram fabricadas pelo processo de Vacuum Assisted Resin Transfer Molding (VARTM), t?pico para este tipo de componente. Uma compara??o do peso das duas p?s foi realizada, e a p? de fibra de carbono apresentou 45% do peso da p? de fibra de vidro. Ensaios est?ticos de flex?o foram realizados nas p?s para v?rios percentuais do carregamento de projeto e as deflex?es medidas foram comparadas com os valores obtidos nas simula??es num?ricas por elementos finitos. Uma boa concord?ncia foi observada entre os valores de deflex?o medidos e calculados. Em resumo, os resultados obtidos neste trabalho confirmam que a baixa densidade combinada com elevadas propriedades mec?nicas das fibras de carbono s?o atrativas para a produ??o de p?s de aerogeradores de grande porte
378

Effect of atmospheric ice accretion on the dynamic performance of wind turbine blades

Alsabagh, Abdel Salam January 2017 (has links)
Atmospheric icing presents serious challenges to the development of wind power of the wind energy industry in cold regions. The potential detrimental impact on the safe operation of wind turbines and the energy harvest hasn't been fully understood and requires further investigation. This thesis presents the research on icing profiles under different weather conditions and their impact on natural frequency, fatigue life, and lift and drag of the wind turbine blade. The research aims to develop a further understanding of the effect of atmospheric ice accretion on the structural integrity and aerodynamic performance of wind turbine blades through numerical and aerodynamic investigations to address the challenges facing the industry. A 5-MW NREL (National Renewable Energy Laboratory) wind turbine blade was selected for this study, due to availability of required geometric design parameters and experimental data for verification. The turbine rotor and its three blades were modelled and numerically simulated with commercial finite element software ANSYS. Three icing scenarios were chosen according to the ISO Standard and the corresponding icing profiles were developed to investigate their influence on vibrational behaviours of the wind turbine blade and rotor under different weather conditions. Icing loads were applied on the leading edge of the blade and natural frequency results were compared between clean and iced blades. It was found that harsh icing weather drove the natural frequency down to the near resonance limit, which could lead to significant issue on structural integrity of the wind turbine. The effect of atmospheric ice accretion with additional load due to varying wind speeds on the fatigue life of the wind turbine blade has been investigated. Significant reduction of fatigue life was found due to the increase of the von Mises stresses. Finally, computational fluid dynamics (CFD) analysis was carried out to investigate the effect of atmospheric ice accretion on the aerodynamic performance of typical 1-MW and 5-MW wind turbine blades. Results of the drag and lift coefficients and power production under different icing scenarios were obtained for five angles of attack. Compared with the results of the clean aerofoil profile, remarkable reduction in the power generation was observed due to the accreted ice at various aerofoil sections in the spanwise direction of the blade, demonstrating the detrimental impact of atmospheric icing on energy harvest for the wind energy industry.
379

Avaliação de estratégias de controle adaptativo do gerador síncrono de ímã permanente aplicado em sistema de energia eólica / Evaluation of adaptive control strategies of permanent magnet synchronous generator applied in wind power system

Pena, Danilo de Santana 18 July 2015 (has links)
Made available in DSpace on 2016-08-31T13:33:43Z (GMT). No. of bitstreams: 1 DaniloSP_DISSERT.pdf: 1541140 bytes, checksum: a3ab0c19a32a7eaf392690513de9a9a5 (MD5) Previous issue date: 2015-07-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The objective of this study is to evaluate different strategies for adaptive control in order to contribute to better performance controllers with synchronous generators with uncertainties of the parameters or disturbances. The permanent magnet synchronous generators are growing in the market for wind power generation, this being the necessary motivation for choosing this plant. A study and analysis of subsystems of wind energy conversion are performed, and the model of the wind turbine, the mechanical transmission system and synchronous generator are described. The project strategy with conventional control is performed and will be the target of comparison for the implemented adaptive control strategies / O objetivo deste trabalho é avaliar diferentes estratégias de controle adaptativo a fim de contribuir para a melhoria do desempenho de controladores de geradores síncronos com incertezas dos parâmetros ou perturbações. Os geradores síncronos de ímã permanente estão crescendo rapidamente no mercado de geração de energia eólica, sendo a motivação necessária para a escolha desta planta. Um estudo e análise dos subsistemas de conversão de energia eólica são realizados, sendo descrito o modelo da turbina eólica, do sistema de transmissão mecânico e do gerador síncrono. O projeto com estratégia de controle convencional é abordado e será alvo de comparação para as estratégias de controle adaptativo implementadas
380

Análise Trifásica de Sistemas de Distribuição com Modelos de Turbinas Eólicas Tipo IV / Three-phase analysis of turbine models with distribution systems Wind Type IV

Rocha, Ednardo Pereira da 30 January 2015 (has links)
Made available in DSpace on 2016-08-31T13:33:44Z (GMT). No. of bitstreams: 1 EdnardoPR_DISSERT.pdf: 2329567 bytes, checksum: ab9bc3145d3823983047e9d57956c8d0 (MD5) Previous issue date: 2015-01-30 / Fundação de Apoio a Pesquisa do Estado do Rio Grande do Norte / The connection of wind generators might cause significant influences in the profile voltages, voltage unbalance, loading and the electrical losses in radial power distribution systems. This fact requires a specific study, called Hosting Capacity, which aims to analyze the maximum limit of the power increase on the network that makes the performance of the system acceptable to the established quality limits. This work shows an IEEE radial distribution system behavior, composed of 13 bus, in steady state, when a synchronous wind machine is engaged on the bus 680 in two ways: directly connected to the network and connected through the frequency converter. For each type of connection the power factor was varied from 0.9 capacitive to inductive 0.9. The parameters analyzed in connection bar were the degree of voltage unbalance, the losses in the system and the profile of voltages on the bus 680 for each case . The simulations were performed using the program Distribution Network Analysis with Generation Aeolian-Electric - ANAREDGEE, which was developed and validated with own results of the IEEE. It was found that there was a reduction in the degree of unbalance for all simulated situations, when compared to the original value of the system status, not exceeded the limits determined by imbalances entities NEMA, ANSI, IEEE and ANEEL. Regarding the profile of voltages in the various system buses, there was a slight decrease in some situations. In the original system, the voltage level of the phase B in the bus 680 exceeded the 5% voltage given by ANEEL, with a value of 1.0529 p.u. With the machine connected directly, there was an increase of this value in all simulations with different power factor, while the connection through frequency converter might causa a reduction of the phase B voltage levels to below 1.05 pu in situations where the power factors were equal to 0.9 capacitive and unitary. The system losses were reduced in all cases, but showed lower values when the synchronous machine was integrated into the system by frequency convertor. It was also observed a significant reduction in the degree of system imbalance after connecting the synchronous machine, this reduction, in most cases, occurred in proportion to the increase in power injected into the connection bar / A conexão de geradores eólio-elétricos pode causar influências significativas no perfil de tensões, desequilíbrio de tensão, no carregamento e nas perdas elétricas em sistemas de distribuição de energia radiais. Este fato requer um estudo específico, denominado Hosting Capacity, que tem por finalidade analisar o limite máximo do incremento de potência na rede que torna a performance do sistema aceitável para os limites de qualidade estabelecidos. Este trabalho demonstra o comportamento do sistema de distribuição radial do IEEE, composto de 13 barras, em regime permanente, quando uma máquina eólica síncrona é acoplada na barra com o maior nível de tensão do sistema, de duas formas distintas: diretamente conectada à rede e conectada por meio de conversor de frequência. Para cada tipo de conexão o fator de potência foi variado de 0.9 capacitivo a 0.9 indutivo. Os parâmetros analisados na barra de conexão foram o grau de desequilíbrio de tensão, as perdas no sistema e o perfil das tensões. As simulações foram realizadas através do programa Análise de Redes de Distribuição com Geração Eólio-Elétrica - ANAREDGEE, que foi desenvolvido e validado com resultados próprios do IEEE. Verificou-se que houve uma redução no grau d e desequilíbrio para todas as situações simuladas, quando comparadas ao valor da situação original do sistema, não superado os limites de desequilíbrios determinados por entidades como NEMA, ANSI, IEEE e ANEEL. Com relação ao perfil das tensões nas diversas barras do sistema, houve uma ligeira diminuição em algumas situações. No sistema original, o valor de tensão na fase B da barra 680 superava os 5% de sobretensão determinado pela ANEEL, apresentando um valor de 1,0529 p.u. Com a máquina diretamente conectada houve um aumento deste valor em todas as simulações com diferentes fatores de potência, enquanto que a conexão por meio de conversor de frequência possibilitou uma diminuição dos níveis de tensão da fase B para valores abaixo de 1,05 p.u. nas situações em que os fatores de potência eram iguais a 0.9 capacitivo e unitário. As perdas no sistema foram reduzidas em todos os casos, entretanto apresentaram menores valores quando a máquina síncrona era integrada ao sistema por meio de conversor de frequência. Foi observado também uma redução considerável do grau de desequilíbrio do sistema após a conexão da máquina síncrona, esta redução, na maioria dos casos, se deu de forma proporcional ao aumento da potência injetada na barra de conexão

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