929 resultados para Maximum Power Point Tracking (mppt)
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Pós-graduação em Engenharia Elétrica - FEIS
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This paper presents an analysis of an irreversible Otto cycle aiming to optimize the net power through ECOP and ecological function. The studied cycle operates between two thermal reservoirs of infinite thermal capacity, with internal irreversibilities derived from non-isentropic behavior of compression and expansion processes, irreversibilities from thermal resistance in heat exchangers and heat leakage from the high temperature reservoir to the low temperature reservoir. Analytical expressions are applied for the power outputs optimized by the ECOP, by the ecological function and by the maximum power criteria, in conjunction with a graphic analysis, in which some cycle operation parameters are analyzed for an increased comprehension of the effects of the irreversibilities in the optimized power.
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Membranes of Poly(2,5-benzimidazole) (ABPBI), prepared by polycondensation in polyphosphoric acid, were characterized from the fuel cell application point of view: mechanical properties of the membranes for different acid doping levels, thermal stability, permeability for the different gases/vapors susceptible of use in the cell (hydrogen, oxygen, methanol and ethanol), electro-osmotic water drag coefficient, oxidation stability to hydroxyl radicals, phosphoric acid leaching rate and, finally, in-plane membrane conductivity. ABPBI membranes presented an excellent thermal stability, above 500 degrees C in oxygen, suitable mechanical properties for high phosphoric acid doping levels, a low methanol and ethanol limiting permeation currents, and oxygen permeability compared to Nafion membranes, and a low phosphoric acid leaching rate when exposed to water vapor. On the contrary, hydrogen permeation current was higher than that of Nafion, and the chemical stability was very limited. Membrane conductivity achieved 0.07 S cm(-1) after equilibration with a humid environment. Fuel cell tests showed reasonable good performances, with a maximum power peak of 170 mW cm(-2) for H-2/air at 170 degrees C operating under a humidified hydrogen stream, 39.9 mW cm(-2) for CH3OH/O-2 at 200 degrees C for a methanol/water weight ratio of 1: 2, and 31.5 mW cm(-2) for CH3CH2OH/O-2 at the same conditions than for methanol. (C) 2012 The Electrochemical Society. [DOI: 10.1149/2.014207jes] All rights reserved.
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This study investigates the promoting effect of PtSnIr/C (1:1:1) electrocatalyst anode, prepared by polymeric precursor method, on the ethanol oxidation reaction in a direct ethanol fuel cell (DEFC). All of the materials used were 20% metal m/m on carbon. X-ray photoelectron spectroscopy (XPS) analysis showed the presence of Pt, PtOH2, PtO2, SnO2 and IrO2 at the electrocatalyst surface, indicating a possible decorated particle structure. X-ray diffractometry (XRD) analysis indicated metallic Pt and Ir as well as the formation of an alloy with Sn. Using the PtSnIr/C electrocatalyst prepared here with two times lower loading of Pt than PtSn/C E-tek electrocatalyst, it was possible to obtain the same maximum power density found for the commercial material. The main reaction product was acetic acid probably due to the presence of oxides, in this point the bifunctional mechanism is predominant, but an electronic effect should not be discarded.
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The installation of induction distributed generators should be preceded by a careful study in order to determine if the point of common coupling is suitable for transmission of the generated power, keeping acceptable power quality and system stability. In this sense, this paper presents a simple analytical formulation that allows a fast and comprehensive evaluation of the maximum power delivered by the induction generator, without losing voltage stability. Moreover, this formulation can be used to identify voltage stability issues that limit the generator output power. All the formulation is developed by using the equivalent circuit of squirrel-cage induction machine. Simulation results are used to validate the method, which enables the approach to be used as a guide to reduce the simulation efforts necessary to assess the maximum output power and voltage stability of induction generators. (C) 2011 Elsevier Ltd. All rights reserved.
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This study investigates the promoting effect of PtSnIr/C (1:1:1) electrocatalyst anode, prepared by polymeric precursor method, on the ethanol oxidation reaction in a direct ethanol fuel cell (DEFC). All of the materials used were 20% metal m/m on carbon. X-ray photoelectron spectroscopy (XPS) analysis showed the presence of Pt, PtOH2, PtO2, SnO2 and IrO2 at the electrocatalyst surface, indicating a possible decorated particle structure. X-ray diffractometry (XRD) analysis indicated metallic Pt and Ir as well as the formation of an alloy with Sn. Using the PtSnIr/C electrocatalyst prepared here with two times lower loading of Pt than PtSn/C E-tek electrocatalyst, it was possible to obtain the same maximum power density found for the commercial material. The main reaction product was acetic acid probably due to the presence of oxides, in this point the bifunctional mechanism is predominant, but an electronic effect should not be discarded.
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Bone-anchored hearing implants (BAHI) are routinely used to alleviate the effects of the acoustic head shadow in single-sided sensorineural deafness (SSD). In this study, the influence of the directional microphone setting and the maximum power output of the BAHI sound processor on speech understanding in noise in a laboratory setting were investigated. Eight adult BAHI users with SSD participated in this pilot study. Speech understanding in noise was measured using a new Slovak speech-in-noise test in two different spatial settings, either with noise coming from the front and noise from the side of the BAHI (S90N0) or vice versa (S0N90). In both spatial settings, speech understanding was measured without a BAHI, with a Baha BP100 in omnidirectional mode, with a BP100 in directional mode, with a BP110 power in omnidirectional and with a BP110 power in directional mode. In spatial setting S90N0, speech understanding in noise with either sound processor and in either directional mode was improved by 2.2-2.8 dB (p = 0.004-0.016). In spatial setting S0N90, speech understanding in noise was reduced by either BAHI, but was significantly better by 1.0-1.8 dB, if the directional microphone system was activated (p = 0.046), when compared to the omnidirectional setting. With the limited number of subjects in this study, no statistically significant differences were found between the two sound processors.
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La presente tesis doctoral propone un conjunto de ensayos de corta duración destinados a cubrir la ausencia de estándares internacionales específicamente adaptados a la tecnología y al panorama fotovoltaico actual que indiquen como realizar los procedimientos de control de calidad para comprobar que las grandes centrales fotovoltaicas ejecutadas responden a las expectativas establecidas durante la fase de proyecto. Dichos ensayos buscan, desde el punto de vista estrictamente técnico, obtener en un corto periodo de tiempo (típicamente una semana) resultados altamente repetitivos y representativos del comportamiento de la instalación bajo análisis, a la vez que minimizar al máximo la incertidumbre global, aspectos fundamentales para los procedimientos de control general de la calidad de una central. Los ensayos propuestos comprueban tanto el comportamiento general de la central, en términos de su capacidad de producción energética, como el de sus principales componentes, generadores fotovoltaicos e inversores, en términos de potencia máxima y eficiencia, respectivamente. También se aconseja una revisión de la calidad y seguridad de la instalación y de los materiales empleados en la ejecución de la central para evitar un envejecimiento prematuro de los mismos. Todos los ensayos recogidos en el texto se apoyan en la experiencia recopilada por el “Grupo de Sistemas Fotovoltaicos del Instituto de Energía Solar de la Universidad Politécnica de Madrid”, que ha estado involucrado en procedimientos de control de calidad de unas 50 centrales fotovoltaicas, con una potencia acumulada cercana a 250 MW, la mayoría de ellas instaladas en España. ABSTRACT This PhD thesis proposes a set of short-duration tests to establish quality control procedures to ensure that large photovoltaic plants fulfil the initial expectations. The motivation for this work is the lack of international standards specifically adapted to the present photovoltaic technology and its state of the art. From a strict technical point of view, these tests seek to obtain highly repetitive and representative results about the behaviour of the installation under study in a short period of time (typically one single week); and to minimize the global uncertainty. These are the two keys aspects required in quality control procedures. The proposed tests evaluate the general behaviour of the photovoltaic plants, in terms of energy production, as well as the particular behaviour of their main devices, photovoltaic arrays and inverters, in terms of maximum power and efficiency, respectively. A review of the installation quality and safety, and the employed materials in its execution to avoid premature aging is also recommended. The tests here presented are based on the experience accumulated by the “Grupo de Sistemas Fotovoltaicos del Instituto de Energia Solar de la Universidad Politecnica de Madrid”. This group has been involved in quality control procedures of about 50 photovoltaic plants, with an accumulated power close to 250 MW, most of them installed in Spain.
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This paper presents an envelope amplifier solution for envelope elimination and restoration (EER), that consists of a series combination of a switch-mode power supply (SMPS), based on three-level voltage cells and a linear regulator. This cell topology offers several advantages over a previously presented envelope amplifier based on a different multilevel topology (two-level voltage cells). The topology of the multilevel converter affects to the whole design of the envelope amplifier and a comparison between both design alternatives regarding the size, complexity and the efficiency of the solution is done. Both envelope amplifier solutions have a bandwidth of 2 MHz with an instantaneous maximum power of 50 W. It is also analyzed the linearity of the three-level cell solution, with critical importance in the EER technique implementation. Additionally, considerations to optimize the design of the envelope amplifier and experimental comparison between both cell topologies are included.
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An electrodynamic tether system for power generation at Jupiter is presented that allows extracting energy from Jupiter's corotating plasmasphere while leaving the system orbital energy unaltered to first order. The spacecraft is placed in a polar orbit with the tether spinning in the orbital plane so that the resulting Lorentz force, neglecting Jupiter's magnetic dipole tilt, is orthogonal to the instantaneous velocity vector and orbital radius, hence affecting orbital inclination rather than orbital energy. In addition, the electrodynamic tether subsystem, which consists of two radial tether arms deployed from the main central spacecraft, is designed in such a way as to extract maximum power while keeping the resulting Lorentz torque constantly null. The power-generation performance of the system and the effect on the orbit inclination is evaluated analytically for different orbital conditions and verified numerically. Finally, a thruster-based inclination-compensation maneuver at apoapsis is added, resulting in an efficient scheme to extract energy from the plasmasphere of the planet with minimum propellant consumption and no inclination change. A tradeoff analysis is conducted showing that, depending on tether size and orbit characteristics, the system performance can be considerably higher than conventional power-generation methods.
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Short-term variability in the power generated by large grid-connected photovoltaic (PV) plants can negatively affect power quality and the network reliability. New grid-codes require combining the PV generator with some form of energy storage technology in order to reduce short-term PV power fluctuation. This paper proposes an effective method in order to calculate, for any PV plant size and maximum allowable ramp-rate, the maximum power and the minimum energy storage requirements alike. The general validity of this method is corroborated with extensive simulation exercises performed with real 5-s one year data of 500 kW inverters at the 38.5 MW Amaraleja (Portugal) PV plant and two other PV plants located in Navarra (Spain), at a distance of more than 660 km from Amaraleja.
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La capacidad de transporte es uno de los baremos fundamentales para evaluar la progresión que puede llegar a tener un área económica y social. Es un sector de elevada importancia para la sociedad actual. Englobado en los distintos tipos de transporte, uno de los medios de transporte que se encuentra más en alza en la actualidad, es el ferroviario. Tanto para movilidad de pasajeros como para mercancías, el tren se ha convertido en un medio de transporte muy útil. Se encuentra dentro de las ciudades, entre ciudades con un radio pequeño entre ellas e incluso cada vez más, gracias a la alta velocidad, entre ciudades con gran distancia entre ellas. Esta Tesis pretende ayudar en el diseño de una de las etapas más importantes de los Proyectos de instalación de un sistema ferroviario: el sistema eléctrico de tracción. La fase de diseño de un sistema eléctrico de tracción ferroviaria se enfrenta a muchas dudas que deben ser resueltas con precisión. Del éxito de esta fase dependerá la capacidad de afrontar las demandas de energía de la explotación ferroviaria. También se debe atender a los costes de instalación y de operación, tanto costes directos como indirectos. Con la Metodología que se presenta en esta Tesis se ofrecerá al diseñador la opción de manejar un sistema experto que como soluciones le plantee un conjunto de escenarios de sistemas eléctricos correctos, comprobados por resolución de modelos de ecuaciones. Correctos desde el punto de vista de validez de distintos parámetros eléctrico, como de costes presupuestarios e impacto de costes indirectos. Por tanto, el diseñador al haber hecho uso de esta Metodología, tendría en un espacio de tiempo relativamente corto, un conjunto de soluciones factibles con las que poder elegir cuál convendría más según sus intereses finales. Esta Tesis se ha desarrollado en una vía de investigación integrada dentro del Centro de Investigaciones Ferroviarias CITEF-UPM. Entre otros proyectos y vías de investigación, en CITEF se ha venido trabajando en estudios de validación y dimensionamiento de sistemas eléctricos ferroviarios con diversos y variados clientes y sistemas ferroviarios. A lo largo de los proyectos realizados, el interés siempre ha girado mayoritariamente sobre los siguientes parámetros del sistema eléctrico: - Calcular número y posición de subestaciones de tracción. Potencia de cada subestación. - Tipo de catenaria a lo largo del recorrido. Conductores que componen la catenaria. Características. - Calcular número y posición de autotransformadores para sistemas funcionando en alterna bitensión o 2x25kV. - Posición Zonas Neutras. - Validación según normativa de: o Caídas de tensión en la línea o Tensiones máximas en el retorno de la línea o Sobrecalentamiento de conductores o Sobrecalentamiento de los transformadores de las subestaciones de tracción La idea es que las soluciones aportadas por la Metodología sugieran escenarios donde de estos parámetros estén dentro de los límites que marca la normativa. Tener la posibilidad de tener un repositorio de posibles escenarios donde los parámetros y elementos eléctricos estén calculados como correctos, aporta un avance en tiempos y en pruebas, que mejoraría ostensiblemente el proceso habitual de diseño para los sistemas eléctricos ferroviarios. Los costes directos referidos a elementos como subestaciones de tracción, autotransformadores, zonas neutras, ocupan un gran volumen dentro del presupuesto de un sistema ferroviario. En esta Tesis se ha querido profundizar también en el efecto de los costes indirectos provocados en la instalación y operación de sistemas eléctricos. Aquellos derivados del impacto medioambiental, los costes que se generan al mantener los equipos eléctricos y la instalación de la catenaria, los costes que implican la conexión entre las subestaciones de tracción con la red general o de distribución y por último, los costes de instalación propios de cada elemento compondrían los costes indirectos que, según experiencia, se han pensado relevantes para ejercer un cierto control sobre ellos. La Metodología cubrirá la posibilidad de que los diseños eléctricos propuestos tengan en cuenta variaciones de coste inasumibles o directamente, proponer en igualdad de condiciones de parámetros eléctricos, los más baratos en función de los costes comentados. Analizando los costes directos e indirectos, se ha pensado dividir su impacto entre los que se computan en la instalación y los que suceden posteriormente, durante la operación de la línea ferroviaria. Estos costes normalmente suelen ser contrapuestos, cuánto mejor es uno peor suele ser el otro y viceversa, por lo que hace falta un sistema que trate ambos objetivos por separado. Para conseguir los objetivos comentados, se ha construido la Metodología sobre tres pilares básicos: - Simulador ferroviario Hamlet: Este simulador integra módulos para construir esquemas de vías ferroviarios completos; módulo de simulación mecánica y de la tracción de material rodante; módulo de señalización ferroviaria; módulo de sistema eléctrico. Software realizado en C++ y Matlab. - Análisis y estudio de cómo focalizar los distintos posibles escenarios eléctricos, para que puedan ser examinados rápidamente. Pico de demanda máxima de potencia por el tráfico ferroviario. - Algoritmos de optimización: A partir de un estudio de los posibles algoritmos adaptables a un sistema tan complejo como el que se plantea, se decidió que los algoritmos genéticos serían los elegidos. Se han escogido 3 algoritmos genéticos, permitiendo recabar información acerca del comportamiento y resultados de cada uno de ellos. Los elegidos por motivos de tiempos de respuesta, multiobjetividad, facilidad de adaptación y buena y amplia aplicación en proyectos de ingeniería fueron: NSGA-II, AMGA-II y ɛ-MOEA. - Diseño de funciones y modelo preparado para trabajar con los costes directos e indirectos y las restricciones básicas que los escenarios eléctricos no deberían violar. Estas restricciones vigilan el comportamiento eléctrico y la estabilidad presupuestaria. Las pruebas realizadas utilizando el sistema han tratado o bien de copiar situaciones que se puedan dar en la realidad o directamente sistemas y problemas reales. Esto ha proporcionado además de la posibilidad de validar la Metodología, también se ha posibilitado la comparación entre los algoritmos genéticos, comparar sistemas eléctricos escogidos con los reales y llegar a conclusiones muy satisfactorias. La Metodología sugiere una vía de trabajo muy interesante, tanto por los resultados ya obtenidos como por las oportunidades que puede llegar a crear con la evolución de la misma. Esta Tesis se ha desarrollado con esta idea, por lo que se espera pueda servir como otro factor para trabajar con la validación y diseño de sistemas eléctricos ferroviarios. ABSTRACT Transport capacity is one of the critical points to evaluate the progress than a specific social and economical area is able to reach. This is a sector of high significance for the actual society. Included inside the most common types of transport, one of the means of transport which is elevating its use nowadays is the railway. Such as for passenger transport of weight movements, the train is being consolidated like a very useful mean of transport. Railways are installed in many geography areas. Everyone know train in cities, or connecting cities inside a surrounding area or even more often, taking into account the high-speed, there are railways infrastructure between cities separated with a long distance. This Ph.D work aims to help in the process to design one of the most essential steps in Installation Projects belonging to a railway system: Power Supply System. Design step of the railway power supply, usually confronts to several doubts and uncertainties, which must be solved with high accuracy. Capacity to supply power to the railway traffic depends on the success of this step. On the other hand is very important to manage the direct and indirect costs derived from Installation and Operation. With the Methodology is presented in this Thesis, it will be offered to the designer the possibility to handle an expert system that finally will fill a set of possible solutions. These solutions must be ready to work properly in the railway system, and they were tested using complex equation models. This Thesis has been developed through a research way, integrated inside Citef (Railway Research Centre of Technical University of Madrid). Among other projects and research ways, in Citef has been working in several validation studies and dimensioning of railway power supplies. It is been working by a large range of clients and railways systems. Along the accomplished Projects, the main goal has been rounded mostly about the next list of parameters of the electrical system: - Calculating number and location of traction substations. Power of each substation. - Type of Overhead contact line or catenary through the railway line. The wires which set up the catenary. Main Characteristics. - Calculating number and position of autotransformers for systems working in alternating current bi-voltage of called 2x25 kV. - Location of Neutral Zones. - Validating upon regulation of: o Drop voltages along the line o Maximum return voltages in the line o Overheating/overcurrent of the wires of the catenary o Avoiding overheating in the transformers of the traction substations. Main objective is that the solutions given by the Methodology, could be suggest scenarios where all of these parameters from above, would be between the limits established in the regulation. Having the choice to achieve a repository of possible good scenarios, where the parameters and electrical elements will be assigned like ready to work, that gives a great advance in terms of times and avoiding several tests. All of this would improve evidently the regular railway electrical systems process design. Direct costs referred to elements like traction substations, autotransformers, neutral zones, usually take up a great volume inside the general budget in railway systems. In this Thesis has been thought to bear in mind another kind of costs related to railway systems, also called indirect costs. These could be enveloped by those enmarked during installation and operation of electrical systems. Those derived from environmental impact; costs generated during the maintenance of the electrical elements and catenary; costs involved in the connection between traction substations and general electric grid; finally costs linked with the own installation of the whole electrical elements needed for the correct performance of the railway system. These are integrated inside the set has been collected taking into account own experience and research works. They are relevant to be controlled for our Methodology, just in case for the designers of this type of systems. The Methodology will cover the possibility that the final proposed power supply systems will be hold non-acceptable variations of costs, comparing with initial expected budgets, or directly assuming a threshold of budget for electrical elements in actual scenario, and achieving the cheapest in terms of commented costs from above. Analyzing direct and indirect costs, has been thought to divide their impact between two main categories. First one will be inside the Installation and the other category will comply with the costs often happens during Railway Operation time. These costs normally are opposed, that means when one is better the other turn into worse, in costs meaning. For this reason is necessary treating both objectives separately, in order to evaluate correctly the impact of each one into the final system. The objectives detailed before build the Methodology under three basic pillars: - Railway simulator Hamlet: This software has modules to configure many railway type of lines; mechanical and traction module to simulate the movement of rolling stock; signaling module; power supply module. This software has been developed using C++ and Matlab R13a - Previously has been mandatory to study how would be possible to work properly with a great number of feasible electrical systems. The target comprised the quick examination of these set of scenarios in terms of time. This point is talking about Maximum power demand peaks by railway operation plans. - Optimization algorithms. A railway infrastructure is a very complex system. At the beginning it was necessary to search about techniques and optimization algorithms, which could be adaptable to this complex system. Finally three genetic multiobjective algorithms were the chosen. Final decision was taken attending to reasons such as time complexity, able to multiobjective, easy to integrate in our problem and with a large application in engineering tasks. They are: NSGA-II, AMGA-II and ɛ-MOEA. - Designing objectives functions and equation model ready to work with the direct and indirect costs. The basic restrictions are not able to avoid, like budgetary or electrical, connected hardly with the recommended performance of elements, catenary and safety in a electrical railway systems. The battery of tests launched to the Methodology has been designed to be as real as possible. In fact, due to our work in Citef and with real Projects, has been integrated and configured three real railway lines, in order to evaluate correctly the final results collected by the Methodology. Another topic of our tests has been the comparison between the performances of the three algorithms chosen. Final step has been the comparison again with different possible good solutions, it means power supply system designs, provided by the Methodology, testing the validity of them. Once this work has been finished, the conclusions have been very satisfactory. Therefore this Thesis suggest a very interesting way of research and work, in terms of the results obtained and for the future opportunities can be created with the evolution of this. This Thesis has been developed with this idea in mind, so is expected this work could adhere another factor to work in the difficult task of validation and design of railway power supply systems.
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An important functional and evolutionary constraint on the physical performance of vertebrates is believed to be the trade-off between speed and endurance capacity. However, despite the pervasiveness of physiological arguments, most studies have found no evidence of the trade-off when tested at the whole-animal level. We investigated the existence of this trade-off at the whole-muscle level, the presumed site of this physiological conflict, by examining inter-individual variation in both maximum power output and fatigue resistance for mouse extensor digitorum longus (EDL) muscle using the work-loop technique. We found negative correlations between several measures of in vitro maximum power output and force production with fatigue resistance for individual mouse EDL muscles, indicating functional trade-offs between these performance parameters. We suggest that this trade-off detected at the whole-muscle level has imposed an important constraint on the evolution of vertebrate physical performance.
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Human development requires a broad balance between ecological, social and economic factors in order to ensure its own sustainability. In this sense, the search for new sources of energy generation, with low deployment and operation costs, which cause the least possible impact to the environment, has been the focus of attention of all society segments. To do so, the reduction in exploration of fossil fuels and the encouragement of using renewable energy resources for distributed generation have proved interesting alternatives to the expansion of the energy matrix of various countries in the world. In this sense, the wind energy has acquired an increasingly significant role, presenting increasing rates of power grid penetration and highlighting technological innovations such as the use of permanent magnet synchronous generators (PMSG). In Brazil, this fact has also been noted and, as a result, the impact of the inclusion of this source in the distribution and sub-transmission power grid has been a major concern of utilities and agents connected to Brazilian electrical sector. Thus, it is relevant the development of appropriate computational tools that allow detailed predictive studies about the dynamic behavior of wind farms, either operating with isolated load, either connected to the main grid, taking also into account the implementation of control strategies for active/reactive power generation and the keeping of adequate levels of voltage and frequency. This work fits in this context since it comprises mathematical and computational developments of a complete wind energy conversion system (WECS) endowed with PMSG using time domain techniques of Alternative Transients Program (ATP), which prides itself a recognized reputation by scientific and academic communities as well as by electricity professionals in Brazil and elsewhere. The modeling procedures performed allowed the elaboration of blocks representing each of the elements of a real WECS, comprising the primary source (the wind), the wind turbine, the PMSG, the frequency converter, the step up transformer, the load composition and the power grid equivalent. Special attention is also given to the implementation of wind turbine control techniques, mainly the pitch control responsible for keeping the generator under the maximum power operation point, and the vector theory that aims at adjusting the active/reactive power flow between the wind turbine and the power grid. Several simulations are performed to investigate the dynamic behavior of the wind farm when subjected to different operating conditions and/or on the occurrence of wind intensity variations. The results have shown the effectiveness of both mathematical and computational modeling developed for the wind turbine and the associated controls.
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We consider a linear precoder design for an underlay cognitive radio multiple-input multiple-output broadcast channel, where the secondary system consisting of a secondary base-station (BS) and a group of secondary users (SUs) is allowed to share the same spectrum with the primary system. All the transceivers are equipped with multiple antennas, each of which has its own maximum power constraint. Assuming zero-forcing method to eliminate the multiuser interference, we study the sum rate maximization problem for the secondary system subject to both per-antenna power constraints at the secondary BS and the interference power constraints at the primary users. The problem of interest differs from the ones studied previously that often assumed a sum power constraint and/or single antenna employed at either both the primary and secondary receivers or the primary receivers. To develop an efficient numerical algorithm, we first invoke the rank relaxation method to transform the considered problem into a convex-concave problem based on a downlink-uplink result. We then propose a barrier interior-point method to solve the resulting saddle point problem. In particular, in each iteration of the proposed method we find the Newton step by solving a system of discrete-time Sylvester equations, which help reduce the complexity significantly, compared to the conventional method. Simulation results are provided to demonstrate fast convergence and effectiveness of the proposed algorithm.