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Transient engine model for calibration using two-stage regression approachKhan, Muhammad Alam Z. January 2011 (has links)
Engine mapping is the process of empirically modelling engine behaviour as a function of adjustable engine parameters, predicting the output of the engine. The aim is to calibrate the electronic engine controller to meet decreasing emission requirements and increasing fuel economy demands. Modern engines have an increasing number of control parameters that are having a dramatic impact on time and e ort required to obtain optimal engine calibrations. These are further complicated due to transient engine operating mode. A new model-based transient calibration method has been built on the application of hierarchical statistical modelling methods, and analysis of repeated experiments for the application of engine mapping. The methodology is based on two-stage regression approach, which organise the engine data for the mapping process in sweeps. The introduction of time-dependent covariates in the hierarchy of the modelling led to the development of a new approach for the problem of transient engine calibration. This new approach for transient engine modelling is analysed using a small designed data set for a throttle body inferred air ow phenomenon. The data collection for the model was performed on a transient engine test bed as a part of this work, with sophisticated software and hardware installed on it. Models and their associated experimental design protocols have been identi ed that permits the models capable of accurately predicting the desired response features over the whole region of operability. Further, during the course of the work, the utility of multi-layer perceptron (MLP) neural network based model for the multi-covariate case has been demonstrated. The MLP neural network performs slightly better than the radial basis function (RBF) model. The basis of this comparison is made on assessing relevant model selection criteria, as well as internal and external validation ts. Finally, the general ability of the model was demonstrated through the implementation of this methodology for use in the calibration process, for populating the electronic engine control module lookup tables.
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Modélisation de l’arc électrique dans un disjoncteur à vide / Modelling of the electric arc in a vacuum interrupterLanglois, Yilin 05 November 2010 (has links)
Un modèle numérique d’un arc électrique diffus dans un disjoncteur à vide à champ magnétique axial (AMF) a été développé dans le but de mieux comprendre à terme la transition d’un mode de fonctionnement diffus de l’arc vers un mode plus concentré. Le comportement du plasma d’arc a été simulé depuis la sortie de la zone de mélange cathodique jusqu’à l’entrée de la gaine anodique. Le modèle bidimensionnel est basé sur un système d’équations hydrodynamiques à deux fluides non magnétisés (ions et électrons), incluant les équations de conservation d’énergie ionique et électronique. Il est démontré que les processus d’ionisation et de recombinaison et les effets visqueux sont négligeables. Les transferts radiatifs ne sont pas considérés en première approximation. Outre les forces dues au champ AMF, le modèle inclut les forces dues aux trois composantes du champ magnétique induit par l’arc. Deux régimes d’écoulement des ions, supersonique (aux faibles densités de courant) et subsonique (aux fortes densités de courant), sont considérés. Près de la cathode, les conditions aux limites sont spécifiées à partir de résultats de la littérature. A proximité de l’anode, elles sont basées sur une description simplifiée de la gaine anodique. Les résultats de simulation présentés mettent en évidence une constriction du courant et un comportement différent des ions aux faibles et aux fortes densités de courant, et renseignent sur l’influence de divers paramètres (intensité du courant, distance interélectrode). Ce travail présente également une étude expérimentale, basée sur des visualisations par vidéo rapide de l’arc et des mesures pyrométriques de la température de la surface de l’anode / A model of a diffuse arc in a vacuum circuit breaker with an axial magnetic field (AMF) has been developed with the ultimate aim to better understand the transition of the arc from a diffuse mode to a more confined mode. The interelectrode plasma is simulated from the exit of the mixing region on the cathode side to the entrance of the anode sheath. The two-dimensional model is based on the solution of a system of two-fluid (ions and electrons) hydrodynamic equations, including in particular the energy balance equations relative to both the ions and the electrons, which are treated as non-magnetized particles. It is demonstrated that ionisation and recombination processes, as well as viscous effects, can be neglected. Radiation losses are not taken into account in a first approximation. In addition to the forces due to the AMF, the model considers the forces created by the three components of the magnetic field induced by the arc current. The possibility of both supersonic (at low current density) and subsonic (at high current density) ionic flow regimes is considered. On the cathode side, the boundary conditions are specified using results from the literature. On the anode side, they are based on a simplified description of the anode sheath. The simulation results presented show a constriction of the current lines, emphasize the differences in the behaviour of the ions at low and high current densities, and provide some insight on the influence of various operating parameters (arc current, gap length). The present work comprises also an experimental study, based on high-speed camera visualisations of the arc and measurements of the temperature at the anode surface
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Fonctionnement hydrodynamique du bassin tertiaire du Bas-Dauphiné entre la Drôme et la Varèze (Drôme et Isère, Sud-Est de la France) : Etude géochimique et isotopique / Hydrodynamic survey of molassic basin of Bas-Dauphiné between Drôme and Varèze rivers (Drôme and Isère, South-eastern France)Cave, Tiffanie 19 December 2011 (has links)
L’aquifère molassique du Bas-Dauphiné est situé le long de la vallée du Rhône, dans le Sud-Est de la France. Cet aquifère d’une superficie proche de3000 km², et d’une épaisseur moyenne de 400m renferme une eau d’excellente qualité, utilisée par de nombreuses collectivités pour l’alimentation en eau potable. Cependant certains secteurs montrent une forte vulnérabilité de la nappe aux activités agricoles. L’utilisation d’outils géochimiques etisotopiques a permis de préciser le fonctionnement hydrodynamique de l’aquifère. Dans un premier temps, nous avons montré que la stratification des écoulements décrite par De La Vaissière (2006) sur la partie drômoise de l’aquifère s’étend au secteur isérois. Les eaux les plus profondes ont des vitesses de circulation de l’ordre du mètre par an alors que les flux superficiels ont des vitesses de circulations d’une centaine de mètres par an. D’autre part, le marquage des nappes superficielles et des rivières par des teneurs faibles en tritium (de 3 à 4 UT) et forte en magnésium (jusqu’à 18 mg/L)indique un apport d’eaux anciennes, issues de l’aquifère molassique vers ces eaux superficielles. La définition de deux pôles d’eaux et l’application d’une équation de mélange couplés à la réalisation de bilans hydrogéologique a permis d’appréhender les volumes échangés. Il apparaît finalement que les réservoirs d’eaux superficiels constituent l’exutoire principal de l’aquifère molassique. L’utilisation des éléments traces a mis en avant le rôleessentiel du temps de séjour des eaux dans l’aquifère ainsi que des conditions d’oxydo-réduction dans l’acquisition de la minéralisation. L’évaluation de la qualité naturelle des eaux de la nappe a montré l’impact des activités agricoles sur l’aquifère, avec prés de 80% des échantillons ayant une teneur en nitrates supérieure à la concentration naturelle supposée. L’étude des teneurs en pesticides conforte ce constat. De plus l’étude de l’évolution des concentrations en polluants montre une dégradation de la ressource. / The molassic basin of Bas-Dauphiné is located in south-eastern France, in the Rhône valley. With an averagethickness of about 400 m, and a surface area of about 2900 km², this aquifer is an important groundwaterresource for freshwater supply and agriculture. However, this resource is also vulnerable and is impacted byhuman activities. The use of geochemical and isotopic analyses made it possible to understand the hydrodynamicsurvey of the aquifer. Firstly, we showed the stratification of the groundwater previously described in thesouthern part of the molassic aquifer could be extended to the north. The groundwater flow velocity is about onemeter / year for the deepest flow and around 100-200 meter /year for the shallowest flow. Secondly, superficialaquifers and rivers are marked by low tritium activities (3 to 4 UT) and high magnesium concentrations (until 18mg/L), which indicate ancient molassic water contribution. The definition of two water types and the applicationof a mixing equation combined with hydrogeological balances lead to an estimation of the contribution of thedeep aquifer to the shallow aquifer. It is finally established that surface water (aquifers and rivers) constitute themain outlet of the molassic aquifer. The use of trace elements shows the importance of the groundwaterresidence time and of redox conditions in the water mineralization. The assessment of baseline quality shows theimpact of agricultural activities upon the aquifer, with nearly 80 % of samples showing higher nitrateconcentration than the maximal natural concentration. This is confirmed by the study of pesticidesconcentrations. Furthermore, the evolution of pollutants concentrations points out a deterioration of the resource.
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[en] NEW HEURISTICS AND AN INTEGER PROGRAMMING APPROACH TO AN INEXACT GRAPH MATCHING PROBLEM / [pt] NOVAS HEURÍSTICAS E UMA ABORDAGEM POR PROGRAMAÇÃO INTEIRA PARA UM PROBLEMA DE CORRESPONDÊNCIA INEXATA DE GRAFOSALEXANDRE ROCHA DUARTE 26 March 2004 (has links)
[pt] Esta dissertação apresenta novos algoritmos aproximados e
uma abordagem exata para a resolução de um problema de
correspondência inexata de grafos. O problema considerado é
o de correspondência entre um grafo representando um modelo
genérico e outro representando dados a serem reconhecidos.
Assumi-se que o grafo dos dados possui mais vértices que o
do modelo. A motivação para o estudo desse problema vem de
problemas de reconhecimento de cenas, que consistem na
caracterização dos objetos envolvidos em uma determinada
cena, assim como das relações existentes entre eles. Uma
aplicação para este problema na área de reconhecimento de
imagens médicas é a de efetuar-se o reconhecimento de
estruturas 3D do cérebro humano, a partir de imagens
obtidas por ressonância magnética. Tais imagens são
previamente processadas por algum método de segmentação
automática e o processo de reconhecimento consiste na busca
da correspondência estrutural entre a imagem e um modelo
genérico, tipicamente definido como um atlas de imagens
médicas. Foram propostos novos algoritmos aproximados, tais
como um algoritmo construtivo guloso aleatorizado, um
procedimento de reconexão de caminhos e um GRASP que
combina estes com uma técnica de busca local. Além disso,
foi proposta uma formulação original do problema como um
problema de programação linear inteira, que permitiu a
resolução de algumas instâncias de forma exata. / [en] This dissertation presents new approximation algorithms and
an exact approach to the solution of an inexact graph
matching problem. The problem consists in finding the best
match between a generic model graph and a graph
representing an image, the latter with more nodes than the
former. The motivation for studying this problem comes from
a scene recognition problem, which consists in
characterizing objects involved in a given scene and the
relationships between them. An application of this problem
appears in the analysis of medical images and consists in
recognizing 3-dimensional structures in the human brain
using images obtained by magnetic resonance. Such images
must be previously processed by an automatic segmentation
method and the recognition process consists in the search
of an structural matching between the image and a generic
model, typically defined as an atlas of medical images.
New heuristics are proposed, such as a greedy randomized
construction algorithm, a path relinking procedure and a
GRASP heuristic that combines them with a local search
technique. Furthermore, an original integer formulation
of the problem based on integer multicommodity flows is
proposed, which makes possible the exact solution of medium-
sized instances.
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The Valuation of Corporate Value¡ÐOn the Cases of Taiwan Listing Companies of Steel IndustryYun, Hsiao-Chuan 25 August 2006 (has links)
Abstract
The steel industry has been known as 'The mother of all industries '. With the emerging incidents such as Asian financial meltdown, industrialization of the China, and the policy of macro economic controls by the China government, the stock index of the steel industry has fluctuated violently. Despite the economy of China is to be adjusted upwards, in the foreseen future, the global steel supply will be probably exceed the demand. Such phenomenon definitely causes the pressure on the market that it also attracts much attention of the relevant stockholders. Current research investigates the most suitable model for valuating the stock price of the steel industry that would provide valuating methods to the corporate management and investors for decision making and investment.
This research has studied 19 companies of steel industry of Taiwan listing companies with 6 approaches including the ¡¥Discounted Free Cash Flow Models¡¦, ¡¥Price to Earning Ratio¡¦, ¡¥Price to EBITDA Ratio¡¦, ¡¥Price to Sales Ratio¡¦, ¡¥Price to Book Value Ratio¡¦ and ¡¥Edwards-Bell-Ohlson Model¡¦ to valuate their reasonable intrinsic value from 2000 to 2005. The test of Theil¡¦s U is then applied to evaluate the approaches in order to justify the best valuation model.
This study indicates the following results¡GThe Price to Book Value Ratio is the best valuation model since its smallest Theil¡¦s U value. The Price to Earning Ratio is the most unsuitable model for this evaluation purpose with a highest Theil¡¦s U value.
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採用國際財務報導準則對自由現金流量評價模式之影響 / The impacts of adopting international financial reporting standards on discounted free cash flow model姚文伶 Unknown Date (has links)
因應全球化時代之來臨,為提升會計資訊的透明度及跨國間之可比較性,國際財務報導準則(IFRS)已然成為全球資本市場共通的會計語言。我國為提升企業與資本市場國際競爭力及降低企業赴海外籌資成本,將自2013年起分階段直接採用(Adoption)IFRS。
針對無活絡市場公開報價之權益商品公允價值衡量議題,本研究目的擬以投資者的立場,透過IFRS與我國現行財務會計準則間之主要會計原則差異,探討對自由現金流量折現法評價模型及評價步驟之影響,以提供未來投資者於應用自由現金流量折現法進行企業評價時之參考。
本研究顯示在IFRS與我國現行財務會計準則並存適用下,不論於進行同公司跨期間或不同公司同期間之分析比較時,需先辨識重大會計差異所帶來之潛在影響,並掌握因衡量方法的改變、IFRS 1各項豁免選擇、抑或表達上的重分類等,對財務報表資訊內涵所產生之影響,進而衡酌對自由現金流量評價模式的參數設定調整,以及可能改變對未來現金流量金額、時點及不確定性之預期,如此,方能獲致IFRS所帶來之提升財務資訊可比較性及高透明度等效益。 / With economic globalization, International Financial Reporting Standards(IFRS) is becoming the single set of globally accepted accounting principles to increase the transparency and comparative of financial statements. In keeping with international trends and to increase competitiveness, companies as the 1st phase in Taiwan will adopt IFRS in 2013.
In this study, from the investor point of view, discussed the major differences between IFRS and ROC GAAP, which impact on the discounted free cash flow model and the evaluation steps. To provide the reference for investors when evaluating the company with the discounted free cash flow model.
This study shows that under IFRS and ROC GAAP coexist, it must recognize the potential impact of the significant accounting differences firstly whether in the analysis of the inter-period of the same company or different companies during the same period. Due to control the impact of the information content of financial statements from the change of measurement、how to use exemptions provided by IFRS1 or expression on the re-classification, in consideration of adjusting the parameters of the discounted free cash flow model, and may change the expected amount of future cash flows , point and uncertainties. And then, we will attain the benefit such as enhance comparative and transparency of financial information from adopting IFRS.
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Uma abordagem dirigida por modelos para desenvolvimento de middlewares auto-adaptativos para transmiss?o de fluxo de dados baseado em restri??es de QoS / Uma abordagem dirigida por modelos para desenvolvimento de middlewares auto-adaptativos para transmiss?o de fluxo de dados baseado em restri??es de QoSSilva, Andre Gustavo Pereira da 15 March 2010 (has links)
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Previous issue date: 2010-03-15 / The use of middleware technology in various types of systems, in order to abstract low-level details related to the distribution of application logic, is increasingly common. Among several systems that can be benefited from using these components, we highlight the distributed systems, where it is necessary to allow communications between software components located on different physical machines. An important issue related to the communication between distributed components is the provision of mechanisms for managing the quality of service. This work presents a metamodel for modeling middlewares based on components in order to provide to an application the abstraction of a communication between components involved in a data stream, regardless their location. Another feature of the metamodel is the possibility of self-adaptation related to the communication mechanism, either by updating the values of its configuration parameters, or by its replacement by another mechanism, in case of the restrictions of quality of service specified are not being guaranteed. In this respect, it is planned the monitoring of the communication state (application of techniques like feedback control loop), analyzing performance metrics related. The paradigm of Model Driven Development was used to generate the implementation of a middleware that will serve as proof of concept of the metamodel, and the configuration and reconfiguration policies related to the dynamic adaptation processes. In this sense was defined the metamodel associated to the process of a communication configuration. The MDD application also corresponds to the definition of the following transformations: the architectural model of the middleware in Java code, and the configuration model to XML / A utiliza??o da tecnologia de middleware em diversos tipos de sistemas, com a finalidade de abstrair detalhes de baixo n?vel relacionados com a distribui??o da l?gica da aplica??o, ? cada vez mais frequente. Dentre diversos sistemas que podem ser beneficiados com a utiliza??o desses componentes, podemos destacar os sistemas distribu?dos, onde ? necess?rio viabilizar a comunica??o entre componentes de software localizados em diferentes m?quinas f?sicas. Uma importante quest?o relacionada ? comunica??o entre componentes distribu?dos ? o fornecimento de mecanismos para gerenciamento da qualidade de servi?o. Este trabalho apresenta um metamodelo para modelagem de middlewares baseados em componentes que prov?em ? aplica??o a abstra??o da comunica??o entre componentes envolvidos em um fluxo de dados, independente da sua localiza??o. Outra caracter?stica do metamodelo ? a possibilidade de auto-adapta??o relacionada ao mecanismo de comunica??o utilizado, seja atrav?s da atualiza??o dos valores dos seus par?metros de configura??o, ou atrav?s da sua substitui??o por outro mecanismo, caso as restri??es de qualidade de servi?o especificadas n?o estejam sendo garantidas. Nesse prop?sito, ? previsto o monitoramento do estado da comunica??o (aplica??es de t?cnicas do tipo feedback control loop), analisando-se m?tricas de desempenho relacionadas. O paradigma de Desenvolvimento Dirigido por Modelos foi utilizado para gerar a implementa??o de um middleware que servir? como prova de conceito do metamodelo, e as pol?ticas de configura??o e reconfigura??o relacionadas com o processo de adapta??o din?mica; neste sentido, foi definido o metamodelo associado ao processo de configura??o de uma comunica??o. A aplica??o da t?cnica de MDD corresponde ainda ? defini??o das seguintes transforma??es: do modelo arquitetural do middleware para c?digo em linguagem Java, e do modelo de configura??o para c?digo XML
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Estrutura de ondas para um modelo de escoamento trifásico com viscosidades das fases assimétricas. / Wave structure for a three phase flow model with asymmetric phase viscosities.GUEDES, Maria Joseane Felipe. 23 July 2018 (has links)
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Previous issue date: 2009-04 / CNPq / Neste trabalho é considerado o problema de Riemann para um sistemas de leis
de conservação modelando a recuperação de óleo de um reservatório petrolífero pela
injeção de uma mistura do tipo água e gás. supondo que o mesmo contenha inicialmente
uma mistura do tipo água e óleo. A partir da teoria de Leis de Conservação é
determinada a solução do problema de Riemann considerando os várias casos possíveis
para dados de produção. Para cada um desses dados de produção são considerados
todos os casos possíveis de injeção da mistura água/gás. Para cada caso de produção é
mostrada a existência de estados especiais de injeção separando construções distintas
de soluções no espaço de estados. Além disso, entre esses estados especiais de injeção
um deles é crítico, no sentido que a solução é dada de duas ou três maneiras distintas no
espaço de estados, porém representando a mesma solução no espaço físico - xt. Em geral a solução do problema de Riemann consiste de duas ondas separadas
por um estado intermediário constante quando o dado de produção está próximo de
situações extremas, em que a saturação inicial da água ou do óleo é maximal. Para
estados de produção com uma proporção mais homogénea da mistura de água e óleo a
solução pode consistir de até três ondas para alguns casos de injeção de uma mistura
contendo uma proporção maior de gás do que de água. Nesses casos uma onda não
clássica, i. e. uma onda transicional, deve ser usada. / In this work we consider the Riemann probíem for a system of conservation laws
modeling the oil recovery for a three-phase flow in a porous médium by the injection of
a mixture of water and gas in a reservoir whieh is initially filled with a mixture of water
and oil. Using the theory of conservation laws, the solution of the Rieman problem
is determined considering ali possibilities for the production data. For each of these
production data. ali possible cases for the injected gas/ water mixture are considered
as well. For each production case it is shown the existence of some special injection
data separating distinct constmctions of Solutions in the state space. Moreover, among
these special injection data one of them is criticai in the sense that the wave sequence
that describes the solution can be represented by two or three distinct paths in the
state space, but consisting of the same solution in the physical space - xi. In general
the solution of the Riemann problem consists of a sequence of two waves separated by
one intermediate constant state when the production data are closed to the extreme
situations where the initial water or oil saturations are maximal. For production data
with a more homogeneous initial water and oil proportion, the solution may consists
up to three waves separated by two constant intermediate states for some injected
mixtures containing a hígher proportion of gas than water. In such cases a nonelassical
wave, i. e. a transitional wave, must be used.
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Modelos de programação linear inteira mista para resolver problemas de planejamento da expansão e da operação de sistemas de transmissão de energia elétrica / Mixed integer linear programming models to solve problems of expansion and operation planning of electric energy transmission systemsVillajuan Montes, Cristiam Victor [UNESP] 19 February 2016 (has links)
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Previous issue date: 2016-02-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Os problemas de planejamento da expansão de sistemas de transmissão e de fluxo de potência ótimo são de grande importância na área de sistemas de transmissão de energia elétrica. O primeiro consiste em determinar a expansão ótima do sistema, que deve ocorrer com o menor gasto monetário possível. No problema fluxo de potência ótimo deve-se encontrar o estado de operação do sistema de forma a minimizar um objetivo, no caso, os custos de geração. Ambos problemas possuem modelos de programação não-linear inteira mista. Além disto, o resultado ótimo de ambos deve cumprir com restrições operacionais, como o limite de tensão nas barras, os limites de fluxos nos ramos e os limites dos geradores. Para resolver os problemas citados, neste trabalho são apresentados modelos matemáticos de programação linear inteiro misto, aproximados, baseados em um modelo linearizado de fluxo de carga AC, que considera a presença da potência reativa, das perdas no sistema e magnitudes de tensões nas barras diferentes do valor nominal. Todos os modelos foram escritos na linguagem de modelagem matemática AMPL e resolvidos com o solver comercial CPLEX. Os modelos propostos foram testados com os sistemas IEEE de 14, 30, 57, 118 e 300 barras e com o sistema Garver para o planejamento da expansão de sistemas de transmissão. Os resultados foram comparados utilizando-se um fluxo de carga não linear, para verificar-se a precisão dos modelos propostos. / The transmission network expansion planning and the optimal power flow problems are of great importance in the field of electricity transmission systems. The first consists in determining the optimal expansion of the system, which must be done with the least possible investment. In the optimal power flow problem it must found the operating status of the system in order to minimize an objective, in this case, generation costs. Both problems have mixed-integer nonlinear programming models. In addition, the optimal solution of both must comply with operating constraints, such as the voltage limit on buses, the limits flows in branches and the limits of the generators. To solve the problems cited, in this work are presented approximate mixed integer linear programming models based on a linearized AC load flow model, which considers the presence of reactive power, the losses in the system and of nominal bus voltage magnitudes. All models were written in mathematical modeling language AMPL and solved with the commercial solver CPLEX. The proposed models were tested with the IEEE systems of 14, 30, 57, 118 and 300 buses and with the Garver system for transmission network expansion planning. Results were compared using a nonlinear load flow model, to verify the accuracy of the proposed models.
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Modelos de programação linear inteira mista para resolver problemas de planejamento da expansão e da operação de sistemas de transmissão de energia elétrica /Villajuan Montes, Cristiam Victor January 2016 (has links)
Orientador: Marcos Julio Rider Flores / Resumo: Os problemas de planejamento da expansão de sistemas de transmissão e de fluxo de potência ótimo são de grande importância na área de sistemas de transmissão de energia elétrica. O primeiro consiste em determinar a expansão ótima do sistema, que deve ocorrer com o menor gasto monetário possível. No problema fluxo de potência ótimo deve-se encontrar o estado de operação do sistema de forma a minimizar um objetivo, no caso, os custos de geração. Ambos problemas possuem modelos de programação não-linear inteira mista. Além disto, o resultado ótimo de ambos deve cumprir com restrições operacionais, como o limite de tensão nas barras, os limites de fluxos nos ramos e os limites dos geradores. Para resolver os problemas citados, neste trabalho são apresentados modelos matemáticos de programação linear inteiro misto, aproximados, baseados em um modelo linearizado de fluxo de carga AC, que considera a presença da potência reativa, das perdas no sistema e magnitudes de tensões nas barras diferentes do valor nominal. Todos os modelos foram escritos na linguagem de modelagem matemática AMPL e resolvidos com o solver comercial CPLEX. Os modelos propostos foram testados com os sistemas IEEE de 14, 30, 57, 118 e 300 barras e com o sistema Garver para o planejamento da expansão de sistemas de transmissão. Os resultados foram comparados utilizando-se um fluxo de carga não linear, para verificar-se a precisão dos modelos propostos. / Abstract: The transmission network expansion planning and the optimal power flow problems are of great importance in the field of electricity transmission systems. The first consists in determining the optimal expansion of the system, which must be done with the least possible investment. In the optimal power flow problem it must found the operating status of the system in order to minimize an objective, in this case, generation costs. Both problems have mixed-integer nonlinear programming models. In addition, the optimal solution of both must comply with operating constraints, such as the voltage limit on buses, the limits flows in branches and the limits of the generators. To solve the problems cited, in this work are presented approximate mixed integer linear programming models based on a linearized AC load flow model, which considers the presence of reactive power, the losses in the system and of nominal bus voltage magnitudes. All models were written in mathematical modeling language AMPL and solved with the commercial solver CPLEX. The proposed models were tested with the IEEE systems of 14, 30, 57, 118 and 300 buses and with the Garver system for transmission network expansion planning. Results were compared using a nonlinear load flow model, to verify the accuracy of the proposed models. / Mestre
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