Face aux forts besoins de réduction de la consommation énergétique et de l’impact environnemental,le bâtiment d’aujourd’hui vise la performance en s’appuyant sur des sourcesd’énergie de plus en plus diversifiées (énergies renouvelables), une enveloppe mieux conçue(isolation) et des systèmes de gestion plus avancés. Plus la conception vise la basse consommation,plus les interactions entre ses composants sont complexes et peu intuitives. Seule unerégulation plus intégrée permettrait de prendre en compte cette complexité et d’optimiser lefonctionnement pour atteindre la basse consommation sans sacrifier le confort.Les techniques de commande prédictive, fondées sur l’utilisation de modèles dynamiqueset de techniques d’optimisation, promettent une réduction des consommations et de l’inconfort.Elles permettent en effet d’anticiper l’évolution des sources et des besoins intermittentstout en tirant parti de l’inertie thermique du bâtiment, de ses systèmes et autres élémentsde stockage. Cependant, dans le cas du bâtiment, l’obtention d’un modèle dynamique suffisammentprécis présente des difficultés du fait d’incertitudes importantes sur les paramètresdu modèle et les sollicitations du système. Les avancées récentes dans le domaine de l’instrumentationdomotique constituent une opportunité prometteuse pour la réduction de cesincertitudes, mais la conception d’un tel système pour une telle application n’est pas triviale.De fait, il devient nécessaire de pouvoir considérer les problématiques de monitoring énergétique,d’instrumentation, de commande prédictive et de modélisation de façon conjointe.Cette thèse vise à identifier les liens entre commande prédictive et instrumentation dansle bâtiment, en proposant puis exploitant une méthode générique de modélisation du bâtiment,de simulation thermique et de résolution de problèmes d’optimisation. Cette méthodologiemet en oeuvre une modélisation thermique multizone du bâtiment, et des algorithmesd’optimisation reposant sur un modèle adjoint et les outils du contrôle optimal. Elle a étéconcrétisée dans un outil de calcul permettant de mettre en place une stratégie de commandeprédictive comportant des phases de commande optimale, d’estimation d’état et decalibration.En premier lieu, nous étudions la formulation et la résolution d’un problème de commandeoptimale. Nous abordons les différences entre un tel contrôle et une stratégie de régulationclassique, entre autres sur la prise en compte d’indices de performance et de contraintes. Nousprésentons ensuite une méthode d’estimation d’état basée sur l’identification de gains thermiquesinternes inconnus. Cette méthode d’estimation est couplée au calcul de commandeoptimale pour former une stratégie de commande prédictive.Les valeurs des paramètres d’un modèle de bâtiment sont souvent très incertaines. Lacalibration paramétrique du modèle est incontournable pour réduire les erreurs de prédictionet garantir la performance d’une commande optimale. Nous appliquons alors notreméthodologie à une technique de calibration basée sur des mesures de températures in situ.Nous ouvrons ensuite sur des méthodes permettant d’orienter le choix des capteurs à utiliser(nombre, positionnement) et des paramètres à calibrer en exploitant les gradients calculéspar la méthode adjointe.La stratégie de commande prédictive a été mise en oeuvre sur un bâtiment expérimentalprès de Chambéry. Dans le cadre de cette étude, l’intégralité du bâtiment a été modélisé,et les différentes étapes de notre commande prédictive ont été ensuite déployées de mainière séquentielle. Cette mise en oeuvre permet d’étudier les enjeux et les difficultés liées àl’implémentation d’une commande prédictive sur un bâtiment réel.Cette thèse est issue d’une collaboration entre le CEA Leti, l’IFSTTAR de Nantes et leG2ELab, et s’inscrit dans le cadre du projet ANR PRECCISION. / More efficient energy management of buildings through the use of Model Predictive Control(MPC) techniques is a key issue to reduce the environmental impact of buildings. Buildingenergy performance is currently improved by using renewable energy sources, a betterdesign of the building envelope (insulation) and the use of advanced management systems.The more the design aims for high performance, the more interactions and coupling effectsbetween the building, its environment and the conditions of use are important and unintuitive.Only a more integrated regulation would take in account this complexity, and couldhelp to optimize the consumption without compromising the comfort.Model Predictive Control techniques, based on the use of dynamic models and optimizationmethods, promise a reduction of consumption and discomfort. They can generate energysavings by anticipating the evolution of renewable sources and intermittent needs, while takingadvantage of the building thermal inertia and other storage items. However, in the caseof buildings, obtaining a good dynamic model is tough, due to important uncertainties onmodel parameters and system solicitations.Recent advances in the field of wireless sensor networks are fostering the deployment ofsensors in buildings, and offer a promising opportunity to reduce these errors. Nevertheless,designing a sensor network dedicated to MPC is not obvious, and energy monitoring,instrumentation, modeling and predictive control matters must be considered jointly.This thesis aims at establishing the links between MPC and instrumentation needs inbuildings. We propose a generic method for building modeling, thermal simulation andoptimization. This methodology involves a multi-zone thermal model of the building, andefficient optimization algorithms using an adjoint model and tools from the optimal controltheory. It was implemented in a specific toolbox to develop a predictive control strategywith optimal control phases, state estimation phases and model calibration.At first, we study the formulation and resolution of an optimal control problem. We discussthe differences between such a control and a conventional regulation strategy, throughperformance indicators. Then, we present a state estimation method based on the identificationof unknown internal gains. This estimation method is subsequently coupled with theoptimal control method to form a predictive control strategy.As the parameters values of a building model are often very uncertain, parametric modelcalibration is essential to reduce prediction errors and to ensure the MPC performance. Consequently,we apply our methodology to a calibration technique based on in situ temperaturemeasurements. We also discuss how our approach can lead to selection techniques in orderto choose calibrated parameters and sensors for MPC purposes.Eventually, the predictive control strategy was implemented on an experimental building,at CEA INES, near Chambéry. The entire building was modeled, and the different steps ofthe control strategy were applied sequentially through an online supervisor. This experimentgave us a useful feedback on our methodology on a real case.This thesis is the result of a collaboration between CEA Leti, IFSTTAR Nantes andG2ELab, and is part of the ANR PRECCISION project.

Master of Science / Department of Electrical and Computer Engineering / Faryad Darabi Sahneh / Recent experience of Ebola outbreak of 2014 highlighted the importance of immediate response to impede Ebola transmission at its very early stage. To this aim, efficient and effective allocation of limited resources is crucial. Among standard interventions is the practice of following up with physical contacts of individuals diagnosed with Ebola virus disease -- known as contact tracing. In an effort to objectively understand the effect of possible contact tracing protocols, we explicitly develop a model of Ebola transmission incorporating contact tracing. Our modeling framework has several features to suit early–stage Ebola transmission: 1) the network model is patient–centric because when number of infected cases are small only the myopic networks of infected individuals matter and the rest of possible social contacts are irrelevant, 2) the Ebola disease model is individual–based and stochastic because at the early stages of spread, random fluctuations are significant and must be captured appropriately, 3) the contact tracing model is parameterizable to analyze the impact of critical aspects of contact tracing protocols. Notably, we propose an activity driven network approach to contact tracing, and develop a Monte-Carlo method to compute the basic reproductive number of the disease spread in different scenarios. Exhaustive simulation experiments suggest that while contact tracing is important in stopping the Ebola spread, it does not need to be done too urgently. This result is due to rather long incubation period of Ebola disease infection. However, immediate hospitalization of infected cases is crucial and requires the most attention and resource allocation. Moreover, to investigate the impact of mitigation strategies in the 2014 Ebola outbreak, we consider reported data in Guinea, one the three West Africa countries that had experienced the Ebola virus disease outbreak. We formulate a multivariate sequential Monte Carlo filter that utilizes mechanistic models for Ebola virus propagation to simultaneously estimate the disease progression states and the model parameters according to reported incidence data streams. This method has the advantage of performing the inference online as the new data becomes available and estimating the evolution of the basic reproductive ratio R₀(t) throughout the Ebola outbreak. Our analysis identifies a peak in the basic reproductive ratio close to the time of Ebola cases reports in Europe and the USA.

Cette thèse concerne principalement la résolution des problèmes d’inversion dynamiquedans le cadre des systèmes dynamiques non linéaires. Ainsi, un ensemble de techniquesbasées sur l’utilisation des trains de mesures passées et sauvegardées sur une fenêtreglissante, a été développé. En premier lieu, les mesures sont utilisées pour générerune famille de signatures graphiques, qui constituent un outil de classification permettantde discriminer les diverses valeurs des variables à estimer pour un système non linéairedonné. Cette première technique a été appliquée à la résolution de deux problèmes : leproblème d’électolocation d’un robot doté du sens électrique et le problème d’estimationd’état dans les systèmes à dynamiques non linéaires. Outre ces deux applications, destechniques d’inversion à horizon glissant spécifiques au problème de diagnostic des défautsd’éoliennes dans le cadre d’un benchmark international ont été développées. Cestechniques sont basées sur la minimisation de critères quadratiques basés sur des modèlesde connaissance. / This thesis mainly concerns the resolution of dynamic inverse problems involvingnonlinear dynamical systems. A set of techniques based on the use of trains of pastmeasurements saved on a sliding window was developed. First, the measurements areused to generate a family of graphical signatures, which is a classification tool, in orderto discriminate between different values of variables to be estimated for a given nonlinearsystem. This technique was applied to solve two problems : the electrolocationproblem of a robot with electrical sense and the problem of state estimation in nonlineardynamical systems. Besides these two applications, receding horizon inversion techniquesdedicated to the fault diagnosis problem of a wind turbine proposed as an internationalbenchmark were developed. These techniques are based on the minimization of quadraticcriteria based on knowledge-based models.

Submitted by Bruna Rodrigues (bruna92rodrigues@yahoo.com.br) on 2016-10-04T14:03:27Z No. of bitstreams: 1 DissDPL.pdf: 3012901 bytes, checksum: 29c2df84e5e59e8e598fae154f0983d2 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-14T14:18:34Z (GMT) No. of bitstreams: 1 DissDPL.pdf: 3012901 bytes, checksum: 29c2df84e5e59e8e598fae154f0983d2 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-10-14T14:18:43Z (GMT) No. of bitstreams: 1 DissDPL.pdf: 3012901 bytes, checksum: 29c2df84e5e59e8e598fae154f0983d2 (MD5) / Made available in DSpace on 2016-10-14T14:18:52Z (GMT). No. of bitstreams: 1 DissDPL.pdf: 3012901 bytes, checksum: 29c2df84e5e59e8e598fae154f0983d2 (MD5) Previous issue date: 2016-03-04 / Não recebi financiamento / Kalman filters are rooted in the technical literature, as a way of predicting new states in nonlinear systems providing a recursive solution to the problem of linear optimal filtering. Therefore, 56 years after its discovery, many modifications have been proposed in order to obtain better accuracy and speed. Some of these changes are used in this work; these being the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Kalman Filter Cubature (CKF). This work , divided into three distinct parts: Implementation / Comparative analysis of prediction of Kalman filters in complex systems (Series), qualitative analysis of the possible uses of the Kalman filter variants for neural network training and position and velocity determination a displaced object on a simulated plane with some trajectories Having these analyzes key role in fostering the studies cited in the scientific literature , proving the possibility of such algorithms and methods are used for positioning in unstructured environments / Filtros de Kalman estão consagrados na literatura técnica, como uma das formas de prever novos estados em sistemas não-lineares, fornecendo uma solução recursiva para o problema da filtragem ideal linear. Após 56 anos de sua descoberta, muitas modificações e melhorias foram propostas, procurando obter uma maior precisão e velocidade na predição de novos estados. Algumas dessas mudanças são utilizadas neste trabalho; sendo elas o Filtro de Kalman Estendido (EKF), Unscented Kalman Filter (UKF) e Filtro de Kalman de Cubagem Esférica Radial (CKF).O objetivo deste trabalho, divido em três partes distintas, porém complementares: Implementação/Análise comparativa da predição dos Filtros de Kalman em sistemas complexos (Series), Análise qualitativa das possíveis utilizações das variantes do Filtro de Kalman para treinamento de Redes Neurais e Determinação de posição e velocidade de um objeto deslocado sobre um plano simulado. Possuindo essas análises papel fundamental na fomentação dos estudos citados na literatura científica durante o trabalho, e comprovando a possibilidade desses algoritmos/ métodos serem utilizados em tarefas de posicionamento em ambientes não estruturados.

Esta tese apresenta novos algoritmos que resolvem problemas de estimativas filtrada, suavizadora e preditora para sistemas singulares no tempo discreto usando apenas argumentos determinísticos. Cada capítulo aborda inicialmente as estimativas para o sistema nominal e em seguida, as versões robustas para o sistema com incertezas limitadas. Os resultados encontrados podem ser aplicados tanto em sistemas invariantes como variantes no tempo discreto, utilizando a mesma estrutura do filtro de Kalman. Nos últimos anos, uma quantidade significativa de trabalhos envolvendo estimativas singulares foi publicada enfocando apenas a estimativa filtrada sob a justificativa de que a estimativa preditora era de significativa complexidade quando modelada pelo método dos mínimos quadrados. Por este motivo, poucos trabalhos, como NIKOUKHAH et al. (1992) e ZHANG et al. (1998), deduziram a estimativa preditora. Este último artigo apresentou também um algoritmo para a estimativa suavizadora, mas usando o modelo de inovação ARMA. No entanto, até onde foi possível identificar, nenhum trabalho até agora resolveu o problema de estimativa robusta, considerando incertezas nos parâmetros, para sistemas singulares. Para a dedução das estimativas singulares robustas, esta tese tomou como base SAYED (2001), que deduz o filtro de Kalman robusto com incertezas limitadas utilizando uma abordagem determinística, o chamado filtro BDU. Os filtros robustos para sistemas singulares apresentados nesta tese, são mais abrangentes que os apresentados em SAYED (2001). Quando particularizados para o espaço de estados sem incertezas, todos os filtros se assemelham ao filtro de Kalman. / New algorithms to optimal recursive filtering, smoothed and prediction for general time-invariant or time-variant descriptor systems are proposed in this thesis. The estimation problem is addressed as an optimal deterministic trajectory fitting. This problem is solved using exclusively deterministic arguments for systems with or without uncertainties. Kalman type recursive algorithms for robust filtered, predicted and smoothed estimations are derived. In the last years, many papers have paid attention to the estimation problems of linear singular systems. Unfortunately, all those works were concentrated only on the study of filtering problems, for nominal systems. The predicted and smoothed filters are more involved and were considered only by few works : NIKOUKHAH et al. (1992) and ZHANG et al. (1998) had proposed a unified approach for filtering, prediction and smoothing problems which were derived by using the projection formula and were calculated based on the ARMA innovation model, but they had not considered the uncertainties. In this thesis its applied for descriptor systems a robust procedure for usual state space systems developed by SAYED (2001), called BDU filter. It is obtained a robust descriptor Kalman type recursions for filtered, predicted and smoothed estimates. Considering the nominal state space, all descriptor filters developed in this work collapse to the Kalman filter.

Na tentativa de contornar os problemas ainda existentes para a detecção e identificação de erros grosseiros (EGs) no processo de estimação de estado em sistemas elétricos de potência (EESEP), realiza-se, neste trabalho, uma análise da formulação dos estimadores aplicados a sistemas elétricos de potência, em especial, o de mínimos quadrados ponderados, tendo em vista evidenciar as limitações dos mesmos para o tratamento de EGs. Em razão da dificuldade de detectar EGs em medidas pontos de alavancamento, foram também analisadas as metodologias desenvolvidas para identificação de medidas pontos de alavancamento. Através da formulação do processo de EESEP como um problema de álgebra linear, demonstra-se o porquê da impossibilidade de detectar EGs em determinadas medidas redundantes, sendo proposto, na seqüência, um método para identificação de medidas pontos de alavancamento. Para reduzir os efeitos maléficos dessas medidas no processo de EESEP verifica-se a possibilidade de aplicar outras técnicas estatísticas para o processamento de EGs, bem como técnicas para obtenção de uma matriz de ponderação adequada. / To overcome the problems still existent for gross errors (GEs) detection and identification in the process of power system state estimation (PSSE), the formulations of the estimators applied to power systems are analyzed, specially, the formulation of the weighted squares estimator. These analyses were performed to show the limitations of these estimators for GEs processing. As leverage points (LP) represent a problem for GEs processing, methodologies for LP identification were also verified. By means of the linear formulation of the PSSE process, the reason for the impossibility of GEs detection in some redundant measurements is shown and a method for LP identification is proposed. To minimize the bad effects of the LP to the PSSE process, the possibility of applying other statistic techniques for GEs processing, as well as techniques to estimate an weighting matrix are also analyzed.

Made available in DSpace on 2016-08-17T14:52:40Z (GMT). No. of bitstreams: 1 Dissertacao-AntonioAdolphoMartinsRaposo.pdf: 6219934 bytes, checksum: 92f0e1fb7c3d703fcf27aae305b549f2 (MD5) Previous issue date: 2016-02-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / To plan and operate properly a Smart Grid (SG), many new technical considerations in the context of distribution systems, must be considered, for example: stability (due to installation of Distributed Generation (DG), the load and generation dispatch, management of energy storage devices and the assessment of the impact of electric vehicle connection on the distribution system. The main prerequisite for many of these new functions in the distribution system control center is to determine the electrical network state (magnitude and angle of nodal voltages) in real time from measurement devices installed in it. In the transmission system control centers, this task is performed by the state estimation tool. Thus, the Distribution System State Estimation (DSSE) is one of the cornerstones for the implementation of a SG. The presence of a small number of measurements can make the grid unobservable in the context of the DSSE. That is, the state variables (magnitude and angle of the node voltages of all bus) can not be determined from a set of measurements by a state estimator. Due to this, it is usually added a large number of pseudo measurements to the existing measurement plan to ensure observability and to enable the DSSE. A drawback with this strategy is that the accuracy of the estimated state is compromised due to the fact that the errors associated with the pseudo measurements are considerably higher than those relating to real measurements. Consequently, it is necessary to allocate meters (voltage magnitude, active and reactive power flows, current magnitudes, etc.) to guarantee the accuracy of the DSEE. The meter placement problem for the state estimation in the transmission networks is usually carried out with the objective of assuring the observability. On the other hand, the meter placement for the EERD aims to minimize probabilistic index associated with the errors between the true and estimated state vectors. An important component of the method used to solve the meters placement problem is a probabilistic technique used to estimate the objective function. Due to the nonlinear nature of DSSE problem, the best option has been to use the Monte Carlo Simulation (MCS). A disadvantage of the MCS to estimate the objective function of the allocation problem is its high computational cost due to the need to solve a nonlinear state estimation problem for each sample element. The main objective of this dissertation is to propose a probabilistic techniques to improve the computational performance of existing methodologies for meter placement without reducing the accuracy of the estimated ix state. This compromise has been established using two strategies. In the first one, a linear model is used to estimate the state and the MCS is applied to determine the risks of the objective function. In the second one, a closed analytical formula is used to determine the risks based on the linearized model. Furthermore, the improved versions of the meter placement algorithms proposed in this dissertation consider the effect of the correlation among the measurements. The proposed meter placement algorithms were tested in the British distribution system of 95 bus. The tests results demonstrate that the introduction of the proposed strategies in a meter placement algorithm significantly reduced its computational cost. Moreover, it can be observed that there were improvements in accuracy in some cases, because the risk estimates provided by MCS are not accurate with small samples. / Para planejar e operar adequadamente uma Rede Elétrica Inteligente (REI), muitas novas considerações técnicas, no âmbito de sistemas de distribuição, devem ser apreciadas, por exemplo: a estabilidade devido a instalação de Geração Distribuída (GD), o despacho de carga e geração, o gerenciamento de dispositivos de armazenamento de energia e a avaliação do impacto da conexão de veículos elétricos na rede de distribuição. O principal pré-requisito para muitas destas novas funções do centro de controle do sistema de distribuição é a determinação do estado da rede elétrica (módulo e a fase das tensões nodais) em tempo real a partir de dispositivos de medição nela instalados. Em centros de controle de sistemas de transmissão esta tarefa é realizada por ferramentas de estimação de estado. Desta forma, a Estimação de Estado em Redes de Distribuição (EERD) é um dos alicerces para a implantação de uma REI. A presença de um número reduzido de medições pode tornar a rede elétrica não observável no âmbito da EERD. Isto é, as variáveis de estado (módulo e fase das tensões nodais em todas as barras) não podem ser determinadas a partir de um conjunto de medições por um estimador de estado. Devido a isto, geralmente adiciona-se um grande número de pseudo-medições ao plano de medição existente para assegurar a observabilidade e viabilizar a EERD. Um problema com esta estratégia é que a precisão do estado estimado é comprometida devido ao fato de que os erros associados com as pseudo-medições são consideravelmente maiores do que aqueles referentes às medições reais. Consequentemente é necessário alocar medidores (magnitude das tensões, fluxos de potência ativa e reativa, magnitude das correntes, etc.) para garantir a precisão do EERD. O problema de alocação de medidores para a estimação de estado em redes de transmissão é, geralmente, realizado com o objetivo de assegurar a observabilidade. Por outro lado, a alocação de medidores para EERD é realizada visando minimizar índices probabilísticos associados com os erros entre os vetores de estado estimado e verdadeiro. Um componente importante do método usado para resolver o problema de alocação de medidores é a técnica probabilística usada para estimar a função objetivo. Devido à natureza não-linear do problema de EERD, a melhor opção tem sido utilizar a Simulação Monte Carlo (SMC). Uma desvantagem da SMC para estimar a função objetivo do problema de alocação é o seu alto custo computacional devido a necessidade de resolver um problema de estimação de estado não-linear para cada vii elemento da amostra. O principal objetivo desta dissertação é propor técnicas probabilísticas para melhorar o desempenho computacional de metodologias existentes para alocação de medidores sem sacrificar a precisão do estado estimado. Este compromisso foi estabelecido usando-se duas estratégias. Na primeira, um modelo linearizado é usado para estimar o estado e a SMC para determinar os riscos da função objetivo. Na segunda, uma fórmula analítica fechada é usada para determinar os riscos com base no modelo linearizado. Além disso, as versões melhoradas dos algoritmos de alocação propostos nesta dissertação consideram o efeito da correlação entre as medições. As metodologias de alocação propostas foram testadas no sistema de distribuição britânico de 95 barras. Os resultados dos testes demonstraram que a introdução das estratégias propostas em um algoritmo de alocação de medidores reduziu significativamente o seu custo computacional. Além disso, pode-se observar que ocorreram melhorias na precisão em alguns casos, pois as estimativas dos riscos fornecidas pela SMC não são precisas com pequenas amostras.

Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-10-24T14:20:53Z No. of bitstreams: 1 igordelgadodemelo.pdf: 3776690 bytes, checksum: 47e7e8480e1ca6486c2b7b102f002e51 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-11-23T12:14:30Z (GMT) No. of bitstreams: 1 igordelgadodemelo.pdf: 3776690 bytes, checksum: 47e7e8480e1ca6486c2b7b102f002e51 (MD5) / Made available in DSpace on 2018-11-23T12:14:30Z (GMT). No. of bitstreams: 1 igordelgadodemelo.pdf: 3776690 bytes, checksum: 47e7e8480e1ca6486c2b7b102f002e51 (MD5) Previous issue date: 2018-09-21 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho apresenta uma nova metodologia para a estimação de estados harmônicos em redes de distribuição de energia elétrica, a partir da modelagem de problemas de otimização, em uma abordagem estática. Assume-se que medições fasoriais sincronizadas são obtidas continuamente por um número reduzido de PMUs (Phasor Measurement Units) estrategicamente alocadas no sistema. Correntes harmônicas passantes em todos os ramos da rede elétrica são variáveis de estado a serem estimadas em coordenadas retangulares. Valendo-se do uso de leis de Kirchhoff, outras grandezas elétricas são calculadas como fasores de tensão, potências ativa e reativa. Os problemas de otimização são modelados para cada ordem harmônica individualmente e para cada intervalo de tempo em que o algoritmo for executado, com o objetivo de estimar estados harmônicos ao longo do tempo, considerando curvas diárias de carga. A função objetivo é determinada a partir do método dos mínimos quadrados ponderados, almejando minimizar o somatório das diferenças quadráticas entre os valores medidos e os valores correspondentes estimados pelo método proposto. Para as barras não monitoradas por PMUs, potências ativa e reativa são consideradas como restrições de desigualdade com limites inferiores e superiores definidos por fatores percentuais, assumindo incertezas sobre as variações de carregamento e componentes harmônicas a serem estimadas em intervalos de tempo regulares. Os problemas de otimização são resolvidos usando o método de pontos interiores com barreira de segurança adaptado, em que a solução ótima é dada sem violação de restrições, através da introdução de um parâmetro de relaxamento que permite que os valores inferiores e superiores das restrições que atingirem seus respectivos valores limites sejam relaxados para que a solução ótima seja encontrada. Sistemas teste de distribuição de energia elétrica trifásicos, topologicamente radial são utilizados para validação da metodologia proposta. Análises de sensibilidade são consideradas para avaliar o tempo computacional, número de PMUs alocadas, geração distribuída, filtro harmônico e parâmetros usados pelo algoritmo proposto. Vantagens deste trabalho incluem número limitado de PMUs a ser instalado, identificação de múltiplas fontes harmônicas, estimação de curvas diárias de carga e componentes harmônicas ao longo do tempo, com erros de estimação reduzidos. / This work presents a novel methodology for harmonic state estimation in electric power distribution networks, based on optimization problems formulation, in a static approach. It is assumed that synchronized phasor measurements are continuously obtained using a reduced number of PMUs (Phasor Measurement Units) strategically allocated into the system. Harmonic branch currents passing through the branches of the network are the state variables to be estimated in rectangular coordinates. Based on Kirchhoff’s laws, other electrical quantities are calculated, such as voltage phasors, active and reactive powers. An optimization problem is modelled for each harmonic order individually and for each time interval in which the algorithm is executed, with the objective of estimating harmonic states along the time, considering daily load curves. The objective function is determined based on the weighted least squares method, aiming to minimize the sum of the quadratic difference between measured and estimated values by the proposed method. For the buses which are not monitored by PMUs, active and reactive powers are considered as inequality constraints, with lower and upper limits defined by percentage factors, assuming uncertainties over daily load curves and harmonic components to be estimated in regular time intervals. The optimization problems are solved using the modified safety barrier interior point method, in which the optimal solution is provided with no constraints violation, by the introduction of a relaxation parameter which allows the upper and lower bounds of the constraints which reached their corresponding limits to be relaxed in such a way that the optimal solution is obtained. Three-phase electrical distribution test systems, with radial topology are used for the validation of the proposed methodology. Sensitivity analysis are considered in order to evaluate computational time, distributed generation, harmonic filter and parameters used by the proposed algorithm. Advantages of this work include limited number of PMUs to be installed, multiple harmonic sources identification, estimation of daily load curves and harmonic components along the time, with reduced estimation errors.

Orientador: Madson Cortes de Almeida / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-21T03:49:32Z (GMT). No. of bitstreams: 1 Oliveira_WilsonAparecidode_M.pdf: 547322 bytes, checksum: ef149ef455996cf448b79577cdb88728 (MD5) Previous issue date: 2012 / Resumo: Este trabalho apresenta uma metodologia completa para analise de observabilidade de sistemas de energia eletrica. A observabilidade da rede e determinada a partir do traco da matriz de covariancia das medidas estimadas, as variancias dos fluxos estimados permitem a identificacao das ilhas observaveis e a restauracao da observabilidade e realizada a partir das variancias das medidas estimadas. As variancias necessarias sao obtidas da matriz de ganho linearizada regularizada. Alem das medidas disponiveis, na formacao da matriz de ganho regularizada admite-se a existencia de pseudomedidas de angulo em todas as barras da rede. O estimador de estado linearizado regularizado e a metodologia de identificacao de ramos observaveis a partir das variancias dos fluxos estimados foram apresentados em [Almeida, Garcia e Asada, 2011]. As novas contribuicoes deste trabalho sao o mecanismo de verificacao da observabilidade, baseado no traco da matriz de covariancia das medidas estimadas, o mecanismo de restauracao da observabilidade, desenvolvido a partir da analise das variancias das medidas, e a inclusao de medicao fasorial sincronizada na formulacao matematica utilizada / Abstract: The purpose of this work is to present a complete methodology for observability analysis of electric power systems. The observability of the network is determined from the trace of the covariance matrix of the measurement estimate, the variance of the estimated power flow allow the identification of observable islands and the restoration of observability is performed from the variance of the measurement estimate. The variances required are obtained from the regularized linearized gain matrix. Besides the measurements available, in the formation of regularized gain matrix allows the existence of voltage angle pseudomeasurements on all buses of the network. The regularized least squares power system state estimation and the methodology of analysis of the variance of the estimated power flow is based in [Almeida, Garcia e Asada, 2011]. The new contributions of this work are the observability checking mechanism, based on the trace of the covariance matrix of the measurement estimate, the mechanism of restoration of observability, developed from the analysis of variance of the measurement and the inclusion of synchronized phasor measurement in the mathematical formulation utilized / Mestrado / Energia Eletrica / Mestre em Engenharia Elétrica

The study of randomly excited nonlinear dynamical systems forms the focus of this thesis. We discuss two classes of problems: first, the characterization of nonlinear random response of the system before it comes into existence and, the second, assimilation of measured responses into the mathematical model of the system after the system comes into existence. The first class of problems constitutes forward problems while the latter belongs to the class of inverse problems. An outstanding feature of these problems is that they are almost always not amenable for exact solutions. We tackle in the present study these two classes of problems using Monte Carlo simulation tools in conjunction with Markov process theory, Bayesian model updating strategies, and particle filtering based dynamic state estimation methods. It is well recognized in literature that any successful application of Monte Carlo simulation methods to practical problems requires the simulation methods to be reinforced with effective means of controlling sampling variance. This can be achieved by incorporating any problem specific qualitative and (or) quantitative information that one might have about system behavior in formulating estimators for response quantities of interest. In the present thesis we outline two such approaches for variance reduction. The first of these approaches employs a substructuring scheme, which partitions the system states into two sets such that the probability distribution of the states in one of the sets conditioned on the other set become amenable for exact analytical solution. In the second approach, results from data based asymptotic extreme value analysis are employed to tackle problems of time variant reliability analysis and updating of this reliability. We exemplify in this thesis the proposed approaches for response estimation and model updating by considering wide ranging problems of interest in structural engineering, namely, nonlinear response and reliability analyses under stationary and (or) nonstationary random excitations, response sensitivity model updating, force identification, residual displacement analysis in instrumented inelastic structures under transient excitations, problems of dynamic state estimation in systems with local nonlinearities, and time variant reliability analysis and reliability model updating. We have organized the thesis into eight chapters and three appendices. A resume of contents of these chapters and appendices follows. In the first chapter we aim to provide an overview of mathematical tools which form the basis for investigations reported in the thesis. The starting point of the study is taken to be a set of coupled stochastic differential equations, which are obtained after discretizing spatial variables, typically, based on application of finite element methods. Accordingly, we provide a summary of the following topics: (a) Markov vector approach for characterizing time evolution of transition probability density functions, which includes the forward and backward Kolmogorov equations, (b) the equations governing the time evolution of response moments and first passage times, (c) numerical discretization of governing stochastic differential equation using Ito-Taylor’s expansion, (d) the partial differential equation governing the time evolution of transition probability density functions conditioned on measurements for the study of existing instrumented structures, (e) the time evolution of response moments conditioned on measurements based on governing equations in (d), and (f) functional recursions for evolution of multidimensional posterior probability density function and posterior filtering density function, when the time variable is also discretized. The objective of the description here is to provide an outline of the theoretical formulations within which the problems of response estimation and model updating are formulated in the subsequent chapters of the present thesis. We briefly state the class of problems, which are amenable for exact solutions. We also list in this chapter major text books, research monographs, and review papers relevant to the topics of nonlinear random vibration analysis and dynamic state estimation. In Chapter 2 we provide a review of literature on solutions of problems of response analysis and model updating in nonlinear dynamical systems. The main focus of the review is on Monte Carlo simulation based methods for tackling these problems. The review accordingly covers numerical methods for approximate solutions of Kolmogorov equations and associated moment equations, variance reduction in simulation based analysis of Markovian systems, dynamic state estimation methods based on Kalman filter and its variants, particle filtering, and variance reduction based on Rao-Blackwellization. In this review we chiefly cover papers that have contributed to the growth of the methodology. We also cover briefly, the efforts made in applying the ideas to structural engineering problems. Based on this review, we identify the problems of variance reduction using substructuring schemes and data based extreme value analysis and, their incorporation into response estimation and model updating strategies, as problems requiring further research attention. We also identify a range of problems where these tools could be applied. We consider the development of a sequential Monte Carlo scheme, which incorporates a substructuring strategy, for the analysis of nonlinear dynamical systems under random excitations in Chapter 3. The proposed substructuring ensures that a part of the system states conditioned on the remaining states becomes Gaussian distributed and is amenable for an exact analytical solution. The use of Monte Carlo simulations is subsequently limited for the analysis of the remaining system states. This clearly results in reduction in sampling variance since a part of the problem is tackled analytically in an exact manner. The successful performance of the proposed approach is illustrated by considering response analysis of a single degree of freedom nonlinear oscillator under random excitations. Arguments based on variance decomposition result and Rao-Blackwell theorems are presented to demonstrate that the proposed variance reduction indeed is effective. In Chapter 4, we modify the sequential Monte Carlo simulation strategy outlined in the preceding chapter to incorporate questions of dynamic state estimation when data on measured responses become available. Here too, the system states are partitioned into two groups such that the states in one group become Gaussian distributed when conditioned on the states in the other group. The conditioned Gaussian states are subsequently analyzed exactly using the Kalman filter and, this is interfaced with the analysis of the remaining states using sequential importance sampling based filtering strategy. The development of this combined Kalman and sequential importance sampling filtering method constitutes one of the novel elements of this study. The proposed strategy is validated by considering the problem of dynamic state estimation in linear single and multi-degree of freedom systems for which exact analytical solutions exist. In Chapter 5, we consider the application of the tools developed in Chapter 4 for a class of wide ranging problems in nonlinear random vibrations of existing systems. The nonlinear systems considered include single and multi-degree of freedom systems, systems with memoryless and hereditary nonlinearities, and stationary and nonstationary random excitations. The specific applications considered include nonlinear dynamic state estimation in systems with local nonlinearities, estimation of residual displacement in instrumented inelastic dynamical system under transient random excitations, response sensitivity model updating, and identification of transient seismic base motions based on measured responses in inelastic systems. Comparisons of solutions from the proposed substructuring scheme with corresponding results from direct application of particle filtering are made and a satisfactory mutual agreement is demonstrated. We consider next questions on time variant reliability analysis and corresponding model updating in Chapters 6 and 7, respectively. The research effort in these studies is focused on exploring the application of data based asymptotic extreme value analysis for problems on hand. Accordingly, we investigate reliability of nonlinear vibrating systems under stochastic excitations in Chapter 6 using a two-stage Monte Carlo simulation strategy. For systems with white noise excitation, the governing equations of motion are interpreted as a set of Ito stochastic differential equations. It is assumed that the probability distribution of the maximum over a specified time duration in the steady state response belongs to the basin of attraction of one of the classical asymptotic extreme value distributions. The first stage of the solution strategy consists of selection of the form of the extreme value distribution based on hypothesis testing, and, the next stage involves the estimation of parameters of the relevant extreme value distribution. Both these stages are implemented using data from limited Monte Carlo simulations of the system response. The proposed procedure is illustrated with examples of linear/nonlinear systems with single/multiple degrees of freedom driven by random excitations. The predictions from the proposed method are compared with the results from large scale Monte Carlo simulations, and also with the classical analytical results, when available, from the theory of out-crossing statistics. Applications of the proposed method for vibration data obtained from laboratory conditions are also discussed. In Chapter 7 we consider the problem of time variant reliability analysis of existing structures subjected to stationary random dynamic excitations. Here we assume that samples of dynamic response of the structure, under the action of external excitations, have been measured at a set of sparse points on the structure. The utilization of these measurements in updating reliability models, postulated prior to making any measurements, is considered. This is achieved by using dynamic state estimation methods which combine results from Markov process theory and Bayes’ theorem. The uncertainties present in measurements as well as in the postulated model for the structural behaviour are accounted for. The samples of external excitations are taken to emanate from known stochastic models and allowance is made for ability (or lack of it) to measure the applied excitations. The future reliability of the structure is modeled using expected structural response conditioned on all the measurements made. This expected response is shown to have a time varying mean and a random component that can be treated as being weakly stationary. For linear systems, an approximate analytical solution for the problem of reliability model updating is obtained by combining theories of discrete Kalman filter and level crossing statistics. For the case of nonlinear systems, the problem is tackled by combining particle filtering strategies with data based extreme value analysis. The possibility of using conditional simulation strategies, when applied external actions are measured, is also considered. The proposed procedures are exemplified by considering the reliability analysis of a few low dimensional dynamical systems based on synthetically generated measurement data. The performance of the procedures developed is also assessed based on limited amount of pertinent Monte Carlo simulations. A summary of the contributions made and a few suggestions for future work are presented in Chapter 8. The thesis also contains three appendices. Appendix A provides details of the order 1.5 strong Taylor scheme that is extensively employed at several places in the thesis. The formulary pertaining to the bootstrap and sequential importance sampling particle filters is provided in Appendix B. Some of the results on characterizing conditional probability density functions that have been used in the development of the combined Kalman and sequential importance sampling filter in Chapter 4 are elaborated in Appendix C.