Indirect wind estimation onboard unmanned aerial systems (UASs) can be accomplished using existing air vehicle sensors along with a dynamic model of the UAS augmented with additional wind-related states. It is often desired to extract a mean component of the wind the from frequency fluctuations (i.e. turbulence). Commonly, a variation of the KALMAN filter is used, with explicit or implicit assumptions about the nature of the random wind velocity. This dissertation presents an H-infinity (H∞) filtering approach to wind estimation which requires no assumptions about the statistics of the process or measurement noise. To specify the wind frequency content of interest a low-pass filter is incorporated. We develop the augmented UAS model in continuous-time, derive the H∞ filter, and introduce a KALMAN-BUCY filter for comparison. The filters are applied to data gathered during UAS flight tests and validated using a vaned air data unit onboard the aircraft. The H∞ filter provides quantitatively better estimates of the wind than the KALMAN-BUCY filter, with approximately 10-40% less root-mean-square (RMS) error in the majority of cases. It is also shown that incorporating DRYDEN turbulence does not improve the KALMAN-BUCY results. Additionally, this dissertation describes the theory and process for using generalized polynomial chaos (gPC) to re-cast the dynamics of a system with non-deterministic parameters as a deterministic system. The concepts are applied to the problem of wind estimation and characterizing the precision of wind estimates over time due to known parametric uncertainties. A novel truncation method, known as Sensitivity-Informed Variable Reduction (SIVR) was developed. In the multivariate case presented here, gPC and the SIVR-derived reduced gPC (gPCr) exhibit a computational advantage over Monte Carlo sampling-based methods for uncertainty quantification (UQ) and sensitivity analysis (SA), with time reductions of 38% and 98%, respectively. Lastly, while many estimation approaches achieve desirable accuracy under the assumption of known system parameters, reducing the effect of parametric uncertainty on wind estimate precision is desirable and has not been thoroughly investigated. This dissertation describes the theory and process for combining gPC and H-infinity (H∞) filtering. In the multivariate case presented, the gPC H∞ filter shows superiority over a nominal H∞ filter in terms of variance in estimates due to model parametric uncertainty. The error due to parametric uncertainty, as characterized by the variance in estimates from the mean, is reduced by as much as 63%. / Doctor of Philosophy / On unmanned aerial systems (UASs), determining wind conditions indirectly, without direct measurements, is possible by utilizing onboard sensors and computational models. Often, the goal is to isolate the average wind speed while ignoring turbulent fluctuations. Conventionally, this is achieved using a mathematical tool called the KALMAN filter, which relies on assumptions about the wind. This dissertation introduces a novel approach called H-infinity (H∞) filtering, which does not rely on such assumptions and includes an additional mechanism to focus on specific wind frequencies of interest. The effectiveness of this method is evaluated using real-world data from UAS flights, comparing it with the traditional KALMAN-BUCY filter. Results show that the H∞ filter provides significantly improved wind estimates, with approximately 10-40% less error in most cases. Furthermore, the dissertation addresses the challenge of dealing with uncertainty in wind estimation. It introduces another mathematical technique called generalized polynomial chaos (gPC), which is used to quantify and manage uncertainties within the UAS system and their impact on the indirect wind estimates. By applying gPC, the dissertation shows that the amount and sources of uncertainty can be determined more efficiently than by traditional methods (up to 98% faster). Lastly, this dissertation shows the use of gPC to provide more precise wind estimates. In experimental scenarios, employing gPC in conjunction with H∞ filtering demonstrates superior performance compared to using a standard H∞ filter alone, reducing errors caused by uncertainty by as much as 63%.

This paper deals with the modeling of asynchronous motor. Ccomparing the simulation date to reality. And attempts to find an algorithm for calculating the mechanical torque assist state estimation engine.

Ce travail de thèse traite de la problématique d’estimation des défauts et de l’étathybride pour une classe de systèmes linéaires à commutations. L’objectif est de développerune méthode afin de synthétiser un observateur et un estimateur dédiésrespectivement à l’estimation de l’état hybride et des défauts. Après la présentationd’un état de l’art sur les techniques d’estimation, de stabilité et de diagnosticpour les systèmes linéaires à commutations, la thèse est scindée en deux parties.La première partie propose une méthode d’estimation de l’état continu et desdéfauts dans le cas où l’état discret du système est connu. En se basant sur unetransformation de coordonnées qui découple un sous-ensemble de l’état du systèmedes défauts, nous avons synthétisé dans un premier temps un observateur hybridepour estimer l’état continu du système, et dans un second temps, un estimateurpermettant la reconstruction des défauts. L’estimateur de défauts proposé dépendde la dérivée de la sortie du système. Pour cette raison, un différenciateur robusteet exact basé sur des techniques des modes glissants est utilisé. Dans la secondepartie de ce mémoire, l’état discret du système est supposé inconnu. Une approchebasée sur des méthodes algébriques est proposée afin d’estimer les instants decommutation entre les différents sous-systèmes. Par la suite, l’estimation de l’étathybride (état continu et état discret) et des défauts est considérée dans le cas oùl’état discret du système est inconnu. Ce dernier est reconstruit en se basant surles instant de commutation estimé et sur une séquence de commutation connue.L’état continu du système est estimé en se basant sur une méthode de placementde pôles permettant d’améliorer les performances de la phase transitoire. Enfin, enexploitant des résultats trouvés dans la première partie, l’estimation des défautsest considérée en estimant la sortie du système avec un différenciateur algébrique.Ce différenciateur donne des résultats plus intéressants vis-à-vis du bruit par rapportau différenciateur basé sur les techniques des modes glissants utilisé dans lapremière partie. / This work deals with the problem of estimation of fault and hybrid state for a classof switched linear systems. The objective is to develop a method to synthesize anobserver and an estimator dedicated respectively to the estimation of the hybridstate and the faults. After presenting a state of the art for estimation, stabilityand diagnostic techniques for switched linear systems, the report is divided intotwo parts. The first part proposes a method for estimating the continuous stateand the faults in the case where the discrete state of the system is known. Basedon a coordinate transformation which decouples a subset of the state of the systemof faults, we first synthesized a hybrid observer to estimate the continuous stateof the system and, in a second step, an estimator allowing the reconstructionof faults. The proposed fault estimator depends on the derivative of the systemoutput. For this reason, a robust and accurate differentiator based on sliding modetechniques is used. In the second part of this paper, the discrete state of the systemis assumed unknown. An algebraic approach is proposed to estimate the switchingtimes between the different subsystems. Thereafter, the estimation of the hybridstate (continuous and discrete state) and of the faults is considered in the casewhere the discrete state of the system is unknown. The latter is reconstructedfrom the estimated switching times and on a known switching sequence. Thecontinuous state of the system is estimated using a pole placement method allowingimprove the performances of the transient phase. Finally, by exploiting the resultsfound in the first part, the estimation of the faults is considered by estimatingthe output of the system with an algebraic differentiator. This differentiator givesmore interesting results at the noise compared to the differentiator based on thesliding mode techniques used in the first part.

Este trabalho tem como objetivo o desenvolvimento de uma metodologia de monitoramento a partir da alocação de medidores voltada para a estimação de estado harmônico trifásica em sistemas de distribuição de energia elétrica desequilibrados. O algoritmo de estimação de estado harmônico desenvolvido tem como entrada os fasores de tensão e de corrente em pontos pré-definidos de medição sobre os alimentadores em análise. Para a alocação dos medidores, verificou-se a necessidade de a mesma ser realizada e direcionada para este problema, e um algoritmo de otimização em específico foi desenvolvido utilizando algoritmos genéticos. Para a estimação de estado harmônico, a técnica de Decomposição em Valores Singulares foi utilizada, por ser adequada a sistemas não completamente observáveis. Em relação às simulações, cargas não lineares (ou perturbadoras) foram conectadas ao longo dos alimentadores testes do IEEE de 13, 34 e 37 barras, considerando configuração trifásica assimétrica para as linhas e cargas desbalanceadas. Todas as simulações computacionais foram realizadas dispondo do programa DIgSILENT PowerFactory. Os resultados satisfatórios encontrados denotam que o desempenho do estimador desenvolvido é dependente dos pontos de medição pré-definidos a partir da alocação dos medidores realizada. Pela metodologia implementada e aplicada, o algoritmo de estimação de estado harmônico veio a corretamente calcular todas as variáveis de estado e, consequentemente, os sistemas testes em análise tornaram-se completamente observáveis para todas as fases e ordens harmônicas caracterizadas. / This research aims for the development of a monitoring methodology through the allo-cation of meters in order to perform a three-phase harmonic state estimation in unbalanced distribution systems. The harmonic state estimation algorithm developed has voltage and current phasors as inputs at predefined measurement points on the feeders about analysis. For an allocation of the meters, there was a need for it to be performed and directed to this problem, and a specific optimization algorithm was developed using Genetic Algorithms. For a harmonic state estimation, the Singular Value Decomposition technique was made, because it is suitable for systems that are not completely observable. Regarding the simulations, the non-linear (or disturbing) loads were connected along the test feeders of the IEEE of 13, 34 and 37 bus, considering the three-phase asymmetric configuration for lines and loads. All computational simulations were performed in the DIgSILENT PowerFactory software. The satisfactory results found note that the performance of the developed estimator depends on the pre-defined measurement points from the allocation of the realized meters. By the applied methodology, the harmonic state estimation algorithm came to correctly calculate all the state variables and, consequently, the test systems about analysis became fully observable for all phases and harmonic orders characterized.

Neste trabalho propõe-se uma metodologia off-line, prática e eficiente, para detectar, identificar e corrigir erros em parâmetros série e shunt de linhas de transmissão. As linhas de transmissão, ou ramos do modelo barra-ramo, suspeitas de estarem com EPs são identificadas através do Índice de Suspeita (IS). O IS de um ramo é a relação entre o número de medidas incidentes a esse ramo, cujos resíduos normalizados são maiores que um valor pré-estabelecido, e o número total de medidas incidentes a esse ramo. Usando várias amostras de medidas, os parâmetros dos ramos suspeitos são estimados, de forma seqüencial, via um estimador de estado e parâmetros baseado nas equações normais, que aumenta o vetor de variáveis de estado para inclusão dos parâmetros suspeitos. Resultados numéricos de diversas simulações, com os sistemas de 14, 30 e 57 barras do IEEE, têm demonstrado a alta precisão e confiabilidade da metodologia proposta, mesmo na ocorrência de erros múltiplos (em mais de um parâmetro) em ramos adjacentes, como também em linhas de transmissão paralelas com compensação série. Comprovou-se a viabilidade prática da metodologia proposta através da aplicação da mesma, para depuração (detecção, identificação e correção) dos valores dos parâmetros de dois subsistemas da Hydro-Québec Trans-Énergie. / A practical and efficient off-line approach to detect, identify and correct series and shunt branch parameter errors is proposed in this thesis. The branches suspected of having parameter errors are identified by means of the Suspicious Index (SI). The SI of a branch is the ratio between the number of measurements incident to that branch, whose normalized residuals are larger than one specified threshold value, and the total number of measurements incident to that branch. Using several measurement snapshots, the suspicious parameters are sequentially estimated, via an augmented state and parameter estimator which increases the V-\'teta\' state vector for the inclusion of suspicious parameters. Several simulation results (with IEEE 14, 30 and 57 bus systems) have demonstrated the high accuracy and reliability of the proposed approach to de al with single and multiple parameter errors in adjacent and non-adjacent branches, as well as in parallel transmission lines with series compensation. The proposed approach is confirmed by tests performed in two subsystems of the Hydro-Québec Trans-Énergie.

Esta dissertação apresenta um estudo dos filtros de Kalman para sistemas singulares em tempo discreto. Novos algoritmos são formulados para as estimativas filtradas, preditoras e suavizadas com as correspondentes equações de Riccati para sistemas singulares variantes no tempo. Nesta dissertação considera-se também uma aproximação do problema de filtragem de Kalman como um problema determinístico de ajuste ótimo de trajetória. A formulação proposta permite considerar um atraso no sinal de medida, sendo permitida a correlação entre os estados e os ruídos da medida. Apresentam-se também as provas da estabilidade e da convergência destes filtros. / This dissertation presents a study of Kalman filters for singular systems in discrete time. New algorithms are developed for the Kalman filtered, predicted and smoothed estimate recursions with the corresponding Riccati equations for time-variant singular systems. This dissertation addresses the Kalman filtering problem as a deterministic optimal trajectory fitting problem. The problem is formulated taking into account one delay in the measured signals and correlations between state and measurement noises. In the final, this work presents the stability and convergence proofs of these filters.

A tendência crescente na geração de harmônicos nos sistemas elétricos de potência tem ganhado atenção especial no planejamento das redes de transporte de energia elétrica, uma vez que os crescimentos observados acontecem em regiões que antes não representavam qualquer tipo de preocupação. Um dos principais fatores que contribuíram para esse novo contexto é a característica distribuída da geração de harmônicos. Devido a essa nova realidade, métodos mais aprimorados para avaliação de desempenho e modelos mais precisos para a representação de equipamentos tornaram-se necessários. Sendo assim, a pesquisa realizada para a elaboração da presente tese fundamentou a sua investigação em três tópicos com o intuído de fornecer contribuições que permitissem uma avaliação mais precisa das redes elétricas, proporcionando, assim, resultados mais aderentes com a realidade existente: Modelagem Agregada de Carga; Equivalentes de Redes; Estimação de Estados das Distorções Harmônicas. Através das contribuições feitas nesses tópicos, torna-se possível a consideração de aspectos que antes eram ignorados na avaliação harmônica das redes de transporte de energia elétrica e, assim, permite-se uma verificação precisa dos impactos da característica distribuída da geração de harmônicos nos sistemas elétricos de potência. / The growing rate of harmonic generation present in the electric power systems has gained special attention in the planning process of power networks. The major factor that contributed for this new context is the increasing harmonic generation observed in regions that did not use to represent any concern in the past. One of the main causes for this new trend is the distributed characteristic of the harmonic generation. In this new environment, sophisticated methods and models have become necessary, in order to precisely represent the electric elements behaviour and to accurately evaluate the systems performance. As a result, the research work presented in this thesis focused in three different topics, in order to provide contributions that would lead to a more accurate performance evaluation of the power networks and that would provide results closer to the values found in the field: Aggregate Load Modeling; Network Equivalents; Harmonic State Estimation. These contributions would allow the consideration of aspects that normally are ignored in the harmonic assessment of power systems. Consequently, the evaluation of the impacts caused by the distributed generation of harmonics becomes more accurate.

Bretas et al. (2009) prova matematicamente, e através da interpretação geométrica, que o erro de medida se divide em componentes detectáveis e não-detectáveis. Demonstra ainda que as metodologias até então utilizadas, para o processamento de Erros Grosseiros (EGs), consideram apenas a componente detectável do erro. Assim, dependendo da amplitude das componentes do erro, essas metodologias podem falhar. Face ao exposto, neste trabalho é proposto uma nova metodologia para processar as medidas portadoras de EGs. Essa proposição será obtida decompondo o erro da medida em duas componentes: a primeira, é ortogonal ao espaço da imagem da matriz jacobiana cuja amplitude é igual ao resíduo da medida, a outra, pertence ao espaço da imagem da matriz jacobiana e que, por conseguinte, não contribui para o resíduo da medida. A relação entre a norma dessas componentes, aqui denominado Índice de Inovação (II), prevê uma nova informação, isto é, informação não contida nas outras medidas. Usando o II, calcula-se um valor limiar (TV) para cada medida, esse limiar será utilizado para inferir se a medida é ou não suspeita de possuir EG. Em seguida, com as medidas suspeitas em mãos, desenvolve-se um índice de filtragem (FI) que será utilizado para identificar qual daquelas medidas tem maior probabilidade de possuir EG. Os sistemas de 14 e 30 barras do IEEE, e o sistema sul reduzido do Brasil de 45 barras, serão utilizados para mostrar a eficiência da metodologia proposta. Os testes realizados com os sistemas acima são: i) O teste de nível de detecção de EG, que consisti em encontrar o valor mínimo de EG que seja detectado usando o TV da medida; ii) O teste onde é adicionado EG de 10 desvios padrões em cada medida, uma por vez, nesse teste o FI da medida é usado para identificar qual medida possui o erro, em seguida à medida com erro é corrigida através do erro normalizado composto (ENC); iii) O teste de EG simples. / Bretas et al. (2009) has proved, using geometric background, that the measurement error can be decomposed into two components the detectable and the undetectable component respectively. Bretas has also demonstrated that the current methodologies used for processing of gross errors (GE), consider only the detectable component of the error. Thus, depending on the magnitude of the undetectable error components, such methods may fail. Given the above explanation, in this work a new methodology for processing the measurements with GE is proposed. This proposition is obtained by decomposing each measurement error into two components: the first, orthogonal to the Jacobian range space, whose magnitude is equal to the measurement residual and the other contained in that space, which does not contribute to the measurement residual. The ratio between the norms of those components was proposed as the measurement Innovation Index (II) which provides the new information a measurement contains regarding the other measurements. Using the II, a threshold value (TV) for each measurement is computed so that one can declare a measurement suspicious of having a GE. Then a filtering index (FI) is proposed to filter up, from the suspicious measurements, the one that has more chances of containing a GE. The IEEE-14 bus system, IEEE-30 bus system, and reduced 45-bus power system of south of Brazil, will be used to demonstrate the accuracy and efficiency of the proposed methodology. Tests conducted with the above systems were: i) The level test for GE detection, which consists in finding the minimum GE value in order it can be detected using the measurement TV; ii) The test where GE of 10 standard deviations is added to each measurement, once at a time, and using the measurement FI to identify which measurement has the error ant the using the composed measurement error (CNE) to correct measurement value; iii) The GE simple test.

Este trabalho de dissertação trata do problema de observabilidade e redundância de medidas para efeito de estimação de estado trifásica. É proposta a extensão de uma metodologia numérica eficiente para análise de observabilidade e identificação de medidas críticas e conjuntos críticos de medidas, desenvolvida para modelagem por fase, a fim de considerar redes trifásicas de energia, nas quais os desbalanços nas cargas e os desequilíbrios na rede são considerados. Ao longo do trabalho apresenta-se uma revisão dos principais conceitos de estimação de estado, observabilidade de redes e redundância de medidas, destacando a importância da estimação de estado trifásica para obtenção de uma operação segura de sistemas elétricos de potência desbalanceados e/ou desequilibrados. Os resultados obtidos em diversos testes realizados, com sistemas trifásicos já empregados em outros trabalhos da área contendo 4, 7 e 38 barras, atestam o adequado desempenho da extensão proposta e são apresentados detalhadamente nesta dissertação. Por fim, o conceito de observabilidade topológica, desenvolvido para modelagem monofásica da rede, é estendido para modelagem trifásica, permitindo um entendimento melhor do problema de observabilidade no contexto de estimação trifásica. / This thesis focuses on the problem of observability and measurement redundancy in the context of three-phase state estimation. It is proposed an extension of an efficient numerical methodology for observability and redundancy analysis, developed for the single-phase network model, in order to consider the three-phase network model, where the unbalanced loads and the asymmetric nature of the system are considered. During this work, a review of the main concepts related to state estimation, network observability and measurement redundancy are presented, highlighting the importance of the three-phase state estimation in order to obtain a reliable operation of unbalanced and/or asymmetric power systems. Simulations results obtained for several cases studies based on three three-phase systems already used in the literature, with 4, 7 and 38 buses, validate the proposed methodology extension and are presented in detail in this thesis. Finally, the concept of topological observability, developed for the single-phase network model, is extended for the three-phase model.

Cette thèse traite de l’analyse et de la synthèse de multimodèles pour la simplification de modèles, l’estimation d’état et le diagnostic des systèmes non linéaires caractérisés par une ou plusieurs échelles de temps. Ces travaux visent, dans un premier temps, à développer une procédure systématique de transformation d’un système non-linéaire en le récrivant sous une forme multimodèle, en évitant quelques inconvénients majeurs : la transformation est réalisée sans perte d’information, le choix de différents points de fonctionnement n’est plus nécessaire, le choix de variables de prémisse est réalisé d’une façon systématique. De plus, la méthode offre le choix entre différents multimodèles. Ce degré de liberté sera utilisé pour faciliter les études de contrôlabilité, d’observabilité et d’analyse de stabilité. Dans un deuxième temps, l’obtention de la forme à perturbations singulières d’un système non linéaire est proposée, en éliminant quelques contraintes structurelles et en rendant l’identification et la séparation des échelles de temps indépendante de la structure du modèle. Dans un troisième temps, la synthèse de plusieurs observateurs robustes vis-à-vis des perturbations, des erreurs de modélisation et des entrées inconnues a été réalisée afin dereconstruire l’état et l’entrée inconnue du système. La difficulté de cette étude provient du fait que le multimodèle utilisé dépend de variables de prémisse non mesurables, situation qui n’est pas intensivement étudiée, alors qu’elle est naturellement issue de l’approche par transformation système non linéaire!multimodèle. Ensuite, le diagnostic de défauts de systèmes est réalisé au moyen de bancs d’observateur à entrées inconnues permettant la génération et la structuration de résidus indicateurs de défauts. Finalement, tous les travaux proposés sont appliqués au modèle d’une station d’´epuration, Activated Sludge Model No.1, qui est largement utilisé dans le domaine du traitement des eaux usées / This thesis deals with analysis and synthesis of multiple model structures for model simplification, state estimation and diagnosis of nonlinear systems represented by one or several time-scales. This work aims, at first, to develop a systematic procedure to transform a nonlinear system into a multiple model form, by avoiding some major drawbacks : the transformation causes no information loss, the choice of the different operating points is no more necessary, the choice of the premise variables is realized in a more systematic way. Furthermore, the method gives the possibility of choosing between different multiplemodel structures. This degree of freedom will be used to ease the controllability, observ-ability, stability analysis studies. Secondly, the derivation of a singularly perturbed form for a multiple time scale non linear system is proposed, by eliminating some structuralconstraints and by making the identification and the separation of the time-scales independent to the model structure. Thirdly, the robust observer synthesis with respect to perturbations, modeling errors and unknown inputs are presented for state and unknowninput estimation. The difficulty of these studies comes from the fact that the multiple model depends on unmeasurable premise variables, this case being not intensively studied, whereas it results naturally from the method of transformation nonlinear system - multiple model. Afterward, fault diagnosis is performed using banks of observer to generate andstructure residual signals. Finally, this works are applied to a model of wastewater treatment plant, Activated Sludge Model No.1 (ASM1) that is largely used in the concerned fiel