Desenvolveu-se neste trabalho um método para projeto e fortalecimento de planos de medição, para efeito de estimação de estados. O método proposto permite a obtenção de planos de medição que além de isentos de medidas críticas e de conjuntos críticos de medidas, garantem a observabilidade do sistema, mesmo com a perda simultânea de 1 ou 2 medidas quaisquer, ou, até mesmo, com a perda de 1 UTR. É um método numérico simples, de fácil implantação, que se baseia na análise da estrutura da matriz resultante da decomposição LDU, que é obtida através da fatoração triangular da matriz Jacobiana. Para comprovar a sua eficiência, vários testes foram realizados, utilizando os sistemas de 14 e 30 barras do IEEE, o sistema de 121 barras da ELETROSUL e o sistema de 383 barras da CHESF. / In this work a method to design and to upgrade Measurements Placement Plan for state estimation is proposed. The proposed method allows the obtention of measurements placement plans that, besides free of both critical measurements and critical sets, maintain the system observability when 1 or 2 measurements are lost, at same time, or even when a Remote Terminal Unit (RTU) is lost. It is a simple numerical method, easy to implement and based on the analysis of the structure of the resultant matrix of the decomposition LDU, that it is obtained through a triangular factorization of the Jacobian matrix. To prove the efficiency of the proposed method, several tests were made using the IEEE 14 and 30-bus systems, a 121-bus system from ELETROSUL and a 383-bus system from CHESF.

O estimador de estado (EE) foi originalmente desenvolvido para lidar com sistemas de transmissão (ST). Desta maneira, sua aplicação em sistemas de distribuição (SD) exige que os métodos clássicos sejam repensados. Este trabalho teve como objetivo avaliar os métodos disponíveis na literatura para a estimação de estado em SD e explorar a fundo um método escolhido. A abordagem escolhida foi a que utiliza as correntes complexas nos ramos como variáveis de estado. Tal abordagem visa tirar proveito das características específicas dos SD, e apresenta um desempenho computacional superior se comparado a soluções que utilizam as tensões como variáveis de estado. Entretanto, tal método ainda se encontra pouco explorado na literatura, de modo que diversas limitações foram identificadas. A principal limitação encontrada foi no que tange à presença de transformadores no sistema, que foi negligenciada nos trabalhos encontrados na literatura. De modo a aumentar a confiabilidade da estimação, além das correntes em todos os ramos, foi considerada a possibilidade de se incluir no vetor de estado variáveis referentes à tensão na subestação (SE). Na presença de transformadores, tal expansão no vetor de estados gerou um acoplamento do modelo matemático. Neste trabalho, foram propostas soluções para lidar com diferentes conexões de transformadores utilizando o estimador com base nas correntes mantendo uma de suas principais características, que é o desacoplamento entre fases. Na ocasião da estimação da tensão na SE, um método de combinação ótima de variáveis de estado foi proposto de modo a contornar o acoplamento gerado no modelo matemático. Sistemas teste do IEEE foram utilizados para avaliar o desempenho do algoritmo implementado. Os resultados obtidos mostraram que a metodologia escolhida foi capaz de estimar o estado do SD com precisão adequada na presença de diferentes tipos de medidas e topologias. Os modelos propostos neste trabalho se mostraram eficazes na incorporação de transformadores com diferentes conexões na formulação do EE. Por fim, o método proposto para lidar com a estimação da tensão na SE de maneira desacoplada na presença de transformadores foi validado e se mostrou mais eficiente computacionalmente quando comparado ao seu análogo acoplado. / The state estimator (SE) was originally developed to deal with transmission networks (TN). Hence, its application in distribution networks (DN) requires the classical methods to be modified. The main aim of this work was to evaluate the methods available in the literature for state estimation in DN and to explore in depth a chosen method. The chosen approach was the one that uses the complex branch currents as state variables. This approach aims to take advantage of the specific characteristics of DN, and presents a superior computational performance when compared to solutions that use voltages as state variables. However, this method is still little explored in the literature, so that several limitations have been identified. The main limitation was in terms of the presence of transformers in the system, which was neglected in the papers found in the literature. In order to increase the reliability of the estimation, in addition to the branch currents, it was considered the posibility of including the substation voltage variables in the state vector. In the presence of transformers, such expansion in the state vector generated a coupled mathematical model. In this work, solutions were proposed to deal with different transformer connections using the branch current SE while keeping one of its main characteristics, that is the decoupling between phases. When the substation voltage is being estimated, an optimal combination of state variables was proposed in order to circumvent the coupling in the mathematical model. IEEE test systems were used to evaluate the performance of the implemented algorithm. The results showed that the chosen methodology was able to estimate the DN state with adequate accuracy in the presence of different types of measurements and topologies. The models proposed in this work proved to be effective in the incorporation of transformers with different connections in the SE formulation. Finally, the proposed method to decouple the branch current SE when dealing with substation voltage estimation in the presence of transformers was validated and proved to be computationally more efficient when compared to its coupled version.

Cette thèse s’inscrit dans le cadre applicatif général de l'analyse de cellules uniques. Afin d’améliorer la sélectivité du tri de cellules uniques, les équipes de FEMTO-ST proposent de contrôler en boucle fermée les trajectoires des cellules entemps réel pendant leur trajet dans les puces dédiées au tri. Dans ce cadre, mes travaux de thèse portent sur une méthode novatrice de détection en temps-réel de la position des cellules, directement intégrée aux puces et basée sur le principephysique de la mesure d'impédance.Lors du passage d’une cellule dans un microcanal, celle-ci vient modifier l’impédance mesurable entre des électrodes placées sur les bords du canal.Une méthode générique permettant de formuler les variations d'impédance en fonction de la position de la particule été proposée (modèledirect).Une méthode d'estimation de la position d’une particule reposant sur les mesures d’impédance a également été proposée (modèle inverse). Celle-ci exploite un filtre de Kalman étendu, permettant la fusion de données en provenance de plusieurspaires d'électrodes, et exploitant les informations disponibles telles que la distribution du bruit de mesure et le modèle dynamique de la particule.La validation de la méthode a été effectuée sur un banc expérimental qui a été développé lors de cette thèse et sur des simulations numériques.Ces travaux montrent la pertinence d’exploiter l’impédancemétrie pour construire un capteur de position de particules immergées dans un microcanal. Cette méthode est une alternative à l’utilisation de microscopes optiques et présente l’avantage d’une grande compacité. / This thesis is part of the general application framework of single cell analysis. In order to improve the selectivity of single cell sorting, FEMTO-ST teams propose to control in closed loop the trajectories of the cells in real time during their journey in the chips dedicated to sorting. In this context, my thesis work focuses on an innovative method for real-time detection of cell position, directly integrated into chips and based on the physical principle of impedance measurement.When a cell passes through a microchannel, it changes the measurable impedance between electrodes placed on the edges of the channel.A generic method for formulating impedance variations as a function of particle position has been proposed (direct model). A method for estimating the position of a particle based on impedance measurements has also been proposed (inverse model). It uses an extended Kalman filter, allowing data from several pairs ofelectrodes to be merged, and exploiting available information such as measurement noise distribution and particle dynamic model. The validation of the method was carried out on an experimental bench that was developed during this thesis and on numerical simulations.This work shows the relevance of using impedance measurement to build a position sensor for particles immersed in a microchannel. This method is an alternative to the use of optical microscopes and has the advantage of being very compact.

The main objective of this thesis is to apply ideas and techniques from modern control theory, especially from robust state estimation and model validation, to various important problems in computer vision. Robust model validation is used in texture recognition where new approaches for classifying texture samples and segmenting textured images are developed. Also, a new model validation approach to motion primitive recognition is demonstrated by considering the motion segmentation problem for a mobile wheeled robot. A new approach to image inpainting based on robust state estimation is proposed where the implementation presented here concerns with recovering corrupted frames in video sequences. Another application addressed in this thesis based on robust state estimation is video-based tracking. A new tracking system is proposed to follow connected regions in video frames representing the objects in consideration. The system accommodates tracking multiple objects and is designed to be robust towards occlusions. To demonstrate the performance of the proposed solutions, examples are provided where the developed methods are applied to various gray-scale images, colored images, gray-scale videos and colored videos. In addition, a new algorithm is introduced for motion estimation via inverse polynomial interpolation. Motion estimation plays a primary role within the video-based tracking system proposed in this thesis. The proposed motion estimation algorithm is also applied to medical image sequences. Motion estimation results presented in this thesis include pairs of images from a echocardiography video and a robot-assisted surgery video.

With the arrival of modern component-based modeling tools for dynamic systems, the differential-algebraic equation form is increasing in popularity as it is general enough to handle the resulting models. However, if uncertainty is allowed in the equations — no matter how small — this thesis stresses that such equations generally become ill-posed. Rather than deeming the general differential-algebraic structure useless up front due to this reason, the suggested approach to the problem is to ask what assumptions that can be made in order to obtain well-posedness. Here, “well-posedness” is used in the sense that the uncertainty in the solutions should tend to zero as the uncertainty in the equations tends to zero. The main theme of the thesis is to analyze how the uncertainty in the solution to a differential-algebraic equation depends on the uncertainty in the equation. In particular, uncertainty in the leading matrix of linear differential-algebraic equations leads to a new kind of singular perturbation, which is referred to as “matrix-valued singular perturbation”. Though a natural extension of existing types of singular perturbation problems, this topic has not been studied in the past. As it turns out that assumptions about the equations have to be made in order to obtain well-posedness, it is stressed that the assumptions should be selected carefully in order to be realistic to use in applications. Hence, it is suggested that any assumptions (not counting properties which can be checked by inspection of the uncertain equations) should be formulated in terms of coordinate-free system properties. In the thesis, the location of system poles has been the chosen target for assumptions. Three chapters are devoted to the study of uncertain differential-algebraic equations and the associated matrix-valued singular perturbation problems. Only linear equations without forcing function are considered. For both time-invariant and time-varying equations of nominal differentiation index 1, the solutions are shown to converge as the uncertainties tend to zero. For time-invariant equations of nominal index 2, convergence has not been shown to occur except for an academic example. However, the thesis contains other results for this type of equations, including the derivation of a canonical form for the uncertain equations. While uncertainty in differential-algebraic equations has been studied in-depth, two related topics have been studied more passingly. One chapter considers the development of point-mass filters for state estimation on manifolds. The highlight is a novel framework for general algorithm development with manifold-valued variables. The connection to differential-algebraic equations is that one of their characteristics is that they have an underlying manifold-structure imposed on the solution. One chapter presents a new index closely related to the strangeness index of a differential-algebraic equation. Basic properties of the strangeness index are shown to be valid also for the new index. The definition of the new index is conceptually simpler than that of the strangeness index, hence making it potentially better suited for both practical applications and theoretical developments.

The discipline usually called `probability theory' can be seen as the theory which describes and sets standard norms to the way we reason about plausibility. From this point of view, this `plausibility theory' is a province of logic, and the following informal proportion subsists: plausibility theory is to the common notion of `plausibility', as deductive logic is to the common notion of `truth'. Some studies in plausibility theory are here offered. An alternative view and mathematical formalism for the problem of induction (the prediction of uncertain events from similar, certain ones) is presented. It is also shown how from plausibility theory one can derive a mathematical framework, based on convex geometry, for the description of the predictive properties of physical theories. Within this framework, problems like state assignment - for any physical theory - find simple and clear algorithms, numerical examples of which are given for three-level quantum systems. Plausibility theory also gives insights on various fashionable theorems, like Bell’s theorem, and various fashionable `paradoxes', like Gibbs' paradox. / QC 20100816

Transformers are very important parts of any electrical network, and their size increase so does their price. Protecting these important devices is a daunting task due to the wide variety of operating conditions. This thesis develops a new protection scheme based on state estimation.The foundation upon which our protection scheme is built is the modeling of the single phase transformer system of equations. The transformer equations are composed of polynomial and differential equations and this system of equations involving the transformer's electrical quantities are modeled into a system of equations such that highest degree of each of the system's equations is quadratic―in a process named Quadratization and then integrated using a technique called Quadratic integration to give a set of algebraic companion equations that can be solved numerically to determine the health of the transformer.

Today's automotive industry is undergoing significant changes in technology due to economic, political and environmental pressures. The shift from conventional internal combustion vehicles to hybrid and plug in hybrid electric vehicles brings with it a new host of technical challenges. As the vehicles become more electrified, and the batteries become larger, there are many difficulties facing the battery integration including both embedded control and supervisory control. A very important aspect of Li-Ion battery integration is the state estimation of the battery. State estimation can include multiple states, however the two most important are the state of charge and state of health of the battery. Determining an accurate state of charge estimation of a battery has been an important part of consumer electronics for years now [1]. In small portable electronics, the state of charge of the battery is used to determine the time remaining on the current battery charge. Although difficult, the estimation is simplified by the relatively low charge and discharge currents (approximately + 3C) of the devices and the non-dynamic duty cycle. Hybrid vehicle battery packs can reach much higher charge and discharge currents (+ 20C) [2]. This higher current combined with a very dynamic duty cycle, large changes in temperature, longer periods without usage and long life requirements make state of charge estimation in Hybrid Electric Vehicles (HEV) much more difficult. There have been a host of methods employed by various previous authors. One of the most important factors in state of charge estimation is having an accurate estimation of the actual capacity (depending on state of health) of the battery at any time [3]. Without having an understanding of the state of health of the battery, the state of charge estimation can vary greatly. This paper proposes a state of charge and state of health estimation based on a dual Extended Kalman Filter (EKF). Employing an EKF for the state estimation of the battery pack not only allows for enhanced accuracy of the estimation but allows the control engineer to develop vehicle performance criteria based not only on the state of charge estimation, but also the state of health.

Power industry is undergoing a transition from the traditional regulated environment to the competitive power market. To have a reliable state estimator (SE) in the power market environment, two major challenges are emerging, i.e. to keep SE running reliably even under a contingency and to run SE over a grid with extremely large size. The objective of this dissertation is to use graph theory to address the above two challenges. To keep SE running reliably under a contingency, a novel topological approach is first proposed to identify critical measurements and examine network observability under a contingency. To advance the classical topological observability analysis, a new concept of contingency observability graph (COG) is introduced and it is proven that a power system network maintains its observability under a contingency if and only if its COG satisfies some conditions. As an application of COG, a two-stage heuristic topological approach is further developed based on the new concept of qualified COG (QCOG) to minimize the number of measurements and RTUs under the constraint that the system remains observable under any single contingency. To overcome the disadvantages of existing SE over extremely large networks, a textured distributed state estimator (DSE), which consists of the off-line textured architecture design and the on-line textured computation, is proposed based on COG and a new concept of Bus Credibility Index (BCI). The textured DSE is non-recursive, asynchronous and avoids central controlling node. Numerical tests verify that the performance of the new textured DSE algorithm improves greatly compared with existing DSE algorithms in respect of bad data detection and identification. Furthermore, the software implementation for DSE is formulated as an information integration problem over regional power markets, and is very challenging because of its size and complexity. A new concept of semantic knowledge warehouse (SKW), together with the proposed concepts of semantic reasoning software component (SRSC) and deduction credibility, is developed to implement such an information integration system.

State estimation plays an important role in modern power system energy management systems. The network observability is a pre-requisite for the state estimation solution. Topological error in the network may cause the state estimation results to be seriously biased. This dissertation studies new schemes to improve the conventional state estimation in the above aspects. A new algorithm for cost minimization in the measurement placement design is proposed in this dissertation. The new algorithm reduces the cost of measurement installation and retains the network observability. Two levels of measurement place- ment designs are obtained: the basic level design guarantees the whole network to be observable using only the voltage magnitude measurement and the branch power flow measurements. The advanced level design keeps the network observable under certain contingencies. To preserve as many substation measurements as possible and maintain the net-work observability, an advanced network topology processor is introduced. A new method - the dynamic utilization of substation measurements (DUSM) - is presented. Instead of seeking the installation of new measurements in the system, this method dynamically calculates state estimation measurement values by applying the current law that regulates different measurement values implicitly. Its processing is at the substation level and, therefore, can be implemented independently in substations. This dissertation also presents a new way to verify circuit breaker status and identify topological errors. The new method improves topological error detection using the method of DUSM. It can be seen that without modifying the state estimator, the status of a circuit breaker may still be verified even without direct power flow measurements. Inferred measurements, calculated by DUSM, are used to help decide the CB status. To reduce future software code maintenance and to provide standard data ex- changes, the newly developed functions were developed in Java, with XML format input/output support. The effectiveness and applicability of these functions are ver-ified by various test cases.