Traffic state estimation (TSE) aims to estimate the time-varying traffic characteristics (such as flow rate, flow speed, flow density, and occurrence of incidents) of all roads in traffic networks, provided with limited observations in sparse time and locations. TSE is critical to transportation planning, operation and infrastructure design. In this new era of “big data”, massive volumes of sensing data from a variety of source (such as cell phones, GPS, probe vehicles, and inductive loops, etc.) enable TSE in an efficient, timely and accurate manner. This research develops a Bayesian-based theoretical framework, along with statistical inference algorithms, to (1) capture the complex flow patterns in the urban traffic network consisting both highways and arterials; (2) incorporate heterogeneous data sources into the process of TSE; (3) enable both estimation and perdition of traffic states; and (4) demonstrate the scalability to large-scale urban traffic networks. To achieve those goals, a Hierarchical Bayesian probabilistic model is proposed to capture spatio-temporal traffic states. The propagation of traffic states are encapsulated through mesoscopic network flow models (namely the Link Queue Model) and equilibrated fundamental diagrams. Traffic states in the Hierarchical Bayesian model are inferred using the Expectation-Maximization Extended Kalman Filter (EM-EKF). To better estimate and predict states, infrastructure supply is also estimated as part of the TSE process. It is done by adopting a series of algorithms to translate Twitter data into traffic incident information. Finally, the proposed EM-EKF algorithm is implemented and examined on the road networks in Washington DC. The results show that the proposed methods can handle large-scale traffic state estimation, while achieving superior results comparing to traditional temporal and spatial smoothing methods.

Dans ce travail, la modélisation, la simulation, l'optimisation dynamique et la commande nonlinéaire d'un procédé industriel de polymérisation en émulsion produisant du polyacétate de vinyle (PVAc) sont étudiées. La réaction est modélisée comme un système à deux phases constitué d'une phase aqueuse et une phase particulaire. Un modèle détaillé est développé pour calculer la masse molaire moyenne en poids, la masse molaire moyenne en nombre et la dispersité. Les moments de chaînes en croissance et terminés sont utilisés pour représenter l'état du polymère et pour calculer la distribution de masse molaire (MWD). L'étude de cas correspond à un réacteur industriel fonctionnant dans une entreprise de produits chimiques à Bogotá. Un réacteur à l'échelle industrielle (11 m3 de capacité) est simulé dans lequel une réaction semi-batch de polymérisation en émulsion de l'acétate de vinyle est effectuée. Le problème d'optimisation dynamique est résolu directement en utilisant un solveur de programmation non linéaire. L'intégration des équations différentielles est faite en utilisant la méthode de Runge-Kutta. Trois problèmes d'optimisation différents sont résolus, depuis le plus simpliste (une seule variable d'optimisation : la température du réacteur) au plus complexe (trois variables d'optimisation : la température du réacteur, le débit de l'amorceur et le débit du monomère) en vue de minimiser le temps final de réaction. Une réduction de 25% du temps de traitement par batchs est réalisée par rapport aux conditions normales de fonctionnement appliquées dans l'entreprise. Les résultats montrent qu'il est possible de minimiser la durée de réaction alors que certaines qualités de polymères souhaitées (conversion, masse molaire et contenu en solides) satisfont les contraintes définies. Une technique de commande non linéaire géométrique à l'aide de la linéarisation entrée/sortie est adaptée à la régulation de la température du réacteur. Un filtre Kalman étendu (EKF) est mis en oeuvre pour estimer les états non mesurés et il est testé dans différents cas, dont une étude de robustesse où des erreurs du modèle sont introduites pour vérifier son bon fonctionnement. Après vérification des performances du régulateur, certains changements d'opération du procédé ont été proposés afin d'améliorer la productivité du procédé et la qualité du polymère. Enfin, le profil de température optimale et les politiques d'alimentation optimales de débits du monomère et de l'amorceur, obtenues dans l'étape d'optimisation dynamique, ont fourni les consignes optimales pour la commande non linéaire. Les résultats montrent que le régulateur non linéaire conçu ici convient pour suivre les trajectoires optimales de température calculées précédemment / In this work, modeling, simulation, dynamic optimization and nonlinear control of an industrial emulsion polymerization process to produce poly-vinyl acetate (PVAc) are proposed. The reaction is modeled as a two-phase system composed of an aqueous phase and a particle phase. A detailed model is used to calculate the weight average molecular weight, the number average molecular weight and the dispersity. The moments of the growing and dead chains are used to represent the state of the polymer and to calculate the molecular weight distribution (MWD). The case study corresponds to an industrial reactor operated at a chemical company in Bogotá. An industrial scale reactor (11 m3 of capacity) is simulated where a semi-batch emulsion polymerization reaction of vinyl acetate is performed. Dynamic optimization problem is solved directly using a Nonlinear Programming solver. Integration of differential equations is made using Runge-Kutta method. Three different optimization problems are solved from the more simplistic (only one control variable: reactor temperature) to the more complex (three control variables : reactor temperature, initiator flow rate and monomer flow rate) in order to minimize the reaction time. A reduction of 25% of the batch time is achieved with respect to the normal operating conditions applied at the company. The results show that is possible to minimize the reaction time while some polymer desired qualities (conversion, molecular weight and solids content) satisfy the defined constraints. A nonlinear geometric control technique by using input/output linearization is adapted to the reactor temperature control. An extended Kalman filter (EKF) is implemented to estimate unmeasured states and it is tested in different cases including a robustness study where model errors are introduced to verify its good performance. After verification of controller performance, some process changes were proposed in order to improve process productivity and polymer quality. Finally, the optimal temperature profile and optimal feed policies of the monomer and initiator, obtained in a dynamic optimization step, are used to provide the optimal set points for the nonlinear control. The results show that the nonlinear controller designed here is appropriate to follow the optimal temperature trajectories calculated previously

Neste trabalho propõe-se um método de análise de observabilidade para estimação de estados e parâmetros em sistemas elétricos de potência, baseado nas equações normais. O método fundamenta-se na fatoração triangular da matriz ganho aumentada e nos conceitos de caminhos de fatoração. O mesmo utiliza rotinas já existentes no processo de estimação, sendo simples, de fácil implementação, rápida execução e não exige a solução de equações algébricas. Para comprovar a sua eficiência vários testes foram realizados, utilizando os sistemas de 6, 14 e 30 barras do IEEE, tendo sido satisfatórios os resultados obtidos. / In this work we propose a method of observability analysis for states and parameters estimation in electric power systems, based on the Normal Equations. The method is based on triangular factoration of the augmented gain matrix and on the concepts of factoration paths. It uses routines that there exist in the estimation process. These routines are simple, of easy implementation, fast execution and it doesn\'t demand the solution of algebraic equations. To prove your efficiency several tests were accomplished, using the 6, 14 and 30-bus IEEE test systems. The obtained results were satisfactory.

With a larger global population and fewer farmers, harvests will have to be larger and easier to manage. By high precision planting, each crop will have the same available area on the field, yielding an even size of the crops which means the whole field can be harvested at the same time. This thesis investigates the possibility for such precision planting in curves. Currently, Väderstads planter collection Tempo, can deliver precision in the centimeter range for speeds up to 20 km/h when driving straight, but not when turning. This thesis makes use of the available sensors on the planters, but also investigates possible improvements by including additional sensors. An Extended Kalman Filter is used to estimate the individual speeds of the planting row units and thus enabling high precision planting for an arbitrary motion. The filter is shown to yield a satisfactory result when using the internal measurement units, the radar speed sensor and the GPS already mounted on the planter. By implementing the filter, a higher precision is obtained compared to using the same global speed for all planting row units.

Esta tese trata do problema de estimativa robusta ótima para sistemas dinâmicos regulares discretos no tempo. Novos algoritmos recursivos são formulados para as estimativas filtradas e preditoras com as correspondentes equações de Riccati. O filtro robusto tipo Kalman e a equação de Riccati correspondente são obtidos numa formulação mais geral, estendendo os resultados apresentados na literatura. O funcional quadrático proposto para deduzir este filtro faz a combinação das técnicas mínimos quadrados regularizados e funções penalidade. O sistema considerado para obtenção de tais estimativas é singular, discreto, variante no tempo, com ruídos correlacionados e todos os parâmetros do modelo linear estão sujeitos a incertezas. As incertezas paramétricas são limitadas por norma. As propriedades de estabilidade e convergência do filtro de Kalman para sistemas nominais e incertos são provadas, mostrando-se que o filtro em estado permanente é estável e a recursão de Riccati associada a ele é uma sequência monótona não decrescente, limitada superiormente pela solução da equação algébrica de Riccati. / This thesis considers the optimal robust estimates problem for discrete-time singular dymanic systems. New recursive algorithms are developed for the Kalman filtered and predicted estimated recursions with the corresponding Riccati equations. The singular robust Kalman type filter and the corresponding recursive Riccati equation arer obtained in their most general formulation, extending the results presented in the literature. The quadratic functional developed to deduce this filter combines regularized least squares and penalty functions approaches. The system considered to obtain the estimates is singular, time varying with correlated noises and all parameter matrices of the underlying linear model are subject to uncertainties. The parametric uncertainty is assumed to be norm bounded. The properties of stability and convergence of the Kalman filter for nominal and uncertain system models are proved, where we show that steady state filter is stable and the Riccati recursion associated with this is a nondecreasing monotone sequence with upper bound.

O presente trabalho tem por objetivo propor uma metodologia de estimação de estado (EE) para sistemas de distribuição de energia que auxilie na identificação das regiões de fornecimento das concessionárias de distribuição que possam conter perdas não técnicas, de modo a orientar as ações para sua redução. As perdas não técnicas de energia elétrica são um grande desafio não só no Brasil como também em outros países em desenvolvimento. Face à dificuldade e ao custo para fiscalizar anualmente toda a área de concessão, faz-se necessário um diagnóstico para avaliar em quais grupos de clientes e regiões encontram-se este tipo de perda. Destarte, fica evidenciada a necessidade do desenvolvimento de uma ferramenta que, além de tratar de uma modelagem completa do sistema, utilize informações provenientes de medições diversas. Para isso, a estimação de estado se torna a metodologia ideal. A metodologia utilizada na estimação de estados foi a dos Mínimos Quadrados Ponderados (do inglês, Weighted Least Squares - WLS) (Schweppe & Wildes, 1970) e algumas técnicas foram aplicadas para permitir a EE em sistemas de distribuição, tais como a utilização da corrente complexa dos trechos como variáveis de estado, que decompõe a estimação de estados em três subproblemas, um para cada fase, permitindo a utilização de uma modelagem trifásica da rede e a introdução de pseudomedidas obtidas dos dados de faturamento dos clientes através de um processo estatístico. O trabalho apresenta exemplos de aplicação, sendo estes em sistemas de distribuição reais, mostrando os resultados obtidos e termina destacando as principais vantagens da metodologia. / This work focuses on the development of a distribution system state estimation (SE) algorithm for application to radial distribution networks which assists the identification of regions of the distribution network containing non-technical energy losses, helping the electric utilities to evaluate and reduce it. Non-technical energy losses represent an important challenge for distribution companies in developing countries, such as Brazil. However, economical limitations and measurement problems make impossible to have a perfect picture of the complete system, then a diagnoses method is required to evaluate which group of consumers and the regions have that type of loss. Therefore, is evidenced the necessity of a tool development which, farther on using the complete system modeling, works with information from various measurement instruments. Consequently, the SE becomes the ideal method. The SE applied is the Weighted Least Square approach (WLS) (Schweppe & Wildes, 1970) and some techniques where applied to allow the SE for distribution systems, such as, using the branch currents as the system state, which decouples the state estimation problem into three sub problems, one for each phase, allowing the three phase system modelling and the introduction of pseudo measurements from historical load data produced based on customer billing data through statistical processes. This work shows the results obtained by applying the computational tool to a real distribution system. Such results are compared with the ones obtained by using other methodologies, and the main advantages of this new methodology are outlined.

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.

The research conducted in this dissertation is divided into two main parts. The first part provides further improvements in power system state estimation and the second part implements Contingency Constrained Optimal Power Flow (CCOPF) in a stochastic multiple contingency framework. As a real-time application in modern power systems, the existing Newton-QR state estimation algorithms are too slow and too fragile numerically. This dissertation presents a new and more robust method that is based on trust region techniques. A faster method was found among the class of Krylov subspace iterative methods, a robust implementation of the conjugate gradient method, called the LSQR method. Both algorithms have been tested against the widely used Newton-QR state estimator on the standard IEEE test networks. The trust region method-based state estimator was found to be very reliable under severe conditions (bad data, topological and parameter errors). This enhanced reliability justifies the additional time and computational effort required for its execution. The numerical simulations indicate that the iterative Newton-LSQR method is competitive in robustness with classical direct Newton-QR. The gain in computational efficiency has not come at the cost of solution reliability. The second part of the dissertation combines Sequential Quadratic Programming (SQP)-based CCOPF with Monte Carlo importance sampling to estimate the operating cost of multiple contingencies. We also developed an LP-based formulation for the CCOPF that can efficiently calculate Locational Marginal Prices (LMPs) under multiple contingencies. Based on Monte Carlo importance sampling idea, the proposed algorithm can stochastically assess the impact of multiple contingencies on LMP-congestion prices.

O presente trabalho tem por objetivo propor uma metodologia de estimação de estado (EE) para sistemas de distribuição de energia que auxilie na identificação das regiões de fornecimento das concessionárias de distribuição que possam conter perdas não técnicas, de modo a orientar as ações para sua redução. As perdas não técnicas de energia elétrica são um grande desafio não só no Brasil como também em outros países em desenvolvimento. Face à dificuldade e ao custo para fiscalizar anualmente toda a área de concessão, faz-se necessário um diagnóstico para avaliar em quais grupos de clientes e regiões encontram-se este tipo de perda. Destarte, fica evidenciada a necessidade do desenvolvimento de uma ferramenta que, além de tratar de uma modelagem completa do sistema, utilize informações provenientes de medições diversas. Para isso, a estimação de estado se torna a metodologia ideal. A metodologia utilizada na estimação de estados foi a dos Mínimos Quadrados Ponderados (do inglês, Weighted Least Squares - WLS) (Schweppe & Wildes, 1970) e algumas técnicas foram aplicadas para permitir a EE em sistemas de distribuição, tais como a utilização da corrente complexa dos trechos como variáveis de estado, que decompõe a estimação de estados em três subproblemas, um para cada fase, permitindo a utilização de uma modelagem trifásica da rede e a introdução de pseudomedidas obtidas dos dados de faturamento dos clientes através de um processo estatístico. O trabalho apresenta exemplos de aplicação, sendo estes em sistemas de distribuição reais, mostrando os resultados obtidos e termina destacando as principais vantagens da metodologia. / This work focuses on the development of a distribution system state estimation (SE) algorithm for application to radial distribution networks which assists the identification of regions of the distribution network containing non-technical energy losses, helping the electric utilities to evaluate and reduce it. Non-technical energy losses represent an important challenge for distribution companies in developing countries, such as Brazil. However, economical limitations and measurement problems make impossible to have a perfect picture of the complete system, then a diagnoses method is required to evaluate which group of consumers and the regions have that type of loss. Therefore, is evidenced the necessity of a tool development which, farther on using the complete system modeling, works with information from various measurement instruments. Consequently, the SE becomes the ideal method. The SE applied is the Weighted Least Square approach (WLS) (Schweppe & Wildes, 1970) and some techniques where applied to allow the SE for distribution systems, such as, using the branch currents as the system state, which decouples the state estimation problem into three sub problems, one for each phase, allowing the three phase system modelling and the introduction of pseudo measurements from historical load data produced based on customer billing data through statistical processes. This work shows the results obtained by applying the computational tool to a real distribution system. Such results are compared with the ones obtained by using other methodologies, and the main advantages of this new methodology are outlined.

<div>Previous studies have shown that implementing trajectory optimization can reduce state estimations errors. These navigation based path planning problems are often diffcult to solve being computationally burdensome and exhibiting other numerical issues, so former studies have often used lower-delity methods or lacked explanatory power.</div><div><br></div><div><div>This work utilizes indirect optimization methods, particularly optimal control theory, to obtain high-quality solutions minimizing state estimation errors approximated by a continuous-time extended Kalman lter. Indirect methods are well-suited to this because necessary conditions of optimality are found prior to discretization and numerical computation. They are also highly parallelizable enabling application to increasingly larger problems.</div></div><div><br></div><div><div>A simple one dimensional problem shows some potential obstacles to solving problems of this type including regions of the trajectory where the control is unimportant. Indirect trajectory optimization is applied to a more complex scenario to minimize location estimation errors of a single cart traveling in a 2-D plane to a goal location and measuring range from a xed beacon. This resulted in a 96% reduction of the location error variance when compared to the minimum time solution. The single cart problem also highlights the importance of the matrix that encodes the linearization of the vehicle's measurement with respect to state. It is shown in this case that the vehicle roughly attempts to maximize the magnitude of its elements. Additionally, the cart problem further illustrates problematic regions of a design space where the objective is not signicantly affected by the trajectory.</div></div><div><br></div><div><div>An aircraft descent problem demonstrates the applicability of these methods to aerospace problems. In this case, estimation error variance is reduced 28.6% relative to the maximum terminal energy trajectory. Results are shown from two formulations of this problem, one with control constraints and one with control energy cost, to show the benets and disadvantages of the two methods. Furthermore, the ability to perform trade studies on vehicle and trajectory parameters is shown with this problem by solving for dierent terminal velocities and different initial locations.</div></div>