This study takes advantage of wide area measurements to propose a centralized nonlinear controller that acts on power system stabilizers, to cooperatively increase the damping of problematic small signal oscillations all over the system. The structure based on decision trees results in a simple, efficient, and dependable methodology that imposes much less computational burden than other nonlinear design approaches, making it a promising candidate for actual implementation by utilities and system operators. Details are given to utilize existing stabilizers while causing minimum changes to the equipment, and warranting improvement or at least no detriment of current system behavior. This enables power system stabilizers to overcome their inherent limitation to act only on the basis of local measurements to damp a single target frequency. This study demonstrates the implications of this new input on mathematical models, and the control functionality that is made available by its incorporation to conventional stabilizers. In preparation of the case of study, a heuristic dynamic reduction methodology is introduced that preserves a physical equivalent model, and that can be interpreted by any commercial software package. The steps of this method are general, versatile, and of easy adaptation to any particular power system model, with the aggregated value of producing a physical model as final result, that makes the approach appealing for industry. The accuracy of the resulting reduced network has been demonstrated with the model of the Central American System. / Ph. D.

Monitoring and protection of power systems is a task that has manifold objectives. Amongst others, it involves performing data mining, optimizing available resources, assessing system stresses, and doing data conditioning. The role of PMUs in fulfilling these four objectives forms the basis of this dissertation. Classification and regression tree (CART) built using phasor data has been extensively used in power systems. The splits in CART are based on a single attribute or a combination of variables chosen by CART itself rather than the user. But as PMU data consists of complex numbers, both the attributes, should be considered simultaneously for making critical decisions. An algorithm is proposed here that expresses high dimensional, multivariate data as a single attribute in order to successfully perform splits in CART. In order to reap maximum benefits from placement of PMUs in the power grid, their locations must be selected judiciously. A gradual PMU placement scheme is developed here that ensures observability as well as protects critical parts of the system. In order to circumvent the computational burden of the optimization, this scheme is combined with a topology-based system partitioning technique to make it applicable to virtually any sized system. A power system is a dynamic being, and its health needs to be monitored at all times. Two metrics are proposed here to monitor stress of a power system in real-time. Angle difference between buses located across the network and voltage sensitivity of buses lying in the middle are found to accurately reflect the static and dynamic stress of the system. The results indicate that by setting appropriate alerts/alarm limits based on these two metrics, a more secure power system operation can be realized. A PMU-only linear state estimator is intrinsically superior to its predecessors with respect to performance and reliability. However, ensuring quality of the data stream that leaves this estimator is crucial. A methodology for performing synchrophasor data conditioning and validation that fits neatly into the existing linear state estimation formulation is developed here. The results indicate that the proposed methodology provides a computationally simple, elegant solution to the synchrophasor data quality problem. / Ph. D.

The enhancement of the reliability, security, and resiliency of electric power systems depends on the availability of fast, accurate, and robust dynamic state estimators. These estimators should be robust to gross errors on the measurements and the model parameter values while providing good state estimates even in the presence of large dynamical system model uncertainties and non-Gaussian thick-tailed process and observation noises. It turns out that the current Kalman filter-based dynamic state estimators given in the literature suffer from several important shortcomings, precluding them from being adopted by power utilities for practical applications. To be specific, they cannot handle (i) dynamic model uncertainty and parameter errors; (ii) non-Gaussian process and observation noise of the system nonlinear dynamic models; (iii) three types of outliers; and (iv) all types of cyber attacks. The three types of outliers, including observation, innovation, and structural outliers are caused by either an unreliable dynamical model or real-time synchrophasor measurements with data quality issues, which are commonly seen in the power system. To address these challenges, we have pioneered a general theoretical framework that advances both robust statistics and robust control theory for robust dynamic state and parameter estimation of a cyber-physical system. Specifically, the generalized maximum-likelihood-type (GM)-estimator, the unscented Kalman filter (UKF), and the H-infinity filter are integrated into a unified framework to yield various centralized and decentralized robust dynamic state estimators. These new estimators include the GM-iterated extended Kalman filter (GM-IEKF), the GM-UKF, the H-infinity UKF and the robust H-infinity UKF. The GM-IEKF is able to handle observation and innovation outliers but its statistical efficiency is low in the presence of non-Gaussian system process and measurement noise. The GM-UKF addresses this issue and achieves a high statistical efficiency under a broad range of non-Gaussian process and observation noise while maintaining the robustness to observation and innovation outliers. A reformulation of the GM-UKF with multiple hypothesis testing further enables it to handle structural outliers. However, the GM-UKF may yield biased state estimates in presence of large system uncertainties. To this end, the H-infinity UKF that relies on robust control theory is proposed. It is shown that H-infinity is able to bound the system uncertainties but lacks of robustness to outliers and non-Gaussian noise. Finally, the robust H-infinity filter framework is proposed that leverages the H-infinity criterion to bound system uncertainties while relying on the robustness of GM-estimator to filter out non-Gaussian noise and suppress outliers. Furthermore, these new robust estimators are applied for system bus frequency monitoring and control and synchronous generator model parameter calibration. Case studies of several different IEEE standard systems show the efficiency and robustness of the proposed estimators. / Ph. D.

Cette thèse porte sur la surveillance des perturbations de la qualité de l’énergie d’un réseau électrique via des techniques paramétriques de traitement du signal. Pour élaborer nos algorithmes de traitement du signal, nous avons traité les problèmes d’estimation des différentes grandeurs du réseau électrique triphasé et de classification des perturbations de la qualité d'énergie. Pour ce qui est du problème d’estimation, nous avons développé une technique statistique basée sur le maximum de vraisemblance. La technique proposée exploite la nature multidimensionnelle des signaux électriques. Elle utilise un algorithme d’optimisation pour minimiser la fonction de vraisemblance. L’algorithme utilisé permet d’améliorer les performances d’estimation tout en étant d’une faible complexité calculatoire en comparaison aux algorithmes classiques. Une analyse plus poussée de l’estimateur proposé a été effectuée. Plus précisément, ses performances sont évaluées sous un environnement incluant entre autres la pollution harmonique et interharmonique et le bruit. Les performances sont également comparées aux exigences de la norme IEEE C37.118.2011. La problématique de classification dans les réseaux électriques triphasés a plus particulièrement concerné les perturbations que sont les creux de tension et les surtensions. La technique de classification proposée consiste globalement en deux étapes : 1) une pré-classification du signal dans l’une des 4 préclasses établis et en 2) une classification du type de perturbation à l’aide de l’estimation des composants symétriques.Les performances du classificateur proposé ont été évaluées, entre autres, pour différentes nombre de cycles, de SNR et de THD. L’estimateur et le classificateur proposés ont été validés en simulation et en utilisant les données d’un réseau électrique réel du DOE/EPRI National Database of Power System Events. Les résultats obtenus illustrent clairement l’efficacité des algorithmes proposés quand à leur utilisation comme outil de surveillance de la qualité d’énergie. / This thesis deals with electric grid monitoring of power quality (PQ) disturbances using parametric signal processing techniques. The first contribution is devoted to the parametric spectral estimation approach for signal parameter extraction. The proposed approach exploits the multidimensional nature of the electrical signals.For spectral estimation, it uses an optimization algorithm to minimize the likelihood function. In particular, this algorithm allows to improve the estimation accuracy and has lower computational complexity than classical algorithms. An in-depth analysis of the proposed estimator has been performed. Specifically, the estimator performances are evaluated under noisy, harmonic, interharmonic, and off-nominal frequency environment. These performances are also compared with the requirements of the IEEE Standard C37.118.2011. The achieved results have shown that the proposed approach is an attractive choice for PQ measurement devices such as phasor measurement units (PMUs). The second contribution deals with the classification of power quality disturbances in three-phase power systems. Specifically, this approach focuses on voltage sag and swell signatures. The proposed classification approach is based on two main steps: 1) the signal pre-classification into one of 4 pre-classes and 2) the signature type classification using the estimate of the symmetrical components. The classifier performances have been evaluated for different data length, signal to noise ratio, interharmonic, and total harmonic distortion. The proposed estimator and classifier are validated using real power system data obtained from the DOE/EPRI National Database of Power System Events. The achieved simulations and experimental results clearly illustrate the effectiveness of the proposed techniques for PQ monitoring purpose.

Esta proposta de pesquisa visa avaliar métodos de projeto de controladores em dois níveis, composto por controladores descentralizados e centralizado, utilizando sinais de medição fasorial sincronizada. Pesquisas iniciais foram realizadas utilizando a abordagem baseada na resolução da equação de Riccati num sistema multimáquinas, considerando aquisição de dados via medição fasorial sincronizada e atrasos de tempo nos canais de comunicação da entrada e da saída do controlador centralizado. Esta pesquisa propõe o projeto e avaliação de controladores centralizados através das abordagens baseadas na resolução da equação de Riccati, Desigualdades Matriciais Lineares e Algoritmos Genéticos. O projeto consiste em obter um controlador centralizado robusto a variações de carga e topologia do sistema, além de possíveis perdas de links de comunicação da entrada e da saída do controlador centralizado com o sistema elétrico. A fim de verificar a eficácia das abordagens de projeto foram utilizados o Sistema Equivalente Sul-Sudeste Brasileiro e o Sistema Simplificado Australiano. Além disso, simulações dinâmicas dos sistemas com aplicação de contingências foram realizadas com o propósito de se avaliar os controladores centralizados obtidos através de um modelo linear. Os resultados alcançados mostram semelhança e eficiência das abordagens quando se consideram múltiplos pontos de operação do sistema. A abordagem baseada em Algoritmos Genéticos se sobressai de acordo com os resultados obtidos para os sistemas-teste mencionados por propiciar um controlador centralizado robusto a múltiplos pontos de operação e possíveis perdas de links de comunicação. / This research proposal aims to compare control design methods on two levels, consisting of centralized and decentralized controllers, using signals synchronized phasor measurement. Initial researches have been conducted using the approach in solving the Riccati equation in a multi-machine system, considering data acquisition via synchronized phasor measurement and time delays in the communication channels of input and output of the centralized controller. This research proposes the design and comparison of centralized controllers through approaches based on resolution of the Riccati equation, Linear Matrix Inequalities and Genetic Algorithms. The project is to achieve a robust centralized controller to load variations and system topology changes and possible loss of communication of the input and output of the centralized controller with the electrical system. In order to verify the effectiveness of design approaches were used the Southern-Southeastern Brazil Equivalent Equivalent and Australian Simplified System. In addition, simulations of the dynamic systems with application of contingency were performed in order to evaluate the centralized controlling obtained by a linear model. The results show similarity and efficiency of the approaches when considering multiple system operating points. The Genetic Algorithms-based approach stands out according to the results obtained for the test systems mentioned, as demonstrated by the results, because it provides a robust centralized controller to multiple points of operation and possible loss of communication links.

Esta proposta de pesquisa visa avaliar métodos de projeto de controladores em dois níveis, composto por controladores descentralizados e centralizado, utilizando sinais de medição fasorial sincronizada. Pesquisas iniciais foram realizadas utilizando a abordagem baseada na resolução da equação de Riccati num sistema multimáquinas, considerando aquisição de dados via medição fasorial sincronizada e atrasos de tempo nos canais de comunicação da entrada e da saída do controlador centralizado. Esta pesquisa propõe o projeto e avaliação de controladores centralizados através das abordagens baseadas na resolução da equação de Riccati, Desigualdades Matriciais Lineares e Algoritmos Genéticos. O projeto consiste em obter um controlador centralizado robusto a variações de carga e topologia do sistema, além de possíveis perdas de links de comunicação da entrada e da saída do controlador centralizado com o sistema elétrico. A fim de verificar a eficácia das abordagens de projeto foram utilizados o Sistema Equivalente Sul-Sudeste Brasileiro e o Sistema Simplificado Australiano. Além disso, simulações dinâmicas dos sistemas com aplicação de contingências foram realizadas com o propósito de se avaliar os controladores centralizados obtidos através de um modelo linear. Os resultados alcançados mostram semelhança e eficiência das abordagens quando se consideram múltiplos pontos de operação do sistema. A abordagem baseada em Algoritmos Genéticos se sobressai de acordo com os resultados obtidos para os sistemas-teste mencionados por propiciar um controlador centralizado robusto a múltiplos pontos de operação e possíveis perdas de links de comunicação. / This research proposal aims to compare control design methods on two levels, consisting of centralized and decentralized controllers, using signals synchronized phasor measurement. Initial researches have been conducted using the approach in solving the Riccati equation in a multi-machine system, considering data acquisition via synchronized phasor measurement and time delays in the communication channels of input and output of the centralized controller. This research proposes the design and comparison of centralized controllers through approaches based on resolution of the Riccati equation, Linear Matrix Inequalities and Genetic Algorithms. The project is to achieve a robust centralized controller to load variations and system topology changes and possible loss of communication of the input and output of the centralized controller with the electrical system. In order to verify the effectiveness of design approaches were used the Southern-Southeastern Brazil Equivalent Equivalent and Australian Simplified System. In addition, simulations of the dynamic systems with application of contingency were performed in order to evaluate the centralized controlling obtained by a linear model. The results show similarity and efficiency of the approaches when considering multiple system operating points. The Genetic Algorithms-based approach stands out according to the results obtained for the test systems mentioned, as demonstrated by the results, because it provides a robust centralized controller to multiple points of operation and possible loss of communication links.

Este trabalho apresenta uma análise de algoritmos computacionais aplicados à estimação de fasores elétricos em SEPs. A medição dos fasores é realizada por meio da alocação de Unidades de Medição Fasorial nestes sistemas e encontra diversas aplicações nas áreas de operação, controle, proteção e planejamento. Para que os fasores possam ser aplicados, são definidos padrões de medição, sincronização e comunicação, por meio da norma IEEE C37.118.1. A norma apresenta os padrões de mensagens, timetag, fasores, sistema de sincronização, e define testes para avaliar a estimação. Apesar de abranger todos esses critérios, a diretriz não define um algoritmo de estimação padrão, abrindo espaço para uso de diversos métodos, desde que a precisão seja atendida. Nesse contexto, o presente trabalho analisa alguns algoritmos de estimação de fasores definidos na literatura, avaliando o comportamento deles em determinados casos. Foram considerados, dessa forma, os métodos: Transformada Discreta de Fourier, Método dos Mínimos Quadrados e Transformada Wavelet Discreta, nas versões recursivas e não-recursivas. Esses métodos foram submetidos a sinais sintéticos, a fim de verificar o comportamento diante dos testes propostos pela norma, avaliando o Total Vector Error, tempo de resposta e atraso e overshoot. Os algoritmos também foram embarcados em um hardware, denominado PC104, e avaliados de acordo com os sinais medidos pelo equipamento na saída analógica de um simulador em tempo real (Real Time Digital Simulator). / This work presents an analysis of computational algorithms applied to phasor estimation in Electrical Power Systems. The phasor estimation process uses the allocation of Phasor Measurement Units in the system and the measures can be used in many control, operation, planing and protection applications. Therefore, the power system phasors are very useful, specially if they have a common time reference, allowing the determination of the system\'s condition at a given time. The procedures necessary for power system\'s phasors estimation and application are defined by IEEE C37.118.1 standard. The standard defines the requirements for phasor estimation, presenting tests and a methodology to evaluate the algorithms performance. Thus, the standard defines the time tag and data patterns, some synchronization methods, and message examples, simplifying the communication requirements. Despite defining all these parts, the standard does not state which estimation algorithm should be used, making room for the use of various methods, since the standard precision is met. In this context, this work analyzes some phasor estimation algorithms defined in the literature, evaluating their behavior for some cases. It was adopted the recursive and non-recursive versions of the methods: Discrete Fourier Transform, Least Squares and Discrete Wavelet Transform. They were submitted to the standard signals, evaluating the Total Vector Error, time delays, and overshoots. The algorithms were also embedded in hardware (named PC104) and evaluated by real time simulated signals, measured by the PC104 using the analog outputs of a Real Time Digital Simulator.

Este trabalho apresenta uma análise de algoritmos computacionais aplicados à estimação de fasores elétricos em SEPs. A medição dos fasores é realizada por meio da alocação de Unidades de Medição Fasorial nestes sistemas e encontra diversas aplicações nas áreas de operação, controle, proteção e planejamento. Para que os fasores possam ser aplicados, são definidos padrões de medição, sincronização e comunicação, por meio da norma IEEE C37.118.1. A norma apresenta os padrões de mensagens, timetag, fasores, sistema de sincronização, e define testes para avaliar a estimação. Apesar de abranger todos esses critérios, a diretriz não define um algoritmo de estimação padrão, abrindo espaço para uso de diversos métodos, desde que a precisão seja atendida. Nesse contexto, o presente trabalho analisa alguns algoritmos de estimação de fasores definidos na literatura, avaliando o comportamento deles em determinados casos. Foram considerados, dessa forma, os métodos: Transformada Discreta de Fourier, Método dos Mínimos Quadrados e Transformada Wavelet Discreta, nas versões recursivas e não-recursivas. Esses métodos foram submetidos a sinais sintéticos, a fim de verificar o comportamento diante dos testes propostos pela norma, avaliando o Total Vector Error, tempo de resposta e atraso e overshoot. Os algoritmos também foram embarcados em um hardware, denominado PC104, e avaliados de acordo com os sinais medidos pelo equipamento na saída analógica de um simulador em tempo real (Real Time Digital Simulator). / This work presents an analysis of computational algorithms applied to phasor estimation in Electrical Power Systems. The phasor estimation process uses the allocation of Phasor Measurement Units in the system and the measures can be used in many control, operation, planing and protection applications. Therefore, the power system phasors are very useful, specially if they have a common time reference, allowing the determination of the system\'s condition at a given time. The procedures necessary for power system\'s phasors estimation and application are defined by IEEE C37.118.1 standard. The standard defines the requirements for phasor estimation, presenting tests and a methodology to evaluate the algorithms performance. Thus, the standard defines the time tag and data patterns, some synchronization methods, and message examples, simplifying the communication requirements. Despite defining all these parts, the standard does not state which estimation algorithm should be used, making room for the use of various methods, since the standard precision is met. In this context, this work analyzes some phasor estimation algorithms defined in the literature, evaluating their behavior for some cases. It was adopted the recursive and non-recursive versions of the methods: Discrete Fourier Transform, Least Squares and Discrete Wavelet Transform. They were submitted to the standard signals, evaluating the Total Vector Error, time delays, and overshoots. The algorithms were also embedded in hardware (named PC104) and evaluated by real time simulated signals, measured by the PC104 using the analog outputs of a Real Time Digital Simulator.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-05-18T13:24:16Z No. of bitstreams: 1 jorgejaviergimenezledesma.pdf: 4002237 bytes, checksum: 74e94889e9e4afbc4463915274bf7e33 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-18T14:07:36Z (GMT) No. of bitstreams: 1 jorgejaviergimenezledesma.pdf: 4002237 bytes, checksum: 74e94889e9e4afbc4463915274bf7e33 (MD5) / Made available in DSpace on 2017-05-18T14:07:36Z (GMT). No. of bitstreams: 1 jorgejaviergimenezledesma.pdf: 4002237 bytes, checksum: 74e94889e9e4afbc4463915274bf7e33 (MD5) Previous issue date: 2017-02-12 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Este trabalho propõe o desenvolvimento de modelos e métodos numéricos, baseados em redes neurais artificiais, para a detecção e localização de áreas com defeitos de alta impedância em sistemas de distribuição. De forma paralela, também é avaliada a eficiência da utilização de diferentes tipos de formas de medição de dados no desempenho do método, que é implementada através de duas etapas. A primeira etapa consiste na adaptação de um programa existente para cálculo de faltas, tendo como objetivo gerar de forma aleatória vários tipos de defeitos, assim como a localização dos mesmos. A metodologia de cálculo de defeitos foi desenvolvida utilizando as equações de injeção de correntes em coordenadas retangulares. Neste programa, também serão considerados os modelos de carga variantes com a tensão durante os defeitos e modelos de diversas gerações distribuídas, convencionais e não convencionais. Em seguida, foi desenvolvido e implementado um método baseado em redes neurais artificiais, para detecção e identificação de faltas, assim como para estimar a localização de faltas em um sistema de distribuição. Esta rede neural possui como entrada módulos e ângulos das tensões e correntes do sistema elétrico, obtidas através das medições fasoriais dos PMUs e/ou IEDs. As saídas da rede neural correspondem à detecção e localização de áreas de defeitos. O método proposto foi desenvolvido no ambiente MatLab® e com o intuito de avaliar sua eficiência, foi testado em alguns sistemas IEEE e em um sistema real. Os resultados obtidos dos estudos são apresentados sob a forma de tabelas e gráficos com suas respectivas acurácias, números de neurônios e as diferentes configurações adotadas. / This work proposes the development of numerical models and methods, based on artificial neural networks, for the detection and localization of high impedance faults in distribution systems. In parallel, the efficiency is also evaluated using different types of measurement data techniques in the performance of the method, which is implemented through two steps. The first step consists in the adaptation of an existing program for calculation of faults, aiming to generate randomly several types of faults, as well as their location. The faults calculation methodology was developed using current injection equations in rectangular coordinates. In this program the models of load variation with the voltage during the faults and a variety of conventional and unconventional models for distributed generation, are considered. Next, a method based on artificial neural networks is developed and implemented for the detection and identification of faults, as well as to estimate the fault location within a distribution system. The neural network inputs are modules and angles of the voltages and currents of the electrical system, obtained from the PMUs and / or IEDs. The outputs of the neural network correspond to the detection and location of faults. The proposed method was developed in MatLab® environment and tested in some IEEE systems and in a real system in order to evaluate its efficiency. The results obtained from the studies was presented in the form of tables and graphs with their respective accuracy, numbers of neurons and the different configurations adopted.

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.