Orientador: Laurence Duarte Colvara / Resumo: Este trabalho apresenta um estudo sobre o controle de Sistema de Energia Elétrica (SEE) com vistas à melhoria da estabilidade transitória por meio da atuação de dispositivos FACTS, neste momento considerando os compensadores em derivação (SVC) e em série (TCSC). Propõe-se a inclusão, em dispositivos pré-existentes, a incorporação de um controle adicional visando atuação em face de transitórios eletromecânicos. A influência dos dispositivos sobre a capacidade de sincronização entre os pares de máquinas, avaliada por meio do fator de efeito é inserida na atuação dinâmica/transitória do sistema. A evolução da trajetória pós-falta do sistema é considerada em relação às fronteiras da chamada Região de Sincronização Positiva (RSP) e simulações foram realizadas usando os sistemas-teste Simétrico de duas áreas e New England para Lei de Controle proposta e conclui-se que esta é efetiva na melhoria da estabilidade transitória do Sistema de Energia Elétrica e, com aprimoramentos, poderá ser incluída em procedimentos de operação em tempo real. / Abstract: The power system transient stability control is approached by means of FACTS devices, and at this first step the SVC and TCSC devices are considered. A certain device acts upon each pair of machines by means of their synchronization capability which is affected by the corresponding transfer admittance as repeated by the FACTS device. This influence is taken into account by means of a parameter named Effect Factor. The boundaries of a region surrounding the stable equilibrium point named Positive Stability Region are used as reference for critical trajectories and the control action intend to reverse the tendency of the trajectory of leaving this region. In view of the shown tested cases the results are very promising since the proposed control has conduced to improvements in fault critical clearing times and so it has potential to be included in online operation procedures. / Doutor

No estudo de estabilidade transitória, as não linearidades inerentes aos sistemas aliadas a grande dimensão do problema, contribuem para que as análises dos sistemas de potência sejam muito complexas. O estudo clássico de estabilidade transitória utiliza soluções numéricas iterativas de um conjunto de equações diferenciais associadas à dinâmica do sistema, visando a obtenção do tempo crítico de abertura. Porém, este não é o processo mais adequado à aplicações em tempo real devido ao esforço computacional exigido em tais iterações numéricas. Os métodos diretos são adequados para análises em tempo real, já que obtêm as informações necessárias sem a solução explícita de equações diferenciais. Dentre os métodos diretos existentes, as idéias de Lyapunov associadas ao princípio de invariância de LaSalle destacam-se por serem métodos energéticos e diretos adequados ao estudo de estabilidade em sistemas não lineares. Baseados em tais idéias, diversos métodos de estimativa da região de estabilidade foram propostos. Dentre estes, o BCU tem sido aceito como o mais eficiente para a determinação do tempo crítico de abertura. Apesar do BCU ser bastante eficiente, existem casos de falha do mesmo. Este trabalho visa eliminar dois problemas relacionados ao BCU: o primeiro problema advém do fato de que nem sempre o máximo de energia potencial ocorre nas vizinhanças do PEBS. O segundo problema está associado aos casos em que a trajetória do sistema gradiente reduzido não passa nas vizinhanças do ponto de equilíbrio de controle. Para solucionar estes dois problemas utiliza-se um método dinâmico para a deteção do “exit point” e o “Shadowing Method” para cálculo do ponto de equilíbrio de controle. Testes com os dois algoritmos mostram que eles encontram soluções para casos de falha do PEBS e BCU, porém problemas de deteção dos pontos de interesse ainda persistem. Alguns métodos alternativos, baseados nos algoritmos citados são propostos, bem como aspectos de melhoria de convergência dos mesmos. / In transient stability assessment, the nonlinearities of the systems and the dimension of the problem contribute to the complexity of the analysis in power systems. The classical numerical solution to obtain the critical clearing time (cct) has been used, but it is time-consuming and not adequate for real-time applications. The direct methods have the adequacy for real-time analysis because they get the necessary information for stability without the explicit solution of the set of differential equations associated to the system dynamics. Among the existing methods of power system transient stability analysis, Lyapunov ideas associated to LaSalle´s invariance principle are very important. Inspired by these ideas, methods to estimate the stability region have been obtained. One of them is the BCU, that has been accepted as the most efficient method in the determination of the critical cct. Despite BCU´s efficiency, it fails in many cases. The main objective of this research is to solve two problems associated to the BCU: the first problem is the fact that not always the maximum of potential energy occurs in the neighborhood of PEBS. The second problem is the fact that in many cases the trajectory of the reduced gradient system does not pass in the neighborhood of the controlling unstable equilibrium point. For the solution of these problems it will be used a dynamic method for the exit point detection and the Shadowing Method to calculate the controlling unstable equilibrium point. Tests have shown that the aforementioned robust algorithms find the solutions for many cases for which BCU and PEBS method fails, but many cases of fail persist. Some alternative methods, based in the mentioned algorithms are proposed, and so, aspects to improve its convergency.

O crescimento da demanda de energia e das interligações entre os Sistemas Elétricos de Potência, assim como a necessidade de prestação de melhores serviços exigem que as técnicas de análise destes sejam cada vez mais rápidas e refinadas. Dentre estas técnicas, as análises de estabilidade transitória através de métodos energéticos são estudadas e o desenvolvimento de técnicas computacionais que permitam a análise em tempo real da estabilidade transitória é o principal objetivo deste trabalho. Os métodos energéticos são métodos diretos adequados à aplicações em tempo real, pois obtém informações a respeito da estabilidade diretamente das equações diferenciais do sistema, sem a necessidade do conhecimento das soluções das equações diferenciais. A aplicação de métodos energéticos aos estudos de estabilidade transitória evoluiu significativamente nos últimos anos. Esta evolução culminou com o desenvolvimento do método BCU. Este método está fundamentado no conceito de ponto de equilíbrio de controle e portanto, garante apenas a existência ou a estabilidade do primeiro \"swing\". Embora este seja um método eficiente, existe uma grande quantidade de casos que são estáveis no primeiro \"swing\", mas o sistema perde a estabilidade em \"swings\" subseqüentes. Para resolver este problema, desenvolveu-se uma técnica de estimativa do parâmetro amortecimento para o caso de uma máquina versus barramento infinito. Estima-se o amortecimento necessário que a máquina deverá possuir tal que a estabilidade nos \"swings\" subseqüentes seja garantida. Esta metodologia é utilizada em conjunto com o BCU garantindo a satisfação da condição de transversalidade exigida no desenvolvimento teórico deste método. Maiores investigações serão necessárias para estimar os amortecimentos em sistemas multimáquinas. / The increase of load demand and interconnection between power systems as well as the necessity of offering better customer services require fast and refined techniques to analyze these systems. In particular, the transient stability analysis is studied and the development of computational techniques suitable to real-time transient stability analysis is the main aim of this work. The energetic methods are direct methods suitable to real-time applications because they obtain qualitative information about the system without the knowledge of the differential equation solutions. The application of energetic methods to the transient stability analysis developed significantly in the last years. This evolution culminated with the development of the BCU method. This method is based on the concept of controlling equilibrium point, therefore it only guarantees the existence of the first swing. In spite of the efficiency of this method, there exists a high number of cases where the BCU predicts stability to the first swing but the system becomes unstable or loses synchronism in future swings. In order to solve this problem, a methodology to estimate the damping coefficient was developed to the machine versus infinite bus case. The damping coefficient that must be applied to the machine to guarantee the stability in future swings is estimated. This methodology is used together with the BCU method guaranteeing the satisfying of the transversality condition required by the BCU theory. Further investigations must be carried out to extend the methodology to multimachine systems.

O método de Lyapunov, também conhecido como método direto, é eficiente para análise de estabilidade transitória em sistemas de potência. Tal método possibilita a análise de estabilidade sem requerer o conhecimento das soluções das equações diferenciais que modelam o problema. A maior desvantagem da utilização dos métodos diretos, é sem dúvida encontrar uma função (V) que satisfaça as condições do Teorema de Lyapunov, ou seja, V > 0 e V \'< ou =\' 0. Durante muitos anos a inclusão das condutâncias de transferência na modelagem do sistema de potência, com a rede reduzida aos nós dos geradores, foi um assunto que despertou interesse em vários pesquisadores. Em 1989, Chiang provou a não existência de uma Função de Lyapunov para sistemas de potência quando as condutâncias de transferência são consideradas. Essas condutâncias de transferência são responsáveis por gerar regiões no espaço de estados onde tem-se V > 0, não satisfazendo as condições do Teorema de Lyapunov. Recentemente, Rodrigues, Alberto e Bretas (2000) apresentaram a Extensão do Princípio de Invariância de LaSalle, onde é permitido que a Função de Lyapunov possua, em algumas regiões limitadas do espaço de estados, a derivada positiva. Neste caso, estas funções passam a ser denominadas Funções de Lyapunov Estendidas (FLE). Neste trabalho, são utilizadas a Extensão do Princípio de Invariância de LaSalle e as Funções de Lyapunov Estendidas para a análise de estabilidade transitória, considerando o efeito das condutâncias de transferência na modelagem do problema. Para isto, são propostas Funções de Lyapunov Estendidas para modelos de sistemas de potência que não apresentam uma Função de Lyapunov no sentido usual. Essas FLE\'s são propostas tanto para sistemas de 1-máquina versus barramento infinito quanto para sistemas multimáquinas. Para a obtenção de boas estimativas do tempo de abertura, nos estudos de estabilidade transitória, é proposto um algoritmo iterativo. Este algoritmo fornece uma boa estimativa local da área de atração do ponto de equilíbrio estável de interesse. / The method of Lyapunov, one of the direct method, is efficient for transient stability analysis of power systems. The direct methods are well-suited for stability analysis of power systems, since they do not require the solution of the set of differential equations of the system model. The great difficulty of the direct methods is to find an auxiliary function (V) which satisfies the conditions of Lyapunov\'s Theorem V > 0 and V \'< or =\' 0. For many years the inclusion of the transfer conductances in the power system model, with the reduced network, is a issue of interest for several researchers. In 1989, Chiang studied the existence of energy functions for power systems with losses and he proved the non existence of a Lyapunov Function for power systems when the transfer conductance is taken into account. The transfer conductances are responsible for generating regions in the state space where the derivative of V is positive. Therefore, the function V is nor a Lyapunov Function, because its derivative is not semi negative definite. Recently, an Extension of the LaSalle\'s Invariance Principle has been proposed by Rodrigues, Alberto and Bretas (2000). This extension relaxes some of the requirements on the auxiliary function which is commonly called Lyapunov Function. In this extension, the derivative of the auxiliary function can be positive in some bounded regions of the state space and, for distinction purposes, it is called, as Extended Lyapunov Function. Inthis work, the Extension of the LaSalle\'s Invariance Principle and the Extended Lyapunov Function are used for the transient stability analysis of power systems with the model taking transfer conductances in consideration. For at purpose in this research, Extended Lyapunov Functions for power system models which do not have Lyapunov Functions in the usual sense are proposed. Extended Lyapunov Functions are proposed for a single-machine-infinite- bus-system and multimachine systems. For obtaining good estimates of the critical clearing time in transient stability analysis, an iterative algorithm is proposed. This algorithm supplies a good local estimate of the attraction area for the post fault stable equilibrium point.

Transient stability analysis is necessary for the planning, operation, and control of power systems. However, its mathematical modeling and time-domain solution is computationally onerous and has attracted the attention of power systems experts and simulation specialists for decades. The ultimate promised goal has been always to perform this simulation as fast as real-time for realistic-sized systems. In this thesis, methods to speedup transient stability simulation for large-scale power systems are investigated. The research reported in this thesis can be divided into two parts. First, real-time simulation on a general-purpose simulator composed of CPU-based computational nodes is considered. A novel approach called Instantaneous Relaxation (IR) is proposed for the real-time transient stability simulation on such a simulator. The motivation of proposing this technique comes from the inherent parallelism that exists in the transient stability problem that allows to have a coarse grain decomposition of resulting system equations. Comparison of the real-time results with the off-line results shows both the accuracy and efficiency of the proposed method. In the second part of this thesis, Graphics Processing Units (GPUs) are used for the first time for the transient stability simulation of power systems. Data-parallel programming techniques are used on the single-instruction multiple-date (SIMD) architecture of the GPU to implement the transient stability simulations. Several test cases of varying sizes are used to investigate the GPU-based simulation. The simulation results reveal the obvious advantage of using GPUs instead of CPUs for large-scale problems. In the continuation of part two of this thesis the application of multiple GPUs running in parallel is investigated. Two different parallel processing based techniques are implemented: the IR method, and the incomplete LU factorization based approach. Practical information is provided on how to use multi-threaded programming to manage multiple GPUs running simultaneously for the implementation of the transient stability simulation. The implementation of the IR method on multiple GPUs is the intersection of data parallelism and program-level parallelism, which makes possible the simulation of very large-scale systems with 7020 buses and 1800 synchronous generators. / Energy Systems

The objective of this thesis is to investigate the transient response and optimal economic dispatch of an isolated power system with wind generators. Different types of wind turbines and the classification of Stability are introduced. Then, the process of Transient stability analysis and the concept of Genetic Algorithms are given for explanation. In this thesis, the practical power system of Kinmen is selected for case study. The disturbances introduced by gusting wind and N-1 system contingency are considered in the transient stability analysis. Furthermore, in order to obtain both accuracy and feasibility of the Optimal power dispatch by using Real-parameter Genetic Algorithms, the simulation results should be tested for the restrictions and requirements of the actual operation.

Due to the consideration of economic dispatch or system operation, the regional severe unbalance between power generation and load demand will introduce large amount of power flow over the inter-area tie lines. The tripping of transmission lines due to power system fault contingency will result in the increase of power flow over the inter-area tie lines, which may violate the constraint of transient stability. The whole power system could be collapsed due to further tripping of more generators unless proper remedy actions are executed in tie. This thesis proposes an effective approach to determine the generators to be tripped for power system protection. All of the generators in the power system are divided into critical group and non-critical group based on the methods of Energy-gap and Impedance-gap. The power flow capability limit of transmission lines on inter-areas have been derived by transient stability analysis. Once fault contingency occurs on the power system, the power flow of transmission lines on inter-area is compared to the above transmission limit to determine the generators in the critical group to be tripped. By this way, the stable operation of power system can be maintained after the contingency. To demonstrate the effectiveness of the proposed methodology, the Taipower system is selected for computer simulation to verify the generator tripping by system transient stability analysis. Different scenarios of system fault contingencies on primary EHV substations with various power flow conditions over the inter-area tie lines have been investigated to confirm the power system performance by applying the proposed generator tripping.

This thesis investigates the impact of high-level penetration of distributed generation especially from the renewable energy sources on the transient stability of the transmission system. Distributed generation is a source of electric power connected to the distribution network or on the consumer side. It is expected that distributed generation grows significantly by the increasing environmental concerns and deregulation in the market. As soon as the increasing penetration level, distributed generation starts to influence the distribution system as well as the transmission system. To investigate the impact of distributed generation with different penetration levels on the transmission system transient stability, simulation scenarios are created and simulations are run on the basis of these scenarios by the implementation of the different distributed generation technologies to the &ldquo / New England&rdquo / test system. Stability indicators are observed to assess the impact on the transient stability. Results are presented throughout the thesis and the impact of the different distributed generation technologies and the different penetration levels on the transient stability is discussed by comparing the stability indicators.

Presently power systems are being operated under high stress level conditions unforeseen at the moment they were designed. These operating conditions have negatively impacted reliability, controllability and security margins. FACTS devices and HVDC transmissions have emerged as solutions to help power systems to increase the stability margins. VSC-HVDC transmissions are of particular interest since the principal characteristic of this type of transmission is its ability to independently control active power and reactive power. This thesis presents various control strategies to improve damping of electromechanical oscillations, and also enhance transient and voltage stability by using VSC-HVDC transmissions. These control strategies are based of different theory frames, namely, modal analysis, nonlinear control (Lyapunov theory) and model predictive control. In the derivation of the control strategies two models of VSC-HVDC transmissions were also derived. They are Injection Model and Simple Model. Simulations done in the HVDC Light Open Model showed the validity of the derived models of VSC-HVDC transmissions and the effectiveness of the control strategies. Furthermore the thesis presents an analysis of local and remote information used as inputs signals in the control strategies. It also describes an approach to relate modal analysis and the SIME method. This approach allowed the application of SIME method with a reduced number of generators, which were selected based on modal analysis. As a general conclusion it was shown that VSC-HVDC transmissions with an appropriate input signal and control strategy was an effective means to improve the system stability. / QC 20110412

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