Até meados da década de setenta a atenção dos técnicos do setor elétrico estava voltada aos problemas advindos da chamada instabilidade de ângulo, onde perturbações mais severas, tais como curtos-circuitos, levam os sistemas a perderem estabilidade. À medida que os sistemas foram ficando mais sobrecarregados, algumas não linearidades tornaram-se mais evidentes e problemas que até então não eram observados passaram a ocorrer. Um desses problemas que passou a despertar maior atenção dos engenheiros de potência foi justamente o problema de colapso de tensão. Tal fenômeno está relacionado à incapacidade do sistema elétrico de prover o balanço entre a potência gerada e a requisitada pelas cargas, devido, principalmente, à limitada capacidade de transmissão, ou ainda, devido a um suporte de potência reativa local inadequada. Neste trabalho pretende-se avaliar o grau de impacto que uma contingência ou uma ação de controle teria sobre um sistema de potência. Para avaliar este grau de impacto pretende-se utilizar os conceitos de coerência de cargas, a partir da matriz de impedância nodal, determinando-se quais barras seriam mais influenciadas por uma certa perturbação no sistema. Quando este número de barras é elevado, indica que a contingência deveria ser classificada como mais grave do que uma contingência com margem baixa, porém de impacto local e de fácil solução. Durante o funcionamento do sistema podem ocorrer eventos que afetam as características de tensão e freqüência, causando inclusive a interrupção do fornecimento de energia. Portanto, o engenheiro de operação deve dispor de ferramentas que controlem e que permitam prever esta situação de risco e tomar medidas para evitá-las. Assim, é de extrema importância, a análise de estabilidade do sistema, a fim de em um futuro próximo, prevenir distúrbios no seu funcionamento normal. / Until the middle of the seventies the attention of the technicians of the electricity sector was focused on the problems arising from instability of the callangle, where the most severe, such as short circuits, take the systems to lose stability. As the systems were getting overloaded, some nonlinearities have become more evident and problems that were not seen until then began to occur. One such problem that has awaken the attention of power engineers was precisely the problem of voltage collapse. This phenomenon is related to the inability of the electric system to provide the balance between power generated and required by the loads, mainly due to the limited transmission capacity, or because a local reactive power support inadequate. This work aims to assess the degree of impact that a contingency or an action of control would have on a system of power. To assess the degree of impact is intended to use the concepts of consistency of loads from the nodal impedance matrix, it was determined that bars would be more influenced by a disturbance in the system. When this number of bars is high, indicates that the contingency should be classified as more serious than a contingency margin with low, but the local impact and easy solution. During operation of system events may occur that affect the characteristics of voltage and frequency, causing even the interruption of power supply. Therefore, the operating engineer should have the tools to monitor and to predict that this situation of risk and take steps to avoid them. It is therefore of extreme importance, the analysis of system stability, so that in the near future, to prevent disturbances in their normal operation.

Nos últimos anos verificou-se um crescimento acentuado da complexidade da avaliação da segurança em Sistemas Elétricos de Potência (SEPs). O aumento das interligações, aliado à operação das redes com altos níveis de carregamento, aumenta a probabilidade de ocorrência de incidentes que podem levar o SEP à instabilidade de tensão, culminando com o colapso de tensão e grandes prejuízos à qualidade do fornecimento de energia elétrica. Neste trabalho foi proposta uma ferramenta rápida para a manutenção da segurança de SEPs no contexto da Estabilidade de Tensão (ET). Para tal, foi desenvolvida uma metodologia rápida para a análise de contingências. Selecionadas as críticas, a eliminação da criticalidade das mesmas é realizada via ações preventivas. Neste contexto, foram desenvolvidas duas abordagens para a seleção de ações preventivas. Na primeira procura-se minimizar o número de controles via técnicas de agrupamento de dados, para eliminar a criticalidade de uma contingência. Na segunda abordagem foi desenvolvida uma estratégia para obtenção de um grupo de controles para eliminar a criticalidade de todas as contingências. Ambas as abordagens baseiam-se em uma metodologia de análise de sensibilidade da margem de ET em relação aos controles preventivos que também foi proposta nesta tese. A eficácia da ferramenta foi comprovada por intermédio de simulações em um SEP. Os resultados foram bastante satisfatórios, os grupos de controles obtidos pela primeira abordagem representam um conjunto mínimo de ações preventivas para eliminar a criticalidade de uma contingência específica. Já na segunda abordagem, foi possível determinar um grupo de controles para a eliminar simultaneamente a criticalidade de todas as contingências. Como produto científico deste doutorado foram obtidas novas metodologias rápidas para a análise de segurança do SEP no contexto da ET. / The complexity of the security assessment in Electric Power Systems (EPS) has received much attention from researches in recent years. The continuous growth in the number of interconnections, allied to networks operating with high loading levels, enhance the probability of incidents that can lead the EPS to voltage instability. Voltage collapse and considerably loss of the electric supply are the principal consequences of this scenery. In this study, we propose a fast tool for supporting the EPS security, in the context of Voltage Stability (VS). To this end, a fast methodology was developed for contingency analysis. Once the critical contingencies are selected, their criticalities are eliminated through the selection of preventive actions. In this context, two approaches were developed. In the first one, we aim at minimizing eh number of controls by using clustering techniques. In this case, the principal objective is to eliminate the criticality of a contingency. In the second approach, we developed a strategy for obtaining a groups of controls in order to eliminate the criticality of all contingencies. Both approaches are based on a methodology for sensitivity analysis of the VS margin with respect to preventive controls which is also proposed in this thesis. The effectiveness of the tool was corroborated by simulations in a EPS. We found the results satisfactory, since the groups of controls achieved by the first approach represent a minimum set of preventive actions that can be taken to eliminate the criticality of a specific contingency. In the second approach, it was possible to determine a minimum group of controls that eliminate the criticality of all contingencies simultaneously. New fast methodologies for security analysis of the EPS in the context of the VS is considered the main scientific product result of this doctorate.

In the context of static Voltage Stability Assessment (VSA), as the power system load grows, bus voltages tend to drop. This reduction may lead to generator or load disconnections caused by undervoltage protection schemes. These events comprise sudden parametric variations that affect the equilibrium diagram and the Voltage Stability Margin (VSM) of power systems. Practical examples of such sudden load changes are caused by the mandatory disconnection of Distributed Generation (DG) units and Undervoltage Load Shedding (ULS). There are no thorough studies in the literature concerning these load parametric variations and the discontinuities that they cause in power system equilibria. This dissertation describes a predictor/corrector scheme specifically designed to handle these discontinuities, so it is possible to evaluate their effect on the VSM of power systems. This method successively calculates the load discontinuities that exist in the equilibrium locus of the system under analysis. It results in the sequence of sudden load variations that happens and their overall impact on the system. When applied to quantify the effect of DG mandatory disconnections and ULS, the proposed predictor/corrector scheme yielded better results than the traditional Continuation Power Flow (CPFLOW), which experienced convergence problems caused by the discontinuities under analysis. However, due to its design, the applicability of the proposed method should be restricted to power systems that go through several successive sudden load changes. In this sense, it should not be regarded as a replacement for the CPFLOW, but rather as a technique that could award this traditional VSA tool with new features to enhance its performance. / No contexto de análise estática de estabilidade de tensão, conforme a carga de um sistema de potência cresce, as tensões nas suas barras tendem a cair. Essa redução pode causar a desconexão de geradores e cargas devido a atuação de proteções de subtensão. Esses eventos representam variações abruptas de demanda que alteram o diagrama de equilíbrio de um sistema e sua Margem de Estabilidade de Tensão (MET). Exemplos práticos dessas variações são causados pelo desligamento mandatório de unidades de Geração Distribuída (GD) e pelo Corte de Carga por Subtensão (CCS). Não há estudos detalhados na literatura que trabalham especificamente com essas variações nos parâmetros da carga, nem com as descontinuidades que elas causam no diagrama de equilíbrio de sistemas de potência. Essa dissertação descreve um procedimento especificamente projetado para lidar com essas descontinuidades, de modo que seja possível avaliar seu efeito na MET de sistemas elétricos. Esse método calcula sucessivamente as descontinuidades de carga que existem no diagrama de equilíbrio do sistema em análise. Ele resulta na sequência de variações súbitas de carga que ocorre e no seu impacto no sistema. Quando o método foi aplicado para quantificar o efeito do desligamento mandatório de GD e do CCS, ele apresentou resultados melhores do que o tradicional Fluxo de Carga Continuado (CPFLOW), o qual sofreu problemas de convergência causados pelas descontinuidades em questão. Entretanto, devido ao seu projeto, o método proposto só deve ser utilizado para sistemas de potência que estão sujeitos a várias sucessivas variações abruptas de carga. Por essa razão, esse método não pode ser considerado um substituto do CPFLOW, mas sim como uma técnica capaz de agregar novas funcionalidades a essa ferramenta tradicional, amentando assim seu horizonte de aplicações.

O objetivo geral deste trabalho é a extensão dos métodos diretos para o estudo de estabilidade de tensão em sistemas de potência. Devido à diversidade dos dispositivos com distinta velocidade de atuação, propriedades de escalas de tempo foram exploradas para viabilizar essa extensão. O presente trabalho de pesquisa tem como contribuições (i) o estabelecimento de uma metodologia geral para análise de estabilidade de sistemas elétricos de potência em escalas de tempo e (ii) a extensão dos métodos diretos para a análise de estabilidade em escalas de tempo de sistemas de potência. Com base na teoria dos sistemas singularmente perturbados, propõe-se um algoritmo geral de análise de estabilidade em escalas de tempo de sistemas elétricos de potência e estabelecem-se os fundamentos teóricos deste algoritmo que validam a decomposição da análise de estabilidade em escalas de tempo. Assim, a análise de estabilidade de um sistema elétrico de potência pode ser decomposta na análise de estabilidade de seus correspondentes subsistemas rápido e lento, de menor ordem. Estes fundamentos preenchem uma lacuna que existia entre as análises de estabilidade no curto-prazo e médio-prazo e estabelece uma relação entre elas. Em particular, o método quase estático (QSS) para análise de estabilidade na escala de médio prazo, que pressupõe que as dinâmicas rápidas são estáveis e a análise de estabilidade transitória são casos particulares do algoritmo proposto. A partir dos fundamentos da decomposição da análise de estabilidade em escalas de tempo, estenderam-se os métodos diretos de análise de estabilidade, em particular o método CUEP, inicialmente desenvolvidos para análises de estabilidade transitória, para o problema de análise de estabilidade no médio prazo via decomposição da análise em escalas de tempo. Essa extensão é importante na medida em que os métodos diretos são rápidos, e viabilizam o desenvolvimento de técnicas de análise de estabilidade de tensão que sejam adequadas para aplicações em tempo real. A metodologia proposta foi testada em sistemas de potência de pequeno porte com bons resultados na avaliação de tempos de atuação dos equipamentos de controle e proteção, fornecendo também um melhor entendimento dos mecanismos de estabilização dos sistemas de potência analisados. / The aim of this study is the extent of direct methods for the study of voltage stability in power systems. Because of the diversity of devices with different speed of action, time-scales properties were explored to enable this extension. This research work has as contributions (i) establishing a general methodology for stability analysis of electric power systems on time scales and (ii) the extent of direct methods for the analysis of stability in time-scales scales of electric power systems. Based on the theory of singularly perturbed systems, we propose a general algorithm of stability analysis in time-scales electric power systems and develop the theoretical foundations of this algorithm to validate the decomposition of stability analysis in time scales. Thus, the stability analysis of a power system can be decomposed in the stability analysis of their corresponding fast and slow subsystems of lower order. These fundamentals fill the gap that existed between the stability analysis in the short-term and mid-term and establishes a relationship between them. In particular, the quasi steady state method (QSS) for stability analysis of the mid-term scale, which presupposes that the fast dynamics are stable and transient stability analysis are particular cases of the algorithm proposed. From the fundamentals of decomposition of time scales stability analysis, the direct methods of stability analysis will be extended, in particular CUEP method initially developed for transient stability analysis, for the mid-term stability problem via time-scale analysis. This extension is important because the direct methods are fast, and enable the development of voltage stability analysis techniques that are suitable for real time applications. The proposed methodology was tested in small power systems with good results in the evaluation of operating times of the control and protection equipment, also providing a better understanding of the stabilization mechanisms of the analyzed power systems.

Este trabalho descreve os métodos e os resultados encontrados a partir da implementação de métodos estáticos para análise da estabilidade de tensão em sistemas elétricos de potência. A determinação da margem de estabilidade de tensão foi feita através do cálculo do menor valor singular da matriz jacobiana associada às equações de fluxo de carga, comumente utilizado como índice estático de colapso de tensão. As não linearidades e descontinuidades relatadas nas referências estudadas e encontradas nos testes realizados, levaram-nos a propor o uso da razão entre o menor e o maior valores singulares da mesma matriz jacobiana, na expectativa de que este índice tivesse um comportamento menos instável do que o menor valor singular, o que não foi confirmado nos testes realizados. Identifica-se também as regiões do sistema elétrico mais afetadas pela instabilidade, o que é feito através da determinação da barra crítica do sistema e da classificação das barras de carga em ilhas de controle de tensão. A barra crítica é identificada através do cálculo do vetor tangente do sistema, conforme proposto nas referências citadas no trabalho. Como alternativa ao vetor tangente para a identificação da barra crítica, propôs-se usar o vetor singular à direita associado ao menor valor singular da matriz jacobiana. A comparação da capacidade de identificação da barra crítica por esses dois vetores mostrou uma clara vantagem do uso do vetor tangente. A rotina para identificação das ilhas de controle de tensão foi adaptada a partir de um método desenvolvido para a análise de coerência em barras de carga, e os resultados encontrados foram bastante satisfatórios. Os métodos implementados foram testados em diversas situações, com o objetivo de se analisar os efeitos dos modelos de carga ZIP com elevadas parcelas de impedância constante, dos limitadores de potência reativa dos geradores e da repartição do incremento da carga de potência ativa entre os geradores. / This work describes the methods and results got from the implementation of static methods for power systems voltage stability analisys. The power system voltage stability margin was predicted by the smallest load flow jacobian\'s singular value, commonly used as a prediction index to voltage stability. lt is investigated the use of ratio of the smallest single value by the biggest one as voltage colapse index, assuming that it\'s less unstable than the singular value itself, specialy near the collapse point. The results presented shown a clear advantage of using the smallest singular value instead of this singular value rate. The identification of the system\'s regions affected by the voltage drop is made by the tangent vector and by the voltage island identification method proposed on this work. Is compared the ability to identify system\'s critical bus by the tangent vector and right singular vetor of the smallest jacobian\'s singular value. In this case, tests results show the superiority of tangent vector. All the simulations presented are compared to allow the analysis of the voltage dependents load models (with high percentual of constant impedances), reactive limiters and generators load sharing efects over the smallest singular value, the rate of the smallest single value by the biggest one, voltage island classification and the critical bus identification.

The power industry has undergone significant restructuring throughout the world since the 1990s. In particular, its traditional, vertically monopolistic structures have been reformed into competitive markets in pursuit of increased efficiency in electricity production and utilization. However, along with market deregulation, power systems presently face severe challenges. One is power system stability, a problem that has attracted widespread concern because of severe blackouts experienced in the USA, the UK, Italy, and other countries. Another is that electricity market operation warrants more effective planning, management, and direction techniques due to the ever expanding large-scale interconnection of power grids. Moreover, many exterior constraints, such as environmental protection influences and associated government regulations, now need to be taken into consideration. All these have made existing challenges even more complex. One consequence is that more advanced power system data analysis methods are required in the deregulated, market-oriented environment. At the same time, the computational power of modern computers and the application of databases have facilitated the effective employment of new data analysis techniques. In this thesis, the reported research is directed at developing computational intelligence based techniques to solve several power system problems that emerge in deregulated electricity markets. Four major contributions are included in the thesis: a newly proposed quantum-inspired particle swarm optimization and self-adaptive learning scheme for radial basis function neural networks; online wavelet denoising techniques; electricity regional reference price forecasting methods in the electricity market; and power system security assessment approaches for deregulated markets, including fault analysis, voltage profile prediction under contingencies, and machine learning based load shedding scheme for voltage stability enhancement. Evolutionary algorithms (EAs) inspired by biological evolution mechanisms have had great success in power system stability analysis and operation planning. Here, a new quantum-inspired particle swarm optimization (QPSO) is proposed. Its inspiration stems from quantum computation theory, whose mechanism is totally different from those of original EAs. The benchmark data sets and economic load dispatch research results show that the QPSO improves on other versions of evolutionary algorithms in terms of both speed and accuracy. Compared to the original PSO, it greatly enhances the searching ability and efficiently manages system constraints. Then, fuzzy C-means (FCM) and QPSO are applied to train radial basis function (RBF) neural networks with the capacity to auto-configure the network structures and obtain the model parameters. The benchmark data sets test results suggest that the proposed training algorithms ensure good performance on data clustering, also improve training and generalization capabilities of RBF neural networks. Wavelet analysis has been widely used in signal estimation, classification, and compression. Denoising with traditional wavelet transforms always exhibits visual artefacts because of translation-variant. Furthermore, in most cases, wavelet denoising of real-time signals is actualized via offline processing which limits the efficacy of such real-time applications. In the present context, an online wavelet denoising method using a moving window technique is proposed. Problems that may occur in real-time wavelet denoising, such as border distortion and pseudo-Gibbs phenomena, are effectively solved by using window extension and window circle spinning methods. This provides an effective data pre-processing technique for the online application of other data analysis approaches. In a competitive electricity market, price forecasting is one of the essential functions required of a generation company and the system operator. It provides critical information for building up effective risk management plans by market participants, especially those companies that generate and retail electrical power. Here, an RBF neural network is adopted as a predictor of the electricity market regional reference price in the Australian national electricity market (NEM). Furthermore, the wavelet denoising technique is adopted to pre-process the historical price data. The promising network prediction performance with respect to price data demonstrates the efficiency of the proposed method, with real-time wavelet denoising making feasible the online application of the proposed price prediction method. Along with market deregulation, power system security assessment has attracted great concern from both academic and industry analysts, especially after several devastating blackouts in the USA, the UK, and Russia. This thesis goes on to propose an efficient composite method for cascading failure prevention comprising three major stages. Firstly, a hybrid method based on principal component analysis (PCA) and specific statistic measures is used to detect system faults. Secondly, the RBF neural network is then used for power network bus voltage profile prediction. Tests are carried out by means of the “N-1” and “N-1-1” methods applied in the New England power system through PSS/E dynamic simulations. Results show that system faults can be reliably detected and voltage profiles can be correctly predicted. In contrast to traditional methods involving phase calculation, this technique uses raw data from time domains and is computationally inexpensive in terms of both memory and speed for practical applications. This establishes a connection between power system fault analysis and cascading analysis. Finally, a multi-stage model predictive control (MPC) based load shedding scheme for ensuring power system voltage stability is proposed. It has been demonstrated that optimal action in the process of load shedding for voltage stability during emergencies can be achieved as a consequence. Based on above discussions, a framework for analysing power system voltage stability and ensuring its enhancement is proposed, with such a framework able to be used as an effective means of cascading failure analysis. In summary, the research reported in this thesis provides a composite framework for power system data analysis in a market environment. It covers advanced techniques of computational intelligence and machine learning, also proposes effective solutions for both the market operation and the system stability related problems facing today’s power industry.

Recently, the widespread use of power system controllers, such as PSS and FACTS controllers, has led to the analysis of their effect on the overall stability of power systems. Many studies have been conducted to allocate FACTS controllers so that they achieve optimal power flow conditions in the context of Optimal Power Flow (OPF) analysis. However, these studies usually do not examine the effect of these controllers on the voltage and angle stability of the entire system, considering that the types of these controllers and their control signals, such as reactive power, current, or voltage, have significant effect on the entire system stability. <br /><br /> Due to the recent transition from government controlled to deregulated electricity markets, the relationship between power system controllers and electricity markets has added a new dimension, as the effect of these controllers on the overall power system stability has to be seen from an economic point of view. Studying the effect of adding and tuning these controllers on the pricing of electricity within the context of electricity markets is a significant and novel research area. Specifically, the link among stability, FACTS controllers and electricity pricing should be appropriately studied and modelled. <br /><br /> Consequently, in this thesis, the focus is on proposing and describing of a novel OPF technique which includes a new stability constraint. This technique is compared with respect to existent OPF techniques, demonstrating that it provides an appropriate modelling of system controllers, and thus a better understanding of their effects on system stability and energy pricing. The proposed OPF technique offers a new methodology for pricing the dynamic services provided by the system's controllers. Moreover, the new OPF technique can be used to develop a novel tuning methodology for PSS and FACTS controllers to optimize power dispatch and price levels, as guaranteeing an adequate level of system security. All tests and comparisons are illustrated using 3-bus and 14-bus benchmark systems.

The number of large-scale wind farms integrated to the power system in Sweden is increasing. Two generator concepts that are widely used are Doubly-Fed Induction Generators (DFIG) and Full Power Converters (FPC). The study is of a quantitative character and the aim of the Master thesis is to compare DFIG-models with FPC-models integrated in an area with high concentration of hydropower. Then it is possible to examine how the dynamics in the power system change depending on the selection of technology (DFIG or FPC) when connecting a wind farm. The power system is simulated during a summer night, i.e., a low load is connected. The Master thesis covers stability analysis of the power system by using rotor angle stability that are split into small-signal stability and transient stability (time-domain simulations) and finally voltage stability to see how the hydropower generators react when varying the power production in the wind farm. The Master thesis concludes that independently of wind turbine technique, integration of a wind farm has slight impact on the stability in the power system compared to a power system without a wind farm, even though the load is low. Further, an integration of a wind farms affects the reactive power production in neighbouring hydropower plants. Finally, when increasing the size of the wind farm the neighbouring hydropower station consume less reactive power which can induce problem with the voltage stability.

Recently, the widespread use of power system controllers, such as PSS and FACTS controllers, has led to the analysis of their effect on the overall stability of power systems. Many studies have been conducted to allocate FACTS controllers so that they achieve optimal power flow conditions in the context of Optimal Power Flow (OPF) analysis. However, these studies usually do not examine the effect of these controllers on the voltage and angle stability of the entire system, considering that the types of these controllers and their control signals, such as reactive power, current, or voltage, have significant effect on the entire system stability. <br /><br /> Due to the recent transition from government controlled to deregulated electricity markets, the relationship between power system controllers and electricity markets has added a new dimension, as the effect of these controllers on the overall power system stability has to be seen from an economic point of view. Studying the effect of adding and tuning these controllers on the pricing of electricity within the context of electricity markets is a significant and novel research area. Specifically, the link among stability, FACTS controllers and electricity pricing should be appropriately studied and modelled. <br /><br /> Consequently, in this thesis, the focus is on proposing and describing of a novel OPF technique which includes a new stability constraint. This technique is compared with respect to existent OPF techniques, demonstrating that it provides an appropriate modelling of system controllers, and thus a better understanding of their effects on system stability and energy pricing. The proposed OPF technique offers a new methodology for pricing the dynamic services provided by the system's controllers. Moreover, the new OPF technique can be used to develop a novel tuning methodology for PSS and FACTS controllers to optimize power dispatch and price levels, as guaranteeing an adequate level of system security. All tests and comparisons are illustrated using 3-bus and 14-bus benchmark systems.

The purpose of the proposed research is to design a Decentralized Voltage/Stability Monitoring and Control System to counteract voltage violations and the impact of disturbances/contingencies on power system voltage stability. A decentralized voltage and stability control system is designed to coordinate the controls of the local secondary voltage control devices and necessary load shedding without requiring information about the rest of the system. The voltage/stability control can be formulated as a multi-objective optimization problem. The control objectives include, but are not limited to: minimization of system active/reactive losses; maximization of the system stability margin; and minimization of the control actions. The constraints of the optimization problem depend on the specifications of the actual system components. For the first time, margin sensitivities of the control actions are included in the control formulation. The concept of using margin sensitivity to evaluate the post-control load margin is presented as a fast and accurate way to assess potential voltage and stability control options. A system decomposition procedure is designed to define the disturbance-affected zone as an independent control subsystem. A normal constraint algorithm is adopted to identify the most suitable control solution in a shorter timeline than the typical utility voltage-control practice. Both steady-state and dynamic simulations are performed to compare the proposed system with typical utility control practices.