This work deals with the issue of evaluating transient stability in the simulation program PSCAD. Factors affecting transient stability were analyzed on a single-machine SMIB model. The results of this analysis confirmed the theoretical assumption that for more accurate results of the analysis of transient stability, it is necessary to consider the mentioned factors. A short circuit was simulated on the IEEE9 test model and subsequently the load angles of the generators were monitored using various methods. The method of reference of the largest generator in the system proved to be a more suitable method for the assessment of relative load angles from the results of the analysis.

[pt] O cálculo de equivalentes dinâmicos baseados em coerência apresenta três etapas básicas: a identificação de geradores coerentes, a redução estática da rede e a agregação dinâmica dos modelos das unidades geradoras coerentes. Esta dissertação trata do problema da agregação dinâmica de modelos de estabilizadores aplicados em reguladores de tensão de geradores coerentes, visando o cálculo de equivalentes dinâmicos precisos para estudos de estabilidade transitória de sistemas de energia elétrica. A determinação de um critério de escolha do melhor modelo equivalente, para uma dada composição de modelos de estabilizadores num grupo de geradores coerentes, é o objetivo principal. O ajuste dos parâmetros dos modelos equivalentes de estabilizadores dos grupos coerentes é realizado, a partir das respostas em freqüência dos modelos individuais de cada grupo, utilizando-se o método de Levenberg-Marquardt, o que caracteriza um problema de otimização multivariável. O desempenho dinâmico dos equivalentes calculados com a metodologia adotada é avaliado em um sistema teste. / [en] The calculation of coherency-based dynamic equivalents has three main steps: the identification of coherent generators, the network reduction and the dynamic aggregation of the coherent generating unit models. This dissertation deals with the problem of dynamic aggregation of power system stabilizer models to calculate coherency-based dynamic equivalents for power system transient stability studies. The determination of a criteria to choose the best equivalent model for a given composition of power system stabilizer models in a group of coherent generators is the main objective. The parameters of the power system stabilizer equivalent models for each group of coherent generating units are adjusted to match the frequency response of the individual models. This multivariable optimization problem is solved using the Levenberg-Marquardt method. The dynamic performance of the equivalents is evaluated in a test system.

The content of this dissertation consists of three parts. In the first part, optimal control strategies are developed for Unified Power Flow Controller (UPFC) following the clearance of fault conditions. UPFC is one of the most versatile Flexible AC Transmission devices (FACTs) that have been implemented thus far. The optimal control scheme is composed of two parts. The first is an optimal stabilization control, which is an open-loop ‘Bang’ type of control. The second is an suboptimal damping control, which consists of segments of ‘Bang’ type control with switching functions the same as those of a corresponding approximate linear system. Simulation results show that the proposed control strategy is very effective in maintaining stability and damping out transient oscillations following the clearance of the fault. In the second part, a new power market structure is proposed. The new structure is based on a two-level optimization formulation of the market. It is shown that the proposed market structure can easily find the optimal solutions for the market while takeing factors such as demand elasticity into account. In the last part, a mathematical programming problem is formulated to obtain the maximum value of the loadibility factor, while the power system is constrained by steady-state dynamic security constraints. An iterative solution procedure is proposed for the problem, and the solution gives a slightly conservative estimate of the loadibility limit for the generation and transmission system.

[pt] Este trabalho, relacionado com a área de modelagem de cargas para estudos de estabilidade transitória de sistemas elétricos, tem por objetivo discutir a adequação dos modelos clássicos normalmente utilizados, bem como o aprimoramento e desenvolvimento de representações para cargas com características específicas. Inicialmente, são enfocados os aspectos das representações clássicas de cargas e, através de desenvolvimentos teóricos e estudos computacionais, ressaltadas as adequações destas estratégias ao contexto atual. Reconhecendo algumas limitações quanto às técnicas para a obtenção dos parâmetros de motores de indução, apresenta- se procedimentos sistematizados para o tratamento destes componentes de carga. Tendo em vista a busca da melhoria de modelos e respostas aos questionamentos a respeito da relevância da inclusão dos efeitos da variação da freqüência sobre as cargas e parâmetros da rede, o trabalho prossegue com investigações nesta direção. Objetivando a análise do desempenho dos modelos simplificados de cargas através de funções algébricas, são discutidas as propostas atuais e verificadas suas adequações aos estudos de estabilidade. Finalmente, considerando a importância atual das cargas conversoras estáticas, são desenvolvidos modelos apropriados e realizados os estudos necessários à incorporação de unidades retificadoras em programas de estabilidade. / [en] This work, involved with the load modeling for electrical system transiente stability analysis, aim to discuss the classical load models normally used, and to develop and improve representations of specific types of loads. Initially, aspects concerned with classical load representations are dealt with aiming to evaluate, through theoretical and computational analyses, the current employment of such models. Knowing that the techiques to obtain induction motor parameters are still deficient, this work presents some systematic procedures for the treatment of such loads. Additionally, it continues seeking improvements in electrical system component models and answers to the questions about the need for inclusion of the frequency variation effects on loads and network parameters. Moreover, it takes into account the tendencies of using simplified load models represented by algebraic expressions. Some recent proposals in this area are discussed and tested with a view to acess the perfomance of the models in stability studies. Finally, considering the present importance of static load converters, it is developed the related models and presented the necessary studies to include rectifier units in stability programs.

Online stability assessment is an important problem that has not been solved completely yet. The purpose of this research is to tackle online transient stability assessment. Currently, most utility companies use step-by-step integration in order to set protective equipment so that they effectively work for critical contingencies. However, there are times an unforeseen contingency may occur which may cause the system to transit and the protective equipment to misoperate and does not isolate the disturbed part of the system. This research introduces a method that automatically determines a group of generators that participate in system separation and hence transient instability. The method consists of four phases: modeling and simulation, critical machines identification, online transient stability assessment, and critical clearing time calculation. In the modeling and simulation phase, the power system is built and the generators’ rotor angles and speeds are captured. In the critical machines identification phase, the average instantaneous rotor accelerating powers, coherency measures, the during-fault rotor angles and speeds characteristics, and the pre- and post-fault rotor angles are used to identify the Severely Disturbed Group (SDG) of machines. The results of this phase are used to calculate the kinetic energy of the SDG and potential energy of another (or possibly the same) group of generators. Utilization and success of the proposed method will be documented using results from the IEEE 39-Bus test system. Each step of each phase will be demonstrated as needed. The proposed method is compared to step-by-step integration and two direct methods. The suitability of the proposed method for operation will be shown in cases where the Y-Bus matrix and rotor angles and speeds are given. The proof of concept of the proposed method was used in simulating the test system and encouraging results of the simulation were published in ‎[1] and ‎[2]. The proof of concept is the foundation of the method proposed in this dissertation to determine transient stability of large-scale power systems.

Neste trabalho, as restrições de estabilidade transitória são incorporadas ao problema de Fluxo de Potência Ótimo (FPO) por meio da aproximação de equações diferenciais do problema de estabilidade por um conjunto de equações algébricas provenientes de procedimentos de integração numérica. Uma contribuição original desta dissertação é a proposição de um procedimento de otimização multi-passos que minimiza problemas de convergência e acelera o processo computacional. O procedimento de otimização proposto foi testado com sucesso num sistema pequeno de 3 geradores, tendo as potências geradas como variáveis de controle. / In this work, transient stability constraints are incorporated into the Optimal Power Flow (OPF) problem by approximating differential equations constraints by a set of equivalent algebraic equations originated from numerical integration procedures. A contribution of this dissertation is the proposal of a multi-step optimization procedure, which minimizes convergence problems and speeds up computation. The proposed optimization procedure was successfully tested on a small 3-machine power system, having the generated powers as control variables.

Nesta pesquisa são analisados os mecanismos que levam um sistema elétrico de potência (SEP) à instabilidade proveniente de uma perturbação de grande porte e as formas de se avaliar diretamente a margem de estabilidade desse sistema quando o mesmo é modelado preservando a estrutura da rede de transmissão. O sistema foi matematicamente modelado por um conjunto de equações algébrico-diferenciais (EAD), que permite modelagens mais compreensivas da carga e da rede e possibilita melhor avaliação da estabilidade de um sistema quando comparado com o modelo de equações diferenciais ordinárias (EDO) utilizado tradicionalmente para o estudo de estabilidade transitória. A avaliação direta da margem de estabilidade do sistema de potência modelado por conjuntos de EAD foi realizada usando métodos diretos de análise com base no conceito de ponto de equilíbrio instável de controle (PEIC). Tais métodos permitem a obtenção da margem deforma local e rápida, sem requerer a integração numérica de equações diferenciais do modelo pós-falta. No entanto, existem alguns problemas abertos para se alcançar a completa fundamentação do método PEIC para modelos de EAD. Assim, neste estudo dá-se um passo nesta direção, mostrando que as definições existentes de PEIC e de outros pontos de interesse podem ser falhas, principalmente quando a trajetória de falta do sistema alcança superfícies singulares. Neste sentido, são propostos a correção destas definições e um método direto de detecção do PEIC. O método proposto é adequado para análise direta de estabilidade angular e de tensão de curto-termos devido a grandes perturbações e capaz de fornecer corretos tempos críticos de abertura e a identificação dos mecanismos de instabilização do sistema de EAD, mesmo quando as trajetórias do sistema alcançam superfícies singulares. / This thesis addresses to the mechanisms that lead an electric power system to instability due to large disturbances and to the methods to assess directly the stability margin when the system is modeled preserving the network structure. The system is modeled by a set of differential-algebraic equations (DAE) that permits more comprehensive models for the load and network and provides a better stability margin assessment when compared to the model of ordinary differential equations (ODE) traditionally used for transient stability analysis. The direct assessment of the stability margin was realized using direct methods based on the controlling unstable equilibrium point (CUEP) concept and permits to assess the margin in a local and fast manner, without requires the time integration of the post-fault system differential equations. Nevertheless, some open problems remain to be solved in order to provide a complete foundation of the CUEP method for DAE power system models. In this research a further step is given in this direction, showing that the existent definitions for the CUEP and other interest points may fail, mainly when the fault-on trajectory reaches singular surfaces. In this sense, it is proposed the correction of these definitions and a new CUEP method that is adequate to the angular and voltage short-term direct stability assessment due to large disturbances; capable to provide precise critical clearing times and the identification of the instability mechanisms for the DAE modeled power system, even in the presence of singular surfaces.

Neste trabalho, as restrições de estabilidade transitória são incorporadas ao problema de Fluxo de Potência Ótimo (FPO) por meio da aproximação de equações diferenciais do problema de estabilidade por um conjunto de equações algébricas provenientes de procedimentos de integração numérica. Uma contribuição original desta dissertação é a proposição de um procedimento de otimização multi-passos que minimiza problemas de convergência e acelera o processo computacional. O procedimento de otimização proposto foi testado com sucesso num sistema pequeno de 3 geradores, tendo as potências geradas como variáveis de controle. / In this work, transient stability constraints are incorporated into the Optimal Power Flow (OPF) problem by approximating differential equations constraints by a set of equivalent algebraic equations originated from numerical integration procedures. A contribution of this dissertation is the proposal of a multi-step optimization procedure, which minimizes convergence problems and speeds up computation. The proposed optimization procedure was successfully tested on a small 3-machine power system, having the generated powers as control variables.

Recent widespread blackouts have indicated the need for more efficient and accurate power system monitoring, control and protection tools. Power system state estimation, which is the major tool that is used nowadays for providing the real-time model of the system, has significant biases resulting mainly from the complexity and geographic spread and separation of an electric power system. Synchrophasor technology is a promising technology that has numerous advantages compared to conventional metering devices. PMUs provide synchronized measurements, where synchronization is achieved via a GPS clock which provides the synchronizing signal with accuracy of 1 μsec. As a result, the computed phasors have a common reference (UTC time) and can be used in local computations, thus distributing the state estimation process. The first part of the work presents a PMU enabled dynamic state estimator (DSE) that can capture with high fidelity the dynamics of the system and extract in real time the dynamic model of the system. The described DSE is performed in a decentralized way, on the substation level based on local measurements which are globally valid. The substation based DSE uses data from relays, PMUs, meters, FDRs etc in the substation only, thus avoiding all issues associated with transmission of data and associated time latencies. This approach enables very fast DSE update rate which can go up to more than 60 executions per second. The distributed state estimation architecture that synchrophasor technology enables, along with the fast sampling rate and the accuracy of the measurements that PMUs provide, enable the computation of the real-time dynamic model of the system and the development of numerous power system applications for more efficient control and protection of the system. In the second part of the work, a transient stability monitoring scheme is presented that utilizes the information given by the dynamic state estimation and enables real-time monitoring of the transient swings of the system and characterizes the stability of the system in real time. In particular, the real-time dynamic model of the system, as given by the DSE, is utilized to evaluate the system's energy function based on Lyapunov's direct method and extract stability properties from the energy function. The two major components of the scheme are a) the calculation of the center of oscillations of the system and b) the derivation of an equivalent, reduced sized model which is used for the calculation of the potential and kinetic energy of the system based on which the stability of the system is determined. Finally, as an application of the transient stability monitoring scheme, an energy based out-of-step protection scheme is proposed. The energy of the generator is continuously monitored and if it exceeds a predefined threshold then instability is asserted and a trip signal can be sent to the generator. The major advantage of the scheme is that the out-of-step condition is predicted before its occurrence and therefore relays can act much faster than today's technology. The scheme is compared to presently available state of the art out-of-step protection schemes in order to verify its superiority.

<p>Utilization of power electronics based controllable systems (or devices) in transmission systems has opened new opportunities for the power industry to optimize utilization of the existing transmission systems, and at the same time to keep high system reliability and security.</p><p>As a member of these controllable systems, Voltage Source Converters-based High Voltage direct current (VSC-HVdc) systems have the ability to rapidly control the transmitted active power, and also to independently exchange reactive power with transmissions systems. Therefore, VSC-HVdcs with a suitable control scheme can offer an alternative means to enhance transient stability, to improve power oscillations damping, and to provide voltage support. An interesting application of this system is the analysis of a power system when a VSC-HVdc is connected in parallel with ac transmission lines.</p><p>This thesis presents the derivation of control strategies to damp power oscillations, to enhance the transient stability and to provide voltage support for a VSC-HVdc. The thesis also formulates a multichoice control strategy and its application when the VSC-HVdc is connected in a synchronous system.</p><p>The control strategy for enhancing transient stability is based on the theory of Control Lyapunov Function. The control strategy for increasing the damping is based on Linear Analysis. A very effective well known way to increase damping in the system is modulating the active power through the HVdc. However, besides the control of active power, the thesis explores an alternative way to mitigate power oscillations by controlling the reactive power. This condition might be very useful when the dc link in the VSC-HVdc system is out of service, but the converter stations are in operating conditions.</p><p>A simple model of VSC-HVdc is considered in order to test the control strategy. The model represents the VSC-HVdc as an element in the power system that provides adequate interaction with other systems elements. The model is intended for analysis of power flows and electromechanical transients. It is then sufficient to consider the power frequency components of voltages and currents represented by phasors that vary with time during transients. The model is valid for symmetrical conditions, i.e. positive sequence phasors are used for the representation of the electrical state.</p>