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.

[pt] A metodologia empregada para o cálculo de equivalentes dinâmicos apresenta três etapas essenciais: a identificação de geradores coerentes, a redução estática da rede e a agregação dinâmica dos modelos das unidades geradoras coerentes. Dentre essas etapas, a última é a que menos tem sido tratada, e que vem requerendo maior desenvolvimento. Esta dissertação trata do problema da agregação dinâmica de modelos de sistemas de excitação de geradores coerentes, visando o cálculo de equivalentes dinâmicos para estudos de estabilidade transitória de sistemas de energia elétrica. O principal objetivo é a determinação de um critério de escolha do melhor modelo equivalente para uma dada composição de modelos de sistemas de excitação num grupo de geradores coerentes. Os parâmetros dos modelos equivalentes dos sistemas de excitação dos grupos de unidades geradoras coerentes são ajustados numericamente a partir das respostas em frequência dos modelos individuais de cada grupo, utilizando-se o método de Levenberg-Marquardt, o que caracteriza um problema de otimização multivariável. Os desempenhos dinâmicos dos equivalentes propostos são avaliados em um sistema teste. / [en] The methodology used to calculate dynamic equivalents has three basic steps: the identification of the coherent groups of generating units, the network reduction and the dynamic aggregation of coherent generator models. Among these steps, the last one has not been studied lately and deserves more development. This disseration deals with the problem of dynamic aggregation of excitaion system models to calculate coherency-based dynamic equivalents for power system transient stability studies. The main objective is the determination of a criteria to choose the best equivalent model for a given composition of excitation system models in a group of coherent generators. The parameters of the excitation system equivalent model for cach group of coherent generating units are numerically adjusted to match the frequency response of the individual models. This is a multivariable otmization problem, which is solved using the Levenberg-Marquardt method. The dynamic performance of the proposed equivalents is evaluated in a test system.

Les systèmes électriques évoluent actuellement vers l'intégration d'une production moins carbonée, éventuellement plus locale. Afin d’explorer les évolutions possibles de ces systèmes sur le long terme, l’exercice prospectif s’appuyant sur des modèles est un outil précieux. Cependant, pour être pertinent, il doit réconcilier des phénomènes spatiaux et temporels à des échelles variées. Ainsi, le fonctionnement du système électrique repose sur un équilibre offre – demande à chaque instant. Afin de corriger les fluctuations de la production ou de la consommation qui surviennent nécessairement, les gestionnaires de réseau mettent en place un certain nombre de régulations dont les durées d’activation sont de l’ordre de quelques secondes à quelques heures. A des échelles de temps encore plus fines le système électrique présente une robustesse interne : le réseau électrique créé un couplage électromagnétique entre les machines synchrones qui leur permet de mutualiser leur inertie respective. Cette inertie, qui constitue une réserve d’énergie cinétique, est instantanément disponible pour faire face aux fluctuations. Pour que les scénarios de long terme proposés ne soient pas en contradiction avec les exigences de robustesse du système électrique, qui permettront son opération, il est nécessaire que l’évaluation de cette robustesse soit intégrée à la modélisation prospective. Dans ce travail, nous proposons un indicateur, calculable au sein des études de prospective, qui évalue la stabilité d’un système électrique, c’est- à-dire son aptitude à revenir au synchronisme suite à une perturbation. Cet indicateur repose sur une description agrégée du réseau de transport et traduit le couplage électromagnétique apporté par le réseau. Associé au modèle bottom-up de la famille MARKAL/TIMES décrivant le système électrique français, cet indicateur de synchronisme et un indicateur quantifiant la réserve cinétique disponible, nous permet d’évaluer les conséquences de la pénétration du renouvelable, notamment sur la robustesse du système électrique. / Power systems are currently facing several issues in order to evolve and integrate less carbon-heavy, and potentially more local, production. Prospective model-based analysis is a precious tool for exploring the possible long-term developments of these systems and comparing their advantages and disadvantages. However, to ensure relevance, it is important to reconcile the spatial and temporal phenomena that occur at various scales. Power system management depends on constantly maintaining a complex supply- demand balance. Meeting this challenge requires anticipating demand variations and power plant availability, combined with regulation systems to resolve remaining discrepancies. These regulations are activated in from a few seconds up to several hours. On shorter timescales, power systems show inherent robustness: the power grid creates an electromagnetic coupling between synchronous machines allowing them to share their inertia. This inertia, which takes the form of kinetic energy, is instantaneously available to face natural demand or supply fluctuations. To ensure that proposed long-term scenarios are consistent with the robustness requirements of power systems, which enable their management, this robustness must be assessed using prospective modeling. In this work, we propose an indicator, calculable within prospective studies, which assesses power system stability, namely its ability to return to synchronism after a perturbation. This indicator is based on an aggregated description of the transportation power grid and describes the electromagnetic coupling brought by the power grid. When combined with a bottom-up model from the MARKAL/TIMES family describing the French power system, this synchronism indicator, along with another indicator quantifying the available kinetic reserve, enables us to assess the consequences of renewable penetration, especially in terms of power system robustness.

O presente trabalho tem como objetivo desenvolver um programa computacional para análise de contingências, no contexto da estabilidade transitória, capaz de identificar as contingências críticas do sistema elétrico de potência via métodos diretos. A análise de estabilidade é realizada em diversas etapas, onde serão aplicados diversos filtros, baseados em métodos de análise de ilhamento, não existência de pontos de equilíbrio, PEBS, BCU e simulação computacional, no domínio do tempo, do sistema. Em cada etapa da análise, os casos serão classificadas como sendo estáveis, instáveis ou incertos segundo diferentes critérios, restando portanto, ao fim de cada etapa, um conjunto menor de possíveis contingências críticas. A metodologia proposta foi desenvolvida para modelos de SEPs com rede reduzida, porém as técnicas discutidas neste trabalho aplicam-se também a modelos que preservam a estrutura do sistema de transmissão. / The main objective of this work is to design a transient stability screening contingency program that is able to identify all critical contingencies in an electric power system using direct methods. The stability assessment is performed through several steps by mean of filters based on islanding detection, nonexistence of equilibrium points, PEBS, BCU and time-domain simulation of the power system. In each step of the analysis, all cases are classified as stable, unstable or uncertain cases by different criteria, resulting at the end of each step in a small number of possible critical contingencies. The proposed methodology was designed for reduced models of electric power systems, but all the techniques discussed in this work are also suitable for preserving structure models.

O presente trabalho tem como objetivo desenvolver um programa computacional para análise de contingências, no contexto da estabilidade transitória, capaz de identificar as contingências críticas do sistema elétrico de potência via métodos diretos. A análise de estabilidade é realizada em diversas etapas, onde serão aplicados diversos filtros, baseados em métodos de análise de ilhamento, não existência de pontos de equilíbrio, PEBS, BCU e simulação computacional, no domínio do tempo, do sistema. Em cada etapa da análise, os casos serão classificadas como sendo estáveis, instáveis ou incertos segundo diferentes critérios, restando portanto, ao fim de cada etapa, um conjunto menor de possíveis contingências críticas. A metodologia proposta foi desenvolvida para modelos de SEPs com rede reduzida, porém as técnicas discutidas neste trabalho aplicam-se também a modelos que preservam a estrutura do sistema de transmissão. / The main objective of this work is to design a transient stability screening contingency program that is able to identify all critical contingencies in an electric power system using direct methods. The stability assessment is performed through several steps by mean of filters based on islanding detection, nonexistence of equilibrium points, PEBS, BCU and time-domain simulation of the power system. In each step of the analysis, all cases are classified as stable, unstable or uncertain cases by different criteria, resulting at the end of each step in a small number of possible critical contingencies. The proposed methodology was designed for reduced models of electric power systems, but all the techniques discussed in this work are also suitable for preserving structure models.

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.

This thesis introduces a new modeling approach that allows very large power systems to be modeled on a real time electro-magnetic transients (EMT) digital simulator with reduced hardware costs. The key step in achieving this is the development of an improved wide-band multi-port equivalent, which reduces a large power network into a small manageable equivalent model that preserves wideband behaviors. This approach has a foundation method that use a two part equivalent in which the high frequency behavior of the equivalenced network is represented by a terminating frequency dependent network equivalent (FDNE), with the low frequency behavior being modeled using a detailed Transient Stability Analysis (TSA) model that only models the electromechanical behavior. This approach allowed the modelling of medium size electric regions up to hundreds of buses in real time. This thesis extends the equivalent by implementing a reduced order of the detailed electromechanical TSA equivalent mentioned above. Coherency based reduction is used for the electromechanical model of the power network to be equivalenced, and is implemented as a Transient Stability Analysis (TSA) type electromechanical equivalent. A challenge in implementing the FDNE is to ensure that it is a passive network, as otherwise its inclusion could lead to unstable simulation. This thesis also introduces a practical procedure to enforce passivity in the FDNE. The validity of the proposed technique is demonstrated by comparing the approach with detailed electromagnetic simulations of the well-known 39 bus New England system and a modified 39 bus system with an HVDC infeed with coupling between the dc line and an adjacent ac line, in addition to a 108 bus ac system. The power of the method is demonstrated by the real-time simulation of a large system with 2300 busses and 139 generators. It has been shown that this approach has the potential to increase by at least one order of magnitude the size of the network that can be modeled and thus on a real time electro-magnetic transients (EMT) digital simulator with reduced hardware costs.

This thesis introduces a new modeling approach that allows very large power systems to be modeled on a real time electro-magnetic transients (EMT) digital simulator with reduced hardware costs. The key step in achieving this is the development of an improved wide-band multi-port equivalent, which reduces a large power network into a small manageable equivalent model that preserves wideband behaviors. This approach has a foundation method that use a two part equivalent in which the high frequency behavior of the equivalenced network is represented by a terminating frequency dependent network equivalent (FDNE), with the low frequency behavior being modeled using a detailed Transient Stability Analysis (TSA) model that only models the electromechanical behavior. This approach allowed the modelling of medium size electric regions up to hundreds of buses in real time. This thesis extends the equivalent by implementing a reduced order of the detailed electromechanical TSA equivalent mentioned above. Coherency based reduction is used for the electromechanical model of the power network to be equivalenced, and is implemented as a Transient Stability Analysis (TSA) type electromechanical equivalent. A challenge in implementing the FDNE is to ensure that it is a passive network, as otherwise its inclusion could lead to unstable simulation. This thesis also introduces a practical procedure to enforce passivity in the FDNE. The validity of the proposed technique is demonstrated by comparing the approach with detailed electromagnetic simulations of the well-known 39 bus New England system and a modified 39 bus system with an HVDC infeed with coupling between the dc line and an adjacent ac line, in addition to a 108 bus ac system. The power of the method is demonstrated by the real-time simulation of a large system with 2300 busses and 139 generators. It has been shown that this approach has the potential to increase by at least one order of magnitude the size of the network that can be modeled and thus on a real time electro-magnetic transients (EMT) digital simulator with reduced hardware costs.

Η παρούσα διπλωματική εργασία έχει ως στόχο την αντιμετώπιση των ηλεκτρομηχανικών ταλαντώσεων οι οποίες εμφανίζονται σε μία σύγχρονη γεννήτρια παραγωγής Ηλεκτρικής Ενέργειας μετά από διαταραχές. Ο συμβατικός έλεγχος για τη διατήρηση της μηχανής σε συγχρονισμό μετά από ξαφνικές αλλαγές φορτίου, βραχυκυκλωμάτων, κλείσιμο διακοπτών ή οποιασδήποτε κατάστασης που μπορεί να προκαλέσει αστάθεια στο Σύστημα της Ηλεκτρικής Ενέργειας, γίνεται με χρήση ελεγκτικών διατάξεων Σταθεροποιητών Συστημάτων Ισχύος σε συνδυασμό με τον Αυτόματο Ρυθμιστή Τάσης (ΑΡΤ/ΣΣΙ). Σκοπός της εργασίας αυτής είναι να σχεδιαστούν και να ρυθμιστούν κατάλληλα οι διατάξεις αυτές, ώστε να εξασφαλίζεται η απόσβεση των ηλεκτρομηχανικών ταλαντώσεων που εμφανίζονται ανάμεσα στην γεννήτρια και το υπόλοιπο σύστημα. Στην εργασία αυτή, αρχικά γίνεται μια εισαγωγή στα είδη των ηλεκτρομηχανικών ταλαντώσεων και την ευστάθεια για δυναμικά Συστήματα Ηλεκτρικής Ενέργειας. Στη συνέχεια αναπτύσσεται το δυναμικό μοντέλο ενός απλού συστήματος μιας γεννήτριας άπειρου ζυγού βασισμένο στο απλοποιημένο μοντέλο 4ης τάξης της σύγχρονης μηχανής. Επειδή το μοντέλο αυτό είναι μη γραμμικό προχωράμε στην εξαγωγή του γραμμικοποιημένου μοντέλου που θα μας βοηθήσει για τον σχεδιασμό του κατάλληλου ελεγκτή. Αξιοποιώντας ιδιότητες του μοντέλου παρουσιάζεται μια συστηματική μέθοδος σχεδίασης του Σταθεροποιητή Συστήματος Ισχύος που είναι βασισμένη στη λογική των ολοκληρωτικών υπολοίπων. Τέλος με τη βοήθεια του λογισμικού SIMULINK του MATLAB προσομοιώνεται το σύστημα σύγχρονης γεννήτριας συνδεδεμένης σε άπειρο ζυγό, που ελέγχεται με την χρήση του Αυτόματου Ρυθμιστή Τάσης και του Σταθεροποιητή Συστήματος Ισχύος σε κατάσταση τυπικής φόρτισης. Εφαρμόζοντας διαταραχές στο σύστημα παρατηρείται η απόκριση του συστήματος και εκτιμάται η λειτουργία του ελεγκτή. / This thesis aims to address the electromechanical oscillations which appear in a synchronous generator after disturbances. The conventional control for maintaining the machine synchronized after sudden load changes, short circuits, switching or any condition which may cause instability phenomena, is achieved by the use of control circuits such as Power System Stabilizers combined with the Automatic Voltage Regulator ( PSS / AVR). The purpose of this work is to design and configure properly these control circuits to ensure the reduction of electromechanical oscillations that occur between the generator and the rest of the system. In the beginning this thesis, an introduction of the types of power system electromechanical oscillations and stability is being discussed. Afterwards, the dynamic model of a simple system of a generator infinite-bus based on simplified 4th order of synchronous machine is being developed. Due to the model nonlinearities, we export the linearized model which helps us to design a suitable controller. Taking into account the model properties, we provide a systematic method for designing a Power System Stabilizer based on the residues method. Finally, using the MATLAB-SIMULINK software, the synchronous generator infinite-bus system is simulated which is controlled by an Automatic Voltage Regulator and a Power System Stabilizer. After applying disturbances, the system response is driven and analyzed along with the controller functioning.

A conexão de geradores em sistemas de distribuição, usualmente chamados de geradores distribuídos, traz novos aspectos técnicos que devem ser analisados pelas empresas distribuidoras, uma vez que os dispositivos de proteção e controle, bem como as técnicas de planejamento e otimização da operação destes sistemas consideram um sistema radial, ou seja, sem a presença de geradores. Em se tratando de geradores síncronos, sabe-se que os sistemas de excitação podem ser equipados com meios para o ajuste automático de tensão, potência reativa ou fator de potência, sendo que três diferentes modos de controle podem ser aplicados a geradores síncronos: regulação de tensão, regulação de potência reativa ou fator de potência e controle de potência reativa ou fator de potência. Ainda, sabe-se que não há um consenso entre as empresas distribuidoras de energia sobre qual o melhor modo de controle destas máquinas, e na maioria dos casos a estratégia de controle de excitação é definida através de um acordo operativo entre a empresa de distribuição de energia e o produtor independente ou autoprodutor que opera o gerador distribuído. Neste contexto, esta dissertação de mestrado tem como objetivo apresentar contribuições com relação à avaliação da estabilidade transitória de geradores síncronos conectados em sistemas de distribuição, avaliando o impacto que os diferentes modos de controle de excitação podem ocasionar, em diferentes condições de operação do sistema. Como parâmetro principal de análise tem-se o tempo crítico de eliminação de falta, obtido através de exaustivas simulações dinâmicas utilizando dados de um sistema real e considerando diferentes condições de operação do sistema, sendo estas: diferentes modos de controle da geração distribuída, modificação do ganho proporcional do controlador de fator de potência, diferentes pontos de operação da geração distribuída, diferentes cenários de carregamento do sistema e diferentes potências de geração. / The connection of generators in distribution systems, commonly called distributed generation, brings new technical issues that must be analyzed by the utilities, since protection and control devices, as well as techniques for system planning and operation optimizing consider radial systems, i.e. without the presence of generators. In the case of synchronous generators, it is known that the excitation systems can be equipped with means for automatic adjustment of voltage, reactive power or power factor, and three different control modes can be applied to synchronous generators: voltage regulation, reactive power or power factor regulation and reactive power or power factor control. It is also known that there is no consensus among the power distribution companies about which is the best control mode for use in these machines, and in most cases the excitation control strategy is defined by an operating agreement between the company and the energy producer that operates the distributed generator. In this context, this work aims to provide contributions about the transient stability of synchronous generators connected to distribution systems, evaluating the impacts that different control modes may result in different system operating conditions. The main analysis parameter is the critical clearing fault time, obtained through extensive simulations using real system data. The different system operating conditions considered in the simulations are: different control modes, variation of the power factor controller proportional gain, different operating points of the distributed generation, different system loadings and power generation.