Academic literature on the topic 'Power systems stability'

The electric power systems in U.S. Navy ships supply energy to sophisticated systems for weapons, communications, navigation and operation. The reliability and survivability of a Shipboard Power System (SPS) are critical to the mission of a Navy ship, especially under battle conditions. When a weapon hits the ship in the event of battle, it can cause severe damage to the electrical systems on the ship. Researchers in the Power System Automation Laboratory (PSAL) at Texas A&M University have developed methods for performing reconfiguration of SPS before or after a weapon hit to reduce the damage to SPS. Reconfiguration operations change the topology of an SPS. When a system is stressed, these topology changes and induced dynamics of equipment due to reconfiguration might cause voltage instability, such as progressive voltage decreases or voltage oscillations. SPS stability thus should be assessed to ensure the stable operation of a system during reconfiguration. In this dissertation, time frames of SPS dynamics are presented. Stability problems during SPS reconfiguration are classified as long-term stability problems. Since angle stability is strongly maintained in SPS, voltage stability is studied in this dissertation for SPS stability during reconfiguration. A test SPS computer model, whose simulation results were used for stability studies, is presented in this dissertation. The model used a new generalized methodology for modeling and simulating ungrounded stiffly grounded power systems. This dissertation presents two new indices, a static voltage stability index (SVSILji) and a dynamic voltage stability index (DVSI), for assessing the voltage stability in static and dynamic analysis. SVSILji assesses system stability by all lines in SPS. DVSI detects local bifurcations in SPS. SVSILji was found to be a better index in comparison with some indices in the literature for a study on a two-bus power system. Also, results of DVSI were similar to the results of conventional bifurcation analysis software when applied to a small power system. Using SVSILji and DVSI on the test SPS computer model, three of four factors affection voltage stability during SPS reconfiguration were verified. During reconfiguration, SVSILji and DVSI are used together to assess SPS stability.

This thesis investigates an important power system phenomenon, voltage stability, by using continuation power flow method. Voltage collapse scenario is presented which can be a serious result of voltage instability and the parameters that affect voltage collapse are discussed. In analyzing power system voltage stability, continuation power flow method is utilized which consists of successive load flows. This method is applied to a sample test system and Turkish Power System and load-voltage curves for several buses are obtained.

Supervisor : Prof. Dr. Roman Kuiava<br>Dissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica. Defesa: Curitiba, 30/08/2016<br>Inclui referências : f. 79-82<br>Área de concentração<br>Resumo: O conceito de estabilidade a tempo finito (ETF) foi criado em 1950. Sistemas dinâmicos cujas trajetórias convergem para o estado de equilíbrio em um tempo finito fazem parte desse conceito. Sistemas chaveados lineares não homogêneos também estõ sendo considerados. Esses sistemas são oriundos de muitas aplicações de controle e para casos aonde sistemas físicos não são descritos por processos unicamente contínuos ou unicamente discretos. Essa dissertação esta concentrada no problema de estabilidade a tempo finito de uma classe de sistemas chaveados lineares não homogêneos contínuos no tempo sob um sinal de chaveamento dependente do tempo seguindo um tempo de permanência T. Uma vez que a estabilidade a tempo finito é garantida, um dos principais resultados dessa dissertação garante que qualquer trajetória do sistema que comece em uma região 1 do espaço de estados, permanecera dentro de 2 _ 1 ao longo de um intervalo de tempo finito, e para qualquer sequencia de chaveamento com tempo de estabelecimento ¯ T _ T. As condições de estabilidade a tempo finito obtidas na forma de inequações matriciais bilineares (BMIs), podem ser transformadas em inequações matriciais lineares (LMIs) por uma sequência de passos que incluem o cálculo dos conjuntos 1 e 2 por meio de um conhecimento prévio dos limites de operação do sistema. Dois exemplos ilustrativos do estudo de estabilidade em sistemas de potência são utilizados para apresentar a validade dos resultados. Palavras-chave: estabilidade a tempo finito, sistemas chaveados não autônomos, inequações matriciais lineares<br>Abstract: The finite-time stability (FTS) concept was created in the 1950. Dynamical systems whose trajectories converge to an equilibrium state in finite time are involved in this concept. Switched non-homogeneous linear systems are being considered. These systems can result from many control applications and for cases where physical systems are not described by simply continuous or simply discrete processes. This dissertation is concerned with the finite-time stability problem of a class of linear continuous-time non-homogeneous switched systems under a time-dependent switching signal constrained by a dwell-time T. Once the finite-time stability is guaranteed, one of the main results of the dissertation guarantees that any system trajectory starting in a subset 1 of the state-space will remain in 2 _ 1 over a finite time interval, and, for any switching sequence with a dwell-time ¯ T _ T. The finite-time stability conditions which provided in the form of bilinear matrix inequalities (BMIs), can be transformed to linear matrix inequalities (LMIs) by means of a step-by-step procedure that includes the computation of the sets 1 and 2 by the knowledge of the system's operating range. Two illustrative examples in power system stability study are used to show the validity of the results. Keywords: finite-time stability, Non-autonomous switched systems, Linear matrix inequalities

CENTRO DE PESQUISA DE ENERGIA ELÉTRICA<br>Na medida em que as redes de transmissão de energia elétrica ficaram mais malhadas, os limites térmicos de linhas e transformadores passaram a restringir menos a transmissão de potência. Similarmente, o uso de sistemas estáticos de compensação de potência reativa e estabilizadores na excitação dos geradores aumentou a capacidade de transmissão de potência nos sistemas antes limitados por problemas de estabilidade angular. Hoje as linhas de transmissão estão mais carregadas e isto deu origem ao problema da instabilidade de tensão.Neste trabalho, as condições de estabilidade de tensão são avaliadas por condições nodais associadas ao máximo fluxo de potência ativa e reativa que pode ser transmitida dos geradores para as cargas. Estas condições nodais são avaliadas por uma ferramenta analítica com base em modelo matemático, simples mas poderoso, de uma direta interpretação física do fenômeno.Índices abrangentes e significativos são obtidos a partir da matriz Jacobiano do sistema. Eles indicam a região de operação na curva V x P, Q , a margem em MVA para o máximo carregamento, a importância relativa entre as barras, uma medida de dificuldade de transmissão, e o índice de influência que relaciona as margens de potência entre dois pontos de operação, o que caracteriza a eficácia ou não, por exemplo, de uma ação de controle. O método proposto nesta tese para reforçar as condições de estabilidade de tensão consiste de três etapas seqüenciais. Primeiramente, avalia-se as condições de estabilidade de tensão determinando-se a barra crítica da rede através do cálculo da margem de potência. Determinase o caminho de transmissão crítico, conceito novo usado neste trabalho, entre os vários existentes para transportar potência de geradores para aquela barra crítica. Determina-se então o ramo crítico deste caminho, conceito introduzido neste trabalho. Um programa de fluxo de potência ótimo é usado para aliviar o carregamento desse ramo crítico. A seqüência começa novamente com a avaliação das condições no novo ponto de operação. Todas as etapas são repetidas até que as margens resultantes sejam julgadas adequadas.Barras de carga, de geração e de tensão controlada por compensadores de potência reativa em paralelo com a rede podem ser eleitas como a barra crítica. Somente o método de avaliação nodal usado é capaz de lidar com qualquer tipo de barra. Da mesma forma, o procedimento proposto para reforçar as condições de estabilidade de tensão é adequado para qualquer tipo de barra.São mostrados inúmeros testes, tanto ilustrativos como com sistemas reais, em pontos de operação também reais, inclusive na situação de iminente colapso de tensão. Verifica-se que o método proposto realmente produz os resultados desejados.<br>As the electric power transmission networks became more interconnected, the thermal limits of lines and transformers restrict less the power transmission. Similarly, the use of static systems of reactive power compensation increases the power transmission capacity in systems whereas before they were limited by problems of angular stability. Actually, transmission lines are more loaded and create the voltage stability problem. In this work, voltage stability conditions are assessment by nodal conditions associated to the maximum active and reactive power flow that can be transmitted from generators to loads.These nodal conditions are assessment using an analytical tool, based on a simple but sound mathematical background, modelling a straightforward physical haracterisation of the phenomena. Comprehensive and meaningful indices are obtained from system Jacobean matrix. They indices indicate the operating region in V x P,Q curve, the MVA margin to the maximum load, the relative importance among buses, the buses loading ranking, a measure of difficult for power transmission, and the influence indices that relates power margins between two operating points, which characterises efficiency or not, for example, of a control action.In order to reinforce voltage stability condition, the thesis proposes a method consisting of three sequential stages. Firstly, voltage stability is analysed, deciding network critical bus using the power margin calculation. Next, the critical transmission path is decided, which is a new concept used in this work, in between several existing used to transport generators power for that critical bus. Then, critical branch is obtained through this path, concept introduced in this work. An optimal power flow program is used to alleviate load flow in the critical branch. The sequence starts again with the stability condition assessment in the new operating point. All stages are repeated until resultant margins are judged suitable. Load, generation and voltage-controlled bus by shunt reactive power compensators could be considered critical bus. The nodal method used is the only one capable of handling any bus type.Several cases are shown, illustrative as well as real systems using real operating points,including imminent voltage collapse situations. It is verified that the proposed method really produces the desired results.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.<br>Cataloged from PDF version of thesis. "Due to the condition of the original material, there are unavoidable flaws in this reproduction. Some pages in the original document contain text that is illegible"--Disclaimer Notice page.<br>Includes bibliographical references (pages 119-128).<br>Loss of stability in electrical power systems may eventually lead to blackouts which, despite being rare, are extremely costly. However, ensuring system stability is a non-trivial task for several reasons. First, power grids, by nature, are complex nonlinear dynamical systems, so assessing and maintaining system stability is challenging mainly due to the co-existence of multiple equilibria and the lack of global stability. Second, the systems are subject to various sources of uncertainties. For example, the renewable energy injections may vary depending on the weather conditions. Unfortunately, existing security assessment may not be sufficient to verify system stability in the presence of such uncertainties. This thesis focuses on new scalable approaches for robust stability assessment applicable to three main types of stability, i.e., long-term voltage, transient, and small-signal stability. In the first part of this thesis, I develop a novel computationally tractable technique for constructing Optimal Power Flow (OPF) feasibility (convex) subsets. For any inner point of the subset, the power flow problem is guaranteed to have a feasible solution which satisfies all the operational constraints considered in the corresponding OPF. This inner approximation technique is developed based on Brouwer's fixed point theorem as the existence of a solution can be verified through a self-mapping condition. The self-mapping condition along with other operational constraints are incorporated in an optimization problem to find the largest feasible subsets. Such an optimization problem is nonlinear, but any feasible solution will correspond to a valid OPF feasibility estimation. Simulation results tested on several IEEE test cases up to 300 buses show that the estimation covers a substantial fraction of the true feasible set. Next, I introduce another inner approximation technique for estimating an attraction domain of a post-fault equilibrium based on contraction analysis. In particular, I construct a contraction region where the initial conditions are "forgotten", i.e., all trajectories starting from inside this region will exponentially converge to each other. An attraction basin is constructed by inscribing the largest ball in the contraction region. To verify contraction of a Differential-Algebraic Equation (DAE) system, I also show that one can rely on the analysis of extended virtual systems which are reducible to the original one. Moreover, the Jacobians of the synthetic systems can always be expressed in a linear form of state variables because any polynomial system has a quadratic representation. This makes the synthetic system analysis more appropriate for contraction region estimation in a large scale. In the final part of the thesis, I focus on small-signal stability assessment under load dynamic uncertainties. After introducing a generic impedance-based load model which can capture the uncertainty, I propose a new robust small signal (RSS) stability criterion. Semidefinite programming is used to find a structured Lyapunov matrix, and if it exists, the system is provably RSS stable. An important application of the criterion is to characterize operating regions which are safe from Hopf bifurcations. The robust stability assessment techniques developed in this thesis primarily address the needs of a system operator in electrical power systems. The results, however, can be naturally extended to other nonlinear dynamical systems that arise in different fields such as biology, biomedicine, economics, neuron networks, and optimization. As the robust assessment is based on sufficient conditions for stability, there is still room for development on reducing the inevitable conservatism. For example, for OPF feasibility region estimation, an important open question considers what tighter bounds on the nonlinear residual terms one can use instead of box type bounds. Also, for attraction basin problem, finding the optimal norms and metrics which result in the largest contraction domain is an interesting potential research question.<br>by Hung Dinh Nguyen.<br>Ph. D.

Power systems are extremely non-linear systems which require substantial modeling and control efforts to run continuously. The movement of the power system in parameter and state space is often not well understood, thus making it difficult or impossible to determine whether the system is nearing instability. This dissertation demonstrates several ways in which the power system stability boundary can be calculated. The power system movements evaluated here address the effects of inter-area oscillations on the system which occur in the seconds to minutes time period. The first uses gain scheduling techniques through creation of a set of linear parameter varying (LPV) systems for many operating points of the non-linear system. In the case presented, load and line reactance are used as parameters. The scheduling variables are the power flows in tie lines of the system due to the useful information they provide about the power system state in addition to being available for measurement. A linear controller is developed for the LPV model using H₂/H∞ with pole placement objectives. When the control is applied to the non-linear system, the proposed algorithm predicts the response of the non-linear system to the control by determining if the current system state is located within the domain of attraction of the equilibrium. If the stability domain contains a convex combination of the two points, the control will aid the system in moving towards the equilibrium. The second contribution of this thesis is through the development and implementation of a pseudo non-linear evaluation of a power system as it moves through state space. A system linearization occurs first to compute a multi-objective state space controller. For each contingency definition, many variations of the power system example are created and assigned to the particular contingency class. The powerflow variations and contingency controls are combined to run sets of time series analysis in which the Lyapunov function is tracked over three time steps. This data is utilized for a classification analysis which identifies and classifies the data by the contingency type. The goal is that whenever a new event occurs on the system, real time data can be fed into the trained tree to provide a control for application to increase system damping.<br>Ph. D.

Power electronics is the enabling technology that can put transportation on a more sustainable pathway. The key problem with power electronic (PE) systems is that they are prone to instability. Classical techniques are insufficient at assessing the stability of these systems, as they do not take into account the uncertain nature of physical systems. This thesis presents the structured singular value (SSV) method as an effective, reliable and robust stability analysis approach that justifiably incorporates uncertainties which are inherently present in physical systems. Although the SSV approach has numerous benefits, it has a few drawbacks that tend to make it hard to apply. Its theoretical framework remains complex. The practical approaches to applying the SSV method to PE systems seem lacking in the literature. The SSV approach is generally applied to linear system models while most systems are non-linear in nature. This thesis demonstrates the applicability of the SSV method to PE systems, by addressing these limitations. The work first brings deeper and clearer insights into key concepts of SSV theory. It demonstrates the significance and usefulness of the robust stability measure (SSV) in the space of multiple parametric uncertainties, through the concept of the hypercube. Secondly, it presents several practical approaches to applying the SSV method to PE systems. Finally, it develops a modelling methodology that converts a non-linear system to an equivalent linear model, suited for SSV analysis. The findings are supported by simulation and experimental results of the buck converter, permanent magnet machine drive, ideal constant power load and resistance-inductance-capacitance systems. This thesis provides the design engineer with some crucial theoretical and practical tools for applying the SSV approach to both linear and non-linear models of PE systems, while showing how to reap the full benefits of the method. It is the author's belief that the SSV method can be used as widely as classical methods, and to great effect.