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Graduate

Thesis (M.S.)--University of Wisconsin--Madison, 1969. / eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Estatística, 2013. / Submitted by Albânia Cézar de Melo (albania@bce.unb.br) on 2013-11-25T13:51:34Z No. of bitstreams: 1 2013_ThiagoRegoSousa.pdf: 2413635 bytes, checksum: bc266470bb858c4d6dda709cba54743c (MD5) / Approved for entry into archive by Guimaraes Jacqueline(jacqueline.guimaraes@bce.unb.br) on 2013-11-26T13:22:51Z (GMT) No. of bitstreams: 1 2013_ThiagoRegoSousa.pdf: 2413635 bytes, checksum: bc266470bb858c4d6dda709cba54743c (MD5) / Made available in DSpace on 2013-11-26T13:22:51Z (GMT). No. of bitstreams: 1 2013_ThiagoRegoSousa.pdf: 2413635 bytes, checksum: bc266470bb858c4d6dda709cba54743c (MD5) / Neste trabalho estendemos a aplicação do modelo combinado AR-GARCH governado por distribuições GEV e apresentado por Zhao et. al. (2011) para um modelo governado por distribuições estáveis, já que estas distribuições podem ser utilizadas para modelar dados de finanças, incluindo os eventos extremos. Além de estimação pelo método Bayesiano explorada por Zhao et. al. (2011), estimamos ambos os modelos também com o método clássico da máxima verossimilhança. Posteriormente investigamos as condições de estacionariedade de um modelo ARMA-power-GARCH com inovações estáveis proposto por Rachev et. al. (2002) e estendemos este modelo derivando as condições de estacionariedade para um modelo assimétrico ARMA-APARCH com inovações estáveis. Esta última generalização nos permitiu implementar uma rotina numérica de estimação de modelos ARMA-APARCH que, ao contrário da conhecida rotina fGARCH apresentada por Wurtz et. al. (2006) estima modelos ARMA-APARCH com distribuição condicional GEV ou estável. ______________________________________________________________________________ ABSTRACT / We extend the application of the GEV-GARCH model given by Zhao et al. (2011) to a model driven by stable distibuitons as they share some similarities in modelling nancial data, including extreme events. We perform both Maximum likelihood and Bayesian estimation of these models. Thereafter, we investigate the stationarity conditions of the ARMA-power-GARCH model with stable innovations proposed by Rachev et. al. (2002) and prove the stationarity conditions for the assymetric model ARMA-APARCH with stable innovations. The last result allowed us to construct a numerical routine to estimate the paramters of an ARMA-APARCH model following stable and GEV distributions.

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

Lyapunov functions are applied to the power system studies. Three types of power system problems are investigated, namely, the determination of asymptotic stability regions of a nonlinear power system for fault and switching transient stability studies, the systematic optimum parameter setting of power system controllers, and the determination of linear and nonlinear optimum stabilising signals as functions of state variables for both nonlinear and linearized power systems. To investigate and construct the transient stability region of a synchronous machine connected to infinite bus through a transmission system after fault and switching, high degree Lyapunov function series generated by Zubov's method is applied. For the optimum parameter setting of a power system, a computation technique based on the method of gradient has been developed to adjust the system parameters simultaneously so as to minimise a system performance function which is evaluated from a Lyapunov function of the second degree. For the computation of the second degree Lyapunov function a method based on the concept of similarity transformation has been developed and applied so that the simultaneous solution of a large number of algebraic equations can be avoided. To determine the optimum stabilizing signals for a power system, the concept of the Lyapunov function of the optimum system is applied. To compute the Lyapunov function of the optimum nonlinear power system, a general iterative scheme and algorithm have been developed. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

In this thesis Liapunov's direct method is applied to transient stability study of power systems. Szego's method is applied to a second order power system in chapter two and a quadratic Liapunov function applied to the same system in chapter three. The hypervolume enclosed by the quadratic V-function is maximized. Changes in the time derivative of the quadratic V function are then made to meet the conditions of Liapunov V and V functions. Finally a maximized modified Liapunov function is constructed from a tentative quadratic function for a three-machine system. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

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Increased attention has been paid in recent years to the means in which the body maintains stability and the subtleties of the neurocontroller. Variability of kinematic data has been used as a measure of stability but these analyses are not appropriate for quantifying stability of dynamic systems. Response of biological control systems depend on both temporal and spatial inputs, so means of quantifying stability should account for both. These studies utilized tools developed for the analysis of deterministic chaos to quantify local dynamic stability of musculoskeletal systems. The initial study aimed to answer the oft assumed conjecture that reduced gait speeds in people with neuromuscular impairments lead to improved stability. Healthy subjects walked on a motorized treadmill at an array of speeds ranging from slow to fast while kinematic joint angle data were recorded. Significant (p < 0.001) trends showed that stability monotonically decreased with increasing walking speeds. A second study was performed to investigate dynamic stability of the trunk. Healthy subjects went through a variety of motions exhibiting either symmetric flexion in the sagittal plane or asymmetric flexion including twisting at both low and high cycle frequencies. Faster cycle frequencies led to significantly (p<0.001) greater instability than slower frequencies. Motions that were hybrids of flexion and rotation were significantly (p<0.001) more stable than motions of pure rotation or flexion. Finding means of increasing dynamic stability may provide great understanding of the neurocontroller as well as decrease instances of injury related to repetitive tasks. Future studies should look in greater detail at the relationships between dynamic instability and injury and between local dynamic stability and global dynamic stability. / Master of Science