On présente une nouvelle approche de simulation pour la fonction de densité conjointe du surplus avant la ruine et du déficit au moment de la ruine, pour des modèles de risque déterminés par des subordinateurs de Lévy. Cette approche s'inspire de la décomposition "Ladder height" pour la probabilité de ruine dans le Modèle Classique. Ce modèle, déterminé par un processus de Poisson composé, est un cas particulier du modèle plus général déterminé par un subordinateur, pour lequel la décomposition "Ladder height" de la probabilité de ruine s'applique aussi. La Fonction de Pénalité Escomptée, encore appelée Fonction Gerber-Shiu (Fonction GS), a apporté une approche unificatrice dans l'étude des quantités liées à l'événement de la ruine été introduite. La probabilité de ruine et la fonction de densité conjointe du surplus avant la ruine et du déficit au moment de la ruine sont des cas particuliers de la Fonction GS. On retrouve, dans la littérature, des expressions pour exprimer ces deux quantités, mais elles sont difficilement exploitables de par leurs formes de séries infinies de convolutions sans formes analytiques fermées. Cependant, puisqu'elles sont dérivées de la Fonction GS, les expressions pour les deux quantités partagent une certaine ressemblance qui nous permet de nous inspirer de la décomposition "Ladder height" de la probabilité de ruine pour dériver une approche de simulation pour cette fonction de densité conjointe. On présente une introduction détaillée des modèles de risque que nous étudions dans ce mémoire et pour lesquels il est possible de réaliser la simulation. Afin de motiver ce travail, on introduit brièvement le vaste domaine des mesures de risque, afin d'en calculer quelques unes pour ces modèles de risque. Ce travail contribue à une meilleure compréhension du comportement des modèles de risques déterminés par des subordinateurs face à l'éventualité de la ruine, puisqu'il apporte un point de vue numérique absent de la littérature. / We discuss a simulation approach for the joint density function of the surplus prior to ruin and deficit at ruin for risk models driven by Lévy subordinators. This approach is inspired by the Ladder Height decomposition for the probability of ruin of such models. The Classical Risk Model driven by a Compound Poisson process is a particular case of this more generalized one. The Expected Discounted Penalty Function, also referred to as the Gerber-Shiu Function (GS Function), was introduced as a unifying approach to deal with different quantities related to the event of ruin. The probability of ruin and the joint density function of surplus prior to ruin and deficit at ruin are particular cases of this function. Expressions for those two quantities have been derived from the GS Function, but those are not easily evaluated nor handled as they are infinite series of convolutions with no analytical closed form. However they share a similar structure, thus allowing to use the Ladder Height decomposition of the Probability of Ruin as a guiding method to generate simulated values for this joint density function. We present an introduction to risk models driven by subordinators, and describe those models for which it is possible to process the simulation. To motivate this work, we also present an application for this distribution, in order to calculate different risk measures for those risk models. An brief introduction to the vast field of Risk Measures is conducted where we present selected measures calculated in this empirical study. This work contributes to better understanding the behavior of subordinators driven risk models, as it offers a numerical point of view, which is absent in the literature.

Este projeto de pesquisa propõe desenvolver um novo modelo e uma nova abordagem para a resolução do problema da otimização Volt/VAr em redes de distribuição de energia elétrica. A otimização Volt/VAr consiste em, basicamente, determinar os ajustes das variáveis de controle tais como bancos de capacitores chaveados, transformadores com comutação de tap sob carga e reguladores de tensão, de modo a satisfazer, simultaneamente, as restrições de carga e de operação para um dado objetivo operacional. Esse problema, matematicamente, foi formulado como um problema de programação não linear, multiperíodo, e com variáveis contínuas e discretas. Algoritmos de programação não linear foram utilizados com o intuito de aproveitar as vantagens das matrizes altamente esparsas montadas ao longo do método de solução. Para utilizar tais algoritmos, as variáveis discretas são tratadas como contínuas por meio da utilização de funções senoidais que penalizam a função objetivo do problema original enquanto estas não convergirem para algum dos pontos pré-definidos no seu domínio. O caráter multiperíodo do problema, contudo, refere-se à consideração de uma restrição que relaciona os ajustes das variáveis de controle para sucessivos intervalos de tempo na medida em que limita o número de operações de chaveamento desses dispositivos para um período de 24-horas. O estudo fundamenta-se, metodologicamente, em métodos do tipo Primal-Dual Barreira-Logarítmica. Para demonstrar a eficiência do modelo proposto e a robustez dessa abordagem, a partir de dados teóricos obtidos de levantamentos bibliográficos, testes foram realizados em sistemas-teste de 10, 69 e 135 barras, e em um sistema de 442 barras do noroeste do Reino Unido. As implementações computacionais foram feitas nos softwares MATLAB, AIMMS e GAMS, utilizando o solver IPOPT como método de solução. Os resultados mostram que a abordagem proposta para a resolução do problema de programação não linear é eficaz para tratar adequadamente todas as variáveis presentes em problemas de otimização Volt/VAr. / This work proposes a new model and a new approach for solving the Volt / VAr optimization problem in distribution systems. The Volt/VAr optimization consists, basically, to determine the settings of the control variables of switched capacitor banks, on-load tap changer transformers and voltage regulators, in order to satisfy both the load and operational constraints, to a given operational objective. The problem is formulated as a nonlinear programming problem, multiperiod, and with continuous and discrete variables. Nonlinear programming algorithms were used in order to take advantage of the highly sparse matrices built along the solution method. The discrete variables are treated as continuous along the solution method by means of the use of sinusoidal functions that penalize the original objective function while the control variables do not converge to any of the predefined discrete points in its domain. The multiperiod, or dynamic, characteristic of the problem, however, refers to the use of a constraint that relates the settings of the control variables for successive time intervals that limits the control devices switching operations number for a period of 24-hours. The study is based, methodologically, on Primal-Dual Logarithmic Barrier method. To demonstrate the effectiveness of the proposed model and the robustness of this approach, the data were obtained from theoretical literature surveys, and tests were performed on test-systems of 10, 69 and 135 buses, and in a 442 buses located in the Northwest of the United Kingdom. The computational implementation was accomplished in the softwares MATLAB, AIMMS and GAMS, using the IPOPT solver as solution method. The results have shown the approach for solving nonlinear programming problems is effective to appropriate cope with all the variables presented in Volt/VAr optimization problems.

Submitted by Marina Teixeira Costa null (marinateixeiracosta@gmail.com) on 2017-02-14T14:27:15Z No. of bitstreams: 1 Dissertação MARINA 12.pdf: 1807218 bytes, checksum: 95bc28b832360cf51847512b47b234d8 (MD5) / Approved for entry into archive by LUIZA DE MENEZES ROMANETTO (luizamenezes@reitoria.unesp.br) on 2017-02-14T15:29:56Z (GMT) No. of bitstreams: 1 costa_mt_me_bauru.pdf: 1807218 bytes, checksum: 95bc28b832360cf51847512b47b234d8 (MD5) / Made available in DSpace on 2017-02-14T15:29:56Z (GMT). No. of bitstreams: 1 costa_mt_me_bauru.pdf: 1807218 bytes, checksum: 95bc28b832360cf51847512b47b234d8 (MD5) Previous issue date: 2016-12-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O problema de Fluxo de Potência Ótimo determina a melhor condição de operação de um sistema elétrico de potência. Há diferentes classes de problemas de Fluxo de Potência Ótimo de acordo com os tipos de funções a serem otimizadas, e os conjuntos de controles e de restrições utilizados. Dentre elas, dá-se destaque ao problema de Fluxo de Potência Ótimo com Restrição de Segurança, o qual é uma importante ferramenta para os Operadores dos Sistemas de Transmissão, tanto para o planejamento operacional, quanto para a precificação da energia. Seu objetivo é minimizar os custos operacionais de geração de energia levando em consideração as restrições decorrentes da operação do sistema sob um conjunto de contingências. Ele é formulado como um problema de otimização não linear, não-convexo de grande porte, com variáveis contínuas e discretas. Neste trabalho investiga-se este problema em relação à sua formulação, dificuldades computacionais e método de solução. Para um tratamento do problema mais próximo à realidade adotam-se alguns controles como variáveis discretas, ou seja, os taps dos transformadores. Estes são tratados através de um método que penaliza a função objetivo quando as variáveis discretas assumem valores não discretos. Desta forma, o problema não linear discreto é transformado em um problema contínuo e o método Primal-Dual Barreira Logarítmica é utilizado em sua resolução. Testes computacionais são apresentados com o problema de Fluxo de Potência Ótimo com Restrição de Segurança associado ao sistema teste IEEE 14 barras em três etapas de teste. Os resultados obtidos e as comparações realizadas comprovam a eficiência do método de resolução escolhido / The Optimum Power Flow problem determines the best operating condition of an electric power system. There are different classes of Optimal Power Flow problems according to the types of functions to be optimized, and the sets of controls and constraints used. Among them, the problem of Optimal Power Flow with Security Constraint is highlighted, which is an important tool for the Transmission System operators, both for operational planning and for energy pricing. Its objective is to minimize the operational costs of power generation taking into account the constraints arising from the operation of the system under a set of contingencies. It is formulated as a nonlinear, nonconvex large optimization problem, of continuous and discrete variables. In this work, the problem in relation to its formulation, computational difficulties and solution method is investigated. For a treatment of the problem closest to the reality, some controls such as discrete variables, i.e. the taps of the transformers, are used. These are treated by a method that penalizes the objective function when the discrete variables assume non-discrete values. Thus, the discrete nonlinear problem is transformed into a continuous problem and the Primal-Dual Logarithmic Barrier method is used in its resolution. Computational tests are performed with the optimal power flow problem with security constraint associated with the test system of IEEE 14 bars in three test stages. The obtained results and the realized comparisons prove the efficiency of the chosen resolution method.

Este projeto de pesquisa propõe desenvolver um novo modelo e uma nova abordagem para a resolução do problema da otimização Volt/VAr em redes de distribuição de energia elétrica. A otimização Volt/VAr consiste em, basicamente, determinar os ajustes das variáveis de controle tais como bancos de capacitores chaveados, transformadores com comutação de tap sob carga e reguladores de tensão, de modo a satisfazer, simultaneamente, as restrições de carga e de operação para um dado objetivo operacional. Esse problema, matematicamente, foi formulado como um problema de programação não linear, multiperíodo, e com variáveis contínuas e discretas. Algoritmos de programação não linear foram utilizados com o intuito de aproveitar as vantagens das matrizes altamente esparsas montadas ao longo do método de solução. Para utilizar tais algoritmos, as variáveis discretas são tratadas como contínuas por meio da utilização de funções senoidais que penalizam a função objetivo do problema original enquanto estas não convergirem para algum dos pontos pré-definidos no seu domínio. O caráter multiperíodo do problema, contudo, refere-se à consideração de uma restrição que relaciona os ajustes das variáveis de controle para sucessivos intervalos de tempo na medida em que limita o número de operações de chaveamento desses dispositivos para um período de 24-horas. O estudo fundamenta-se, metodologicamente, em métodos do tipo Primal-Dual Barreira-Logarítmica. Para demonstrar a eficiência do modelo proposto e a robustez dessa abordagem, a partir de dados teóricos obtidos de levantamentos bibliográficos, testes foram realizados em sistemas-teste de 10, 69 e 135 barras, e em um sistema de 442 barras do noroeste do Reino Unido. As implementações computacionais foram feitas nos softwares MATLAB, AIMMS e GAMS, utilizando o solver IPOPT como método de solução. Os resultados mostram que a abordagem proposta para a resolução do problema de programação não linear é eficaz para tratar adequadamente todas as variáveis presentes em problemas de otimização Volt/VAr. / This work proposes a new model and a new approach for solving the Volt / VAr optimization problem in distribution systems. The Volt/VAr optimization consists, basically, to determine the settings of the control variables of switched capacitor banks, on-load tap changer transformers and voltage regulators, in order to satisfy both the load and operational constraints, to a given operational objective. The problem is formulated as a nonlinear programming problem, multiperiod, and with continuous and discrete variables. Nonlinear programming algorithms were used in order to take advantage of the highly sparse matrices built along the solution method. The discrete variables are treated as continuous along the solution method by means of the use of sinusoidal functions that penalize the original objective function while the control variables do not converge to any of the predefined discrete points in its domain. The multiperiod, or dynamic, characteristic of the problem, however, refers to the use of a constraint that relates the settings of the control variables for successive time intervals that limits the control devices switching operations number for a period of 24-hours. The study is based, methodologically, on Primal-Dual Logarithmic Barrier method. To demonstrate the effectiveness of the proposed model and the robustness of this approach, the data were obtained from theoretical literature surveys, and tests were performed on test-systems of 10, 69 and 135 buses, and in a 442 buses located in the Northwest of the United Kingdom. The computational implementation was accomplished in the softwares MATLAB, AIMMS and GAMS, using the IPOPT solver as solution method. The results have shown the approach for solving nonlinear programming problems is effective to appropriate cope with all the variables presented in Volt/VAr optimization problems.

Neste trabalho é apresentada uma abordagem do Método de Newton associado à função penalidade quadrática e ao método dos conjuntos ativos na solução do problema de Fluxo de Potência Ótimo (FPO). A formulação geral do problema de FPO é apresentada, assim como a técnica utilizada na resolução do sistema de equações. A fatoração da matriz Lagrangeana é feita por elementos ao invés das estruturas em blocos. A característica de esparsidade da matriz Lagrangeana é levada em consideração. Resultados dos testes realizados em 4 sistemas (3, 14, 30 e 118 barras) são apresentados. / This work presents an approach on Newton\'s Method associated with the quadratic penalty function and the active set methods in the solution of Optimal Power Flow Problem (OPF). The general formulation of the OPF problem is presented, as will as the technique used in the equation systems resolution. The Lagrangean matrix factorization is carried out by elements instead of structures in blocks. The characteristic of sparsity of the Lagrangean matrix is taken in to account. Numerical results of tests realized in systems of 3, 14, 30 and 118 buses are presented to show the efficiency of the method.

As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each other, it was brought to our attention that many solution methods apply to nearly all ruin-related quantities. Such a peculiar similarity among their solution methods inspired us to search for a general form that reconciles those seemingly different ruin-related quantities. The stochastic approach proposed in the thesis addresses such issues and contributes to the current literature in three major directions. (1) It provides a new function that unifies many existing ruin-related quantities and that produces more new quantities of potential use in both practice and academia. (2) It applies generally to a vast majority of risk processes and permits the consideration of combined effects of investment strategies, policy modifications, etc, which were either impossible or difficult tasks using traditional approaches. (3) It gives a shortcut to the derivation of intermediate solution equations. In addition to the efficiency, the new approach also leads to a standardized procedure to cope with various situations. The thesis covers a wide range of ruin-related and financial topics while developing the unifying stochastic approach. Not only does it attempt to provide insights into the unification of quantities in ruin theory, the thesis also seeks to extend its applications in other related areas.

As ruin theory evolves in recent years, there has been a variety of quantities pertaining to an insurer's bankruptcy at the centre of focus in the literature. Despite the fact that these quantities are distinct from each other, it was brought to our attention that many solution methods apply to nearly all ruin-related quantities. Such a peculiar similarity among their solution methods inspired us to search for a general form that reconciles those seemingly different ruin-related quantities. The stochastic approach proposed in the thesis addresses such issues and contributes to the current literature in three major directions. (1) It provides a new function that unifies many existing ruin-related quantities and that produces more new quantities of potential use in both practice and academia. (2) It applies generally to a vast majority of risk processes and permits the consideration of combined effects of investment strategies, policy modifications, etc, which were either impossible or difficult tasks using traditional approaches. (3) It gives a shortcut to the derivation of intermediate solution equations. In addition to the efficiency, the new approach also leads to a standardized procedure to cope with various situations. The thesis covers a wide range of ruin-related and financial topics while developing the unifying stochastic approach. Not only does it attempt to provide insights into the unification of quantities in ruin theory, the thesis also seeks to extend its applications in other related areas.

On présente une nouvelle approche de simulation pour la fonction de densité conjointe du surplus avant la ruine et du déficit au moment de la ruine, pour des modèles de risque déterminés par des subordinateurs de Lévy. Cette approche s'inspire de la décomposition "Ladder height" pour la probabilité de ruine dans le Modèle Classique. Ce modèle, déterminé par un processus de Poisson composé, est un cas particulier du modèle plus général déterminé par un subordinateur, pour lequel la décomposition "Ladder height" de la probabilité de ruine s'applique aussi. La Fonction de Pénalité Escomptée, encore appelée Fonction Gerber-Shiu (Fonction GS), a apporté une approche unificatrice dans l'étude des quantités liées à l'événement de la ruine été introduite. La probabilité de ruine et la fonction de densité conjointe du surplus avant la ruine et du déficit au moment de la ruine sont des cas particuliers de la Fonction GS. On retrouve, dans la littérature, des expressions pour exprimer ces deux quantités, mais elles sont difficilement exploitables de par leurs formes de séries infinies de convolutions sans formes analytiques fermées. Cependant, puisqu'elles sont dérivées de la Fonction GS, les expressions pour les deux quantités partagent une certaine ressemblance qui nous permet de nous inspirer de la décomposition "Ladder height" de la probabilité de ruine pour dériver une approche de simulation pour cette fonction de densité conjointe. On présente une introduction détaillée des modèles de risque que nous étudions dans ce mémoire et pour lesquels il est possible de réaliser la simulation. Afin de motiver ce travail, on introduit brièvement le vaste domaine des mesures de risque, afin d'en calculer quelques unes pour ces modèles de risque. Ce travail contribue à une meilleure compréhension du comportement des modèles de risques déterminés par des subordinateurs face à l'éventualité de la ruine, puisqu'il apporte un point de vue numérique absent de la littérature. / We discuss a simulation approach for the joint density function of the surplus prior to ruin and deficit at ruin for risk models driven by Lévy subordinators. This approach is inspired by the Ladder Height decomposition for the probability of ruin of such models. The Classical Risk Model driven by a Compound Poisson process is a particular case of this more generalized one. The Expected Discounted Penalty Function, also referred to as the Gerber-Shiu Function (GS Function), was introduced as a unifying approach to deal with different quantities related to the event of ruin. The probability of ruin and the joint density function of surplus prior to ruin and deficit at ruin are particular cases of this function. Expressions for those two quantities have been derived from the GS Function, but those are not easily evaluated nor handled as they are infinite series of convolutions with no analytical closed form. However they share a similar structure, thus allowing to use the Ladder Height decomposition of the Probability of Ruin as a guiding method to generate simulated values for this joint density function. We present an introduction to risk models driven by subordinators, and describe those models for which it is possible to process the simulation. To motivate this work, we also present an application for this distribution, in order to calculate different risk measures for those risk models. An brief introduction to the vast field of Risk Measures is conducted where we present selected measures calculated in this empirical study. This work contributes to better understanding the behavior of subordinators driven risk models, as it offers a numerical point of view, which is absent in the literature.

Neste trabalho é apresentada uma abordagem do Método de Newton associado à função penalidade quadrática e ao método dos conjuntos ativos na solução do problema de Fluxo de Potência Ótimo (FPO). A formulação geral do problema de FPO é apresentada, assim como a técnica utilizada na resolução do sistema de equações. A fatoração da matriz Lagrangeana é feita por elementos ao invés das estruturas em blocos. A característica de esparsidade da matriz Lagrangeana é levada em consideração. Resultados dos testes realizados em 4 sistemas (3, 14, 30 e 118 barras) são apresentados. / This work presents an approach on Newton\'s Method associated with the quadratic penalty function and the active set methods in the solution of Optimal Power Flow Problem (OPF). The general formulation of the OPF problem is presented, as will as the technique used in the equation systems resolution. The Lagrangean matrix factorization is carried out by elements instead of structures in blocks. The characteristic of sparsity of the Lagrangean matrix is taken in to account. Numerical results of tests realized in systems of 3, 14, 30 and 118 buses are presented to show the efficiency of the method.

The dissertation thesis deal with the design and the optimization of the permanent magnet synchronous machine (SMPM) based on the artificial intelligence. The main target is to apply potential optimization methods on the design procedure of the machine and evaluate the effectiveness of optimization and the optimization usefulness. In general, the optimization of the material properties (NdFeB or SmCo), the efficiency maximization with given nominal input parameters, the cogging torque elimination are proposed. Moreover, the magnet shape optimization, shape of the air gap and the shape of slots were also performed. The well known Genetic algorithm and Self-Organizing migrating algorithm produced in Czech were presented and applied on the particular optimization issues. The basic principles (iterations) and definitions (penalty function and cost function) of proposed algorithms are demonstrated on the examples. The results of the vibration generator optimization (VG) with given power 7mW (0.1g acceleration) and the results of the SMPM 1,1kW (6 krpm) optimization are practically evaluated in the collaboration with industry. Proposed methods are useful for the optimization of PM machines and they are further theoretically applied on the low speed machine (10 krpm) optimization and high speed machine (120 krpm) optimization.