The presented thesis is focused on a set of problems related to managerial decision-making concerning networks (particularly transportation networks), respectively - if we put it more precisely - the thesis focuses on the support of this decision-making by means of quantitative methods. A set of problems related to nets and decision-making concerning their individual parts or elements represents a very complex sphere which has been a subject of research for a number of decades. Out of this sphere, the thesis formulates and elaborates in great detail two problems, which - from the point of view of their practical significance - are important for the decision-making of managers of carriers, or the public sphere, and which have not been published in this form yet. The main point is the problem of how to find a subnet with a limited prolongation of routes between important pairs of vertices. Another problem is a design of a bus route in an area with a low demand. For each of these problems, the thesis offers an exact combinatorial solution method, furthermore a method based on integer linear programming, and - last but not least - also, of course, heuristic methods of solution. All these methods have been tested on a set of networks, which has been created for this purpose in a pseudo-random way in the frame of this thesis. The testing has been focused primarily on the comparison of the results provided by heuristic methods, which are of great importance - with regard to a great computational difficulty of exact methods - for feasible tasks on a larger scale. The tests have proved that the proposed heuristic methods are practically applicable and show results whicheven represent the optimal solution in a number of cases, or are only slightly distant from the optimal solution.

[pt] O uso da representação de modelos completos em estudos de sistemas de potência pode levar a indesejados níveis de esforço computacional e imprecisão devido às incertezas e complexidade dos sistemas modernos. Para endereçar este problema de tratabilidade, métodos de redução de redes buscam criar um modelo simplificado, com dimensão reduzida, de um dado sistema de potência. As técnicas atuais consideram apenas um ponto de operação no processo de redução falhando em desempenho para uma grande variedade de condições operativas. Adicionalmente, a solução para o fluxo de potência CA (não linear) apresenta pior performance computacional, mas melhor precisão quando comparada à sua contraparte linear (solução para fluxo de potência CC). Infelizmente, a aproximação do fluxo de potência CC desconsidera a perda de energia nas linhas e os efeitos das não linearidades devido as mudanças nos níveis de tensão e potências reativas no sistema. Neste contexto, um novo modelo de fluxo de potência equivalente baseado em otimização é proposto. Assim, para superar as limitações relativas a performance computacional e as imprecisões para multiplos cenários operativos, utilizamos o modelo proposto para produzir um método de redução baseado no fluxo CC, que apresenta bom desempenho em variados pontos operativos. Neste caso, a solução de um problema de otimização linear, que considera múltiplos cenários de fluxo CA ou medições do sistema, determina os parâmetros da rede equivalente. Para garantir a precisão do modelo, consideramos um conjunto de cargas artificiais para representar o desbalanço entre os cenários observados e a resposta da rede equivalente. Estas cargas artificiais são funções polinomiais do ponto operativo do sistema, e seus coeficientes são cootimizados com os parâmetros da rede reduzida. A Analise de Componentes Pincipais é utilizada para extrair as componentes relevantes do vetor de cargas que define um ponto operativo, reduzindo a dimensão do modelo, e melhorarando o desempenho out–of–sample. A metodologia é testada contra o equivalente Ward para diferentes condições operativas. Casos de estudo com dados gerados são apresentados com o objetivo de analisar a capacidade de generalização do modelo para diferentes níveis de ruído. Por fim, um caso de estudo com perfís de carga realísticos oriundos de uma companhia de distribuição brasileira é conduzido no sistema de teste IEEE 118–Bus. / [en] The use of full model representation in power system studies may lead to undesirable levels of computational burden and inaccuracy due to modern system complexities and uncertainties. To address the tractability issue, network reduction methods aim to create a simplified model, with reduced dimension, of a given power system. Current techniques consider only one operating point in their reduction process, falling short in properly performing for a wide range of operating conditions. Additionally, a nonlinear AC power flow solution features worse computation performance, but better accuracy when compared against its linearized counterpart (DC power flow solution). Unfortunately, the DC power flow approximation disregards the line losses and nonlinear effects due to changes in voltage levels and reactive power. In this context, we propose a novel optimization–based framework to create equivalent power flow models. Thus, to overcome the computational performance limitations and imprecision for multiple operating scenarios, we use the proposed framework to produce a DC–based network reduction method that performs well in many operating points. The solution of a linear optimization problem, which considers multiple AC power flow scenarios or network measurements, determines the equivalent network parameters. To ensure modeling accuracy, we consider a set of artificial dynamic loads to represent the mismatch between observed scenarios and the response of the equivalent. These artificial loads are polynomial functions of the operating point, and their coefficients are co-optimized with the reduced network parameters. Principal Component Analysis (PCA) is used to extract the relevant components of the load vector defining the operating point, reducing the equivalent model dimensionality, and improving out–of–sample performance. We test the methodology against traditional Ward equivalent for different operating conditions. We present case studies with generated data to investigate the model generalization capability for different noise levels. Finally, we conduct a case study based on realistic load profiles from a Brazilian distribution company within the IEEE 118–Bus test system.

abstract: The holomorphic embedding method (HEM) applied to the power-flow problem (HEPF) has been used in the past to obtain the voltages and flows for power systems. The incentives for using this method over the traditional Newton-Raphson based nu-merical methods lie in the claim that the method is theoretically guaranteed to converge to the operable solution, if one exists. In this report, HEPF will be used for two power system analysis purposes: a. Estimating the saddle-node bifurcation point (SNBP) of a system b. Developing reduced-order network equivalents for distribution systems. Typically, the continuation power flow (CPF) is used to estimate the SNBP of a system, which involves solving multiple power-flow problems. One of the advantages of HEPF is that the solution is obtained as an analytical expression of the embedding parameter, and using this property, three of the proposed HEPF-based methods can es-timate the SNBP of a given power system without solving multiple power-flow prob-lems (if generator VAr limits are ignored). If VAr limits are considered, the mathemat-ical representation of the power-flow problem changes and thus an iterative process would have to be performed in order to estimate the SNBP of the system. This would typically still require fewer power-flow problems to be solved than CPF in order to estimate the SNBP. Another proposed application is to develop reduced order network equivalents for radial distribution networks that retain the nonlinearities of the eliminated portion of the network and hence remain more accurate than traditional Ward-type reductions (which linearize about the given operating point) when the operating condition changes. Different ways of accelerating the convergence of the power series obtained as a part of HEPF, are explored and it is shown that the eta method is the most efficient of all methods tested. The local-measurement-based methods of estimating the SNBP are studied. Non-linear Thévenin-like networks as well as multi-bus networks are built using model data to estimate the SNBP and it is shown that the structure of these networks can be made arbitrary by appropriately modifying the nonlinear current injections, which can sim-plify the process of building such networks from measurements. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017

[pt] O surgimento do fenômeno de estabilidade de tensão na operação dos sistemas elétricos motivou centenas de pesquisadores a desenvolverem métodos que permitam detectar a proximidade à instabilidade de tensão, com eficiência computacional, e tomar medidas acertadas para garantir a operação confiável e segura. Neste trabalho são analisados diferentes métodos que permitem transformar sistemas de grande porte em circuitos simples: o circuito equivalente entre geradores e cargas, baseado no cálculo de correntes de curto-circuito, na técnica de redução de rede pela eliminação de barras intermediárias e no equivalente de Thévenin. É analisada a utilização destes equivalentes na avaliação das condições de estabilidade de tensão com sistemas-testes de 3 e 4 barras. Através de diferentes testes verificou-se que o circuito equivalente entre geradores e cargas e a técnica de redução de rede não podem ser usados para o cálculo de índices de avaliação das condições de estabilidade de tensão, enquanto que, usando circuito equivalente de Thévenin encontrou-se um método que funciona corretamente para barra de carga terminal, barra não-terminal e barra de tensão controlada por gerador. / [en] The emergence of voltage stability phenomenon in the operation of power systems has motivated hundreds of researchers to develop methods to detect the proximity to voltage instability, with computational efficiency and to take all necessary and appropriate measures to ensure reliable and safe operation. In this work, different methods that allow transforming large systems into simple circuits were analyzed, such as the equivalent circuit between generators and loads, based on the calculation of short-circuit currents; the network reduction technique for eliminating intermediate buses; and the Thévenin equivalent. The application of these equivalents on voltage stability assessment of 3 and 4 bus testing systems were extensively tested. At the end, it was verified that that the equivalent circuit between the generator and load, and the network reduction technique, cannot be used for calculating the voltage stability conditions evaluation indexes. However, using Thévenin equivalent circuit, it was found a proper method, which works correctly for terminal buses, transit buses and voltage-controlled buses.