Neste trabalho são descritos e avaliados diferentes modelos de linhas aéreas de transmissão, considerando a variação dos parâmetros da linha com a frequência. Em geral os modelos apresentados são baseados no uso da matriz de admitâncias nodais, com algumas análises complementares empregando o método das características. São testados casos de circuito-aberto, curto-circuito, linha em carga e manobras com chaves. Os resultados de cálculo são comparados com as respostas simuladas nos programas ATP e PSCAD. Também são apresentadas as formulações para o cálculo de parâmetros da linha de transmissão, considerando o efeito pelicular e a resistividade do solo São avaliadas as respostas no domínio do tempo para diferentes modelos equivalentes de linha de transmissão, obtidos do modelo polo-resíduo com passividade da matriz de admitâncias nodais, sendo empregados: i) transformação do modelo racional para uma representação em espaço de estados, ii) construção de uma rede elétrica equivalente com resistências, indutores e capacitores e iii) representação por meio de um equivalente de Norton. Também é analisado o equivalente de Norton obtido dos modelos polo-resíduo com passividade de uma linha equivalente dobrada nas condições em curto-circuito e circuito-aberto. Foi analisada a solução de redes elétricas no domínio da frequência usando uma formulação nodal e sem a necessidade de ajustes intermediários da matriz de admitâncias nodais. As respostas de tensão e corrente são antitransformadas para o domínio do tempo por meio de diferentes formulações baseadas na transformada inversa de Fourier, levando em conta os métodos que mitigam erros de truncamento e discretização. As seguintes formulações foram avaliadas: i) transformada modificada de Fourier, ii) transformada inversa rápida de Fourier e iii) transformada inversa de Fourier com integração semianalítica. É também apresentado um modelo para linhas de transmissão em paralelo, baseado no domínio modal usando uma matriz de transformação constante, juntamente com a aplicação do método de ajuste Vector Fitting com o objetivo de modelar com precisão o efeito de acoplamento mútuo entre linhas. / In this work different overhead transmission lines models are described and evaluated, considering the frequency dependence of parameters. In general, the models are based on the nodal admittance matrix, with some complementary analysis using the method of characteristics. Cases of open-circuit, short-circuit, line connected to a load and switching maneuvers are tested. The calculation results are compared with the simulated responses obtained with the ATP and PSCAD. The formulations for the transmission line parameters are also presented, taking into account the skin effect and the ground return. The time-domain responses for different transmission line models are evaluated. These models are obtained from the passive pole-residue model of the nodal admittance matrix. The equivalent models are: i) state-space representation, ii) electrical network composed of resistors, inductors and capacitors, iii) the Norton\'s equivalent. In addition, an evaluation is performed for the Norton\'s equivalent obtained from the pole-residue models for the open-circuit and short-circuit conditions of a folded line equivalent. On the other hand, the network is solved completely in frequency-domain using a nodal formulation, without the fitting of the nodal admittance matrix. The voltage and current responses are transformed back to the time-domain by different formulations based on the inverse Fourier transform, taking into account methods to minimize errors by truncation and discretization. The formulations investigated are: i) modified Fourier transform, ii) fast Fourier transform, iii) inverse Fourier transform with semianalytic integration. The model for parallel transmission lines is also evaluated, based on modal domain using a constant transformation matrix and the application of the vector fitting method, with emphasis on accurate representation of mutual coupling effects.

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.