Representação de linhas de transmissão por meio de variáveis de estado levando em consideração o efeito da freqüência sobre os parâmetros longitudinais

The main objective of this paper is to show the formulation rule of state matrices when the state-space approach is used to represent a transmission line taking into account its frequency dependent parameters. First, the line is represented through a cascade of pi circuits and the frequency dependence of the longitudinal parameters is synthesized with series and parallel resistors and inductors that are inserted in each pi circuit. After that the cascade is described through state equations. The model will be used to represent a single-phase line taking into account that its parameters are frequency dependents. The simulations are carried out by using Matlab and the results obtained will be compared with results obtained with Microtran.O objetivo deste trabalho é determinar as matrizes de estado que representam uma linha de transmissão cujos parâmetros são considerados variáveis em relação à freqüência. Inicialmente a linha é representada por meio de uma cascata de circuitos pi, sendo que o efeito da freqüência sobre os parâmetros longitudinais da linha é sintetizado por meio de uma associação série e paralela de resistores e indutores que é inserida em cada um dos circuitos pi. Esta cascata é então descrita por meio de variáveis de estado. O modelo será utilizado para representar uma linha monofásica, levando em consideração que os parâmetros da mesma são dependentes da freqüência. As simulações serão realizadas no ambiente Matlab. Para conferir a regra de formação das matrizes de estado, os resultados obtidos com a representação proposta serão comparados com os resultados obtidos com o Microtran.337346Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Atualização das disciplinas de comunicação gráfica para engenharia seguindo a abordagem Project Based Learning (PBL)

The Engineering Graphics Communication disciplines of the Escola Politécnica of the Universidade de São Paulo have undergone constant reformulations over the years. The adoption of the Project-based Learning (PBL) approach seemed to fit perfectly the needs and objectives of such disciplines and has become a goal of the recent offerings. One of the main goals was to provide greater contact, and consequent motivation, of the first year students with subjects related to engineering, such as the design and fabrication of an object fulfilling a task. These students have entered a new environment to them, and most of the subjects of the first years do not contemplate content directly related to engineering. This report presents the data and circumstances most representative of this experience and is intended to be a stimulus and an aid to other disciplines wishing to pursue similar trailsAs disciplinas de Comunicação Gráfica para Engenharia da Escola Politécnica da Universidade de São Paulo têm sofrido constantes reformulações ao longo dos anos. Adotar a abordagem do Aprendizado Baseado em Projetos (Project-based Learning – PBL) pareceu adequar-se perfeitamente às necessidades e aos objetivos de tais disciplinas e tornou-se uma meta dos últimos oferecimentos destas. Uma das principais metas foi proporcionar um maior contato, e consequente motivação, dos alunos do primeiro ano com assuntos mais relacionados à engenharia, como o projeto e a fabricação de um objeto que cumpre uma tarefa. Tais alunos ingressaram em um ambiente novo, e a maioria das disciplinas dos primeiros anos não contempla conteúdos mais diretamente ligados à engenharia. O presente relato apresenta os dados e as circunstâncias mais representativas dessa experiência e pretende ser um estímulo e uma ajuda a outras disciplinas que pretendam caminhar por trilhas semelhantes

Some considerations about a new procedure to derive transmission line parameters concerning three-phase lines

The paper shows an alternative methodology to calculate transmission line parameters per unit length and to apply it in a three-phase line with a vertical symmetry plane. This procedure is derived from a general procedure where the modal transformation matrix of the line is required. In this paper, the unknown modal transformation matrix requested by general procedure is substituted by Clarke's matrix. With the substitution that is shown in the paper, the transmission line parameters can be obtained starting from impedances measured in one terminal of the line. First, the article shows the classical methodology to calculate frequency dependent transmission line parameters by using Carson and Pollaczeck's equations for representing the ground effect and Bessel's functions to represent the skin effect. After that, a new procedure is shown to calculate frequency dependent transmission line parameters directly from currents and voltages of an existing line. Then, this procedure is applied in a non-transposed three-phase transmission line whose parameters have been previously calculated by using the classical methodology. Finally, the results obtained by using the new procedure and by using the classical methodology are compared. The article shows simulation results for typical frequency spectra of switching transients (10 Hz to 10 kHz). Results have shown that procedure has © 2006 IEEE

Corona effect in frequency dependent transmission line models

The inclusion of the corona effect in a frequency dependent transmission line model is proposed in this paper. The transmission line is represented through a cascade of π circuits and the frequency dependence of the longitudinal parameters is synthesized with series and parallel resistors and inductors. The corona effect will be represented using the Gary and Skilling-Umoto models. The currents and voltages along the line are calculated by using state-space technique. To demonstrate the accuracy and validity of the proposed frequency dependent line model, time domain simulations of a 10 km length single-phase line response under energization procedure will be presented. ©2008 IEEE

Analysis of the voltage profile in transmission lines operating with injected third harmonic voltages

This paper analyses the voltage profile along a three-phase transmission line whose power transfer capability was increased by an uprating technique based on the injection of a third harmonic voltage component. The superposition of a third harmonic voltage component with the fundamental component at the sending and receiving ends of the line proposes to increase the amplitude of the fundamental voltage component without exceeding the electrical insulation voltage limits, and thus increasing the power transfer capability. However, this uprating technique can affect the voltage amplitudes significantly along the line. In some cases, these amplitudes can be higher than acceptable values. The study was carried out in Simulink/MatLab® software. Two three-phase uprated transmission lines with voltages of 230 kV and 735 kV were represented by the Bergeron’s line model, then voltage profiles and the voltage waveforms in the time domain at the midpoint of each simulated system were obtained. Results have shown that 230-kV transmission lines with lengths of up to 300 km operating under natural to heavy load conditions can be uprated by the THV technique, whereas 735-kV transmission lines have presented overvoltages along its length when operating between light and natural loading, attesting that this technique is not feasible for this system

Optimization of tower-footing grounding impedance for guyed-V transmission towers

Backflashover is one of the mechanisms by which lightning strikes can cause outages/damages in power systems. In this context, the tower-footing grounding system of transmission towers has an essential role for mitigating overvoltages that may result in backflashovers. The tower-footing grounding systems consists of long conductors, in different shapes and arrangements, buried in either homogeneous or stratified ground in order to obtain the lowest tower-footing grounding impedance. In this paper, the tower-footing grounding impedance of a typical guyed-V transmission tower is evaluated in the frequency domain using full-wave electromagnetic analysis and method of moments (MoM). Various scenarios where the tower-footing grounding system is buried in a homogeneous, a 2-, and a 3-layer stratified soil are studied. Also, the effect of the opening angle between the electrodes in the counterpoise arrangement in reducing the footing impedance is investigated. It is shown that the tower-footing impedance is notably reduced, especially when stratified soil is considered in the analysis

Simplified procedure to estimate the resistance parameters of transmission lines

An alternative and simplified procedure is described to estimate the longitudinal resistances of transmission lines based on the real-time load profile. This method proposes to estimate the resistance parameters from the synchronized measurements of complex currents and complex voltages at the sending and receiving ends of transmission systems. The synchronized measurements can be in practice obtained using phasor measurement units (PMUs). © 2012 Springer-Verlag Berlin Heidelberg