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This thesis presents a method to obtain the per-unit-length electrical parameters of a given overhead transmission line or underground cable in an unbounded space considering the effect of the ground. This is achieved using a two-dimensional conformal mapping technique, which consists of a modified bilinear transformation to map a semi-open half-space problem into a unit circle. The Helmholtz equations describing the quasi-stationary approximation for the electromagnetic field behaviour are solved using finite element method, with the aid of commonly used commercial software program, COMSOL Multiphysics. The per-unit-length resistance, inductance and capacitance are calculated using the proposed mapping method, the truncation of the original space method and then compared with the analytical solution obtained from Carson's approximation for the overhead lines and Wedepohl's formulation for the underground cables. / October 2016

The introduction of synchrophasor technology to the realm of power systems has presented a myriad of novel approaches to age-old problems. In this thesis, the questions of instrument transformer calibration and transmission line parameter estimation have been examined. With synchrophasors offering real-time data for analysis, a solution to each individual problem seems feasible. A quandary however arises due to the fact that calibration methods depend on accurate knowledge of line parameters, and estimation of these parameters depend on calibrated measurements. Traditional methods of determining the parameters may not be the most accurate due to a variety of fluctuations possible on the system, which is why real-time estimation could prove beneficial. This work analyzes each problem and a feasible solution and proposes a method to achieve transducer calibration as well as parameter estimation together, while employing synchronized phasor measurements. / Master of Science

Accurate value of transmission line parameters is important for power system protection applications, especially for distance relays whose zone settings are based on positive sequence line impedance. The research is devoted to estimating transmission line positive-sequence parameters from synchronized or unsynchronized measurements of voltage and current phasors that are obtained at both terminals of the line. The positive sequence parameters including series impedance and shunt admittance can be linearly estimated. The linear least square algorithm has been derived in this dissertation for different transmission line configurations. The algorithm is able to handle both synchronized and unsynchronized measurements and deal with potential synchronization errors by explicitly modeling the synchronization angle. Sample results are reported to demonstrate the effectiveness of the proposed method. Three types of transmission line models depending on line length (long, medium and short) are studied in this dissertation. Chapter 3 uses unsynchronized data for the long transmission line. The derived method can detect the unsynchronized angle and estimate the positive sequence of long line parameters. The proposed method is examined with negative impacts such as errors on currents and voltages data. These errors are added randomly to one set each time to test the robustness of the developed algorithm. The medium transmission line algorithm derivation is presented in chapter 4. This chapter uses a linear least square to estimate the lumped parameters of a medium transmission line. The two different transmission line circuits are used to model the medium line. The first circuit is a single transmission line with two nodes and is used to evaluate the developed algorithm. The second circuit is a double transmission line. These two lines can have the same or different line parameters or line length. The developed algorithm shows that the proposed method achieves highly accurate results for the estimation of positive sequence line parameters. The short transmission line is studied in chapter 5. The short transmission line uses less data than the long or medium lines because in this model the shunt capacitance is omitted. Thus, the linear estimation yields highly accurate results. Case studies are considered to test the robustness of this developed method. The line temperature mainly affects the series resistance, and the developed algorithms in previous three chapters can accurately estimate the transmission line parameters. To simplify the real-time estimation of line resistance and temperature, the series inductance, and shunt capacitance can be treated as constant and known values. Chapter 6 provides such studies of estimating resistance by treating inductance and capacitance as known values.

Orientador: Sérgio Kurokawa / Banca: Afonso José do Prado / Banca: Lourenço Matias / Resumo: O objetivo deste projeto é o desenvolvimento de um modelo de linha de transmissão bifásica diretamente no domínio do tempo, que leve em consideração o efeito da freqüência sobre seus parâmetros longitudinais, utilizando os conceitos de variáveis de estado. Os parâmetros longitudinais, variáveis em relação à freqüência, serão aproximados por funções racionais, cujos pólos e resíduos deverão ser determinados por meio do algoritmo vector fitting. Em seguida, as funções racionais que descrevem o comportamento dos parâmetros longitudinais serão associadas com um circuito elétrico equivalente, que será inserido em cada um dos circuitos π, constituindo uma grande quantidade de cascata de circuitos π. O modelo será utilizado para a realização de simulações de transitórios resultantes das operações de manobras e chaveamentos que ocorrem em uma linha bifásica com plano de simetria vertical. Os resultados serão comparados com os resultados obtidos com programas computacionais do tipo EMTP (cascata de circuitos π inserida no EMTP). Ao término do projeto teremos a nossa disposição um modelo de linha de transmissão que não necessita do uso de simuladores do tipo EMTP. / Abstract: The objective of this work is to implement a computational model of two-phase transmission line in time domain taking into account its frequency dependent longitudinal parameters. The line is represented through a cascade of π circuits and the frequency dependence of the longitudinal parameters is approximated by a rational functions that can be associated with an equivalent circuit representation and this equivalent circuit is inserted in each π circuit. After that the cascade is described through state equations. Validating the model, a frequency dependent two-phase line is represented by a cascade of π circuits. The model will be use for typical switching transients in a two-phase transmission line with a vertical symmetrical plan. The simulations were carried out using state space techniques and an EMTP program (in this case, the cascade was inserted in the EMTP program). It is observed that the simulation results obtained with state space representation are in agreement with those results obtained with EMTP. / Mestre

Made available in DSpace on 2014-06-11T19:22:33Z (GMT). No. of bitstreams: 0 Previous issue date: 2009-03-09Bitstream added on 2014-06-13T19:08:07Z : No. of bitstreams: 1 yamanaka_fnr_me_ilha.pdf: 596127 bytes, checksum: 6456b9483b4e3ac56e9f1fded745845f (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O objetivo deste projeto é o desenvolvimento de um modelo de linha de transmissão bifásica diretamente no domínio do tempo, que leve em consideração o efeito da freqüência sobre seus parâmetros longitudinais, utilizando os conceitos de variáveis de estado. Os parâmetros longitudinais, variáveis em relação à freqüência, serão aproximados por funções racionais, cujos pólos e resíduos deverão ser determinados por meio do algoritmo vector fitting. Em seguida, as funções racionais que descrevem o comportamento dos parâmetros longitudinais serão associadas com um circuito elétrico equivalente, que será inserido em cada um dos circuitos π, constituindo uma grande quantidade de cascata de circuitos π. O modelo será utilizado para a realização de simulações de transitórios resultantes das operações de manobras e chaveamentos que ocorrem em uma linha bifásica com plano de simetria vertical. Os resultados serão comparados com os resultados obtidos com programas computacionais do tipo EMTP (cascata de circuitos π inserida no EMTP). Ao término do projeto teremos a nossa disposição um modelo de linha de transmissão que não necessita do uso de simuladores do tipo EMTP. / The objective of this work is to implement a computational model of two-phase transmission line in time domain taking into account its frequency dependent longitudinal parameters. The line is represented through a cascade of π circuits and the frequency dependence of the longitudinal parameters is approximated by a rational functions that can be associated with an equivalent circuit representation and this equivalent circuit is inserted in each π circuit. After that the cascade is described through state equations. Validating the model, a frequency dependent two-phase line is represented by a cascade of π circuits. The model will be use for typical switching transients in a two-phase transmission line with a vertical symmetrical plan. The simulations were carried out using state space techniques and an EMTP program (in this case, the cascade was inserted in the EMTP program). It is observed that the simulation results obtained with state space representation are in agreement with those results obtained with EMTP.

Renewable energy is playing an increasingly significant role in power system operation and stability assessment with its numerous penetration expansion. This is not only brought by its uncertain power output and inverter-based equipment structures but also its operation characteristics like Low Voltage Ride Through (LVRT). It is thus necessary to take these characteristics into consideration and further to find more adaptive schemes to implement them for more effective analysis and safer power system operation. All the aforementioned is based on the accurate identification of the system fundamental information. In this dissertation, a systematic approach is proposed to find the valid system model by estimating the transmission line parameters in the system with PMU measurements. The system transient stability assessment is conducted based on this validated model. The constrained stability region is estimated with Lyapunov functions family based method in the center of angles reference frame considering renewables LVRT as operation limits. In order to integrate the LVRT constraints, a polytopic inner approximation mechanism is introduced to linearize and organize the transformed constraints in state space, which brings much scalability to the whole process. From the voltage stability perspective, an approach to adaptively adjust LVRT settings of the renewable energy sources in the system is formulated to guarantee the system load margin and thus the voltage security. A voltage prediction method is introduced for critical renewable energy sources identification. Estimation methods based on interpolation and sensitivities are developed and conducted for saving computation effort brought by continuation power flows. Multiple test cases are studied utilizing the proposed approaches and results are demonstrated. / Doctor of Philosophy / Renewable energy utilization is continuously rising nowadays. They are clean but highly dependent on natural resources, which causes their uncertainty and intermittence in electric power output. The power system, on the other hand, is designed for schedulable and controllable power generators, which make the traditional methods for system operation and analysis of the system stability much less effective facing the trend of renewables integration. In this dissertation, a series of systematic approaches are proposed firstly identify the system parameters for more accurate system modeling through PMU measurements, then to assess the system transient stability considering the renewable energy sources operation limits, and finally to adaptively adjust these operation limit for improving the system voltage security. The operation limits are transferred into the form in terms of system states. Linearization and approximation methods are also introduced to enhance the scalability of the processes. Multiple test cases are studied with the proposed approaches and the results demonstrate their effectiveness and efficiency.