A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi-phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model. © 2012 IEEE.

A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model © 2003-2012 IEEE.

Equivalent representation of mutual coupling in transmission lines by discrete element

This paper describes a computational model based on lumped elements for the mutual coupling between phases in transmission lines without the explicit use of modal transformation matrices. The self and mutual parameters and the coupling between phases are modeled using modal transformation techniques. The modal representation is developed from the intrinsic consideration of the modal transformation matrix and the resulting system of time-domain differential equations is described as state equations. Thus, a detailed profile ofthe currents and the voltages through the line can be easily calculated using numerical or analytical integration methods. However, the original contribution of the article is the proposal of a time-domain model without the successive phase/mode transformations and a practical implementation based on conventional electrical circuits, without the use of electromagnetic theory to model the coupling between phases. © 2003-2012 IEEE.

Um modelo de linha de transmissão bifásica desenvolvido diretamente no domínio das fases

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimação dos parâmetros de linha de transmissão a partir de um segmento de linha discretizado

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modal transformation obtained from Clarke's matrix - Asymmetrical three-phase case

Some constant matrices can be used as phase-mode transformation matrices for transposed three-phase transmission lines. Clarke's matrix is one of these options. Its application as a phase-mode transformation matrix for untransposed three-phase transmission lines has been analyzed through error and frequency scan comparisons. Based on an actual untransposed asymmetrical three-phase transmission line example, a correction procedure is applied searching for better results from the Clarke's matrix applicaton as a phase-mode transformation matrix. The error analyses are carried out using Clarke's matrix and the new transformation matrices obtained from the correction procedure. Applying Clarke's matrix, the relative errors of the eigenvalue matrix elements can be considered negligible and the relative values of the off-diagonal elements are significant. If the the corrected transformation matrices are used, the relative values of the off-diagonal elements are decreased. Based on the results of these analyses, the homopolar mode is more sensitive to the frequency influence than the two other modes related to three-phase lines. © 2007 IEEE.

Modal transformation applied to double three-phase transmission lines

Double three-phase transmission lines are analyzed in this paper using a modal transformation model. The main attribute of this model is the use of a single real transformation matrix based on line geometrical characteristics and the Clarke matrix. Because of this, for any line point, the electrical values can be accessed for phase domain or mode domain using the considered transformation matrix and without convolution methods. For non-transposed symmetrical lines the errors between the model results and the exact modes are insignificant values. The eigenvector and eigenvalue analyses for transposed lines search the similarities among the three analyzed transposition types and the possible simplifications for a non-transposed case.

Modal transformation analyses for double three-phase transmission lines

Eigenvector and eigenvalue analyses are carried out for double three-phase transmission lines, studying the application of a constant and real phase-mode transformation matrix and the errors of this application to mode line models. Employing some line transposition types, exact results are obtained with a single real transformation matrix based on Clarke's matrix and line geometrical characteristics. It is shown that the proposed technique leads to insignificant errors when a nontransposed case is considered. For both cases, transposed and nontransposed, the access to the electrical values (voltage and current, for example) is provided through a simple matrix multiplication without convolution methods. Using this facility, an interesting model for transmission line analysis is obtained even though the nontransposed case errors are not eliminated. The main advantages of the model are related to the transformation matrix: single, real, frequency independent, and identical for voltage and current.

Step by step analyses of Clarke's matrix correction procedure for untransposed three-phase transmission line cases

The correction procedure for Clarke's matrix, considering three-phase transmission line analyzes, is analyzed step by step in this paper, searching to improve the application of this procedure. Changing the eigenvectors as modal transformation matrices, Clarke's matrix has been applied to analyses for transposed and untransposed three-phase transmission line cases. It is based on the fact that Clarke's matrix is an eigenvector matrix for transposed three-phase transmission lines considering symmetrical and asymmetrical cases. Because of this, the application of this matrix has been analyzed considering untransposed three-phase transmission lines. In most of these cases, the errors related to the eigenvalues can be considered negligible. It is not true when it is analyzed the elements that are not in main diagonal of the quasi-mode matrix. This matrix is obtained from the application of Clarke's matrix. The quasi-mode matrix is correspondent to the eigenvalue matrix. Their off-diagonal elements represent couplings among the quasi-modes. So, the off-diagonal quasi-mode element relative values are not negligible when compared to the eigenvalues that correspond to the coupled quasi-modes. Minimizing these relative values, the correction procedure is analyzed in detail, checking some alternatives for the correction procedure application.

Eigenvalue analyses of two parallel lines using a single real transformation matrix

For a typical non-symmetrical system with two parallel three phase transmission lines, modal transformation is applied using some examples of single real transformation matrices. These examples are applied searching an adequate single real transformation matrix to two parallel three phase transmission line systems. The analyses are started with the eigenvector and eigenvalue studies, using Clarke's transformation or linear combinations of Clarke's elements. The Z C and parameters are analyzed for the case that presents the smallest errors between the exact eigenvalues and the single real transformation matrix application results. The single real transformation determined for this case is based on Clarke's matrix and its main characteristic is the use of a unique homopolar reference. So, the homopolar mode becomes a connector mode between the two three-phase circuits of the analyzed system. ©2005 IEEE.

Análise modal baseada apenas na resposta: decomposição no domínio da frequência

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Expression of matrix metalloproteinases, type IV collagen, and interleukin-10 in rabbits treated with morphine after lamellar keratectomy

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chemical Composition of Lipids Present in Cat and Dog Oocyte by Matrix-Assisted Desorption Ionization Mass Spectrometry (MALDI- MS)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Proteoliposomes Harboring Alkaline Phosphatase and Nucleotide Pyrophosphatase as Matrix Vesicle Biomimetics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Kinetic Analysis of Substrate Utilization by Native and TNAP-, NPP1-, or PHOSPHO1-Deficient Matrix Vesicles

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)