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This paper presents a method for analyzing electromagnetic transients using real transformation matrices in three-phase systems considering the presence of ground wires. So, for the Z and Y matrices that represent the transmission line, the characteristics of ground wires are not implied in the values related to the phases. A first approach uses a real transformation matrix for the entire frequency...
The results presented in this paper are based on a research about the application of approximated transformation matrices for electromagnetic transient analyses and simulations in transmission lines. Initially, it has developed the application of a single real transformation matrix for a double three-phase transmission lines, because the symmetry of the distribution of the phase conductors and the...
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...
Single real transformation matrices can change the Z and Y matrices into diagonal ones for transposed three-phase lines. Considering non-transposed non-symmetrical three-phase lines, the errors between the Clarkepsilas matrix application results (called quasi-modes) and the eigenvectors are negligible. In this text, some other analyses are performed for two line designs. So, the arithmetic media among...
The application of modal transformation models for transmission lines have been analyzed extensively because in mode domain there are facilities in representation of frequency dependent line parameters. Because the determination of exact modal transformation matrices for general cases is not a simple task, simplifications about these applications can be considered. Using non-transposed three-phase...
Clarkepsilas matrix has been applied as a phase-mode transformation matrix to three-phase transmission lines substituting the eigenvector matrices. Considering symmetrical untransposed three-phase lines and the frequency range into 10 kHz, some transient simulations have been made with the application of this single real matrix. An actual symmetrical three-phase line on untransposed conditions is...
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...
Clarke's matrix has been used as an eigenvector matrix for transposed three-phase transmission lines and it can be applied as a phase-mode transformation matrix for transposed cases. Considering untransposed three-phase transmission lines, Clarke's matrix is not an exact eigenvector matrix. In this case, the errors related to the diagonal elements of the Z and Y matrices can be considered negligible,...
Clarke's matrix is an eigenvector matrix for transposed three-phase transmission lines and its application as a phase-mode transformation matrix for untransposed three-phase transmission lines has been studied using error and frequency scan analyses. Considering untransposed asymmetrical three-phase transmission lines, a correction procedure is applied searching for better results from the Clarke's...
For typical symmetrical systems with three-phase double-circuit transmission lines or two parallel three-phase double-circuit transmission lines, single real transformation matrix is applied. The objective is to determine Z (impedance) and Y (admittance) diagonal matrices in the mode domain. The proposed analyses are based on eigenvector and eigenvalue studies, using linear combinations of Clarke...
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