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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...
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,...
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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