Clarke extended methodology for two parallel three-phase double-circuit lines

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 matrix elements. This methodology originates from techniques used for single three-phase transmission lines. Using the proposed extended techniques, Z and Y diagonal matrices are obtained for transposed cases of three-phase double-circuit line systems (6 order transformation matrix). For two parallel three-phase double-circuit lines (12 order transformation matrix), only two nondiagonal elements are not zero in mode matrices. For future development, the objective is to investigate the proposed single real transformation matrix application to nontransposed cases.