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.