Alternative Modal Analysis of N-coupled Multi-conductor Power Lines

Cables and overhead lines are key components in electric power systems, with conductors belonging to those components being electromagnetically coupled. Time-domain analysis of steady-state and transient regimes in cables and power lines usually requires the use of frequency-domain modal analysis techniques where mode decoupling is achieved by solving an eigenvalue-eigenvector matrix problem. In this article, an alternative method is developed for the modal analysis of n-coupled multi-conductor transmission lines employing a simple intuitive approach. The method provides a speedy solution of the eigenvalue-eigenvector problem based on an initial guess for the modal transformation matrix; the accuracy of the method can be controlled and improved easily by iterating the proposed algorithm a few times. The method is exemplified with vertical and triangular single-circuit three-phase transmission lines choosing the Clarke matrix as the initial approximation for the modal transformation.