On the modal analysis of asymmetrical three-phase transmission lines using standard transformation matrices

Fortescue´s transformation, Clarke´s transformation and Karrenbauer´s transformation are all well-known tools which can be used to conduct a modal analysis of perfectly balanced transposed three-phase power transmission lines. For untransposed asymmetrical lines, however, such standard transformations fail. Nevertheless, all these transformation matrices can still play an important role in determining a first order approximation of the exact modal transformation. This paper shows how this can be done by employing a perturbation technique approach. In addition to the theoretical aspects discussed, some application examples concerning a vertical and a triangular line are also presented for illustrative purposes