Time Domain Simulations of Overhead Transmission Lines Using A Custom Real and Constant Transformation Matrix

Modal transformation is widely used in the transient analysis of power systems. Some applications of modal transformation are in fault location and protection sizing in smart grid and transmission networks. While some techniques such as the Universal Line Model use it indirectly, other techniques use modal transformation to represent multiconductor systems directly in the time domain e.g. the lumped parameter model. Time domain simulations require real and constant transformation matrices. The direct implementation of modal transformation matrices in time domain simulations is not trivial because they are frequency-dependent. Techniques such as Vector Fitting can be used to fit frequency-dependent data into time-domain simulations. This paper uses direct search algorithms to find an optimal real and frequency-constant transformation matrix. The presented results demonstrate that the proposed approach leads to accurate time domain simulations in lines with vertical, symmetrical, and asymmetrical configurations.