A frequency-dependent multiconductor transmission line model with collocated voltage and current propagation

This research contributes to developing a time domain and a frequency domain formulations to solve electromagnetic transients in power system with multiconductor overhead transmission lines. The time domain solution introduces a frequency dependent transmission line model “FDLM”. For the development of the FDLM a fundamental constraint is added to the classical line equations to maintain the symmetry between electric and magnetic fields. As a result, voltage waves and current waves travel together and the characteristic impedance remains uniform along the line. With this premise, a constant real transformation matrix can be obtained to diagonalize the line functions with high accuracy. This feature can greatly facilitate the line modelling as opposed to the existing line models which require complex frequency dependent transformation matrices for their diagonalization. The use of a single constant real transformation matrix for the voltage and current waves which is exact over the frequency range enables FDLM to provide higher accuracy and numerical efficiency than the existing line models while it complies with the physical system. The accuracy of the FDLM is assessed through comparisons with a newly developed Discrete Time Fourier Series frequency domain solution. This methodology is based on the correct specification of the time window and frequency window widths. Guidelines are provided for this set up which avoids the typical Gibbs and aliasing errors related to the classical frequency domain solutions. The proposed frequency domain solution is simpler to implement than the most commonly used numerical Laplace transform solution while it does not require further considerations to use damping factors or windowing functions.Applied Science, Faculty ofElectrical and Computer Engineering, Department ofGraduat