Rigorous calculation method for resonance frequencies in transmission line responses

Abstract

This study presents a new, generalised method for the calculation of resonance frequencies (RFs) in transmission line (TL) responses. The proposed method calculates the RF of any propagation mode and is applicable to all types of TL configurations, taking also into account the effect of the source and load impedances as well as of possible transpositions or cross-bondings. The results are validated with the corresponding results obtained from frequency-domain transient simulations and laboratory measurements, whereas simple theoretical formulas for both overhead lines and underground cables are also investigated, revealing their limited accuracy. Practical cases of engineering interest are demonstrated, where the required single or multiple RFs are accurately calculated by the proposed method. Finally, the performance of the presented methodology is thoroughly examined incorporating two diagonalisation approaches for the calculation of the modal propagation velocities.

Optimization of Lumped Parameter Models to Mitigate Numerical Oscillations in the Transient Responses of Short Transmission Lines

“…where V k (s) and V m (s) are voltages at the sending and receiving ends in the frequency domain and s = jω is the complex angular frequency (rad/s). To clarify the results, the abscissa is normalized by the fundamental f 0 and harmonic f h frequencies expressed by [6,22]:…”

Analysis of the resonance phenomenon in unmatched power cables with the resonance surface response

“…With frequency-dependent per-unit-length (p.u.l.) parameters comes a frequencydependent propagation speed [13], and to determine the resonance frequency of such cables a numerical solution is indispensable [14,15]. The paper [14] gives an ecient method to calculate the resonance frequency for transmission lines connected to resistive loads, however, it cannot be applied to reactive loads.…”

“…parameters comes a frequencydependent propagation speed [13], and to determine the resonance frequency of such cables a numerical solution is indispensable [14,15]. The paper [14] gives an ecient method to calculate the resonance frequency for transmission lines connected to resistive loads, however, it cannot be applied to reactive loads. Knowledge on the resonance frequency is useful in many of the applications aforementioned, notably for resonance damping methods based on notch lters [3], which are likely to be reactive.…”

Control of superconducting dc transmission systems and solution of coupled electrothermal superconducting cable model

“…In case of the short circuit scenarios, ∆z and ∆t were taken equal to 82.5 m and 0.275 µs, respectively. Finally for the frequency at which calculations are conducted, analysis of [170] has been used.…”

“…Given w is the number of conducting layers, C, G, L and R are w ×w matrices, representing the per-unit length capacitance, conductance, inductance and resistance matrices of the transmission line [2,169], at the frequency of interest [170]. 1 n corresponds to the identity matrix of the same order.…”