Rigorous calculation method for resonance frequencies in transmission line responses

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.