Derivation of Theoretical Formulas of the Frequency Component Contained in the Overvoltage Related to Long EHV Cables

Abstract

Recent studies of long EHV cables show the importance of performing temporary overvoltage analyses. As the switching of EHV cables can trigger temporary overvoltages, it is important to find the dominant frequency component contained in the switching overvoltages of these cables. Since there are no theoretical formulas to find the dominant frequency, it is generally found by means of time domain simulations or frequency scans. The derivation of theoretical formulas has been desired as the formulas would be useful in verifying the results of time domain simulations or frequency scans. Additionally, the formulas could eliminate the necessity of building simulation models of some network components. In order to address this need, this paper derives theoretical formulas to find the dominant frequency in long cable energization overvoltages. The accuracy and practical usefulness of the formulas are confirmed by comparing with the results of time domain simulations.

Rigorous calculation method for resonance frequencies in transmission line responses

“…The results are in good agreement with those obtained by frequency-domain (FD) transient simulations [16]. Comparisons with theoretical formulas [2,13] are also presented, indicating their limitations. Next, the proposed method is applied in a series of practical cases, where the required RFs are successfully calculated.…”

“…The lumped parameter matrix is converted to a pul distributed form in order to be considered as part of the TL. This is done by using (7), which associates the DF derived by a lumped and a distributed electrical circuit [13]. Next, according to (8), the distributed parameter matrix is added to the pul series impedance matrix of the TL.…”

“…The preceding matrices are used in (4) for the calculation of the modal propagation velocity, whereas the same procedure can also be applied to cross-bonded cables [13,21]. However, the discontinuities associated with line conductor transposition and cable cross-bonding can also generate forward and backward propagation waves, and therefore originate new RFs [22].…”

“…This is mainly determined by the coupling of the excitation injection and the presence of possible groundings as well as of transposition and cross-bonding schemes [9,10,24]. In most practical cases, however, it is assumed that the aerial and coaxial modes dominate in OHTLs and cable systems, respectively [13,[22][23][24].…”

“…More specifically, for overhead transmission lines (OHTLs), RFs have been derived through simple equations, neglecting the influence of the source impedance [2]. For underground cables, a more sophisticated approach has been developed, incorporating the connected lumped elements at the TL sending end, restricted however to symmetrical cross-bonding systems only [13].…”