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

Recent studies of long extremely high-voltage (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. In addition, 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 them with the results of time-domain simulations.