Simplified formulae for the estimation of the positive-sequence resistance and reactance of three-phase cables for different frequencies

The installation of HVAC underground cables became more common in recent years, a trend expected to continue in the future. Underground cables are more complex than overhead lines and the calculation of their resistance and reactance can be challenging and time consuming for frequencies that are not power frequency. Software packages capable of performing exact calculations of these two parameters exist, but simple equations able to estimate the reactance and resistance of an underground cable for the frequencies associated to a transient or a resonance phenomenon would be helpful. This paper proposes new simplified formulae capable of calculating the positive-sequence resistance and reactance of a cable for frequencies associated to temporary overvoltages, slow-front overvoltages and resonance phenomena. The calculation of a cable´s resistance and reactance is made using a simplified series impedance matrix. The proposed formulae are validated by means of sensitivity tests and comparisons with generic cables. The paper finishes with an example demonstrating the estimation of the resonance frequency associated to a cable energisation using the formulae previously developed.