Simplified frequency-dependent formulae for series-impedance matrices of single-core HVAC cables

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. Different methods exist for estimating the impedance of single-core cables. The IEC60287-1-1 standard presents equations that may be use for power frequencies, whereas the loop-method, based on Bessel equations, is typically used for higher frequencies. Simplifications of the reference formula using Bessel equations exist, but they still have some complexity, e.g., hyperbolic cotangents and hyperbolic cosecants are used. Moreover, the series impedance matrix that is designed with these equations and used to estimate the resistance and reactance, requires the summation of at least eight different terms, all calculated in a different way. This paper simplifies the equations used in the loop method, by means of expansions in Taylor series, with other further simplifications that can be made for typical cable thicknesses and materials.