A Simple Innovative Method to Calculate the Magnetic Field Generated by Twisted Three-Phase Power Cables

This paper firstly examines the consolidated analytical methodologies available in literature for the calculation of the magnetic field generated by a twisted three-phase conductor arrangement carrying balanced three-phase currents. Such literature methodologies consist of an exact analytical expression of the RMS magnetic induction given in the form of complicated Bessel-function series and of an approximation of such exact expression where only the first term of the series is considered. Subsequently, a simple innovative approximated formula for the RMS magnetic induction generated by twisted three-phase power cables is obtained by means of an heuristic procedure. This formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by the case of a twisted three-phase power cable used for power distribution at the medium voltage level.