Cylindrical multipole expansion for periodic sources with applications for three-phase power cables

This paper presents a cylindrical multipole expansion for periodic sources with applications for three-phase power cables. It is the aim of the contribution to provide some analytical solutions and techniques that can be useful in the calculation of cable losses. Explicit analytical results are given for the fields generated by a three-phase helical current distribution and which can be computed efficiently as an input to other numerical methods such as, for example, the Method of Moments. It is shown that the field computations are numerically stable at low frequencies (such as 50 Hz) as well as in the quasi-magnetostatic limit provided that sources are divergence-free. The cylindrical multipole expansion is furthermore used to derive an efficient analytical model of a measurement coil to measure and estimate the complex valued permeability of magnetic steel armour in the presence of a strong skin-effect. (Less)