Eddy-current losses in unbonded tubes

A series solution for the eddy-current loss in thin isolated cable sheaths, busbar enclosures, water cooling pipes etc. has been developed using Carter´s method. The theory, which takes into account the magnetic field set up by the tube eddy currents themselves, can be applied to any system where the primary conductor current within a tube is coaxial with the tube, and the materials are nonmagnetic but not necessarily of equal dimensions or resistance. For convenience, the paper provides loss curves for the most common arrangements, i.e. 3-phase flat and trefoil. Results obtained using existing simplified formulas are compared with the computed results, and are shown to be in error by 10% and upwards for diameter/spacing ratios of more than 0.2 and values of frequency/tube-resistance greater than unity. The theory has been further extended to thick-walled tubes for which a correction factor has been derived.