Analytical and Experimental Assessment of the Effect of Current Harmonics on the Heating of a Flat Rectangular Busbar

Higher harmonics can increase conductor temperature even when the total current root mean square (RMS) value remains unchanged, because Joule losses depend on frequency and the spatial distribution of current density. This study develops a compact analytical model of the heating of an isolated, flat rectangular copper busbar and assesses its predictions against laboratory measurements. A one-dimensional solution of the electromagnetic field and heat conduction equation yields a dimensionless heating coefficient for each harmonic and a weighted superposition rule for an arbitrary spectrum. The experimental assessment was limited to a copper busbar with a cross-section of 40 mm × 10 mm at a current of approximately 400 A with temperature rise predictions referenced to the 50 Hz experiment. Eight measurement tests covered four spectra with a fundamental frequency of 50 Hz and single-frequency excitations from 100 to 250 Hz. Nine temperature channels and the actual current spectra were recorded. For the controlled mixed spectra, the relative error of the analytical prediction with respect to the measured relative temperature rise ranged from −3.1% to +0.4%. Under excitation at 100–250 Hz, the analytical model underestimated the measured rise by 3.4–8.8%. The model can be useful for rapidly assessing the effect of harmonic spectra on the ampacity of strip conductors.