Ac Hysteresis Loop Depending on the Phase Angle of the Higher Harmonic Induction

For the design of high efficiency electric machines, analysis of higher harmonic frequency components of the magnetic induction is necessary. We have measured ac magnetic properties of non-oriented silicon steel under harmonic frequencies ranging from $3^rd$ (180 Hz) to $9^th$(540 Hz) and harmonic amplitude components from 10% to 50% of the total amplitude ($B_max$=1.5T). From the experiment, it is found that, if the magnetic induction waveform has above $9^th$ harmonic frequency components of the magnetic induction, the core losses only depended on the harmonic amplitude component, but if harmonic frequency becomes lower than 9th harmonic frequency, the core losses depend on the phase angle and the harmonic amplitude, and phase angle should be considered in the design of electric machine.