Abstract：This paper proposes an engineering method for fast calculating the PWM-induced harmonic losses in interior permanent magnet synchronous machines (IPMSMs) with hairpin windings obtained from the simplification of the quick calculation method of PWM-induced harmonic losses in permanent magnets and silicon steel sheets proposed earlier. Based on the basic rule that harmonic losses are proportional to the square of harmonic voltages, the frequency-domain small-signal time-harmonic finite element analysis is used to establish the functional relationships between harmonic losses and the square of harmonic voltages. Thus, harmonic losses in the stator and rotor with the spectra of harmonic voltages in the stator and rotor reference frames can be fast calculated, respectively. In addition, the proposed algorithm based on the frequency-domain small-signal analysis is applied to calculate PWM-induced harmonic AC copper losses for the IPMSMs with hairpin windings. As a result, the PWM-induced harmonic losses over the entire working condition can be estimated in a few minutes. The efficiency maps are compared under the sinusoidal current source (SCS) supply, considering PWM-induced harmonic losses and the measured efficiency, the proposed method can reduce the maximum deviation of the computational efficiency under SCS supply from 4% to about 1% at low speed and light load working conditions and improve the calculation accuracy of efficiency in the entire working area.
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