Unified analytical equation for theoretical determination of the harmonic components of modern PWM strategies

Pulse width modulation (PWM) is a key element of a voltage source inverter, inverter which is widely used for electric motor control and electric energy conversion. Several PWM methods have been proposed in the literature, focusing on performance, ease of implementation, and maximization of the transfer ratio. The difference between most of the proposed modulation methods like sine-triangular, SVM, and 120° - 60° - 30° Discontinuous PWM consists in the redistribution of the time-length applied for the zero voltage vectors during a fundamental frequency period. This paper presents a unified analytical equation for determining the theoretical spectra components for all the carrier based PWM methods with redistributed zero space vector time-length using the double Fourier integral analysis. The proposed unified equation can also be used for determination of the phase and line-to-line voltage spectra when the modulator works in over-modulation region. Moreover, the effect of the DC-link voltage ripple on the line-to-line voltage spectra is also considered. The experimental results show a very good agreement with the theoretically calculated spectra.