Generic analytical solution for calculating the harmonic characteristics of multilevel sinusoidal PWM inverter

This paper presents the derivation of a generic analytical solution for calculating the harmonic characteristics of multilevel sinusoidal pulse width modulation (SPWM) inverter. This generic solution has advantages over previously published solution since the phase shifts of all the carriers can be made arbitrary. This feature gives a high degree of freedom for evaluating the harmonic structure of a multilevel SPWM inverter with different carrier phase combinations. A multilevel SPWM waveform is decomposed into a series of positive and negative DC biased PWM (DBPWM) waveforms. A 3-dimensional model for describing each individual DBPWM is first derived. After applying the double Fourier series to each waveform, the multilevel SPWM output is then obtained by summing all the DBPWM outputs. The validity of the solution is verified using Pspice simulations