Leveraging Fourier Theory of Jumps for Analysis of Power Quality in PWM Inverters

The sine-triangle PWM (STPWM) technique is undoubtedly a foundational facet in power electronics engineering figuring in almost all standard & introductory textbooks. Notwithstanding, the authors recognize that certain analytical facets of STPWM are intentionally kept out of the textbook discourse in view of the mathematical complexity and intractability involved, as those developments often entail the Double-Fourier series, which is typically deemed esoteric at (under)graduate levels. This paper aims to depart from this convention and leverage an alternative, the Fourier Theory of Jumps (FTJ), an analytical tool that is more easily accessible for academic students & practicing engineers as compared to its double-Fourier counterpart, and examine STPWM to shed light on the following facets—(a) comparison of naturally- and regularly-sampled STPWM, and exact analytical evaluation of fundamental & harmonic voltages in 2-level PWM voltage, (b) a closer examination of symmetrically- and asymmetriccally-sampled variants in the realm of regularly-sampled STPWM, and (c) impact of phase shift on fundamental & harmonic voltages in 3-level PWM voltage. These are pertinent topics especially when the PWM is implemented practically on a digital processor, which is commonplace today. Detailed numerical and simulation results are provided, to verify the analytical development. A key objective of this work is to add academic & educational value to the subject of STPWM and enhance its analytical comprehensibility through a critical examination of results derived via FTJ & the accompanying discussions/inferences, to benefit academic beginners making a foray into the subject.