A comparison of harmonic modeling methods with application to control of switched systems with active filtering

Many harmonic modeling approaches have been introduced in the literature, such as generalized state-space averaging, dynamic phasors, extended harmonic domain, and harmonic state-space. They are capable of capturing both the transient evolution and the steady-state of harmonics. They model the frequency coupling nature of a system and can expose the frequency couplings within interconnected components. By these modeling techniques, a linear time-periodic system can be converted into a linear time-invariant system, which allows the use of traditional analysis and control methods. This paper presents a state of the art of harmonic modeling approaches. Its contribution is to clearly establish the links between the different approaches, in particular through the specification of the decomposition of non-periodic signals in generalized Fourier series with time-varying coefficients. This paper also shows the advantages of harmonic modeling to analyse the frequency couplings within associated systems and to the control with active filtering.