A comparison of harmonic modeling methods with application to the interconnection and the control of switched systems

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 highlight the frequency couplings within interconnected components. By these modeling techniques, a linear time-periodic model can be converted into a linear time-invariant model, 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 strong links between the different literature approaches and to develop a general harmonic methodology that unifies them. A rigorous theoretical framework for the modeling, analysis and control of linear time-varying systems with an arbitrary number of harmonics is developed. In particular, a harmonic model is proposed from which all the literature models can be easily derived. This paper also deals with the harmonic modeling of switched affine systems. It shows the advantages of harmonic modeling to analyze the frequency couplings within associated switched systems and to the control with active filtering.