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.

文献中已经引入了许多谐波建模方法，例如广义状态空间平均，动态相量，扩展谐波域和谐波状态空间。它们能够捕获瞬态演变和谐波的稳态。他们对系统的频率耦合特性进行建模，并且可以突出互连组件内的频率耦合。通过这些建模技术，可以将线性时间周期模型转换为线性时间不变模型，从而可以使用传统的分析和控制方法。本文介绍了谐波建模方法的最新技术。它的作用是清楚地在不同的文献方法之间建立牢固的联系，并发展统一它们的通用谐波方法。建立了严格的理论框架，用于建模，分析和控制具有任意数量谐波的线性时变系统。特别是，提出了一个谐波模型，从中可以容易地得出所有文献模型。本文还涉及仿射系统的谐波建模。它显示了谐波建模的优点，可以分析相关开关系统内的频率耦合，并通过有源滤波来控制。