Abstract
In practice, because of different factors, the supply voltage (especially in the distribution level) almost always has some degrees of imbalance and harmonic pollution. With increasing the level of these power quality issues in recent years, their monitoring and compensation using custom power devices have received much attention. In addition, modern power converter based renewable energy sources are expected to provide some ancillary services to mitigate these power quality issues. These tasks and requirements often involve using a signal processing tool for the online detection of the fundamental sequence components and harmonics of the voltage and/or current signals. The typical choice for this purpose is the discrete Fourier transform as it offers a fast computational speed. It, however, may not be a very attractive solution for applications where the selective extraction of a few frequency components is required as it demands a high computational effort. In such scenarios, using time-domain signal decomposition algorithms is more desirable. Generally speaking, these algorithms are nonlinear feedback control systems, which include two or more dynamically interactive frequency-adaptive filters tuned to concerned frequency components. The complex structure of these algorithms, however, makes them complicated to analyze, especially for those who are not experienced in this field. This article aims to address this difficulty by developing harmonic models for these algorithms and investigating them. To this end, three case studies are considered. Through a harmonic linearization procedure, developing harmonic models for them is shown. The accuracy of these models is then investigated, and performing the harmonic stability analysis using them is demonstrated.