Frequency characteristics of the d-q synchronous-frame current reference generation methods for active power filter

The d-q harmonics detection algorithms are dominant methods to generate current reference for active power filter (APF). They are often processed in synchronous frame and time domain. This paper researches the frequency characteristics of d-q synchronous transformation which are quite related to the design of close loop regulator and analysis of the performance. Intuitively, the synchronous transformation is explained with amplitude modulation (AM) in this paper. Then the synchronous filter is proven as time-invariant linear transformation and modeled with transfer functions in stationary frame and frequency domain. The frequency-domain analytical models imply that the synchronous transformation has an equivalent effect of frequency transformation, with which the synchronous filter achieves a band pass filter from the low pass filter in synchronous frame. To simplify the analytical model, an instantaneous positive/negative sequence frame is proposed as an expansion of symmetrical components theory. Based on these frequency analytical models, the synchronous filter is compared with the traditional filters in stationary frame. Further more, the d-q harmonics detection methods are improved to get rid of the inherent coupling of synchronous transformation. Typical examples are given to verify previous analysis and comparison. Simulation and experimental results are also given.