A Generalized Harmonic Extraction Algorithm Based on Multi-Window Average Filter Under Synchronous Rotating Frame

Abstract

Various harmonic extraction algorithms have been proposed to improve the steady-state and dynamic performance for active power filter. However, it is difficult to select a suitable method for a certain load current scenario. This article analyses the general characteristics of the harmonic extraction based on the “frequency shift” characteristic by Park transform, and it can be transformed into a low-pass filter under the synchronous rotating frame (SRF) for design. Starting from the typical average filter, a general FIR filter structure called multi-window average (MWA) is proposed. According to the actual load current components, aiming at the shortest delay, the design process and guideline are given. Combined with SRF, the MWA structure can generalize recursive discrete Fourier transform (RDFT), cascade delayed signal cancellation (CDSC) and their derived algorithms, which proves the equivalence between time-based harmonic extraction methods and frequency-based ones. Moreover, using the MWA structure can effectively reduce the complexity of the CDSC algorithm. The experiment proves that the typical RDFT and CDSC harmonic extraction can be equivalently realized by using the SRF-based structure. Under the presence of 6 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> + 1 and 12 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> − 2 harmonics, the proposed harmonic extraction time can reach 1/4 fundamental cycle. While greatly reducing the dynamic response time, the MWA structure reveals inherent unity among various harmonic extraction algorithms for the first time.