Fast and Flexible Selective Harmonic Extraction Methods Based on the Generalized Discrete Fourier Transform

Abstract

Selective harmonic extraction plays an important role in power quality assessment, harmonic compensation, and so on. Among the various methods, discrete Fourier transform (DFT)-based algorithms has found wide and popular applications due to advantages like simplicity and excellent selectively filtering properties. However, DFT suffers from disadvantages like slow dynamics and sensitivity to frequency variations. In order to alleviate these drawbacks, an improved and extended DFT—generalized DFT (GDFT) is proposed. It is revealed in this paper that the conventional DFT can be viewed as a comb filter connected in series with complex resonators, and DFT relies on the mechanism of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pole-zero cancellation</i> for harmonic extraction. More importantly, the key reason behind the DFT slow transient responses is the large delay introduced by the comb filter. Therefore, this paper proposed to reconfigure the comb filter according to specific harmonic patterns of the input signal for improving the dynamic responses and system flexibility. The proposed GDFT not only maintains the advantages of simplicity and selectively filtering properties but also features fast transients, around 0.3 fundamental cycle for typical applications, which is much shorter than the one-cycle settling time of the conventional DFT. A phase-locked-loop block is also incorporated into the harmonic-detection system to deal with possibly large frequency variations in practical applications. Extensive tests are provided to validate effectiveness of the proposed method.