{'fraction_non_alphanumeric': 0.02125919869174162, 'fraction_numerical': 0.0, 'mean_word_length': 5.545454545454546, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
From real to complex FLL with unbalance and harmonic distortion compensation

This work presents a model-based frequency-locked loop (FLL) for three-phase systems subject to unbalance and harmonic distortion conditions. It is based on a pretty general model of a three-phase AC reference signal comprising a set of harmonic oscillators. Likewise, the proposed synchronization scheme comprises a set of adaptive harmonic oscillators to estimate the corresponding harmonic components. The proposed scheme considers three different types of harmonic oscillators that distinguish among the sequences involved on each harmonic component, which leads to a less demanding computational effort. The harmonic oscillators of higher order are grouped in a harmonic compensation mechanism dedicated to coping with the harmonic content of the reference signal. Therefore, the main contributions of this work are (i) the incorporation of a complex gain to accelerate the dynamic response of the scheme, (ii) the derivation of sequence-specific oscillators, and (iii) the stability analysis based on Lyapunov’s approach, which shows that the proposed scheme is globally stable provided the bandwidth of the frequency estimator is bounded.