{'fraction_non_alphanumeric': 0.028595458368376788, 'fraction_numerical': 0.010092514718250631, 'mean_word_length': 5.230366492146596, '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}}
A Novel Method for Stochastic Measurement of Harmonics at Low Signal-to-Noise Ratio

This paper presents a digital stochastic instrument for the measurement of the harmonics of mains voltages and currents. The instrument operation is based on stochastic analog-to-digital (A/D) conversion and accumulation, with a novel hardware structure tailored for harmonic measurements. A theoretical approach in determining measurement uncertainty is first presented, and the accuracy trends with varying signal-to-noise ratios (SNRs) are then analyzed. Using this theoretical analysis, the relative standard uncertainty of measurement is found to be 0.32% at -10-dB SNR and less than 0.01% at 20-dB SNR. The method and the predicted uncertainty for 50 harmonics are first validated by simulation. The proposed technique is then implemented into a newly developed prototype instrument that was coupled with a coreless current measurement transformer. Calibration shows high linearity of the coreless transformer and, hence, of the whole instrument in a wide range of primary signals. Experimental results, which measure low-level and highly distorted currents, confirm both the theory and simulation.