Power quality monitoring equipment is inevitably faced with the problem of data loss and is vulnerable to the interference of noise or bad data. We propose a harmonic data recovery method that is based on graph clustering and non-negative matrix factorization (NMF) under multiple constraints. Compared with the existing harmonic data recovery methods, the proposed method can effectively recover lost data and it has a strong anti-interference ability, especially for the recovery of harmonic data with interference. In the recovery of data loss, noisy interference tests and bad data interference tests, the presented recovery algorithm has high accuracy within 60% for continuous missing data. In an environment with SNR = 50, this method has high recover reliability and accuracy within 15% for situations involving bad data interference.

To improve the detection speed for wide-frequency dense signals (WFDSs), a fast minimization algorithm (FMA) was proposed in this study. Firstly, this study modeled the WFDSs and performed a Taylor-series expansion of the sampled model. Secondly, we simplified the sampling model based on the augmented Lagrange multiplier (ALM) method and then calculated the augmented Lagrange function of the sampling model. Finally, according to the alternating minimization strategy, the Lagrange multiplier vector and the sparse block phasor in the function were iterated individually to realize the measurement of the original signal components. The results show that the algorithm improved the analysis accuracy of the WFDS by 35% to 46% on the IEEE C37.118.1a-2014 standard for the wide-frequency noise test, harmonic modulation test, and step-change test, providing a theoretical basis for the development of the P-class phasor measurement unit (PMU).