Aiming to solve the problem of dense-frequency signals in the power system caused by the growing proportion of new energy, this paper proposes a dense-frequency signal-detection method based on the primal–dual splitting method. After establishing the Taylor–Fourier model of the signal, the proposed method uses the sparse property of the coefficient matrix to obtain the convex optimization form of the model. Then, the optimal solution of the estimated phasor is obtained by iterating over the fixed-point equation, finally acquiring the optimal estimation result for the dense signal. When representing the Taylor–Fourier model as a convex optimization form, the introduction of measuring-error entropy makes the solution of the model more rigorous. It can be further verified through simulation experiments that the estimation accuracy of the primal–dual splitting method proposed in this paper for dense signals can meet the M-class PMU accuracy requirements.

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.