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This paper proposes a novel algorithm for the voltage fluctuation detection of a power system based on sparse representation modeling. The contents of this research mainly include: (1) By first constructing a proper objective function of the frequency and phase, we convert the fundamental signal estimation problem to a simple mathematical convex optimization problem, which can be easily solved using an exhaustive search strategy. (2) From the viewpoint of signal restoration, we regard the voltage fluctuation detection as a signal inpainting problem and then develop an l 0 norm-based optimization equation that exploits the sparsity prior of fluctuation component to recover the desired representation vector. (3) With the assumption that the voltage envelope changes smoothly, we establish an l 2 norm-based regularization equation to further improve the regularity of the result. Experimental results show that the proposed algorithm performs well on demodulating the fundamental signal and voltage fluctuation component, with good ability of noise robustness, when compared to the classical Hilbert transform-based detection method and square demodulation method. [ABSTRACT FROM AUTHOR]