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We study low-latency detections of sparse false data injection attacks in power grids, where an adversary can maliciously manipulate power grid operations by modifying measurements at a small number of smart meters. When a power grid is under attack, the detection delay, which is defined as the time difference between the occurrence and detection of the attack, is critical to power grid operations. A shorter detection delay can shorten the response time, thus prevent catastrophic impacts from the attack. The objective of this paper is to develop low-latency false data detection algorithms that can minimize the detection delay subject to constraints on false alarm probability. The false data injection can be modeled with a sparse attack vector, with each non-zero element corresponding to one meter under attack. Since neither the support nor the values of the sparse attack vector is known, a new orthogonal matching pursuit cumulative sum (OMP-CUSUM) algorithm is proposed to identify the meters under attack while minimizing the detection delay. In order to recover the support of the sparse vector, we develop a new stopping condition for the iterative OMP algorithm by analyzing the statistical properties of the power grid measurements. Theoretical analysis and simulation results show that the proposed OMP-CUSUM algorithm can efficiently identify the meters under attack, and reliably detect false data injections with low delays while maintaining good detection accuracy.