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This paper proposes a novel method for fault location in distribution networks using compressive sensing. During fault and prefault voltages are measured by smart meters along the feeders. The voltage sag vector and impedance matrix produce a current vector that is sparse enough with one nonzero element. This element corresponds to the bus at which a fault occurs. Due to the limited number of smart meters installed at primary feeders, our system equation is underdetermined. Therefore, the \ell ^1-norm minimization method is used to calculate the current vector. Primal-dual interior point (PDIP) and the log barrier algorithm (LBA) are utilized to solve the optimization problem with and without measurement noises, respectively. Our proposed method is implemented on a real 13.8-kV, 134-bus distribution network when single-phase, three-phase, double-phase, and double-phase-to-ground short circuits occur. Simulation results show the robustness of the proposed method in noisy environments and satisfactory performance for various faults with different resistances. [ABSTRACT FROM AUTHOR]