This paper proposes a novel method for fault location in distribution networks using compressive sensing. During-and pre-fault 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 limited number of smart meters installed at primary feeders, our system equation is underdetermined. Therefore, the ℓ 1 -norm minimization method is used to calculate the current vector. Primal-Dual interior point (PDIP) and 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.Index Terms-fault location, distribution networks, smart meters, compressive sensing, ℓ 1 and stable ℓ 1 -norm minimization
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