This paper proposes a fault-section location method based on sparse measurements, aimed at asymmetrical faults. A virtual current vector is defined to indicate the faulted section, which is sufficiently sparse except that the fault position corresponding entries are nonzero. To simplify the algorithm, the virtual vector is fixed by amplitudes of voltages and impedances and the feasibility is demonstrated. The Bayesian Compressive Sensing theory is introduced to reduce the number of required intelligent electronic devices (IEDs). In addition, the minimal number of IEDs and their allocation are discussed. The performance of the proposed method is validated in a 69-bus, 12.66 kV distribution system with six distributed generations (DGs) in response to various fault scenarios. The simulation results show that the method is robust for single-phase, double-phase, and double-phase to ground faults with high resistance under noisy condition. Furthermore, the method is applicable for networks with inverter interfaced DGs.