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Various methods have been proposed in the past for locating faults on distribution systems, which generally entail iterative procedures. This paper presents novel fault-location algorithms for overhead distribution systems that provide a unified solution that eliminates or reduces iterative procedures applicable to all types of faults. Two types of methods, respectively, for nonradial systems and radial systems have been proposed by utilizing voltage and current measurements at the local substation. The proposed methods are based on the bus impedance matrix, through which the substation voltage and current quantities can be expressed as a function of the fault location and fault resistance, a solution to which yields the fault location. The methods are developed in phase domain and, consequently, are naturally applicable to unbalanced systems. The assumptions made are that the distribution network parameters and topology are known so that the bus impedance matrix can be developed. Simulation studies have demonstrated that both types of methods are accurate and quite robust to load variations and measurement errors.