The topology of power grid will change when a failure occurs, which may cause the power system to lose its observability. Existing identification method ignores the influence of this special condition on accuracy of fault location. If the fault can be located accurately, the protection strategy will be taken after failure to prevent the expansion of the fault. In this paper, calculation method of unbalanced current in conventional power grid structure is analyzed, and the relationship between unbalanced current and fault line after fault is studied. Further, several possible phasor measurement unit (PMU) configurations are analyzed, the relationship between PMU configuration position and power system being not observable after fault is discussed, and the variation rule of the unbalanced current value under the condition of losing observability is revealed. By using the unbalanced current calculated value to derive the fault location, a fault location method is proposed, and a fault location process is developed. A 35-node power system is built with BPA simulation software to compare the location effect under different PMU configuration positions. Results show that the proposed method can accurately locate the fault. The proposed method is applicable to the wide-area backup protection with action information from protection devices, and extends the application of short-circuit fault location.