The area of vulnerability (AOV) of point of common coupling (PCC) can directly reflect the issue of voltage sag caused by faults in power system. In order to calculate the area of vulnerability more accurately and faster, this paper proposes a new fault positions method based on interpolation, which overcomes the blindness of setting fault points. The influence of transformer winding connections on voltage sag is also taken into account. Short-circuit calculation is adopted and transfer matrix representing the transfer law of transformer on voltage sag is deduced firstly. Then, the principle and implementation flow of the new method are presented in detail. Finally, the new method is applied to a regional power system of China, and graphic result of the area of vulnerability is displayed under balanced and unbalanced faults.