Single phase line-broken (SPLB) fault is one kind of high impedance fault (HIF). When a SPLB fault occurs, there are four scenarios: SPLB fault with neither side conductors grounded (SPLB-NSCG), with source side conductor grounded only (SPLB-SSCG), with load side conductor grounded only (SPLB-LSCG), with both side conductors grounded (SPLB-BSCG). Traditional HIF detection methods using current or voltage characteristics have low sensitivity to SPLB fault. In this paper, voltage characteristics are analysed firstly in the cases of the first three scenarios of SPLB fault, respectively. Theoretical analysis finds that the voltage at both the sides of the disconnection point is significantly different. A high sensitive SPLB fault detection method based on differential voltage is proposed for radial distribution network with different data synchronization ability. Finally, SPLB fault location methods based on centralized intelligent mode feeder automation (FA) and intelligent distributed mode FA are proposed. Simulations based on PSCAD verify that the proposed SPLB fault detection method is feasible, highly sensitive and immune to the neutral grounded mode, fault scenarios and fault resistance.