With the extensive installation of intelligent electronic devices with bi-directional fault monitoring capabilities, richer fault direction information can be collected and utilized to achieve an accurate fault diagnosis. In this paper, we consider the fault diagnosis problem in active distribution systems with distributed generators connected, such as rotating electrical machine power sources and centralized inverter interfaced renewable energy resources. The fault diagnosis problem is modeled as a linear integer programming problem with an objective to minimize the numbers of fault zones and false alarms. A novel functional form is derived to capture the expected alarms sent by bi-directional fault monitoring devices to be compared with the actual alarms received by the dispatch center. Uncertainties in both the monitoring and communication stages are considered in the model by formulating the numbers of false alarms in the objective function. Three types of suspected false alarms can be detected: "missing alarms", "distorted alarms", and "reverse alarms". By solving the developed optimization model for fault diagnosis, false alarms and suspected fault zones can be found. Case studies in a modified IEEE 33-bus system and a 55-bus system in Guangzhou, China are carried out in several different scenarios with multiple faults to demonstrate the performance of the proposed model. Numerical tests show that the proposed approach is superior in computational time such that it can be used for real-time fault diagnosis in active distribution systems. INDEX TERMS Active distribution system, bi-directional fault monitoring devices, fault diagnosis, linear integer programming.