To ensure the safe operation of the active distribution network (ADN), accurate fault diagnosis and location are crucial to improve the reliability indices and reduce the outage time. This paper proposes a characteristic model-based method for the single phase to earth fault in the ADN system. Firstly, the characteristic model of the fault factor extracts the phasor distribution characteristics of the voltage and current along the distribution feeder line and estimates the current contribution of DG units to the fault point. Based on the minimum entropy theory, the solution of nonlinear characteristic model is transformed to a single-objective optimization of the characteristic entropy and the diagnosis criteria is formulated. Then, the two-stage fault location scheme for single phase fault is proposed. The fault diagnosis stage estimates the suspicious fault section to reduce the search area and the fault location stage locates the exact fault distance. The Fibonacci search algorithm is utilized for fault location to the optimize iterative and minimize the respond time. The proposed scheme is general for all DG types and overcomes the requirement of its individual model parameters. The proposed method is validated in the IEEE 34-bus distribution test system using the phasor measurement unit (PMU). Test results of the model-based diagnosis and location method can reveal accurate fault location and rapid response at different fault impedance and small time delay comparing with the radial basis function neural network (RBF), and wavelet neural network (WNN) method.