A considerable portion of the events occurring in distribution systems are high-impedance faults (HIFs), which are rarely detected by conventional overcurrent and overload protection. HIF draws non-predictable currents from the network, occasionally leading to arcing. Existing HIF detection methods focus on the transient properties of HIF and define it as a feature extraction problem, hence requiring measurements with high resolution. Alternatively, we propose using the static properties of HIF for its detection. We show that regardless of the HIF transient behavior, its effective current and average power will affect the system static state variables. Thus, we define the HIF detection in a static framework, realized using a central state estimator. The distribution system state estimation model is augmented to allow for HIF detection across the entire system. The IEEE 13-bus and 123-bus systems are selected to evaluate the effectiveness of the proposed approach to HIF detection, where system observability is also investigated.