Reachability-based Time-domain Distance Protection

Distance relays detect faults on transmission lines from local voltage and current measurements. In this paper, we characterize the set of time-domain measurements a distance relay can observe during a fault as a reachable set. We define corresponding fault tests in terms of set-based state estimation. This allows us to model the full network as an RLC circuit with voltage and current sources. In general, computing reachable sets and set-based state estimates is intractable. For each fault type, we construct a reduced-order, two-dimensional model in terms of the apparent voltage and current seen by the relay. This makes all computations efficient, aligns with standard quantities in distance protection, and allows us to define instantaneous fault tests in terms of unsolved differential equations.