Observability challenges in sparse estimation of fault events

Sparse state estimation methods enable the location of network events using limited data. For instance, recent works use sparse recovery techniques to locate various faults with a small number of measurements. This paper addresses the question of sparse state estimation observability. A well-known result is that observability may be determined using the sensing matrix spark. This paper shows that sparse events can be uniquely located even when the spark uniqueness condition is not met. This result stems from the specific structure of sparse events, which imposes additional constraints on the non-zero entries of the sparse vectors. Analytic conditions are derived for the observability of a single short to ground. These conditions are shown to be both sufficient and necessary. The observability criterion is demonstrated on the IEEE 30 system. It is shown that for this system, five sensors are sufficient to uniquely locate any single short-to-ground.