Necessary and sufficient conditions for observability in power systems

The notion of observability, is a measure of how well internal states of a system can be reconstructed using a given set of measurements. In this paper, we derive necessary and sufficient conditions for observability in a power system. Deriving sufficient conditions for observability is quite difficult and algebraic observability is often used as a surrogate tool for observability. We show that algebraic observability is necessary but not sufficient for observability. It is also shown that standard measurement sets of at least one voltage measurement, and paired active and reactive power measurements may lead to unobservability for certain measurement configurations. Using a nonlinear transformation and properties of graph theory, a set of sufficient conditions are derived for observability. These conditions are shown to be dependent on the topological properties as well as the type of available measurements. The efficiency and robustness of the proposed approach is also discussed. All results are validated using an IEEE-14 bus system. The proposed method can be utilized off-line as a planning tool during the initial stages of measurement system design as well as on-line prior to state estimation.