Application of Detectability Analysis for Power System Dynamic State Estimation

In this paper, detectability analysis is studied and extended to guide selection of measurements for the dynamic state estimation (DSE) of a synchronous machine. To make sure that the DSE converges, past studies suggested that enough measurements must be available to make the system observable. In this paper, the convergence condition is relaxed via detectability analysis to reduce the number of required measurements. Because the objective of the DSE is to estimate the current states as time progresses, it is shown that a DSE observer can converge not only for an observable system but also for an unobservable system if the eigenvalues corresponding to the unobservable states are stable. Simulation results using the IEEE 10-machine, 39-bus system show that the unscented-Kalman-filter-based DSE can converge when measurements are chosen such that the unobservable states have stable eigenvalues. In comparison with observability analysis, the proposed application of detectability analysis can reduce the number of measurements required for the existence of a DSE observer.