A Data-Driven Koopman Approach for Power System Nonlinear Dynamic Observability Analysis

A prerequisite to dynamic state estimation of a stochastic nonlinear dynamic model of a power system is its observability analysis. However, due to the model nonlinearity, the traditional methods either suffer from a poor estimation accuracy if a linear approximation is performed or yield an extremely complicated procedure if the Lie-derivative method is applied to a large-scale power system. To address these weaknesses, we propose a new data-driven Koopman-based observability method by revealing the link that exists between the Koopman operator and the Lie-derivative in the Koopman canonical coordinates. This enables the proposed data-driven method not only to be fully derivative-free, which alleviates its implementation complexity but also overcomes the model nonlinearity and inaccuracy of the system. Furthermore, as an important byproduct, the proposed observability analysis scheme provides a valuable guide for the selection of the observables of the Koopman operator, which is a major difficulty for the application of this operator. Finally, we demonstrate the excellent performance of the proposed method on several IEEE standard test systems.