Physics-Informed Dynamic Mode Decomposition for Power Systems Dynamic State Estimation with Uncertainties

This study investigates the improvement of power system dynamic state estimation accuracy under uncertainties by incorporating the physics of the energy conservation law into the classical dynamic mode decomposition (DMD). DMD, a data-driven technique for deriving reduced-order models and coherent structures from measurements, faces challenges in accurate state estimation when uncertainties arise. Based on Kirchhoff's current law and Ohm's law, the general energy conservation law of a power system is first mathematically derived. Subsequently, this derived physical law is applied to the DMD optimization process utilizing matrix-theoretic principles. By incorporating the energy conservation law, the linear operator is constrained to an energy conservation manifold, effectively addressing uncertainties through a weighted energy transformation matrix and a regularizer. Comparative case studies demonstrate the superior performance of piDMD over classical DMD in power system dynamic state estimation under different levels of noisy measurements and generator modeling details.