Data-driven transient stability analysis using the Koopman operator

• Published in: International journal of electrical power & energy systems Vol. 162; p. 110307
• Main Authors: Matavalam, Amar Ramapuram, Hou, Boya, Choi, Hyungjin, Bose, Subhonmesh, Vaidya, Umesh
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01-11-2024
• Subjects: Koopman operator; Power systems; Reproducing kernel Hilbert space; Transient stability; Koopman operator; Reproducing kernel Hilbert space; Power systems; Transient stability
• ISSN: 0142-0615
• DOI: 10.1016/j.ijepes.2024.110307

We present data-driven methods for power system transient stability analysis using a unit eigenfunction of the Koopman operator. We show that the Koopman eigenfunction with unit eigenvalue can identify the region of attraction of the post-fault stable equilibrium. We then leverage this property to estimate the critical clearing time of a fault. We provide two data-driven methods to estimate said eigenfunction; the first method utilizes time averages over long trajectories, and the second method leverages nonparametric learning of system dynamics over reproducing kernel Hilbert spaces with short bursts of state propagation. Our methods do not require explicit knowledge of the power system model, but require a simulator that can propagate states through the power system dynamics. Numerical experiments on three power system examples demonstrate the efficacy of our method.
•We propose a data-driven method for power system transient stability analysis using the Koopman operator.•We relate the computation of the eigenfunction of Koopman operator to the time-domain simulation.•We provide two data-driven methods to construct the Koopman eigenfunction.