Koopman Operator Applicalion to power Systems Integrating Wind Energy

Koopman modal analysis is a spectral theory for identifying single-frequency oscillatory modes called Koopman modes, extracted from a set of spatio-temporal dynamic observables. It is based on an operator which transforms a finite dimensional non-linear system into a linear infinite dimensional system. Because of its infinite dimensionality, an infinite number of modes with single frequencies may be obtained. The purpose of this paper is to explore this operator for the study of the angular transient stability of a power system integrating wind energy. A two-areas electric network, comprising four machines and a wind farm is considered. Koopman modal analysis is performed using different observables. The results are compared to linear modal analysis. Variable and fixed speed wind turbine technologies are tested with increased wind penetration levels. Inherent inter-area and local oscillations are subsequently characterized.