Locating the source of forced oscillations on the basis of Lyapunov modal analysis

Abstract

Based on the recently proposed Lyapunov modal analysis framework, this study proposes a method for locating the source of forced oscillation in power system when its frequency is close to the natural oscillation of the system. This method combines the selective modal analysis and spectral decomposition of Lyapunov functions, which characterize the energy of voltage perturbation. The proposed modal indicators characterize the energy of voltage disturbances accumulated from the forced oscillation in the nodes. Based on the corresponding spectral decomposition, the part corresponding to the resonance between the forced oscillation and the natural oscillation is subtracted from this energy. “Non-resonant” part of the index calculated in each node of the network allows visualizing the profile of “non-resonant” energy on the power grid graph. Based on the obtained profile it is possible to solve the inverse problem and determine the location of the source of forced oscillations. In a test experiment with IEEE 68 bus system, forced oscillations at a frequency close to the system’s natural oscillation were introduced in different nodes of the system. Profiles of the “non-resonant” part of the energy are obtained on the network graph, from which the location of the source of the forced oscillation can be determined. The profile of the proposed modal indicator on the network graph can be obtained either from a known model of the system or from the measured data.