Residual dynamic mode decomposition based prediction of sustained low frequency oscillations in power grid

Abstract

The application of dynamic mode decomposition (DMD) for obtain the Koopman operator has been widely adopted to reveal the spectral features of dynamics in the power grid system. However, due to spurious eigenvalues, its application remains limited. Furthermore, with application to measurements from PMUs, data-driven approaches find their suitability. In this paper, recently proposed residual DMD (ResDMD), with kernel parameters have been explored as data-driven approach to predict the dynamics of states corresponding to low frequency oscillations (LFO). The ResDMD has the ability to compute spectra and pseudospectra of general Koopman operators with high order convergence guaranteed. This in turn is achieved with dictionary provided by kernalised extended DMD (kEDMD) to be used with ResDMD. The robust and verification of Koopmanism is demonstrated on synthetic LFO signals and measured PMUs data. The analyzed window examples of signals/data include mixed mode of LFO (sustained) and excitation of mode (transition to nonlinearity). The results are supported with approximated spectral properties, prediction of states analyzed for different window length (different size of samples), sampling rate and initial state condition for dynamics representation.