Inference of modes for linear stochastic processes
This work addresses mode inference for dynamical systems like power networks, but it appears incremental as it applies known methods to a specific domain.
The paper tackles the problem of inferring modes (damping rates, frequencies, and shapes) for linear stochastic processes from real-time observations, motivated by detecting oscillations in AC electrical networks.
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For a real mode, we wish to infer its damping rate and mode shape. For a complex mode, we wish to infer its frequency, damping rate and (complex) mode shape. Their amplitudes and correlations are encoded in a mode covariance matrix. The work is motivated and illustrated by the problem of detection of oscillations in power flow in AC electrical networks. Suggestions of other applications are given.