Inferring Power System Frequency Oscillations using Gaussian Processes

Synchronized data provide unprecedented opportunities for inferring voltage frequencies and rates of change of frequencies (ROCOFs) across the buses of a power system. Aligned to this goal, this work puts forth a novel framework for learning dynamics after small-signal disturbances by leveraging the tool of Gaussian processes (GPs). We extend results on inferring the input and output of a linear time-invariant system using GPs to the multi-input multi-output setup by exploiting power system swing dynamics. This physics-aware learning technique captures time derivatives in continuous time, accommodates data streams sampled potentially at different rates, and can cope with missing data and heterogeneous levels of accuracy. While Kalman filter-based approaches require knowing all system inputs, the proposed framework handles readings of system inputs, outputs, their derivatives, and combinations thereof on an arbitrary subset of buses. Relying on minimal system information, it further provides uncertainty quantification in addition to point estimates for dynamic grid signals. The required spatiotemporal covariances are obtained by exploring the statistical properties of approximate swing dynamics driven by ambient disturbances. Numerical tests verify that this technique can infer frequencies and ROCOFs at non-metered buses under (non)-ambient disturbances for a linearized dynamic model of the IEEE 300-bus benchmark.