Neural Posterior Estimation for Empirical Power System Time Series

Methods for state and parameter estimation are widely used to analyze complex systems, such as power systems. Estimating parameters is often necessary for follow-up simulations or effective control. Bayesian approaches allow us to go beyond point estimates and include domain knowledge when identifying parameters. However, such Bayesian approaches are often limited to simulated settings and not well-tuned for noisy, empirical data. We propose to investigate power systems, specifically the power grid frequency dynamics, as an important empirical use case with non-trivial data. Within our article, we introduce the concept of Simulation-Based Inference (SBI) for power grid frequency dynamics. Furthermore, we identify an amortized Neural Posterior Estimator (NPE), using recent normalizing flow architectures, as a suitable method for Bayesian parameter inference. We initially validate the model based on simulated observations and demonstrate the usability of amortized NPE on stochastic models for power grid frequency. Next, we apply the estimation method on empirical frequency data from European synchronous areas and quantify how it outperforms three baseline models based on newly designed posterior predictive checks. Finally, we carry out a detailed analysis of the inferred posterior distributions, in terms of time-dependency and correlations, providing some additional consistency checks. Overall, we demonstrate how Bayesian inference can be carried out and quantified in a complex, noisy, empirical setting.