Flow-based Polynomial Chaos Expansion for Uncertainty Quantification in Power System Dynamic Simulation

TL;DR

This paper introduces flow-based Polynomial Chaos Expansion, a novel method that improves uncertainty quantification in power system simulations by accurately modeling complex input distributions using normalising flows.

Contribution

It proposes a unified framework combining normalising flows with PCE for better input uncertainty representation and introduces the Map Smoothness Index to assess map quality.

Findings

Flow-based PCE improves accuracy over traditional methods.

Smoother transformations lead to more reliable uncertainty quantification.

Validated on IEEE 14-bus and Great Britain systems.

Abstract

The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power system dynamics, its accuracy depends critically on the faithful representation of input uncertainty, an assumption that is oftern violated in practice due to correlated, non-Gaussian, and otherwise complex data distributions. In contrast to purely data-driven surrogates that often overlook rigorous input distribution modelling, this paper introduces flow-based PCE, a unified framework that couples expressive input modelling with efficient uncertainty propagation. Specifically, normalising flows are employed to learn an invertible transport map from a simple base distribution to the empirical joint distribution of uncertain inputs, and this map is then integrated directly into the PCE construction. In addition, the Map Smoothness Index (MSI) is introduced as a new metric to quantify the quality of the learned map, and smoother transformations are shown to yield more accurate PCE surrogates. The proposed Flow-based PCE framework is validated on benchmark dynamic models, including the IEEE 14-bus system and the Great Britain transmission system, under a range of uncertainty scenarios.