# Efficient Polynomial Chaos Expansion for Uncertainty Quantification in Power Systems

arXiv: https://arxiv.org/abs/1910.06498 · HTML: https://mlsanity.com/paper/1910.06498/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2019.

## Built on by (most cited first, 3 of 3)

- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [Bayesian tomography using polynomial chaos expansion and deep generative networks](https://mlsanity.com/paper/2307.04228/) (2023)
- [Bayesian full waveform inversion with sequential surrogate model refinement](https://mlsanity.com/paper/2505.03246/) (2025)

## Abstract (arXiv)

Growing uncertainty from renewable energy integration and distributed energy resources motivate the need for advanced tools to quantify the effect of uncertainty and assess the risks it poses to secure system operation. Polynomial chaos expansion (PCE) has been recently proposed as a tool for uncertainty quantification in power systems. The method produces results that are highly accurate, but has proved to be computationally challenging to scale to large systems. We propose a modified algorithm based on PCE with significantly improved computational efficiency that retains the desired high level of accuracy of the standard PCE. Our method uses computational enhancements by exploiting the sparsity structure and algebraic properties of the power flow equations. We show the scalability of the method on the 1354 pegase test system, assess the quality of the uncertainty quantification in terms of accuracy and robustness, and demonstrate an example application to solving the chance constrained optimal power flow problem.