Efficient Polynomial Chaos Expansion for Uncertainty Quantification in Power Systems

TL;DR

This paper introduces a modified polynomial chaos expansion method that significantly improves computational efficiency for uncertainty quantification in large power systems, maintaining high accuracy and enabling practical applications.

Contribution

A novel, scalable PCE algorithm that exploits sparsity and algebraic properties to enhance efficiency without sacrificing accuracy in power system uncertainty analysis.

Findings

Successfully applied to the 1354-bus test system

Achieved high accuracy and robustness in uncertainty quantification

Enabled efficient solution of chance constrained optimal power flow

Abstract

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.