  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.
