Arbitrary polynomial chaos-based power system dynamic analysis with correlated uncertainties

This paper proposes a novel method based on arbitrary Polynomial Chaos (aPC) to evaluate how parameter and variable uncertainty impacts on the dynamic response of power systems. The method defines a set of orthogonal polynomials that approximate the relationship between the sources of uncertainties, such as the power generation of renewable energy resources, and the system dynamic response. Measurement data can be directly utilized to construct the aPC model without any prior knowledge of the probability distribution of the uncertainty. A whitening transformation method is also integrated to decouple correlated data sets and thus avoid errors caused by distribution fitting. Finally, to avoid numerical issues common to polynomial chaos methods, the kmeans++ clustering is embedded in the aPC. The accuracy and computational efficiency of the proposed method are validated through the WECC 3-machine 9-bus system and the IEEE 69-machine 300-bus system.