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

• Published in: International journal of electrical power & energy systems Vol. 157; p. 109806
• Main Authors: Li, Xingrui, Liu, Chengxi, Wang, Chenxu, Milano, Federico
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2024
• Subjects: Arbitrary polynomial chaos; K-means++ clustering; Power system dynamics; Renewable energy sources; Uncertainty quantification; Whitening transformation; Arbitrary polynomial chaos; Uncertainty quantification; Renewable energy sources; K-means++ clustering; Power system dynamics; Whitening transformation
• ISSN: 0142-0615
• DOI: 10.1016/j.ijepes.2024.109806

•Arbitrary polynomial chaos is proposed to quantify the effect of uncertainty on the dynamic response of power systems.•Whitening transformation is integrated as preprocessing to tackle the correlation of uncertainties.•K-means++ clustering is adopted to avoid matrix singularity when attempting different combinations of collocation points. 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 k-means++ 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.