Probabilistic load flow calculation based on sparse polynomial chaos expansion

• Published in: IET generation, transmission & distribution transmission & distribution, 2018-06, Vol.12 (11), p.2735-2744
• Main Authors: Sun, Xin, Tu, Qingrui, Chen, Jinfu, Zhang, Chengwen, Duan, Xianzhong
• Format: Article
• Language: English
• Subjects: chaos; compressed sensing; compressive sensing technique; Copula theory; curse‐of‐dimensionality problem; generalised polynomial chaos expansion; gPCE‐based scheme; load flow; load flow output distribution; PLF; PLF method; polynomials; probabilistic load flow calculation; probability; probability statistics estimation; Research Article; sparse polynomial chaos expansion; statistical analysis
• ISSN: 1751-8687; 1751-8695; 1751-8695
• DOI: 10.1049/iet-gtd.2017.0859

A probabilistic load flow (PLF) method based on the sparse polynomial chaos expansion (PCE) is presented here. Previous studies have shown that the generalised polynomial chaos expansion (gPCE) is promising for estimating the probability statistics and distributions of load flow outputs. However, it suffers the problem of curse-of-dimensionality in high-dimensional applications. Here, the compressive sensing technique is applied into the gPCE-based scheme, from which the sparse PCE is built as the surrogate model to perform the PLF in an accurate and efficient manner. The dependence among random input variables is also taken into consideration by making use of the Copula theory. Consequently, the proposed method is able to handle the correlated uncertainties of high-dimensionality and alleviate the computational effort as of popular methods. Finally, the feasibility and the effectiveness of the proposed method are validated by the case studies of two standard test systems.