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access icon free Probabilistic load flow calculation based on sparse polynomial chaos expansion

© The Institution of Engineering and Technology
Received 01/06/2017, Accepted 12/03/2018, Revised 29/01/2018, Published 16/03/2018

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.

Inspec keywords: polynomials; chaos; load flow; statistical analysis; probability; compressed sensing

Other keywords: PLF method; PLF; compressive sensing technique; curse-of-dimensionality problem; Copula theory; gPCE-based scheme; load flow output distribution; generalised polynomial chaos expansion; probability statistics estimation; sparse polynomial chaos expansion; probabilistic load flow calculation

Subjects: Power systems; Other topics in statistics; Algebra

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