Probabilistic Load Flow Analysis Based on Sparse Polynomial Chaotic Expansion

Abstract

To aim at the deficiencies of the traditional second-order polynomial chaotic expansion with more input variables and larger calculation quantities applied in power systems probabilistic load flow (PLF) calculation, an improved PLF method is proposed based on sparse polynomial chaotic expansion theory in this paper. In this method, to obtain the sparse expression of the polynomial chaotic expansion (PCE) and reduce calculation quantity, the quadratic cross terms in the second-order PCE are eliminated by Sobol sensitivity analysis. And then, Nataf transformation is used to control the correlation among non-normal input variables. Through comparison on computational efficiency between probabilistic collocation point method and random sampling method in the sparse polynomial chaotic expansion, the probabilistic collocation point method is selected to suit samples allocation. By applying in IEEE-9, IEEE-30, and IEEE-118 standard test systems, respectively, the results show that the proposed method can dramatically reduce the deterministic PLF calculations quantity compared with the traditional stochastic response surface method (SRSM), and possesses the same accuracy as Monte Carlo method, and is an effective solving method for some high-dimensional input variable systems.