Probabilistic load flow considering correlations of input variables following arbitrary distributions

For the purpose of accurately calculating probabilistic load flow (PLF) with correlated input variables following arbitrary distributions, this paper proposes a Latin hypercube sampling (LHS) based PLF method, which combines kernel density estimation with Nataf transformation to improve the calculation performance. First, enhanced kernel density estimation with adaptive-bandwidth is established to precisely depict arbitrary distributions, including the atypical probability density functions (PDF) of power injections from renewable energies such as wind and photovoltaic. Then, considering the correlations of renewable energies and the difficulties of kernel density estimation dealing with correlativity, Gauss-Hermite integral based Nataf transformation is proposed to handle the problem. The proposed method is demonstrated to be feasible and practicable in modified IEEE 14 and IEEE 118 systems with additional wind and photovoltaic power. The results suggest that proposed method is prominent in efficiency and accuracy, and applicable to arbitrary distributions of power injections in PLF calculation.