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• An improved method considering correlated stochastic variables is proposed for PLF. • A twice-permutation technique is proposed to ensure the desired correlations. • Singular value decomposition extends the scope of the method. As the increasing integration of large-scale renewable energy sources in power systems, the stochastic characteristics of loads and renewable energy systems become much more complex and impacts power systems much more than ever. Probabilistic load flow analysis is a powerful tool to discover the stochastic characteristics of power systems. There are two important issues for probabilistic load flow analysis based on Monte Carlo simulation: (i) How to generate random samples with the specific distribution and correlation; and (ii) how to make the simulation method to work well even when the correlation matrices are not positive definite. In order to handle the two issues, Nataf transformation combined with Latin hypercube sampling and singular value decomposition method is proposed for solving probabilistic load flow problems with correlated variables in this paper. By using the singular value decomposition (SVD), the proposed method works well even when the correlation matrices are not positive definite. And the twice-permutation technique based on SVD ensures that the samples have the desired correlations. The investigation on modified IEEE 14-bus system and modified IEEE 118-bus system shows that the proposed method is accurate and efficient. [ABSTRACT FROM AUTHOR]