Probabilistic load flow (PLF) analyses the probability behaviour of the power injected and demanded in an electrical network, providing cumulative results of the power flowing through its lines. However, the probability behaviour analysis is not complete if the correlation between load demands has not been considered. Environmental or social factors can lead to such correlation. This paper proposes an analytical method to solve the PLF considering load demand correlation. It is based on the use of cumulants and Gram-Charlier expansion. The development proposed in the paper has been proved, the consistency of the method has been checked and the influence of the correlation in the solution of the PLF is shown. (C) 2014 Elsevier B.V. All rights reserved.