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Open access transmission has created a deregulated power market and brought new challenges to system planning. This paper proposes a new method to compute a probabilistic load flow in extensive power systems for the purpose of using it as a quick screening tool to determine the major investment on improving transmission system inadequacy. This innovative method combines the concept of Cumulants and Gram-Charlier expansion theory to obtain probabilistic distribution functions of transmission line flows. It has significantly reduced the computational time while maintaining a high degree of accuracy. This enables probabilistic analysis of power flow problems to be treated objectively and allows quantitative assessment of system reliability.