This paper presents a new formulation and solution approach to a probabilistic optimal power flow (POPF) problem. In this formulation, system demand is taken as a random vector of correlated variables, which allows us to consider the dependence between load types and locations. The POPF is clearly formulated and the optimality conditions are considered as a general nonlinear probabilistic transformation. A first-order second-moment method (FOSMM) is used to find their statistical characteristics. Computer results, and their comparisons to Monte Carlo simulation (MCS) approach, demonstrate the accuracy of our proposed methodology.