The increased penetration of intermittent renewable energy sources and random loads has caused many uncertainties in the power system. It is essential to analyze the effect of these uncertain factors on the behavior of the power system. This study presents a new powerful approach called probability-boxes (p-boxes) to consider these uncertainties by combining interval and probability simultaneously. The proposed method is appropriate for problems with insufficient information. In this paper, the uncertainty of distribution functions is modeled according to the influence of natural factors such as light intensity and wind speed. First, the p-boxes load flow problem is studied using an appropriate point estimation method to calculate statistical moments of probabilistic load flow (PLF) outputs. Then, the Cornish-Fisher expansion series is used to obtain the probability bounds. The proposed approach is analyzed on the IEEE 14-bus, and IEEE 118-bus test systems consist of loads, solar farms, and wind farms as p-boxes input variables. The obtained results are compared with the double-loop sampling (DLS) approach to show the proposed method's precision and efficiency.