The uncertainty of multiple power loads and re-newable energy generations in power systems increases the complexity of power flow analysis for decision-makers. The chance-constraint method can be applied to model the optimi-zation problems of power flow with uncertainty. This paper develops a novel solution approach for chance-constrained AC optimal power flow (CCACOPF) problem based on the da-ta-driven convexification of power flow and the fast algorithm for scenario technique (FAST). This method is computationally effective for mainly two reasons. First, the original nonconvex AC power flow constraints are approximated by a set of learn-ing-based quadratic convex ones. Second, FAST is a more ad-vanced distribution-free scenario-based solution method using far less scenarios than the conventional one, retaining a high confidence level. Eventually, the CCACOPF is converted into a computationally tractable convex optimization problem. The simulation results on IEEE test cases indicate that 1) the pro-posed solution method can excel the conventional one and ro-bust program in computational efficiency, 2) the data-driven convexification of power flow is effective in approximating original complex AC power flow.
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