This study tackles a risk-limiting scheduling problem of non-renewable power generation for large power systems, and addresses potential violations of the security constraints owing to the volatility of renewable power generation and the uncertainty of load demand. To cope with the computational challenge that arises from the probabilistic constraints in the considered problem, a computationally efficient solution algorithm that involves a bisection method, an off-line constructed artificial neural network (ANN) and an on-line point estimation method is proposed and tested on the IEEE 118-bus system. The results of tests and comparisons reveal that the proposed solution algorithm is applicable to large power systems in real time, and the solution obtained herein is much better than the conventional optimal power flow (OPF) solution in obtaining a much higher probability of satisfying the security constraints.