The escalating threat of climate change is driving the electric power system through a profound transition toward net-zero emissions. During this transition, the most noticeable characteristic is the large-scale integration of renewable generation sources, which has increased almost fourfold over the past ten years (from 6% to more than 30%). Although renewable energy brings clean power, its inherent uncertain generation leads to potential power grid instability. Hence, dealing with the newly integrated uncertainty in modern power system operations is vital. Classical approaches to handling uncertainties include chance-constrained programming and robust optimization. However, chance-constrained programming is effective often when the distribution knowledge is accessible, whereas solutions from robust optimization are often criticized for conservatism. To this end, distributionally robust optimization improves robust optimization and chance-constrained programming by considering distributional misspecification. Nevertheless, the misspecification may also arise during dataset collection. Intuitively, sample sets with different quality will lead to diverse estimations for uncertainties. This warrants considering the dataset collection misspecification issue in detail, which has only emerged recently. One promising solution is to adopt the notion of statistical feasibility to account for the misspecification in dataset collection. Specifically, on top of chance-constrained programming, guaranteeing statistical feasibility modifies the original chance constraints by incorporating a confidence level requirement concerning dataset collection uncertainty. The modified chance constraints are dealt with from a robust optimization view by using purely data-driven methods, which improves statistically feasible robust optimization practicability. Compared with robust optimization, considering the confidence level grants decision-makers the flexibility in balancing cost-effectiveness and conservativeness. This chapter introduces statistical feasibility and provides its implementation to three typical power system operation tasks with different scales, including thermostatically controlled load scheduling, economic dispatch, and unit commitment, showcasing the effectiveness and scalability of robust operation with a statistical feasibility guarantee. Looking into the future, it is evident that the statistically feasible robust methods will contribute to sample efficient data-driven modern power system operation with high penetration of renewable energy.