Abstract: In modern power systems, the large-scale integration of renewable energy sources such as wind and photovoltaic power generation, along with uncertainties like random failures of system components, is increasing. The N-1 security criterion only considers the failure of a single system component and has gradually been extended to the N-k security criterion, which accounts for all combinations of up to k simultaneous component outages. Therefore, based on existing research, a new N-1-Δk security criterion is proposed. This is an extended version of the N-1 security criterion and differs from the N-k standard in that the scale of contingencies considered per hour is determined by assessing the potential risks of hourly contingencies. Additionally, four potential risk assessment criteria are introduced, and a two-stage adjustable robust unit commitment model is developed, incorporating a constant to control the conservatism of the N-1-Δk security criterion. The improved Benders decomposition method is employed to solve the model, with additional maximum feasible subsystem cut planes generated in each iteration to enhance algorithm performance.