The accidental outages of generating units are increasing rapidly around the world due to extreme weather, cyber attacks and some manual misoperations, which are seriously impacting the stable and secure operation of urban power systems. To enhance the system resilience, more attentions are paid to regulating flexible loads (FLs) in demand-side by utilizing the progressed Internet of Things technologies. However, most previous control methods of FLs are based on the detected frequency deviations or voltage violations, i.e., the regulation on FLs are implemented after the imbalance really happens. This may lead to the expansion of the accident influence and cause large-scale blackouts. To address this issue, this paper proposes an anticipatory control method of FLs to provide faster-than-real-time contingency reserve for the power system. Firstly, a reconstructed power system model after accidental outages is proposed to quantify the disturbance of generating units' outages. Then, an evaluation method of the system frequency deviation nadir is developed to prejudge the most serious damage caused by accidental outages. On this basis, an anticipatory control method of FLs is proposed to impede the fast drop of the system frequency and decrease the harm of accidental outages. Finally, the effectiveness of the proposed method is verified by numerical studies, where the evaluation accuracy of the system frequency nadir can reach about 95% and the maximum system frequency deviation can be reduced about 50%.