Abstract The accidental outages of generating units are increasing in power systems, which can bring huge power shortage suddenly and lead to severe system oscillations. The secure operation of power systems sometimes cannot be guaranteed only by regulating traditional generating units, due to the rapid regulation requirement of making up for power shortage. To address this issue, this paper proposes using emergency demand response (DR) to provide contingency reserve capacities by adjusting the power consumption of flexible loads (FLs). Firstly, in order to analyze the dynamic regulation process of power systems in accidental outages, the power system model in faulty condition is reconstructed to obtain the regulation power from well-running generators. On this basis, FLs are modelled and integrated into the novel reconstructed power system model to be as an alternative method of making up for the fast regulation capacities. Considering that the inevitable communication time-delay probably leads to the slowdown of response speed and endangers the system security, an adaptive time-delay control (ATDC) scheme is proposed and integrated into the control process of aggregated FLs. In this manner, the regulation speed of FLs can be accelerated, the control precision of response capacities can be improved, and the power system frequency deviations caused by time-delay can be decreased. Finally, the proposed models and methods are verified by numerical studies. The results in the test system show that the frequency deviations can be decreased effectively from −0.3276 Hz to −0.1337 Hz in accidental outages by using the ATDC scheme of FLs.