In recent decades, the number of smart digital controllers employed in electric power systems has increased drastically. Either from the modernization of existing analog ones or the introduction of new, data-driven, or even optimization-based controllers, they are now dominating the behavior of power systems. However, this introduces a challenge in the simulation of power system dynamics, as the existing numerical simulation methods are very time-consuming when tackling the resulting hybrid differential-algebraic systems. In this paper, a novel interpolation-based method is proposed for performing fast and accurate dynamic simulations of electric power systems equipped with smart digital controllers. This method fully exploits the potential of variable time-step integration methods without requiring a time-step reduction in the case of discrete events stemming from digital controllers. Therefore, it accelerates the numerical simulation of large-scale systems containing many non-equation-based smart digital controllers, while maintaining accuracy. The performance of the proposed method is showcased using both conventional and smart digital controllers.