In modern electric power systems there are thousands of control devices, spanning from low-voltage distribution networks to high-voltage transmission networks, that manage the energy flows, ensure the secure operation and stabilize the system. To analyze the performance and assess the impact of controllers on the electricity grid, time-domain simulations are most frequently used. In recent decades, all the new controllers introduced in electric power systems are digital controllers and their analog counterparts are gradually being replaced. Nevertheless, many of the most frequently employed controllers are still modeled in time-domain simulations as analog (continuous) systems, employing transfer functions or differential-algebraic equations. This approach introduces a discrepancy between the real response of digital controllers and the simulated one. In this paper, we investigate the impact that correctly modeling digital controllers has on simulation accuracy and performance.