  In this paper, we extend a circuit-based, current-voltage power flow
formulation to include frequency deviations and implicitly model generator
primary and secondary control actions as a function of their temporal
dependence. This includes extending the slack bus generator model(s) to better
represents its true behavior with frequency controls. These implicit models
obviate the need for outer iteration loops and improve the robustness of the
simulation convergence when frequency deviations are considered. The simulation
framework is highly scalable and is demonstrated on 85k+ bus systems.
