  Achieving robust and scalable convergence for simulation of realistic power
flow cases can be challenging. One specific issue relates to the disconnected
solution space that is created by the use of piecewise-discontinuous models of
power grid devices that perform control mechanisms. These models are generally
resolved by outer iteration loops around power flow, which can result in
solution oscillations, increased iteration count, divergence or even
convergence to a solution in an unstable operational region. This paper
introduces a continuously differentiable model for device control mechanisms
that is incorporated within the power flow formulation. To ensure robust power
flow convergence properties, recently introduced homotopy methods are extended
to include these continuous models. The scalability and efficacy of the
proposed formulation is demonstrated on several large-scale test cases that
represent the US Eastern Interconnect network, the Synthetic USA, and the
Nigerian grid.
