  Many power systems operation and planning computations (e.g., transmission
and generation switching and placement) solve a mixed-integer nonlinear problem
(MINLP) with binary variables representing the decision to connect devices to
the grid. Binary variables with nonlinear AC network constraints make this
problem NP-hard. For large real-world networks, obtaining an AC feasible
optimum solution for these problems is computationally challenging and often
unattainable with state-of-the-art tools today. In this work, we map the MINLP
decision problem into a set of equivalent circuits by representing binary
variables with a circuit-based continuous switch model. We characterize the
continuous switch model by a controlled nonlinear impedance that more closely
mimics the physical behavior of a real-world switch. This mapping effectively
transforms the MINLP problem into an NLP problem. We mathematically show that
this transformation is a tight relaxation of the MINLP problem. For fast and
robust convergence, we develop physics-driven homotopy and Newton-Raphson
damping methods. To validate this approach, we empirically show robust
convergences for large, realistic systems ($>$ 70,000 buses) in a practical
wall-clock time to an AC-feasible optimum. We compare our results and show
improvement over industry-standard tools and other binary relaxation methods.
