Continuous Switch Model and Heuristics for Mixed-Integer Nonlinear Problems in Power Systems

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.