AC Dynamics-aware Trajectory Optimization with Binary Enforcement for Adaptive UFLS Design

The high penetration of distributed energy resources, resulting in backfeed of power at the transmission and distribution interface, is causing conventional underfrequency load shedding (UFLS) schemes to become nonconforming. Adaptive schemes that update UFLS relay settings recursively in time offer a solution, but existing adaptive techniques that obtain UFLS relay settings with linearized or reduced-order model formulations fail to capture AC nonlinear network behavior. In practice, this will result in relays unable to restore system frequency during adverse disturbances. We formulate an adaptive UFLS problem as a trajectory optimization and include the full AC nonlinear network dynamics to ensure AC feasibility and time-coordinated control actions. We include binary decisions to model relay switching action and time-delayed multi-stage load-shedding. However, this formulation results in an intractable MINLP problem. To enforce model tractability, we relax these binary variables into continuous surrogates and reformulate the MINLP as a sequence of NLPs. We solve the NLPs with a homotopy-driven method that enforces near-integer-feasible solutions. We evaluate the framework on multiple synthetic transmission systems and demonstrate that it scales efficiently to networks exceeding 1500+ nodes with over 170k+ continuous and 73k+ binary decision variables, while successfully recovering binary-feasible solutions that arrest the frequency decline during worst-case disturbance.