Convex Inner Approximations for Safe AC Dispatch With Device Dynamics

Overview & Synopsis

Safe AC dispatch requires both feasible operating points and enough ramping capability to reach the next target. This paper constructs convex inner approximations that connect nonlinear network feasibility, constrained device response, and dispatch-interval tracking. A fixed-point certificate enforces AC operating limits under bounded load uncertainty. Componentwise response envelopes convert heterogeneous device dynamics into affine conditions on measured states and power references. A command governor then combines these conditions with available ramping capability and a hard terminal-error bound. It selects an admissible target through a minimum-deviation objective and holds the corresponding reference while reserved fast regulation remains active. The resulting quadratic program optimizes controllable references and auxiliary variables. Tests on the IEEE 39- and 118-bus systems include 96 single-target executions and 64 transitions in continuous dispatch sequences at five- and fifteen-minute intervals. All 160 transitions satisfy the AC constraints, independent balancing-generator capability checks, and the prescribed regulation-adjusted terminal accuracy. Complete admission-cycle medians are 3.45 and 8.79 ms. A connected synthetic system with 3,200 buses and 1,000 generating units extends the computational assessment to 999 independent references, with a median cycle time of \LargeMedian{} s. The construction provides a tractable link between available ramping capability and safe, timely execution of AC dispatch.