Certified AC Dispatch over Load Sets and in Continuous Time: Verified Feasibility and Optimality Gaps

An optimal power flow dispatch is computed for one forecast load but operated while loads change and automatic generation control absorbs forecast errors. We certify operation over load sets: a parametric Krawczyk test proves a power-flow solution for a dispatch or affine policy, Taylor models prove every limit, and load-affine Lagrangian bounds bound its relative regret by ε, with the bound maximized exactly over the set. Each piece of a ramped schedule under a box of regional forecast errors is such a set. On eight benchmark systems at ε = 1%, a rule interpolating three optimal power flows is certified for ±5% load-level swings at 78% of the test loads on average, against 57% for a secant through them and 44% for participation factors. Under the hourly optimal dispatch, some sampled one-percent regional error violates an operational threshold in 44% of the hours; certificate-designed schedules are certified on 98.0% of the time along the forecast and, with one balancing unit, proven feasible under every such error on 54.0% (none on three systems, at least 98.8% on four). On a modified 2000-bus Texas grid, 98.6% of 1272 hours are certified along the forecast.