Aggregate Regulation Regions with Joint Response Calibration and Network Constraints

Network-feasible regulation headroom does not ensure that aggregated resources can deliver a dispatch instruction within its activation window. This study combines joint response calibration with robust linear network constraints to construct an aggregate regulation region. A maximum standardized shortfall score provides simultaneous lower response bounds from independent calibration episodes. These bounds enter a robust command-space model, and directional linear programs generate an inner approximation with guaranteed active increment and capacitive reactive support. All results are obtained on the public 33-bus feeder with an explicitly specified synthetic response generator (400 training, 800 calibration and 2000 test episodes per scenario) and are not operational performance figures. In this benchmark, boundary-command delivery failure at 95% nominal coverage ranges from 1.95% to 4.25%; the compound scenario reduces region area by 19.15%, and fixed 0.8 derating yields 11.85% delivery failure there. Sensitivity sweeps over response dispersion, correlation and activation time keep joint-calibrated failure below 5%, whereas fixed derating reaches 39%. Full-boundary AC checks on 2000 episodes show no violation. Under an abrupt response shift, frozen calibration fails in 73% of episodes; an alarm-and-reset recalibration restores about 3%. Findings are limited to a balanced static feeder and synthetic responses.