Distributed coordination for transmission-distribution systems with nonlinear flexibility aggregation

High shares of distributed energy resources (DERs) transform distribution systems into active participants in integrated transmission and distribution (ITD) operations. Linear models enable scalable distribution-level flexibility aggregation but can misclassify AC feasible operating points, whereas direct nonlinear aggregation becomes costly, especially in multiperiod ITD coordination. This paper reformulates transmission-distribution coordination within a hierarchical optimization framework and introduces a non-iterative predictor-corrector aggregation method. By leveraging path-following techniques from real-time optimal control, the approach achieves tractable computation with guaranteed error bounds. Across 24 radial distribution-network cases and seven meshed variants, including the real KIT Campus North grid, the proposed method yields substantially lower sampled false- and lost-flexibility rates than linear surrogates and a convex relaxation. On two 24-period ITD testcases, the formulation reduces end-to-end wall-clock time by factors of 6 relative to the corresponding centralized formulation, primarily through dimensionality reduction.