Power grids are changing because many small devices — rooftop solar panels, batteries, and electric vehicle chargers — now inject or draw power at the distribution level. This makes distribution networks “active” partners in wider grid operation. The paper studies how to summarize each distribution area’s true capabilities, so a transmission system operator (TSO) can schedule flows without needing all the low-level details.

The researchers frame the problem as a hierarchical optimization: each distribution system operator (DSO) computes a compact “flexibility set” that describes which power exchanges at the TSO–DSO interface can be safely realized inside the distribution network. Linearized models are fast for this aggregation but can be wrong. They can overestimate the set (a false flexibility that leads to infeasible commands) or underestimate it (lost flexibility that wastes resources). Exact nonlinear aggregation is more accurate but becomes very costly, especially when planning over multiple time periods.

To bridge that gap, the authors propose a non-iterative predictor–corrector aggregation method. It borrows path-following ideas from real-time optimal control to build local nonlinear surrogates of each DSO’s feasible set. These surrogates preserve the underlying alternating-current (AC) powerflow constraints and come with guaranteed error bounds. The method works for both radial and meshed distribution networks and is designed to let DSOs precompute their flexibility in parallel across space and time.

The paper reports testing across 24 radial network cases and seven meshed variants, including a real network (KIT Campus North). Compared with simple linear surrogates and a convex relaxation, the proposed method gave substantially lower sampled rates of false and lost flexibility. In multi-period tests (two cases with 24 periods), the hierarchical formulation cut end-to-end wall-clock time by about a factor of six compared to a corresponding centralized nonlinear program. The authors also report general 5–7× speedups versus state-of-the-art nonlinear solvers such as IPOPT, mainly from reducing problem dimension. An open-source implementation accompanies the work.