Convergence of the exact AC-PF fixed-point map

Determine whether the exact AC power-flow fixed-point map converges, in order to clarify whether the observed convergence behavior arises from the AC power-flow formulation or from the mapping implemented by the trained deep neural network.

Background

The paper develops a fixed-point formulation in which a deep neural network trained on basecase AC power-flow data predicts post-contingency states for single-line outages. Convergence is certified for the neural-network-based map using sufficient self-mapping and contraction conditions, but these results do not establish convergence of the corresponding fixed-point iteration when the exact AC power-flow map is used instead of the trained neural network.

The authors identify this as a key unresolved question because answering it would separate convergence behavior attributable to the underlying AC power-flow formulation from behavior introduced by approximation through the trained neural network. The paper also mentions extending the formulation to multi-line contingencies and topology reconfiguration, but that aspiration does not itself state an explicit unknown and is therefore not included as a separate problem.