Efficient constraint learning for data-driven active distribution network operation

Scheduling flexible sources to promote the integration of renewable generation is one fundamental problem for operating active distribution networks (ADNs). However, existing works are usually based on power flow models, which require network parameters (e.g., topology and line impedance) that may be unavailable in practice. To address this issue, we propose an efficient constraint learning method to operate ADNs. This method first trains multilayer perceptrons (MLPs) based on historical data to learn the mappings from decisions to constraint violations and power loss. Then, power flow constraints can be replicated by these MLPs without network parameters. We further prove that MLPs learn constraints by formulating a union of disjoint polytopes to approximate the corresponding feasible region. Thus, the proposed method can be interpreted as a piecewise linearization method, which also explains its desirable ability to replicate complex constraints. Finally, a two-step simplification method is developed to reduce its computational burden. The first step prunes away unnecessary polytopes from the union above. The second step drops redundant linear constraints for each retained polytope. Numerical experiments based on the IEEE 33- and 123-bus test systems validate that the proposed method can achieve desirable optimality and feasibility simultaneously with guaranteed computational efficiency.