Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow

The security-constrained optimal power flow (SCOPF) is fundamental in power systems and connects the automatic primary response (APR) of synchronized generators with the short-term schedule. Every day, the SCOPF problem is repeatedly solved for various inputs to determine robust schedules given a set of contingencies. Unfortunately, the modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs, which are hard to solve. To address this challenge, leveraging the wealth of available historical data, this paper proposes a novel approach that combines deep learning and robust optimization techniques. Unlike recent machine-learning applications where the aim is to mitigate the computational burden of exact solvers, the proposed method predicts directly the SCOPF implementable solution. Feasibility is enforced in two steps. First, during training, a Lagrangian dual method penalizes violations of physical and operations constraints, which are iteratively added as necessary to the machine-learning model by a Column-and-Constraint-Generation Algorithm (CCGA). Second, another different CCGA restores feasibility by finding the closest feasible solution to the prediction. Experiments on large test cases show that the method results in significant time reduction for obtaining feasible solutions with an optimality gap below 0.1%.