Structured Equilibrium Learning for OPF Imitation

We study structured equilibrium learning for optimal power flow (OPF) imitation: an offline OPF solver supplies supervision for learning a voltage-to-reactive-power map describing approximated OPF operating points, while distributed energy resources (DERs) update their reactive power setpoints based on accessible voltage measurements to steer the power network toward one of them. We show that the collectively monotonic structure of the voltage-to-reactive-power maps is the key enabler for ensuring the stability and robustness of the closed-loop system. This motivates us to construct neural network-based surrogates with collectively monotonic structure for these maps in the learning task and implement them for reliable closed-loop deployment. We evaluate the proposed method under different communication scenarios through a case study on the UCSD 49-bus power network with AC power flow simulations, unseen and perturbed load/generation profiles, and up to 1\% voltage measurement noise. The combined evidence suggests that low supervised prediction error alone may be insufficient for closed-loop deployment and that structural constraints help to shape desirable closed-loop behavior.