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Improving Learned AC-OPF Feasibility under Distribution Shift with PF-in-the-Loop Correction
Afia Afrin, Omid Ardakanian
TL;DR
Learned AC-OPF can be fast, but feasibility may degrade under distribution shift, and existing methods do not use PF-realized violations to revise predicted controls. The paper tests a simple PF-in-the-loop correction filter and reports substantially improved feasibility across three predictor families, with modest runtime overhead.
Problem
Learned AC-OPF methods can be fast, but prediction accuracy does not ensure operational feasibility when conditions differ from training.
Source: §1 · p. 1Method
A simple, model-agnostic filter searches predicted controls and evaluates candidates through nonlinear power flow, using PF-realized residuals and a separate hard-feasibility check.
Source: §1 · p. 1, §2 · pp. 2–3Results
Mean feasibility rate increases by 54.0% for DeepOPF, 79.9% for PINN, and 0.1% for FSNet across OOD scenarios, while corrected pipelines remain faster than the 219.7 ms single-start PDIPM reference on case14.
Source: §4 · p. 5Takeaways & Limitations
Across three predictor families, PF-realized-state feedback substantially improves feasibility under distribution shift and serves as a design probe rather than a new AC-OPF solver.
Source: §1 · p. 1, §6 · p. 5Evaluation uses one test network, four constructed shifts, and selected checkpoints; the local search has no guarantee of finding feasibility within its budget and ignores generation cost.
Source: §5 · p. 5
Abstract
from arXiv · showhide
Learning-based AC-OPF enables fast dispatch, yet its feasibility can degrade under distribution shift. We analyze three state-of-the-art methods and identify a shared deployment-time limitation: none use feedback from the power-flow (PF)-realized state to ensure feasibility of the predicted control. Using a simple PF-in-the-loop feasibility restoration filter, we empirically show that such feedback substantially improves hard feasibility across four out-of-distribution scenarios with modest runtime overhead.
1 Introduction
Learned AC-OPF can produce fast, economical dispatch, but feasibility may degrade when operating conditions shift from training. The paper identifies missing deployment-time feedback from the PF-realized state and introduces a simple filter to address it.
1 Introduction
- Learned AC-OPF is faster than conventional iterative solvers, but dispatch optimality alone does not ensure operational feasibility under distribution shift.Shifts may involve loads, generation availability, or network parameters differing from training conditions.Source: §1 · p. 1
- Prior work incorporates physics through reconstruction, physics-informed networks, differentiable correction, inference-time feasibility procedures, or architectures for structural shifts; STORM-OPF reports stressed OOD feasibility degradation despite added stressed training samples.The cited approaches include predict-and-reconstruct [Chen et al., 2022; Zamzam and Baker, 2020], physics-informed methods [Nellikkath and Chatzivasileiadis, 2022], and other strategies [Donti et al., 2021; Nguyen and Donti, 2026; Arowolo and Cremer, 2026].Source: §1 · p. 1
- The proposed model-agnostic filter searches over predicted controls and evaluates each candidate through nonlinear power flow.It is intended to use realized violations to revise the current dispatch.Source: §1 · p. 1
- PF-realized constraint feedback substantially improves AC-OPF reliability under distribution shift, with modest runtime overhead.The authors frame this empirical finding as a design implication for learned controls.Source: §1 · pp. 1–2
2 Methodology
The PF-in-the-loop layer sits between an AC-OPF predictor and the power system, using the predicted controls and network instance to assess the PF-realized state. It restores feasibility by adjusting controls against operating-limit violations, with a fixed PF budget and no general convergence claim.
2 Methodology
- The model-agnostic layer accepts predicted controls and a network instance, then uses PF-realized operating-limit violations to guide control correction.Controls determine the PF-solved voltage state; generator outputs and branch currents are reconstructed from that state.Source: §2 · p. 2
- A converged power flow can satisfy power balance yet violate generator, bus-voltage, or branch-loading limits, so acceptance uses a separate HardFeasible check.The correction score is the norm of the positive parts of residuals at the PF-realized state; a lower score alone does not ensure every tolerance is met.Source: §2 · pp. 2–3
- The filter differentiates the violation score with respect to controls through the PF state, using autograd for partial derivatives and the implicit function theorem for PF sensitivity.The Newton–Raphson Jacobian and control derivatives are computed analytically using Pandapower’s dSBus_dV(·) function.Source: §2 · p. 3
- Control changes are measured in scaled coordinates, and Polyak’s step size chooses the shortest local-model step toward zero violation without step-size tuning.Power controls use the widest generator active-power range, floored at 1 MW, as their reference scale; voltage controls use 0.1 p.u.Source: §2 · p. 3
- The filter is intended to isolate deployment-time feedback rather than claim algorithmic superiority, and its nonconvex violation objective supports no general convergence claim.Its feasibility recovery and computational cost are assessed empirically under a fixed PF budget.Source: §2 · p. 3
3 Experimental Setup
The experiments evaluate three learned AC-OPF methods on a single IEEE-14 bus system using nominal training data and in-distribution and shifted test scenarios. They measure hard feasibility, operating cost, and runtime against optimization references.
3 Experimental Setup
- Three predictors—DeepOPF, PINN, and FSNet—are evaluated on the IEEE-14 bus system.The system represents a small approximation of the American power grid as of 1962.Source: §3 · p. 3
- Four out-of-distribution scenarios and one in-distribution scenario each contain 1,000 test instances; models are trained only on nominal samples.The shifts represent extreme weather, light load, geographic load redistribution, and heavy load; in-distribution loads are perturbed within [0.9, 1.1] of base values.Source: §3 · p. 4
- The correction filter is invoked only after a failed hard-feasibility check, with a budget of up to 40 power-flow evaluations.Control bounds include generator active-power limits and PV- and slack-bus voltage limits.Source: §3 · p. 4
3.1 Evaluation Metrics
- Hard feasibility requires convergent nonlinear AC power flow and satisfaction of applicable generator, voltage, and line or transformer loading limits.The evaluation applies specified numerical tolerances to voltage, loading, and generator bounds.Source: §3.1 · p. 4
- Operating cost is reported relative to optimization references only for feasible dispatches, using samples where both the method and reference are feasible.Ratios from columns with different feasible subsets are not direct paired before-and-after comparisons.Source: §3.1 · p. 4
- Learned-pipeline runtime includes inference, any activated correction, and power-flow verification; single-start PDIPM provides the solve-time reference.PDIPM-MS runs five initializations and retains the cheapest feasible result, but its higher runtime is not used for comparison.Source: §3.1 · pp. 4–5, §3 · p. 4, Table 1 · p. 5
4 Results
Across the four out-of-distribution scenarios, the filter improves mean feasibility for DeepOPF, PINN, and FSNet, while corrected pipelines remain faster than single-start PDIPM.
4 Results
- Mean feasibility rate increases by 54.0%, 79.9%, and 0.1% for DeepOPF, PINN, and FSNet, respectively, across OOD scenarios.All corrected pipelines remain faster than the 219.7 ms single-start PDIPM reference on case14, at around 33–70 ms per sample.Source: §4 · p. 5
5 Limitations
The evaluation is limited to one network, four constructed shifts, and selected checkpoints; the filter has no guarantee of finding a feasible point within its budget and does not optimize generation cost.
5 Limitations
- Evaluation covers one network, four constructed shifts, and selected checkpoints; larger systems and topology changes remain untested.The filter may encounter non-convergent power-flow candidates, has no guarantee of finding feasibility within its budget, and ignores generation cost.Source: §5 · p. 5
6 Conclusion
The paper identifies absent deployment-time feedback from power-flow-realized states as a shared limitation of learned AC-OPF methods. A simple training-free correction improves feasibility across three predictor families, while future work may integrate feedback into training and address cost, runtime, and fallback policies.
6 Conclusion
- Across three predictor families, training-free power-flow feedback substantially improves feasibility under distribution shift; the filter is a design probe, not a new solver.Future work includes integrating feedback into training, studying the runtime–feasibility tradeoff, preserving dispatch cost, and pairing bounded correction with an optimization fallback.Source: §6 · p. 5