Optimal Power Flow

Momentum

3 papers in the last four weeks, level with the four weeks before. 0.0% of all new papers.

Jul 13Week of Sep 28

Latest papers 14

Sep 24, 2026eess.SY

GridSFM: A Foundation Model for Solving AC Optimal Power Flow

We introduce GridSFM, a framework that combines a pretrained foundation model across grid topologies with physics-informed fine-tuning for solving AC Optimal Power Flow (AC-OPF) at scale. It is a

15

million parameter physics-inspired graph neural network pretrained across

54

topologies of

500

4{,}000

buses. Our model attains a

2.45\%

zero-shot generation-cost error on a

10{,}000

bus case held-out operating conditions with no degradation as system size grows. Building on this, we pair the pretrained backbone with a physics-informed fine-tuning design based on Newton's method for power flow. With only

100

solved instances, GridSFM adapts to unseen grids up to

10{,}000

buses. We show it out performs single topology, dedicated neural network models that are trained more data, both in terms of cost and solver iterations when deployed as warm starting points. In designing this foundation model, we overcome the fact that the feasible set for AC-OPF can be disconnected. This is an obstruction that prevents any continuous neural network from approximating the solution map. To do so, we lift the problem and relax its constraints with logarithmically penalized slacks. We prove that the resulting elastic feasible set is contractible, that the AC-OPF minimizers remain minimizers of the elastic problem above an explicit penalty threshold, and that projecting an approximate solution back onto the AC-OPF feasible set is well posed. We release all models, data, and code so that the community can build on a shared starting point for AC-OPF.

Luke Bhan, Weiwei Yang, Margaret Capetz +1

University of California, San Diego · Microsoft Research · University of Washington

Neural Surrogate Modeling Optimal Power Flow Physics-Informed GNNs Power Systems

Ask PDF

Sep 15, 2026eess.SY

Unified Heterogeneous Graph Neural Network solver for Power Flow, Optimal Power Flow and State Estimation

Power Flow (PF), Optimal Power Flow (OPF), and State Estimation (SE) are fundamental problems in power system analysis, but solving them is computationally expensive. Graph Neural Networks (GNNs) have been proposed as fast surrogates, yet existing solvers are trained for a single problem at a time, producing narrow models that must be rebuilt for each new task. We propose a more general approach: a single Heterogeneous Residual Gated Graph Convolutional Network that solves all three problems with one shared backbone. Rather than learning one mapping, the model learns a reusable representation of how the network behaves, from which PF, OPF, and SE can each be estimated. Trained jointly on the three problems across diverse topologies and loading conditions, and evaluated on the IEEE 14-bus and 118-bus systems, the shared model matches the accuracy of task-specific GNN solvers and stays robust on unseen loading levels and topologies. These results show that a single model can capture the basic operation of a power network and serve several analysis tasks at once, a first step toward a foundation model for power systems.

Ferran Bohigas-Daranas, Hamid Latif-Martínez, Eduardo Prieto-Araujo +2

Heterogeneous GNNs Multi-Task Learning Optimal Power Flow Power Systems

Ask PDF

Sep 14, 2026cs.LG

Scaling Laws for Physics-Aware ACOPF Surrogate Learning

Learning-based surrogates for AC optimal power flow (ACOPF) promise large speedups over classical solvers, but their operational value depends on physical feasibility as much as predictive accuracy. Physics-aware objectives such as the augmented Lagrangian (AL) improve constraint satisfaction at additional per-step cost, yet how this trade-off behaves with scale is uncharacterized. We sweep model and dataset sizes under both MSE and AL training, and characterize how constraint violation changes with network size across grids. Both objectives improve as power laws, but at different rates: MSE is governed primarily by model capacity, while AL is balanced across both. Violation grows roughly twice as fast with network size under MSE as under AL. On matched hardware, AL reduces violation by nearly

30\times

for an order of magnitude more training time, with negligible added memory. The training objective determines not only where a surrogate lands but how its quality evolves with scale.

Yijiang Li, Emon Dey, Stefano Fenu +3

Argonne National Laboratory Lemont, USA · Oak Ridge National Laboratory Oak Ridge, USA

Neural Surrogate Modeling Optimal Power Flow Augmented Lagrangian Method Scaling Laws

Ask PDF

Aug 31, 2026cs.LG

Certified Safety Radii in Forecast-Error Space for Wasserstein Distributionally Robust Small Signal Stability-Constrained AC Optimal Power Flow via Lifted Spectrahedral Containment

Directly robustifying small-signal stability in AC optimal power flow is challenging since the stability boundary in the original uncertainty space is implicit, highly nonconvex, and changes with the operating decision. This paper exploits an alternative geometry. For a fixed model-specific stability certificate admitting suitable physical lifts, the small-signal stability requirement becomes an affine positive semidefinite constraint in the lifted variables, thereby defining a convex certified safe region. Instead of approximating the nonlinear instability boundary itself, we optimize a sample-wise safe radius in the original uncertainty space and certify, in the lifted space, that the entire power-flow image of the corresponding uncertainty ball is contained in the convex stability region. To this end, a componentwise Perron certificate guarantees existence, uniqueness, and Jacobian regularity of the target AC power-flow branch throughout each ball. An adjoint elimination then provides an exact affine-quadratic representation of the stability-relevant quantities, while rigorous matrix remainder bounds convert their nonlinear variation into finite robust PSD constraints. The resulting radii are certified lower bounds on the distances from empirical samples to failure and can therefore be coupled directly to the distance-based reformulation of a Wasserstein distributionally robust chance constraint, without directly approximating the instability boundary. Numerical studies demonstrate the effectiveness of the proposed framework.

Ziqi Zhang, Xi Chen

College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China

Optimal Power Flow Distributionally Robust Optimization Certified Robustness

Ask PDF

Aug 25, 2026eess.SY

Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration

The proliferation of distributed energy resources (DERs) in distribution grids enables the active coordination of these assets to reduce costs and enable cleaner operations. Realizing this potential requires solving multiphase AC optimal power flow (AC-OPF) quickly across varying loads, DER availabilities, and topology reconfigurations, at much greater speed and scale than conventional nonlinear solvers. Learning-based surrogates can offer millisecond inference, yet existing methods target largely balanced transmission systems and do not scale to the multiphase, unbalanced, and reconfigurable nature of distribution feeders at utility scale. We present the Penalty + Sequential Linearized Feasibility Seeking (SLFS) algorithm, a self-supervised learning framework for multiphase distribution AC-OPF under switch-induced topology changes. Penalty+SLFS requires no labeled optimal solutions and trains directly from the AC-OPF objective and constraints through a differentiable fixed-point power flow solver, avoiding expensive label generation and admitting robust training procedures. Topology changes are handled efficiently using Sherman-Morrison-Woodbury updates of the admittance-matrix inverse, while an M-step Jacobian approximation accelerates differentiation through the power flow solver. At inference, SLFS repairs any infeasible predictions, providing feasibility guarantees with low computational overhead. On IEEE feeders ranging from 13 to 8,500 nodes, Penalty+SLFS achieves negligible optimality gaps and near-zero constraint violations, delivers up to three orders of magnitude speedups over IPOPT, and remains robust under large distributional shifts, demonstrating a viable path toward real-time, topology-aware AC-OPF for large-scale distribution grids.

Hoang T. Nguyen, Shaohui Liu, Reetam Sen Biswas +4

Massachusetts Institute of Technology, Cambridge, MA, USA. · GE Vernova Advanced Research Center, Niskayuna, NY, USA.

Neural Surrogate Modeling Self-Supervised Learning Optimal Power Flow Power Systems

Ask PDF

Aug 10, 2026cs.AI

GENCO - A Unified Neural Solver Embedded in a Development Framework for Steady-State Grid Analysis

Foundation models are transforming business workflows and boosting productivity, yet they remain largely absent from engineering domains such as power system analysis, where strict physical consistency must be enforced. We present GENCO (GEometric Neural Corrective Optimizer), a unified neural solver for steady-state transmission grid analysis that handles power flow (PF), optimal power flow (OPF), and state estimation (SE) within a single architecture and shared network representation. To support advances in neural power system solvers, we introduce the open-source GridFM Development Framework, which standardizes synthetic data generation and training in a low-code environment. We also release large-scale datasets with millions of PF and OPF scenarios across diverse grid topologies to support reproducible benchmarking. We evaluate GENCO on the PFDelta and OPFData benchmarks against state-of-the-art neural solvers and classical solvers, including Newton-Raphson and IPOPT, as well as on real-world Hydro-Québec SCADA data. For large-scale PF, GENCO recovers the full AC operating state, including voltage magnitudes and reactive power that DC-PF cannot provide, while matching DC-PF-level active power-balance residuals. It achieves up to 30x speedups over Newton-Raphson at only 2x the runtime of DC-PF. For OPF, it achieves up to 85x speedups over IPOPT while improving feasibility, optimality, and runtime over DC-OPF. For SE, GENCO is more robust than classical weighted least squares to noisy measurements and network parameter errors, and always returns a high-quality estimate even when weighted least squares fails to converge. Together, the unified architecture and development framework provide a new approach to large-scale steady-state grid analysis, lowering the barrier to entry for power system engineers and marking a step toward Grid Foundation Models.

Alban Puech, Matteo Mazzonelli, Tamara R. Govindasamy +19

IBM Research · Reliability and Risk Engineering Laboratory, ETH Zurich, Switzerland · Hydro-Qu´ebec Research Institute, Canada +3

Neural Surrogate Modeling Optimal Power Flow Power Systems

Ask PDF

Jul 24, 2026cs.LG

FMOPF: Latent Flow Matching with Constraint-Aware Interaction Priors for AC Optimal Power Flow

AC optimal power flow determines the minimum-cost generation dispatch under nonlinear power balance constraints and is solved thousands of times daily in electricity market operations. Learning a direct mapping from load conditions to OPF solutions can accelerate this computation, yet with deepening renewable penetration, a single optimal dispatch is no longer sufficient. Operators require a characterization of the distribution of feasible near-optimal solutions for risk quantification, sensitivity analysis, and multi-objective trade-off assessment. Supervised neural networks provide fast point predictions but cannot capture this conditional distribution. Diffusion-based generative models can sample diverse solutions in principle, yet existing methods operating in the raw state space exhibit degraded solution quality and fail to scale beyond medium-sized systems. We identify the root cause as the conflation of two distinct tasks within a single model. Compressing the high-dimensional OPF solution manifold is one task, and learning the conditional mapping from loads to that manifold is another. This paper presents FMOPF, a framework that resolves this conflation by decoupling compression from generation through latent flow matching and by explicitly modeling load-state coupling through a Constraint-Aware Interaction Prior Network. Experiments on four IEEE test systems demonstrate that FMOPF provides the most effective Newton-Raphson warm starts, achieves the lowest tail risk among generative methods, and is the first such method to scale to systems with several hundred buses while preserving full feasibility. Ablation studies confirm that the latent generation pipeline is a necessary condition for physical feasibility and that the interaction prior functions as a late-stage tail-risk controller.

Zhilin Huang

China Southern Power Dispatching and Control Center, China Southern Power Grid

Constrained Generative Modeling Flow Matching Uncertainty Quantification Optimal Power Flow Constrained Optimization Power Systems

Ask PDF

Jun 4, 2026cs.AI

Multi-ResNets for Subspace Preconditioning in Constrained Optimization

We propose MResOpt, a staged residual neural network architecture for constrained optimization problems. Our architecture fits within predict-complete-correct pipelines and decomposes constraint satisfaction by priority through intermediate re-completion and stage-aware losses. The framework enables domain-informed ordered constraint satisfaction which allows the network to utilize ordinal structure when present. Under an idealized infinite-width regime, we show that our design behaves as sequential Gaussian Process regression. On synthetic QP, QCQP, and SOCP benchmarks, the staged architecture improves high-priority constraint satisfaction across convex and non-convex settings. On line-flow-constrained AC optimal power flow, we introduce a physics-motivated constraint ordering and show that MResOpt supports a learned division of labor that keeps iterates on the equality manifold, achieving substantially lower high-priority violation than reprojected baselines while remaining computationally efficient.

Merve Karakas, Christopher J. Williams, Emmanuel O. Balogun +3

UCLA · University of Oxford · Sunrun† +1

Residual Learning Learning to Optimize Optimal Power Flow Constrained Optimization Constraint Satisfaction

Ask PDF

Jun 2, 2026cs.LG

Rethinking Neural Width for Alternating Current Optimal Power Flow Proxies

Deep learning proxies for Alternating Current Optimal Power Flow (ACOPF) lack systematic methods for determining architectural size. This paper conducts a constructive thought experiment to answer a fundamental inquiry: how wide must a neural network be to almost accurately approximate the ACOPF manifold? We introduce a Loss-Guided Neural Densification (LG-ND) algorithm that incrementally discovers necessary capacity by expanding only when the current deep neural network topology fails to improve further. Empirical results across various IEEE systems show that LG-ND achieves performance parity with literature baselines using up to ten times fewer neurons per layer. Such architectural minimalism is critical for the formal verification required in safety-critical grid operations.

Dhruvi Khandelwal, Anurag Basistha, Ayushi Jolotia +1

Department of Electrical Engineering, National Institute of Technology Kurukshetra, India. · Indraprastha Institute of Information Technology Delhi, India. · Department of Electrical Engineering, Indian Institute of Technology Roorkee, India.

Neural Surrogate Modeling Optimal Power Flow Constrained Optimization Neural Network Approximation Theory Neural Architecture Search Neural Network Expressivity

Ask PDF

May 22, 2026cs.LG

Scalable Heterogeneous Graph Foundation Models for Data-Driven Optimal Power Flow in Smart Grids

Fast and reliable optimal power flow (OPF) approximation is important for power system operation, yet heterogeneous OPF graph models are often evaluated either with architecture-specific implementations or on limited training corpora. This paper presents a large-scale heterogeneous graph-learning workflow, built on HydraGNN, for data-driven OPF surrogate modeling and graph foundation-model (GFM) development. The workflow preserves buses, generators, loads, shunts, alternating-current (AC) lines, transformers, and device-to-bus relations and provides a common implementation for distributed preprocessing, multi-graphics-processing-unit (GPU) training, hyperparameter optimization (HPO), and downstream adaptation. Using approximately three million heterogeneous graphs from ten Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms (PGLib-OPF) cases spanning 14 to 13,659 buses, we compare six heterogeneous graph neural network (GNN) families under a common HPO campaign on Frontier, resulting in two compact HeteroSAGE and HeteroHEAT models (~1.6-1.7 million parameters) that achieve the lowest observed validation MSE. Strong and weak scaling using up to 1,024 Frontier nodes show that 256 nodes (corresponding to 1,024 AMD MI250X GPUs) provides the best time-to-solution balance for the measured workload. Two downstream tasks evaluate task adaptation on the IEEE 118-bus case: a classification task to distinguish nominal operating conditions from artificially generated extreme-overload conditions and N-1 single-component-outage regression to predict bus voltage magnitude and phase angle. Partial fine-tuning provides the strongest balance between predictive performance and computational requirements.

Massimiliano Lupo Pasini, Yijiang Li, Kibaek Kim +1

Computational Sciences and Engineering Division, Oak Ridge National Laboratory, 1 Bethel Valley Road, Oak Ridge, TN 37831, USA

Neural Surrogate Modeling Heterogeneous GNNs Optimal Power Flow Graph Foundation Models Constrained Optimization Power Systems

Ask PDF

May 7, 2026cs.LG

WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers

Solving AC Optimal Power Flow (AC-OPF) is of central importance in electricity market operations, where interior-point methods (IPMs) such as IPOPT are the standard solvers. A growing body of work uses machine learning to predict primal warm-start iterates, reporting iteration reductions of 30-46%. We show that these reported gains rest on an inappropriate evaluation baseline: prior methods benchmark against the flat start

V_m = 1, V_a = 0

, whereas the solver's actual default - the variable-bound midpoint

(l+u)/2

- is near-optimal for log-barrier centrality. Against this corrected baseline, no primal-only warm-start method reduces solver iterations. We trace the failure to a geometric property of interior-point methods: primal prediction accuracy is anticorrelated with convergence speed, and providing the ground-truth optimal solution

x^*

without dual variables causes the solver to diverge. Oracle experiments establish that the complete primal-dual-barrier state

(x^*, λ^*, z^*, μ^*)

reduces IPOPT iterations from 23 to 3 - an 85% reduction that is structurally inaccessible to primal-only methods. To enable rigorous evaluation of warm-start methods on this task, we release a benchmark suite comprising dual-labeled AC-OPF datasets with IPOPT-extracted solutions, a corrected evaluation protocol, and WARP - a topology-conditioned encode-process-decode interaction network that predicts the full interior-point state

(\hat{x}, \hatλ, \hat{z}, \hatμ)

on the heterogeneous constraint graph. WARP achieves a 76% reduction in IPOPT iterations while natively accommodating N-1 contingency topology variations without retraining.

Dhruv Suri, Helgi Hilmarsson, Shourya Bose

Pravah

Primal-Dual Optimization Graph Neural Networks Optimal Power Flow Constrained Optimization Power Systems

Ask PDF

May 4, 2026cs.LG

LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning

AC optimal power flow (ACOPF) is foundational yet computationally expensive in power grid operations, driving learning-based surrogates for large-scale grid analysis. These surrogates, however, often fail to generalize across network topologies, a critical gap for deployment on grids not seen during training and for routine operational what-if studies. We introduce LUMINA-Bench, a comprehensive benchmark suite for ACOPF surrogate learning covering multi-topology pretraining, transfer, and adaptation. The benchmark evaluates homogeneous and heterogeneous architectures under single- and multi-topology learning settings using unified metrics that capture both predictive accuracy and physics-informed constraint violations. We additionally compare constraint-aware training objectives, including MSE, augmented Lagrangian, and violation-based Lagrangian losses, to characterize accuracy-robustness trade-offs across settings. Data processing, training, and evaluation frameworks are open-sourced as the LUMINA suite to support reproducibility and accelerate future research on feasibility-aware OPF surrogates.

Hongwei Jin, Keunju Song, Zeeshan Memon +5

Mathematics and Computer Science Division, Argonne National Laboratory · Department of Electronic Engineering, Sogang University · Department of Computer Science, Emory University +1

Neural Surrogate Modeling Benchmark Design Optimal Power Flow Constrained Optimization Power Systems

Ask PDF

May 3, 2026cs.LG

Towards Systematic Generalization for Power Grid Optimization Problems

AC Optimal Power Flow (ACOPF) and Security-Constrained Unit Commitment (SCUC) are fundamental optimization problems in power system operations. ACOPF serves as the physical backbone of grid simulation and real-time operation, enforcing nonlinear power flow feasibility and network limits, while SCUC represents a core market-level decision process that schedules generation under operational and security constraints. Although these problems share the same underlying transmission network and physical laws, they differ in decision variables and temporal coupling, and prior learning-based approaches address them in isolation, resulting in disjoint models and representations.We propose a learning framework that jointly models ACOPF and SCUC through a shared graph-based backbone that captures grid topology and physical interactions, coupled with task-specific decoders for static and temporal decision-making. Training includes solver supervision with physics-informed objectives to enforce AC feasibility and inter-temporal operational constraints. To evaluate generalization, we assess cross-case transfer on unseen grid topologies for ACOPF and SCUC without retraining, and systematic generalization on the UC-ACOPF problem using unsupervised, physics-based objectives and a power-dispatch consensus mechanism. Experiments across multiple grid scales demonstrate improved performance and transferability relative to existing learning-based baselines, indicating that the model can support learning across heterogeneous power system optimization problems.

Zeeshan Memon, Yijiang Li, Hongwei Jin +2

Emory University Atlanta, GA, USA · Argonne National Laboratory Lemont, IL, USA

Optimal Power Flow Constrained Optimization Compositional Generalization Power Systems

Ask PDF

Aug 30, 2025eess.SY

Solving Conic Programs over Sparse Graphs using a Variational Quantum Approach: The Case of the AC Optimal Power Flow

Conic programs arising in physics, quantum information, machine learning, and engineering are often defined over sparse graphs. Although such problems can be solved in polynomial time using classical interior-point solvers, the computational complexity scales unfavorably with graph size. We propose a variational quantum paradigm for solving conic programs, including quadratically constrained quadratic programs and semidefinite programs. We encode primal variables via the state of a parameterized quantum circuit (PQC) and dual variables via the probability mass function associated with a second PQC. The Lagrangian function can thus be expressed as scaled expectations of quantum observables. We pursue approximately stationary points of the Lagrangian by minimizing/maximizing the Lagrangian over the parameters of the first/second PQC. This is accomplished in a hybrid fashion: gradients are estimated using the two PQCs, while their parameters are updated classically using a primal-dual method. We propose permuting primal variables so that related observables have a banded form, enabling efficient measurement. We provide a complexity analysis that is useful to determine which problem types may enjoy quantum advantage. The framework is applied to the AC OPF problem, a large-scale optimization problem central to electric power system operation. Numerical tests on the IEEE 57-node system using PennyLane's simulator show that the proposed doubly variational quantum framework can find high-quality OPF solutions. While this demonstration does not yield a quantum speedup, the results serve as a proof-of-concept and highlight challenges toward practical quantum advantage. Although showcased for OPF, the framework has broader scope, including conic programs with many variables and constraints, problems defined over sparse graphs, and training quantum machine learning models to satisfy constraints.

Thinh Viet Le, Mark M. Wilde, Vassilis Kekatos

Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47906, USA · School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA

Optimal Power Flow Constrained Optimization Variational Quantum Algorithms

Ask PDF

Momentum

Related topics

Latest papers 14