AC Power Flow Contingency Analysis Using a Single Deep Neural Network

The continuous evolution of next-generation power systems, characterized by the high penetration of renewable energy resources and dynamic topology variations, poses formidable challenges to traditional N-1/N-2 contingency analysis in terms of computational efficiency and scalability. While deep learning-based methods offer accelerated inference, existing studies predominantly treat contingency analysis as a pure regression problem, often overlooking the physical essence of grid operation and engineering requirements of real-world scenarios. To bridge this gap, this paper proposes a physics and prompt-guided graph foundation model (PhyPro-FM) for generalizable and engineering-viable contingency analysis. The proposed architecture integrates graph neural networks with a learnable global query mechanism and, notably, introduces a prompt-guided learning paradigm. By leveraging historical snapshots as few-shot prompts, the model dynamically captures correlations between target and historical operating conditions, significantly enhancing generalization capabilities under unseen topologies. Furthermore, we design a physics-informed training mechanism that prioritizes branch power flow errors over nodal voltage errors, aligning the optimization objective with critical grid security constraints. To ensure engineering applicability, a physics-informed inference mechanism is also developed, incorporating a residual-based correction module and a specialized post-processing strategy for singular branches to circumvent numerical instability. Comprehensive experiments demonstrate that PhyPro-FM outperforms state-of-the-art methods in accuracy and generalization, validating its superior physical consistency and robustness for practical engineering applications.

Machine Learning (ML) methods promise a fast solution process for Optimal Power Flow (OPF). While inconsistent test cases, implementations, and evaluation metrics across existing studies make it challenging to determine which algorithmic advances are most critical for real-world deployment. To this end, we propose ML-OPF-Bench, a unified benchmark for AC- and DC-OPF that evaluates representative ML algorithms under a consistent pipeline, stress-tests them across system sizes, distribution shifts, and resource budgets, and ranks them with a multi-objective framework. We find that prediction accuracy alone is not a reliable indicator of operational feasibility. Under heavily loaded, congested conditions, even the strongest in-distribution performers lose their advantage, while feasibility is maintained largely by post-processing that enforces the target constraints rather than by the underlying pure ML predictor. Data scaling shows that prediction accuracy and constraint violations follow different trajectories, whereas compute scaling shows that returns diminish and that larger models do not consistently perform better. These results expose critical trade-offs among ML methods' speed, accuracy, and feasibility, and offer practical guidance for future ML-OPF design. We open-source the benchmark as an extensible Python package for integrating new learning-based OPF algorithms and evaluating them under the same standard as the existing baselines.

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 $500$ to $4{,}000$ 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.