# AC Power Flow Contingency Analysis Using a Single Deep Neural Network

arXiv: https://arxiv.org/abs/2609.30859 · HTML: https://mlsanity.com/paper/2609.30859/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 15 of 15)

- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [Physics-Guided Deep Neural Networks for Power Flow Analysis](https://mlsanity.com/paper/2002.00097/) (2020)
- [Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks](https://mlsanity.com/paper/2103.14779/) (2021)
- [Certifying Incremental Quadratic Constraints for Neural Networks via Convex Optimization](https://mlsanity.com/paper/2012.05981/) (2020)
- [ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networks](https://mlsanity.com/paper/2404.04375/) (2024)
- [PSSE Redux: Convex Relaxation, Decentralized, Robust, and Dynamic Approaches](https://mlsanity.com/paper/1708.03981/) (2017)
- [Scalable Learning for Optimal Load Shedding Under Power Grid Emergency Operations](https://mlsanity.com/paper/2111.11980/) (2021)
- [Fast and Reliable N-k Contingency Screening with Input-Convex Neural Networks](https://mlsanity.com/paper/2410.00796/) (2024)
- [Linear Approximations to AC Power Flow in Rectangular Coordinates](https://mlsanity.com/paper/1512.06903/) (2015)
- [Optimal Design of Volt/VAR Control Rules of Inverters using Deep Learning](https://mlsanity.com/paper/2211.09557/) (2022)
- [Improved Physics-Informed Neural Network based AC Power Flow for Distribution Networks](https://mlsanity.com/paper/2409.09466/) (2024)
- [AMPS: An Augmented Matrix Formulation for Principal Submatrix Updates with Application to Power Grids](https://mlsanity.com/paper/1706.03147/) (2017)
- [Contingency Analysis Based on Partitioned and Parallel Holomorphic Embedding](https://mlsanity.com/paper/2104.02880/) (2021)

## Abstract (arXiv)

Contingency analysis using the AC power flow (AC-PF) model is a critical tool for accurate grid security assessment, but its computational burden increases with the number of operating scenarios and outage configurations to evaluate. Recent ML-based approaches typically require outage-specific training data, leading to offline training costs that scale with the number of contingencies. This work proposes a framework that reuses a single ML model trained solely on basecase AC-PF data to estimate post-contingency operating states under arbitrary single-line outages. The proposed approach formulates post-contingency state prediction as a fixed-point iteration. If the ML model is a deep neural network (DNN), we derive sufficient conditions that guarantee convergence and develop semidefinite programming (SDP) formulations to certify these conditions for a given DNN. Numerical tests on the IEEE 118-bus system demonstrate that the proposed SDP formulations are tight, that the certified conditions hold for all tested contingencies, and that the resulting method produces accurate post-contingency state estimates within only a few iterations.