# ML OPF wiki

# Machine Learning for Solving Optimal Power Flow Problems

This page contains a list of papers on developing machine learning schemes for solving optimal power flow problems, organized in sections by the algorithmic structure. Anyone can submit an edit (indeed, very welcome to do so!), which will then be reviewed and published.

## Survey and Overview Papers

- B. Jiang, Q. Wang, S. Wu, Y. Wang, and G. Lu, "Advancements and Future Directions in the Application of Machine Learning to AC Optimal Power Flow: A Critical Review," Energies, vol. 17, no. 6, p.1381, 2024.
- M. Zhao and M. Barati, "Synergizing Machine Learning with ACOPF: A Comprehensive Overview," arXiv preprint arXiv:2406.10428, 2024.
- H. Khaloie, M. Dolanyi, J. F. Toubeau and F. Vallée, "Review of Machine Learning Techniques for Optimal Power Flow",
*Available at SSRN 4681955*. - V. Kekatos and M. K. Singh, "Deep Learning Techniques for Solving Optimal Power Flow Problems".
- M. Chen and S. H. Low, “Machine Learning for Solving Optimal Power Flow Problems”, tutorial at ACM SIGMETRICS / IFIP Performance, Mumbai, India, June 6-10, 2022.
- M. Chen and S. H. Low, “Machine Learning for Solving Optimal Power Flow Problems”, tutorial at IEEE SmartGridComm, October 31 - November 3, Glasgow, Scotland, 2023.
- F. Fioretto, "Integrating Machine Learning and Optimization to Boost Decision Making", in Proceedings off the
*31st International Joint Conference on Artificial Intelligence (IJCAI), Vienna, Australia, Jul. 23-29, 2022.* - G. Huang, G, F. Wu and C. Guo, "Smart grid dispatch powered by deep learning: a survey", in Frontiers of Information Technology & Electronic Engineering, pp. 1 - 14, 2022.
- L. Xie, X. Zheng, Y. Sun, T. Huang and T. Bruton, "Massively Digitized Power Grid: Opportunities and Challenges of Use-inspired AI", arXiv preprint arXiv:2205.05180, 2022.
- B. Amos, "Tutorial on amortized optimization for learning to optimize over continuous domains", arXiv preprint arXiv:2202.00665.
- P. V. Hentenryck, "Machine Learning for Optimal Power Flows", in Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications, 62 - 82, Oct. 2021.
- P. L. Donti and J. Z. Kolter, "Machine Learning for Sustainable Energy Systems", in Annual Review of Environment and Resources 2021, vol: 46, 2021.
- M. Massaoudi, H. Abu-Rub, S. S. Refaat, I. Chihi and F. S. Oueslati, "Deep Learning in Smart Grid Technology: A Review of Recent Advancements and Future Prospects", in IEEE Access, vol. 9, pp. 54558-54578, Apr. 2021.
- J. Kotary, F. Fioretto and P. V. Hentenryck, "End-to-End Constrained Optimization Learning: A Survey", arXiv preprint arXiv:2103.16378, 2021.
- G. Ruan, H. Zhong, G. Zhang, Y. He, X. Wang and T. Pu, "Review of Learning-Assisted Power System Optimization", in CSEE Journal of Power and Energy Systems, vol. 7, no. 2, pp. 221 - 231, Mar. 2021.
- L. Duchesne, E. Karangelos and L. Wehenkel, "Recent Developments in Machine Learning for Energy Systems Reliability Management", in Proceedings of IEEE, vol. 108, no. 9, pp. 1656-1676, Oct. 2020.
- F. Hasan, A. Kargarian and A. Mohammadi, "A Survey on Applications of Machine Learning for Optimal Power Flow", in Proceedings of 2020 IEEE Texas Power and Energy Conference (TPEC), College Station, TX, USA, Feb. 6 - 7, 2020.
- L. Yin, Q. Gao, L. Zhao, B. Zhang, T. Wang, S. Li and H. Liu, "A review of machine learning for new generation smart dispatch in power systems", Engineering Applications of Artificial Intelligence, vol. 88, 103372, 2020.

## The Learning-based End-to-end Framework

The idea behind the **end-to-end** framework is to train the ML model to output solutions directly from the input instance.

#### Supervised Learning-based Schemes

##### Security-constrained optimal power flow

- N. Popli, E. Davoodi, F. Capitanescu, and L. Wehenkel, "On the robustness of machine-learnt proxies for security constrained optimal power flow solvers", 2023.
- Y. Yu, Y. Gao, Y. Li, and Y. Yan, "Interpretable data‐driven contingency classification for real‐time corrective security‐constrained economic dispatch",
*IET Renewable Power Generation, 2023.* - S. Park and P. Van Hentenryck, "Self-Supervised Learning for Large-Scale Preventive Security Constrained DC Optimal Power Flow",
*arXiv preprint arXiv:2311.18072, 2023.* - W. Chen, S. Park, M. Tanneau and P. V. Hentenryck, "Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch", arXiv preprint arXiv:2112.13469, 2021.
- A. Velloso and P. V. Hentenryck, "Combining Deep Learning and Optimization for Preventive Security-Constrained DC Optimal Power Flow", in IEEE Transactions on Power Systems, vol. 36, no. 4, pp. 3618 - 3628, Jul, 2021.
- X. Pan, T. Zhao, M. Chen and S. Zhang, "DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow", in IEEE Transactions on Power Systems, vol. 36, no. 3, pp. 1725 - 1735, May. 2021.
- M. Giuntoli, V. Biagini and M. Chioua, "Artificial intelligence and optimization: a way to speed up the security constraint optimal power flow", in Automatisierungstechnik, vol. 68, issue 12, pp. 1035 - 1043, 2020.
- Y. Sun, X. Fan, Q. Huang, X. Li, R. Huang, T. Yin and G. Lin, "Local feature sufficiency exploration for predicting security-constrained generation dispatch in multi-area power systems", in Proceedings of the 17th IEEE International Conference on Machine Learning and Applications (ICMLA). Orlando, FL, USA, Dec. 17 - 20, 2018.
- J. Rahman, C. Feng and J. Zhang, "Machine Learning-Aided Security Constrained Optimal Power Flow", in Proceedings of 2020 IEEE Power & Energy Society General Meeting, Montreal, Canada, Aug. 2 - 6, 2020.

##### DC Optimal Power Flow

- T. Zhao, X. Pan, M. Chen and S. H. Low, "Ensuring DNN Solution Feasibility for Optimization Problems with Linear Constraints", in Proc.ICLR, accepted for publication. [final version to be available ]
- A. Stratigakos, S. Pineda, J. M. Morales, and G. Kariniotakis, "Interpretable Machine Learning for DC Optimal Power Flow with Feasibility Guarantees", 2023.
- W. Chen, M. Tanneau, and P. Van Hentenryck, "End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch",
*arXiv preprint arXiv:2304.11726, 2023.* - M. Kim and H. Kim, H, "Projection-aware Deep Neural Network for DC Optimal Power Flow Without Constraint Violations",
*Proceedings of the 12th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm)*, Oct. 25-28, virtual conference, 2022. - M. Li, S. Kolouri and J. Mohammadi, "Learning to Solve Optimization Problems with Hard Linear Constraints", arXiv preprint arXiv:2208.10611, 2022.
- H. Wu and Xu, Z, "Fast DC Optimal Power Flow Based on Deep Convolutional Neural Network",
*in Proceedings of the5th International Electrical and Energy Conference (CIEEC)*, Apr. 1-4, Tokyo, Japan, 2022. - T. Zhao, X. Pan, M. Chen and S. H. Low, "Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems", arXiv preprint arXiv:2112.08091, 2021.
- T. Zhao, X. Pan, M. Chen, A. Venzke, and S. H. Low, "DeepOPF+: A Deep Neural Network Approach for DC Optimal Power Flow for Ensuring Feasibility", in Proceedings of the 11th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2020), virtual conference, Nov. 11 - 13, 2020.
- L. Duchesne, E. Karangelos, A. Sutera and L. Wehenkel, "Machine Learning for Ranking Day-ahead Decisions in the Context of Short-term Operation Planning", Electric Power Systems Research, vol. 189, pp.106548, Dec. 2020.
- X. Pan, T. Zhao and M. Chen, "DeepOPF: Deep Neural Network for DC Optimal Power Flow", arXiv:1905.04479, May 11th, 2019.
- X. Pan, T. Zhao and M. Chen, "DeepOPF: Deep Neural Network for DC Optimal Power Flow", in Proceedings of the 10th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2019), Beijing, China, Oct. 21 - 24, 2019.
- A. Garg, M. Jalali, V. Kekatos and N. Gatsis, "Kernel-based learning for smart inverter control", in Proceedings of the 6th IEEE Global Conference on Signal and Information Processing (GlobalSIP), Anaheim, CA, Nov. 26 - 29, 2018.

##### AC Optimal Power Flow

###### a. Physics-based Neural Networks

- J. Wang and P. Srikantha, "Data-driven AC Optimal Power Flow with Physics-informed Learning and Calibrations," arXiv preprint arXiv:2404.09128, 2024.
- M. Gao, J. Yu, Z. Yang, and J. Zhao. "A Physics-Guided Graph Convolution Neural Network for Optimal Power Flow",
*IEEE Transactions on Power Systems (early access),*2023. - R. Nellikkath and C. Spyros, "Physics-informed neural networks for AC optimal power flow", in Proceedings of Power Systems Computation Conference (PSCC), 27th June to 1st July, Porto, Portugal, 2022.
- T. Falconer and L. Mones, "Leveraging power grid topology in machine learning assisted optimal power flow", in IEEE Transactions on Power Systems (early access), 2022.
- Y. Zhai, H. Ye, L. Zhang, and Y. Ge, "Model Information-Aided Deep Learning for Corrective AC Power flow",
*in Proceedings of the IEEE Power & Energy Society General Meeting (PESGM), Jul. 17-21,*Denver, Colorado, 2022. - M. K. Singh, V. Kekatos. Chen, and G. B. Giannakis, "Learning to Solve the AC-OPF using Sensitivity-Informed Deep Neural Networks", accepted for publication in IEEE Transactions on Power Systems (early access). Also available on arXiv preprint arXiv:2103.14779, 2021.
- X. Lei, Z. Yang, J. Yu, J. Zhao, Q. Gao and H. Yu, "Data-Driven Optimal Power Flow: A Physics-Informed Machine Learning Approach", in IEEE Transactions on Power Systems, vol. 36, no. 1, pp. 346 - 354, Jan. 2021.
- M. K. Singh, S. Gupta , V. Kekatos, G. Cavraro and A. Bernstein, "Learning to Optimize Power Distribution Grids using Sensitivity-Informed Deep Neural Networks", in Proceedings of the 11th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2020), virtual conference, Nov. 11 - 13, 2020.

###### b. Advanced Neural Network Architectures

- Q. Tran, J. Mitra, and N. Nguyen," Learning model combining of convolutional deep neural network with a self-attention mechanism for AC optimal power flow,"
*Electric Power Systems Research*,*231*, p.110327, 2024. - S. Zeng, Y. Kim, Y. Ren, and K. Kim, "QCQP-Net: Reliably Learning Feasible Alternating Current Optimal Power Flow Solutions Under Constraints",
*arXiv preprint arXiv:2401.06820, 2024.* - C. Li, A. Kies, K. Zhou, M. Schlott, O. El Sayed, M. Bilousova and H. Stöcker, "Optimal Power Flow in a highly renewable power system based on attention neural networks",
*Applied Energy*, vol.*359*, p.122779, 2024. - A. Rosemberg, M. Tanneau, B. Fanzeres, J. Garcia, and P. Van Hentenryck, "Learning Optimal Power Flow value functions with input-convex neural networks," Electric Power Systms Research, vol. 235, p.110643, 2024.
- J. Han, Q. Wang, C. Yang, M. Niu, C. Yang, L. Yan, and Li, Z, "FRMNet: A Feasibility Restoration Mapping Deep Neural Network for AC Optimal Power Flow"
*IEEE Transactions on Power Systems, (early access), 2024.* - A. P. Surani and R. Sahetiya, "Graph Convolutional Neural Networks for Optimal Power Flow Locational Marginal Price",
*arXiv preprint arXiv:2301.09038, 2023.* - E. Liang, M. Chen and S. H. Low, "Low Complexity Homeomorphic Projection to Ensure Neural-Network Solution Feasibility for Optimization over (Non-) Convex Set", In
*Proc. ICML, Hawaii, USA, Jul. 23-29, 2023.* - E. Liang and M. Chen, "Generative Learning for Solving Non-Convex Problem with Multi-Valued Input-Solution Mapping", in Proceedings of 12th International Conference on Learning Representations (ICLR), accepted for publication.
- Y. Jia, X. Bai, L. Zheng, Z. Weng and Y. Li, "ConvOPF-DOP: A Data-driven Method for solving AC-OPF based on CNN considering different operation patterns", accepted for publication in IEEE Transactions on Power Systems (early access), 2022.
- S. Liu, C. Wu, and H. Zhu, "Topology-aware Graph Neural Networks for Learning Feasible and Adaptive AC-OPF Solutions", arXiv preprint arXiv:2205.10129, 2022.
- M. Mostafa, K. Baker, M. H. Dinh and F. Fioretto, "Learning Solutions for Intertemporal Power Systems Optimization with Recurrent Neural Networks", in Proc.PMAPS, pp. 1-6. IEEE, 2022.
- S. Liu, C. Wu and H. Zhu, "Graph Neural Networks for Learning Real-Time Prices in Electricity Market", arXiv preprint arXiv:2106.10529, 2021.
- K. Yang, W. Gao and R. Fan, "Optimal Power Flow Estimation Using One-Dimensional Convolutional Neural Network", in Proceedings of 2021 North American Power Symposium (NAPS), College Station, TX, USA, Nov. 14 -16, 2021.
- D. Owerko, F. Gama and A. Ribeiro, "Optimal Power Flow Using Graph Neural Networks", in Proceedings of the 45th International Conference on Acoustics, Speech and Signal Processing (ICASSP), Barcelona, Spain, May 4 - 8, 2020.

###### c. Non-neural network methods

- P. Pareek and H.D. Nguyen, "Gaussian Process Learning-based Probabilistic Optimal Power Flow", in IEEE Transactions on Power Systems, vol. 36, no. 1, pp. 541 - 544, Jan. 2021.
- M. Jalali, V. Kekatos, N. Gatsis and D. Deka, "Designing Reactive Power Control Rules for Smart Inverters Using Support Vector Machines", IEEE Transactions on Smart Grid, vol. 11, no. 2, pp. 1759 - 1770, Mar. 2020.
- O. Sondermeijer, R. Dobbe, D. Arnold, C. Tomlin and T. Keviczky, "Regression-based inverter control for decentralized optimal power flow and voltage regulation", arXiv preprint arXiv:1902.08594, 2019.
- S. Karagiannopoulos, P. Aristidou and G. Hug, "Data-driven Local Control Design for Active Distribution Grids using off-line Optimal Power Flow and Machine Learning Techniques", in IEEE Transactions on Smart Grid, vol. 10, no. 6, pp. 6461 - 6471, Nov. 2019.
- G. Neel, Z. Wang and A. Majumdar, "Machine Learning for AC Optimal Power Flow", In Proceedings of the 36th International Conference on Machine Learning Workshop, Long Beach, CA, USA, Jun. 10 - 15, 2019.

###### d. Fully-connected Neural Networks

- Z. A. Wubale, and M. G. Yenealem, "Predicting Ac Optimal Power Flow Solutions Using Artificial Neural Network",
*Available at SSRN 4816310*. - G. Chen and J. Qin, "On the Choice of Loss Function in Learning-based Optimal Power Flow",
*arXiv preprint arXiv:2402.00773, 2024.* - Y. Song, G. Chen, and H. Zhang, "Constraint learning-based optimal power dispatch for active distribution networks with extremely imbalanced data",
*CSEE Journal of Power and Energy Systems, vol. 10, no. 1, Jan. 2024.* - A. Unlu and M. Peña, "Combined MIMO Deep Learning Method for ACOPF with High Wind Power Integration"
*Energies*,*17*(4), p.796, 2024. - A. V. Konstantinov, and L. V. Utkin, "A New Computationally Simple Approach for Implementing Neural Networks with Output Hard Constraints",
*arXiv preprint arXiv:2307.10459, 2023.* - H. Liang and C. Zhao, "DeepOPF-U: A Unified Deep Neural Network to Solve AC Optimal Power Flow in Multiple Networks",
*arXiv preprint arXiv:2309.12849, 2023.* - R. Cristian, P. Harsha, G. Perakis, B. L. Quanz, and I. Spantidakis, "End-to-End Learning for Optimization via Constraint-Enforcing Approximators", In
*Proceedings of the AAAI Conference on Artificial Intelligence*(AAAI), Washington, DC, USA, Feb 7-14,, 2023. - M. Kim, H. Kim, "Self-supervised Equality Embedded Deep Lagrange Dual for Approximate Constrained Optimization",
*arXiv preprint arXiv:2306.06674, 2023.* - L. Zheng, X. Bai, Z. Weng, and Y. Jia, "A hybrid physical-data approach for solving dynamic optimal power flow considering uncertainties and different topology configurations",
*Energy Reports*, vol.*9*, pp.333-345, Sep. 2023. - X. Pan, W. Huang, M. Chen and S. H. Low, "DeepOPF-AL: Augmented Learning for Solving AC-OPF Problems with a Multi-Valued Load-Solution Mapping", in Proceedings of the 14th ACM International Conference on Future Energy Systems (ACM e-Energy 2023), accpeted for publication. [ final version to be available ]
- S. Park, W. Chen, T. W. Mak, and V. P. Hentenryck, "Compact Optimization Learning for AC Optimal Power Flow",
*arXiv preprint arXiv:2301.08840, 2023.* - X. Lei., J. Yu, H. Aini, and W. Wu, "Data-driven alternating current optimal power flow: A Lagrange multiplier based approach",
*Energy Reports*, vol.*8*, pp. 748 - 755, Nov. 2022. - M. Klamkin, M. Tanneau, T. W. Mak and P. V. Hentenryck, "Active Bucketized Learning for ACOPF Optimization Proxies", arXiv preprint arXiv:2208.07497, 2022.
- M. Zhou, M. Chen and S. H. Low, "DeepOPF-FT: One Deep Neural Network for Multiple AC-OPF Problems with Flexible Topology", IEEE Transactions on Power Systems, accepted for publication. [ final version to be available ]
- Z. Dong, K. Hou, Z. Liu, X. Yu, H. Jia, and C. Zhang. "A Sample-Efficient OPF Learning Method Based on Annealing Knowledge Distillation",
*IEEE Access, vol. 10, pp. 99724 - 99733, Sep.*2022. - X. Pan, W. Huang, M. Chen and S. H. Low, "DeepOPF-AL Augmented Learning for Solving AC-OPF Problems with Multiple Load-Solution Mappings", arXiv preprint arXiv:2206.03365, 2022.
- P. S. Torre and P. H-Gonzalez, "Decentralized Optimal Power Flow for Time-Varying Network Topologies Using Machine Learning", in Proceedings of Power Systems Computation Conference (PSCC), 27th June to 1st July, Porto, Portugal, 2022.
- A. Lotfi and M. Pirnia, "Constraint-Guided Deep Neural Network for Solving Optimal Power Flow", in Proceedings of Power Systems Computation Conference (PSCC), 27th June to 1st July, Porto, Portugal, 2022.
- Y. Li, C. Zhao and C. Liu, "Model-Informed Generative Adversarial Network (MI-GAN) for Learning Optimal Power Flow", arXiv preprint arXiv:2206.01864, 2022.
- T. H. A. Cheung, M. Zhou and M Chen，"Learning-based AC-OPF Solvers on Realistic Network and Realistic Loads", arXiv preprint arXiv:2205.09452, 2022.
- W. Huang, X. Pan, M. Chen and S. H. Low, "DeepOPF-V: Solving AC-OPF Problems Efficiently", IEEE Transactions on Power Systems, vol. 37, no. 1, pp. 800 - 803, Jan. 2022. Also available on as technical report: arXiv preprint arXiv:2103.11793, 2021.
- M. Dolanyi, K. ESIM, K. Bruninx, J.F. Toubeau and E. Delaru, "Capturing Electricity Market Dynamics in the Optimal Trading of Strategic Agents using Neural Network Constrained Optimization", In Proceedings of the 35th Annual Conference on Neural Information Processing Systems (NeurIPS), virtual conference, Dec. 14, 2021.
- S. D. Jongh, S. Steinle, A. Hlawatsch, F. Mueller, M. Suriyah and T. Leibfried, "Neural Predictive Control for the Optimization of Smart Grid Flexibility Schedules", In Proceedings of the 56th International Universities Power Engineering Conference (UPEC), Middlesbrough, United Kingdom, Aug. 31 - Sept. 3, 2021.
- Y. Jia and X. Bai, "A CNN Approach for Optimal Power Flow Problem for Distribution Network", In Proceedings of Power System and Green Energy Conference (PSGEC), Shanghai, China, Aug. 20 - 22, 2021.
- G. Huang, L. Liao, L. Cheng and W. Hua, "Learning Optimal Power Flow with Infeasibility Awareness", In Proceedings of the 38th International Conference on Machine Learning Workshop, virtual conference, Jul. 23, 2021.
- R. Sadnan and A. Dubey, "Learning Optimal Power Flow Solutions using Linearized Models in Power Distribution Systems", In Proceedings of IEEE 48th Photovoltaic Specialists Conference (PVSC), Fort Lauderdale, FL, USA, Jun. 20 - 25, 2021.
- J. Rahman, C.Feng and J. Zhang, "A learning-augmented approach for AC optimal power flow", accepted for publication in International Journal of Electrical Power & Energy Systems, vol. 130, pp. 106908, Mar. (Publication time Sept) 2021.
- M. K. Singh, S. Gupta and V. Kekatos, "Machine Learning for Optimal Inverter Operation in Distribution Grids", in Proceedings of the 55th Annual Conference on Information Sciences and Systems (CISS), Baltimore, MD, USA, Mar. 24 - 26, 2021.
- M. Chatzos, T. W. Mak and P. V. Hentenryck, "Spatial Network Decomposition for Fast and Scalable AC-OPF Learning", accepted for publication in IEEE Transactions on Power Systems (early access), 2021.
- T. W. Mak, F. Fioretto and P. V. Hentenryck, "Load Embeddings for Scalable AC-OPF Learning", arXiv preprint arXiv:2101.03973, 2021.
- Y. Chen, S. Lakshminarayana, C. Maple and H. V. Poor, "A Meta-Learning Approach to the Optimal Power Flow Problem Under Topology Reconfigurations", arXiv preprint arXiv:2012.11524, 2020.
- A. Zamzam and K. Baker, "Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow", in Proceedings of the 11th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2020), virtual conference, Nov. 11 - 13, 2020.
- S. Gupta , V. Kekatos and M. Jin, "Deep Learning for Reactive Power Control of Smart Inverters under Communication Constraints", in Proceedings of the 11th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2020), virtual conference, Nov. 11 - 13, 2020.
- X. Pan, M. Chen, T. Zhao and S. H. Low, "DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems", arXiv preprint arXiv:2007.01002, 2020.
- M. Chatzos, F. Fioretto, T. W.K. Mak and P. V. Hentenryck, "High-Fidelity Machine Learning Approximations of Large-Scale Optimal Power Flow", arXiv preprint arXiv:2006.1635, 2020.
- Y. Zhou, B. Zhang, C. Xu, T. Lan, R. Diao, D. Shi, Z. Wang and W. Lee, "Deriving Fast AC OPF Solutions via Proximal Policy Optimization for Secure and Economic Grid Operation", arXiv preprint arXiv:2003.12584, 2020.
- F. Fioretto, T. Mak and P. V. Hentenryck, "Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods", in Proceedings of the 34th AAAI Conference on Artificial Intelligence, New York, USA, Feb. 7 - 12, 2020.
- F. Fioretto, P. V. Hentenryck, T. W. Mak, C. Tran, F. Baldo and M. Lombardi, "Lagrangian Duality for Constrained Deep Learning", arXiv preprint arXiv:2001.09394, 2020.

##### Distributed Optimal Power Flow

- T. W. Mak and C. Minas, T. Mathieu and P. V. Hentenryck, "Learning Regionally Decentralized AC Optimal Power Flows with ADMM",
*arXiv preprint arXiv:2205.03787, 2022.* - D. S. Sarma, L. Cupelli, F. Ponci, and A. Monti, "Distributed Optimal Power Flow with Data-Driven Sensitivity Computation", In Proceedings of IEEE Madrid PowerTech, Madrid, Spain, 28 June - 2 July, 2021.
- F. Guo, B. Xu, W. -A. Zhang, C. Wen, D. Zhang and L. Yu, "Training Deep Neural Network for Optimal Power Allocation in Islanded Microgrid Systems: A Distributed Learning-Based Approach", accepted for publication in IEEE Transactions on Neural Networks and Learning Systems (early access), 2021.
- R. Dobbe, O. Sondermeijer, D. Fridovich-Keil, D. Arnold, D. Callaway and C. Tomlin, "Towards Distributed Energy Services: Decentralizing Optimal Power Flow with Machine Learning", in IEEE Transactions on Smart Grid, vol. 11, no. 2, pp. 1296 - 1306, Mar. 2020.

##### Stochastic Optimal Power Flow

- M. Mitrovic, A. Lukashevich, P. Vorobev, V. Terzija, V, S. Budennyy, Y. Maximov, and D. Deka, "Data-driven stochastic AC-OPF using Gaussian process regression",
*International Journal of Electrical Power & Energy Systems*, vol.*152*, pp.109249, Oct. 2023. - L. Zhang, D. Tabas, and B. Zhang, "An Efficient Learning-Based Solver for Two-Stage DC Optimal Power Flow with Feasibility Guarantees,"
*arXiv preprint arXiv:2304.01409, 2023.* - S. Gupta, S. Misra, D. Deka, and V. Kekatos, "DNN-based policies for stochastic AC OPF",
*Electric Power Systems Research*, vol.*213*, p.108563, Dec. 2022.

#### Unsupervised Learning-based Schemes

- T. B. Lopez-Garcia, and J. A. Domínguez-Navarro, "Optimal Power Flow with Physics-informed Typed Graph Neural Networks",
*IEEE Transactions on Power Systems, (early access), 2024.* - J. Kotary and F. Fioretto, "Learning Constrained Optimization with Deep Augmented Lagrangian Methods," arXiv preprint arXiv:2403.03454, 2024.
- M. Klamkin, M. Tanneau, and P. Van Hentenryck, "Dual Interior-Point Optimization Learning," arXiv preprint arXiv:2402.02596, 2024.
- M. Tanneau and P. Van Hentenryck, "Dual Lagrangian Learning for Conic Optimization," arXiv preprint arXiv:2402.03086, 2024.
- M. Yang, G. Qiu, J. Liu, Y. Liu, T. Liu, Z. Tang, L. Ding, Y. Shui, and K. Liu, "Topology-Transferable Physics-Guided Graph Neural Network for Real-Time Optimal Power Flow," IEEE Transactions on Industrial Informatics, 2024.
- M. Saffari, M. Khodayar, and M.E. Khodayar, "Physics-Informed Graph Capsule Generative Autoencoder for Probabilistic AC Optimal Power Flow," IEEE Transactions on Emerging Topics in Computational Intelligence, 2024.
- B.N. Giraud, A. Rajaei, and J.L. Cremer, "Constraint-driven deep learning for Nk security constrained optimal power flow," Electric Power Systems Research, vol. 235, p.110692, 2024.
- D. A. Perez-Rosero, A. M. Álvarez-Meza, and G. Castellanos-Dominguez, "A Regularized Physics-Informed Neural Network to support Data-Driven Nonlinear Constrained Optimization", 2024.
- W. Huang, M. Chen, and S. H. Low, “Unsupervised Learning for Solving AC Optimal Power Flows: Design, Analysis, and Experiment", IEEE Transactions on Power Systems, accepted for publication.
- A. S. Marcial and M. Perninge, "An Unsupervised Neural Network Approach for Solving the Optimal Power Flow Problem", 2023.
- G. Qiu, M. Tanneau, and P. Van Hentenryck, "Dual Conic Proxies for AC Optimal Power Flow",
*arXiv preprint arXiv:2310.02969, 2023.* - K. Chen, S. Bose, and Y. Zhang, "Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality," In Proceedings of the IEEE Global Communications Conference Dec 4, 2022.
- M. Yang, J. Liu, G. Qiu, T. Liu, and Z. Tang, "AC Optimal Power Flows: Combining Lagrangian Dual and physics-Guided Graph Neutral Networks," IEEE Transaction on Industrial Informatics (early access), 2022.
- S. Park and P. V. Hentenryck, "Self-Supervised Primal-Dual Learning for Constrained Optimization,"
*arXiv preprint arXiv:2208.09046, 2022.* - K, Chen, S. Bose and Y. Zhang, "Unsupervised Deep Learning for AC Optimal Power Flow via Lagrangian Duality",
*arXiv preprint arXiv:2212.03977, 2022* - J. Wang and P. Srikantha. Fast Optimal Power Flow With Guarantees Via an Unsupervised Generative Model.
*IEEE Transactions on Power Systems (early access), 2022.* - D. Owerko, F. Gama and A. Ribeiro, "Unsupervised Optimal Power Flow Using Graph Neural Networks",
*arXiv preprint arXiv:2210.09277, 2022.* - W. Huang and M. Chen, "DeepOPF-NGT: A Fast Unsupervised Learning Approach for Solving AC-OPF Problems without Ground Truth", In Proceedings of the 38th International Conference on Machine Learning Workshop, virtual conference, Jul. 23, 2021.
- P. L. Donti, D. Rolnick and J. Z. Kolter, "DC3: a learning method for optimization with hard constraints", in Proceedings of 9th International Conference on Learning Representations (ICLR), virtual conference, May 3 – 7, 2021.
- H. Lange, B. Chen, M. Berges, and S. Kar, "Learning to Solve AC Optimal Power Flow by Differentiating through Holomorphic Embeddings", arXiv preprint arXiv:2012.09622, 2020.

#### Reinforcement Learning-based Schemes

- G. Tsaousoglou, P. Ellinas, J.S. Giraldo, and E. Varvarigos, "Distributed sequential optimal power flow under uncertainty in power distribution systems: A data-driven approach," Electric Power Systems Research, vol. 235, p.110816, 2024.
- T. Wolgast and A. Nieße, "Learning the Optimal Power Flow: Environment Design Matters," arXiv preprint arXiv:2403.17831, 2024.
- B. Feng, J. Zhao, G. Huang, Y. Hu, H. Xu, C. Guo, and Z. Chen, "Safe deep reinforcement learning for real-time AC optimal power flow: A near-optimal solution," CSEE Journal of Power and Energy Systems
*(early access)*, 2024. - P. Wu, C. Chen, D. Lai, J. Zhong, and Z. Bie, "Real-Time Optimal Power Flow Method via Safe Deep Reinforcement Learning Based on Primal-Dual and Prior Knowledge Guidance",
*IEEE Transactions on Power Systems (easrly access), 2024.* - Z. Fan, W. Zhang, and W. Liu, "Data-Efficient Deep Reinforcement Learning-Based Optimal Generation Control in DC Microgrids",
*IEEE Systems Journal, vol. 18, no. 1, 2024.* - Z. Yan and Y. Xu, "Real-Time Optimal Power Flow with Linguistic Stipulations: Integrating GPT-Agent and Deep Reinforcement Learning",
*IEEE Transactions on Power Systems, vol. 39, no. 2, Mar. 2024.* - T. Wu, A. Scaglione, and D. Arnold, "Constrained Reinforcement Learning for Stochastic Dynamic Optimal Power Flow Control",
*arXiv preprint arXiv:2302.10382, 2023.* - Z. Yi, Y. Xu, and C. Wu, "Model-Free Economic Dispatch for Virtual Power Plants: An Adversarial Safe Reinforcement Learning Approach",
*IEEE Transactions on Power Systems, (ealy access) 2023.* - P. Wu, C. Chen, D. Lai, and J. Zhong, "A Safe DRL Method for Fast Solution of Real-Time Optimal Power Flow",
*arXiv preprint arXiv:2308.03420, 2023.* - A. R. Sayed, X. Zhang, G. Wang, C. Wang, and J. Qiu, "Optimal Operable Power Flow: Sample-efficient Holomorphic Embedding-based Reinforcement Learning",
*IEEE Transactions on Power Systems, (early access) 2023.* - A. R. Sayed, C. Wang, H. Anis, and T. Bi, "Feasibility constrained online calculation for real-time optimal power flow: A convex constrained deep reinforcement learning approach",
*IEEE Transactions on Power Systems (ealy access) 2022.* - Z. Wang, J. H. Menke, F. Schäfer, M. Braun and A. Scheidler, "Approximating multi-purpose AC optimal power flow with reinforcement trained artificial neural network.,"
*Energy and AI*,*7*, p.100133., 2022. - A. R. Sayed, C. Wang, H. Anis and T. Bi, "Feasibility Constrained Online Calculation for Real-Time Optimal Power Flow: A Convex Constrained Deep Reinforcement Learning Approach",
*IEEE Transactions on Power Systems (early access), 2022.* - L. Zeng, M. Sun, X. Wan, Z. Zhang, R. Deng and Y. Xu, "Physics-Constrained Vulnerability Assessment of Deep Reinforcement Learning-based SCOPF," accepted for publication in IEEE Transactions on Power Systems (early access), 2022.
- H. Zhen, H. Zhai, W. Ma, L. Zhao, Y. Weng, Y. Xu, J. Shi and X. He, "Design and tests of reinforcement-learning-based optimal power flow solution generator", accepted for publication in Energy Reports, 8, pp.43-50, 2022.
- Z. Wang, J-H. Menke, F. Schäfer, M. Braun, A. Scheidler, "Approximating multi-purpose AC Optimal Power Flow with reinforcement trained Artificial Neural Network," accepted for publication in Energy and AI, 100133, Vol. 7, 2022.
- Z. Yan and Y. Xu, "A Hybrid Data-driven Method for Fast Solution of Security-Constrained Optimal Power Flow," accepted for publication in IEEE Transactions on Power Systems (early access),2022.
- Z. Wang, J.H. Menke, F. Schäfer, M. Braun and A. Scheidler, "Approximating multi-purpose AC optimal power flow with reinforcement trained artificial neural network", Energy and AI, vol. 7, p.100133, 2022.
- Z. Yan and Y. Xu, "Real-Time Optimal Power Flow: A Lagrangian based Deep Reinforcement Learning Approach", in IEEE Transactions on Power Systems, letter paper, vol 35, no. 4, pp. 3270 - 3273, Jul. 2020.
- H. Zhen, Zhai H, W. Ma, L. Zhao, Y. Weng, Y. Xu, J. Shi, X. He, "Design and tests of reinforcement-learning-based optimal power flow solution generator", In Proceedings of 8th International Conference on Power and Energy Systems Engineering (CPESE), Fukuoka, Japan, Sept. 10 – 12 2021.
- Y. Zhou, W. J. Lee, R. Diao, and D. Shi, "Deep Reinforcement Learning Based Real-Time AC Optimal Power Flow Considering Uncertainties", accepted for publication in Journal of Modern Power Systems and Clean Energy (early access), 2021.
- J. H. Woo, L. Wu, J-B. P and J. H. Roh, "Real-Time Optimal Power Flow Using Twin Delayed Deep Deterministic Policy Gradient Algorithm", in IEEE Access, vol. 8, pp. 213611 - 213618, Nov. 2020.
- E. R. Sanseverino, M. L. Di Silvestre, L. Mineo, S. Favuzza, N. Q. Nguyen and Q. T. Tran, "A multi-agent system reinforcement learning based optimal power flow for islanded microgrids", in Proceedings of IEEE 16th International Conference on Environment and Electrical Engineering (EEEIC), Florence, Italy, Jun. 7 - 10, 2016.

#### Neural Network Robustness and Worst-case Performance

- K. Zuo, M. Sun, Z. Zhang, P. Cheng, G. Strbac, and C. Kang, "Transferability-Oriented Adversarial Robust Security-Constrained Optimal Power Flow," IEEE Transactions on Smart Grid, 2024.
- L. Piloto, S. Liguori, S. Madjiheurem, M. Zgubic, S. Lovett, H. Tomlinson, S. Elster, C. Apps, and S. Witherspoon, "CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations",
*arXiv preprint arXiv:2403.17660, 2024.* - W. Chen, H. Zhao, M. Tanneau, and P. Van Hentenryck, "Compact Optimality Verification for Optimization Proxies," arXiv preprint arXiv:2405.21023, 2024.
- R. Nellikkath, M. Tanneau, P. Van Hentenryck, and S. Chatzivasileiadis, "Scalable Exact Verification of Optimization Proxies for Large-Scale Optimal Power Flow," arXiv preprint arXiv:2405.06109, 2024.
- I. Murzakhanov and S. Chatzivasileiadis, "GPU-Accelerated Verification of Machine Learning Models for Power Systems",
*arXiv preprint arXiv:2306.10617, 2023.* - M. H. Dinh, F. Fioretto, M. Mohammadian and K. Baker, "An Analysis of the Reliability of AC Optimal Power Flow Deep Learning Proxies", In
*IEEE PES Innovative Smart Grid Technologies Latin America (ISGT-LA)*(pp. 170-174). IEEEm 2023. - R. Nellikkath, and S. Chatzivasileiadis, "Minimizing Worst-Case Violations of Neural Networks",
*arXiv preprint arXiv:2212.10930, 2022.* - A. Venzke and S. Chatzivasileiadis, "Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications", IEEE Transactions on Smart Grid, vol. 12, no. 1, pp. 383 - 397, Jan. 2021.
- M. H. Dinh, F. Fioretto, Towards, M. Mohammadian and K. Baker, "Understanding the Unreasonable Effectiveness of Learning AC-OPF Solutions", arXiv preprint arXiv:2111.11168, 2021.
- R. Nellikkath and S. Chatzivasileiadis, "Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow", in Proceedings of the 11th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2021), in-Person and Virtual Conference, Aachen, Germany, Oct. 25 - 28, 2021.
- A. Venzke, G. Qu, S. Low and S. Chatzivasileiadis, "Learning Optimal Power Flow: Worst-Case Guarantees for Neural Networks", in Proceedings of the 11th IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (IEEE SmartGridComm 2020), virtual conference, Nov. 11 - 13, 2020.

#### Data Sampling

- M. Klamkin, M. Tanneau, T.W. Mak, and P. Van Hentenryck, "Bucketized Active Sampling for learning ACOPF," Electric Power Systems Research, vol. 235, p.110697, 2024.
- S. Lovett, M. Zgubic, S. Liguori, S. Madjiheurem, H. Tomlinson, S. Elster, C. Apps, S. Witherspoon, and L. Piloto, "OPFData: Large-scale datasets for AC optimal power flow with topological perturbations," arXiv preprint arXiv:2406.07234, 2024.
- I. V. Nadal, and S. Chevalier, "Scalable Bilevel Optimization for Generating Maximally Representative OPF Datasets",
*arXiv preprint arXiv:2304.10912, 2023.* - R. Nellikkath, and S. Chatzivasileiadis, "Enriching Neural Network Training Dataset to Improve Worst-Case Performance Guarantees",
*arXiv preprint arXiv:2303.13228, 2023.* - Z. Hu and H. Zhang. "Optimal Power Flow Based on Physical-Model-Integrated Neural Network with Worth-Learning Data Generation",
*arXiv preprint arXiv:2301.03766,*2023. - J. Kotary, F. Fioretto and P. V. Hentenryck, "Learning Hard Optimization Problems: A Data Generation Perspective", arXiv preprint arXiv:2106.02601, 2021.

## The Hybrid Framework

In the **hybrid** framework, the machine learning model is used to augment the conventional optimization solver with valuable pieces of information.

#### Wart-starting point schemes

(*This scheme* use learning models to predict a wart-start point for iterative algorithms)

- A. Deihim, D. Apostolopoulou, and E. Alonso, "Initial estimate of AC optimal power flow with graph neural networks," Electric Power Systems Research, vol. 234, p.110782, 2024.
- R, Sambharya, G. Hall, B. Amos, and B. Stellato, "Learning to Warm-Start Fixed-Point Optimization Algorithms",
*arXiv preprint arXiv:2309.07835, 2023.* - Y. Cao, H. Zhao, G. Liang, J. Zhao, H. Liao, and C. Yang, "Fast and explainable warm-start point learning for AC Optimal Power Flow using decision tree",
*International Journal of Electrical Power & Energy Systems*, vol.*153*, p.109369, 2023. - R. Sambharya, G. Hall, B. Amos, and B. Stellato, "End-to-End Learning to Warm-Start for Real-Time Quadratic Optimization",
*arXiv preprint arXiv:2212.08260, 2022.* - S. A. Sadat and M. Sahraei-Ardakani, "Initializing Successive Linear Programming Solver for ACOPF using Machine Learning," in Proceedings of 2021 North American Power Symposium (NAPS), College Station, TX, USA, Nov. 14 -16, 2021.
- L. Zhang and B. Zhang, "Learning to Solve the AC Optimal Power Flow via a Lagrangian Approach", arXiv preprint arXiv:2110.01653.
- W. Dong, Z. Xie , G. Kestor and L. Dong, "Smart-PGSim: using neural network to accelerate AC-OPF power grid simulation", in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC '20). IEEE Press, Article 63, 1 – 15, Nov. 2020.
- M. Jamei, L. Mones, A. Robson, L. White, J. Requeima and C. Ududec, "Meta-Optimization of Optimal Power Flow", in Proceedings of the 36th International Conference on Machine Learning Workshop, Long Beach, CA, USA, Jun. 10 - 15, 2019.
- L. Chen and J.E. Tate, "Hot-Starting the AC Power Flow with Convolutional Neural Networks", arXiv preprint arXiv:2004.09342, 2020.
- F. Diehl, "Warm-Starting AC Optimal Power Flow with Graph Neural Networks", in Proceedings of the 33rd Conference on Neural Information Processing Systems (NeurIPS) Workshop, Vancouver, BC, Canada, Dec. 8 - 14, 2019.
- K. Baker, "Learning Warm-Start Points for AC Optimal Power Flow", in Proceedings of IEEE 29th Machine Learning for Signal Processing Conference, Pittsburgh, PA, USA, Oct. 13 - 16, 2019.

#### Constraint simplification schemes

*(This scheme use learning models to simplify the constraints in the optimal power flow problem, including linearizing or convexifying the power flow equations, and representing the chance-constraint or security constrained using learning models)*

- T. Pham and X. Li, "N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Network",
*arXiv preprint arXiv:2402.06226, 2024.* - Z. Fan, L. Lou, J. Zhang, D. Zhou, and Y. Shi, "Improving Linear OPF Model Via Incorporating Bias Factor of Optimality Condition," IEEE Transactions on Power Systems, 2024.
- R. Hu, and Q. Li, "A Data-Driven Optimization Method Considering Data Correlations for Optimal Power Flow Under Uncertainty",
*IEEE Access*, vol.*11*, pp.32041-32050, 2023. - G. Chen, H. Zhang, H. Hui and Y. Song, "Deep-quantile-regression-based surrogate model for joint chance-constrained optimal power flow with renewable generation", arXiv preprint arXiv:2204.04919, 2022.
- J. Liu, Y. Liu, G. Qiu and X. Shao "Learning-Aided Optimal Power Flow Based Fast Total Transfer Capability Calculation", Energies, vol 15, issue 4, pp 1 - 15, 2022.
- R. Hu, and Q. Li, "Optimal operation of power systems with energy storage under uncertainty: A scenario-based method with strategic sampling",
*IEEE Transactions on Smart Grid*, vol.*13, no.*2, pp.1249-1260, 2021. - S. Gupta, V. Kekatos and M. Jin, "Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approach", arXiv preprint arXiv:2105.00429, 2021.
- G. Chen, H. Zhang, H. Hui, N. Dai and Y. Song, "Scheduling thermostatically controlled loads to provide regulation capacity based on a learning-based optimal power flow model", in IEEE Transactions on Sustainable Energy, vol. 12, no. 4, pp. 2459 - 2470, Oct. 2021.
- R. Hu, Q. Li and F. Qiu, "Ensemble Learning Based Convex Approximation of Three-Phase Power Flow," in IEEE Transactions on Power Systems, vol. 36, no. 5, pp. 4042-4051, Sept. 2021.
- Z. Kilwein, F. Boukouvala, C. Laird, A. Castillo, L. Blakely, M. Eydenberg, J. Jalving, and L. Batsch-Smith, "AC-Optimal Power Flow Solutions with Security Constraints from Deep Neural Network Models." In Computer Aided Chemical Engineering, vol. 50, pp. 919 - 925. Elsevier, July, 2021.
- S. Liu, Y. Guo, W. Tang, H. Sun and W. Huang, "Predicting Active Constraints Set in Security-Constrained Optimal Power Flow via Deep Neural Network", in Proceedings of 2021 IEEE Power & Energy Society General Meeting (PESGM), Washington, DC, USA, Jul. 26 - 29, 2021.
- Q. Li, "Uncertainty-Aware Three-Phase Optimal Power Flow Based on Data-Driven Convexification," in IEEE Transactions on Power Systems, vol. 36, no. 2, pp. 1645-1648, Mar. 2021.
- Q. Hou, N. Zhang, D. S. Kirschen, E. Du, Y. Cheng and C. Kang, "Sparse Oblique Decision Tree for Power System Security Rules Extraction and Embedding", in IEEE Transactions on Power Systems, vol. 36, no. 2, pp. 1605 - 1615, Mar. 2021.
- R. Hu, Q. Li, S. Lei, "Ensemble learning based linear power flow", in Proceedings of 2020 IEEE Power & Energy Society General Meeting (PESGM), Montreal, QC, Canada, Aug. 2 - 6, 2020.
- A. Venzke, D. Viola, J. Mermet-Guyennet, G. Misyris and S. Chatzivasileiadis, "Neural Networks for Encoding Dynamic Security-Constrained Optimal Power Flow to Mixed-Integer Linear Programs", arXiv preprint, arXiv:2003.07939, 2020.
- K. Baker and A. Bernstein, "Joint Chance Constraints in AC Optimal Power Flow: Improving Bounds through Learning", in IEEE Transactions on Smart Grid, vol. 10, no. 6, pp. 6376 - 6385, Nov. 2019.
- K. Baker and A. Bernstein. Joint chance constraints reduction through learning in active distribution networks", in Proceedings of the 6th IEEE Global Conference on Signal and Information Processing (GlobalSIP), Anaheim, CA, Nov. 26 - 29, 2018.
- Y. Ng, S. Misra, L. A. Roald and S. Backhaus, "Statistical Learning for DC Optimal Power Flow", in Proceedings of the 20th IEEE Power Systems Computation Conference, Dublin, Ireland, Jun. 11 - 15, 2018.
- L. Halilbašić, F. Thams, A. Venzke, S. Chatzivasileiadis and P. Pinson, "Data-driven Security-Constrained AC-OPF for Operations and Markets", in Proceedings of the 20th IEEE Power Systems Computation Conference, Dublin, Ireland, Jun. 11 - 15, 2018.
- A. Vaccaro and C. A. Cañizares, "A Knowledge-Based Framework for Power Flow and Optimal Power Flow Analyses", in IEEE Transactions on Smart Grid, vol. 9, no. 1, pp. 230 - 239, Jan. 2018.

#### Constraint Screening schemes

*(This scheme using learning models to identify the active or inactice constraints for the optimal power flow problem)*

- Y. Yu, Y. Gao, Y. Li, and Y. Yan, "Interpretable data‐driven contingency classification for real‐time corrective security‐constrained economic dispatch," IET Renewable Power Generation, vol. 18, no. 3, pp. 489-501, 2024.
- S. Bose, K. Chen and Y. Zhang, "Learning to Optimize: Accelerating Optimal Power Flow via Data-driven Constraint Screening",
*arXiv preprint arXiv:2312.07276, 2023.* - S. Misra, L. A. Roald and Y. Ng, "Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets", in INFORMS Journal on Computing, vol. 34, no. 1, pp. 463-480, Jan 2022.
- C. Crozier and K. Baker, "Data-driven Probabilistic Constraint Elimination for Accelerated Optimal Power Flow.," In
*Proceedings of IEEE Power & Energy Society General Meeting (PESGM)*, Denver, CO, USA, Jul. 17-21, 2022. - H. Wu, M. Wang, Z. Xu and Y. Jia, 2022, "Active Constraint Identification Assisted DC Optimal Power Flow," In
*Proceedings of IEEE/IAS Industrial and Commercial Power System Asia (I&CPS Asia), Shanghai, China, Jul. 8-11, 2022.* - S. Liu, Y. Guo, W. Tang, H. Sun, W. Huang and J. Hou, "Varying Condition SCOPF Optimization Based on Deep Learning and Knowledge Graph", accepted for publication in IEEE Transactions on Power Systems (early access), 2022.
- Y. Chen, L. Zhang and B. Zhang, "Learning to Solve DCOPF: A Duality Approach", in Proceedings of Power Systems Computation Conference (PSCC), 27th June to 1st July, Porto, Portugal ,2022.
- T. Pham, T and X. Li, "Reduced Optimal Power Flow Using Graph Neural Network," arXiv preprint arXiv:2206.13591, 2022.
- F. Hasan and A. Kargarian, "Topology-aware Learning Assisted Branch and Ramp Constraints Screening for Dynamic Economic Dispatch", accepted for publication in IEEE Transactions on Power Systems (early access), 2022.
- F. Hasan, A. Kargarian and J. Mohammadi, "Hybrid Learning Aided Inactive Constraints Filtering Algorithm to Enhance AC OPF Solution Time," in IEEE Transactions on Industry Applications, vol. 57, no. 2, pp. 1325-1334, Apr. 2021.
- L. Zhang, Y. Chen and B. Zhang, "A Convex Neural Network Solver for DCOPF with Generalization Guarantees", accepted for publication in IEEE Transactions on Control and Network Systems (early access), 2021; arXiv preprint arXiv:2009.09109, 2020.
- Y. Chen and B. Zhang, "Learning to Solve Network Flow Problems via Neural Decoding", arXiv preprint arXiv:2002.04091, 2020.
- A. Robson, M. Jamei, C. Ududec and L. Mones, "Learning an Optimally Reduced Formulation of OPF through Meta-optimization", arXiv preprint arXiv:1911.06784, 2019.
- D. Deka and S. Misra, "Learning for DC-OPF: Classifying Active Sets Using Neural Nets", Milan, Italy, Jun. 23 - 27, IEEE Milan PowerTech, 2019.
- A. Jahanbani Ardakani and F. Bouffard, "Prediction of umbrella constraints", in Proceedings of IEEE 20th Power Systems Computation Conference, Dublin, Ireland, Jun. 11 - 15, 2018.

#### Learning to optimize schemes

*(This scheme use the learning model to accelerate the iteration process of the iterative algorithms)*

- F. Cengil, H. Nagarajan, R. Bent, S. Eksioglu, and B. Eksioglu, "Learning to Accelerate Tightening of Convex Relaxations of the AC Optimal Power Flow Problem," 2024.
- Y.E. Jang, J. Ban, Y.J. Kim, and C. Chen, "Multi-period Optimal Power Flow Using Decomposition and RL-Based Cutting Planes," Authorea Preprints, 2024.
- F. Cengil, H. Nagarajan, R. Bent, S. Eksioglu and B. Eksioglu, "Learning to accelerate globally optimal solutions to the AC Optimal Power Flow problem", in Proceedings of Power Systems Computation Conference (PSCC), 27th June to 1st July, Porto, Portugal ,2022.
- M. Li, S. Kolouri, and J. Mohammadi, "Learning to Optimize Distributed Optimization: ADMM-based DC-OPF Case Study" In 2023 IEEE Power & Energy Society General Meeting (PESGM), Orlando, the U.S.A, Jul. 16-20, 2023.
- K. Baker, "Emulating AC OPF Solvers With Neural Networks," accepted for publication in IEEE Transactions on Power Systems (early access), 2022
- A. Mohammadi and A. Kargarian, "Learning-Aided Asynchronous ADMM for Optimal Power Flow," in IEEE Transactions on Power Systems, vol. 37, no. 3, pp. 1671 - 1681, May 2022.
- K. Baker K, "Emulating AC OPF solvers for Obtaining Sub-second Feasible, Near-Optimal Solutions", arXiv preprint arXiv:2012.10031, 2020.
- K. Baker, "A Learning-boosted Quasi-Newton Method for AC Optimal Power Flow", arXiv preprint arXiv:2007.06074, 2020.
- D. Biagioni, P. Graf, X. Zhang, A.S. Zamzam, K. Baker and J. King, "Learning-Accelerated ADMM for Distributed Optimal Power Flow", arXiv preprint arXiv:1911.03019, 2019.

#### Adversarial learning schemes

*(This scheme uses adversarial learning to solve the optimal power flow problems)*

- C. Dawson and C. Fan, "Adversarial optimization leads to over-optimistic security-constrained dispatch, but sampling can help"
*arXiv preprint arXiv:2310.06956 ,2023.* - A. Agarwal, L. Pileggi, P. Donti and Z. Kolter, "Employing Adversarial Robustness Techniques for Large-Scale Stochastic Optimal Power Flow", in Proceedings of Power Systems Computation Conference (PSCC), 27th June to 1st July, Porto, Portugal, 2022.
- P. Donti, A. Agarwal, N. V. Bedmutha, L. Pileggi and J. Z. Kolter, "Adversarially robust learning for security-constrained optimal power flow", In Proceedings of the 35th Conference on Neural Information Processing Systems (NeurIPS), virtual conference, poster paper, Dec. 7 - 10, 2021.

## Blog Posts, Talks and Other Materials

- Using Neural Networks for Predicting Solutions to Optimal Power Flow
- Using Meta-optimization for Predicting Solutions to Optimal Power Flow

# Machine Learning for Solving Power Flow Equations

- S. Li, Z. Pan, H. Li, Y. Xiao, M. Liu, and X. Wang, “Convergence criterion of power flow calculation based on graph neural network,” J. Phys.: Conf. Ser., vol. 2703, no. 1, p. 012042, Feb. 2024.
- J. Jalving, M. Eydenberg, L. Blakely, A. Castillo, Z. Kilwein, J. K. Skolfield, F. Boukouvala, and C. Laird, "Physics-informed machine learning with optimization-based guarantees: Applications to AC power flow",
*International Journal of Electrical Power & Energy Systems*,*157*, p.109741, 2024. - P. Pareek, D. Deka, and S. Misra, “Graph-Structured Kernel Design for Power Flow Learning using Gaussian Processes.” arXiv, Aug. 15, 2023.
- S. Chevalier and S. Chatzivasileiadis, “Global Performance Guarantees for Neural Network Models of AC Power Flow.” arXiv, May 04, 2023.
- J. B. Hansen, S. N. Anfinsen, and F. M. Bianchi, “Power Flow Balancing with Decentralized Graph Neural Networks,” in IEEE Transactions on Power Systems, vol. 38, no. 3, pp. 2423–2433, May 2023.
- A. Yaniv, P. Kumar, and Y. Beck, “Towards adoption of GNNs for power flow applications in distribution systems,” Electric Power Systems Research, vol. 216, p. 109005, Mar. 2023.
- M. Yang, G. Qiu, J. Liu and K. Liu, "Probabilistic Power Flow Based on Physics-Guided Graph Neural Networks",
*Available at SSRN 4731825*. - T. B. Lopez-Garcia and J. A. Domínguez-Navarro, “Power flow analysis via typed graph neural networks,” Engineering Applications of Artificial Intelligence, vol. 117, p. 105567, Jan. 2023.
- M. Gao, J. Yu, Z. Yang, and J. Zhao, “Physics Embedded Graph Convolution Neural Network for Power Flow Calculation Considering Uncertain Injections and Topology,” IEEE Transactions on Neural Networks and Learning Systems, pp. 1–12, 2023.
- A. Kody, S. Chevalier, S. Chatzivasileiadis, and D. Molzahn, “Modeling the AC power flow equations with optimally compact neural networks: Application to unit commitment,” Electric Power Systems Research, vol. 213, p. 108282, Dec. 2022.
- T. B. Lopez-Garcia and J. A. Domínguez-Navarro, “Graph Neural Network Power Flow Solver for Dynamical Electrical Networks,” in 2022 IEEE 21st Mediterranean Electrotechnical Conference (MELECON), Jun. 2022, pp. 825–830.
- R. Villena-Ruiz, A. Honrubia-Escribano, and E. Gómez-Lázaro, “Learning Load Flow Analysis in Electric Power Systems: A Case Study in PowerFactory,” in 2022 45th Jubilee International Convention on Information, Communication and Electronic Technology (MIPRO), May 2022, pp. 1357–1362.
- L. Böttcher et al., “Solving AC Power Flow with Graph Neural Networks under Realistic Constraints.” arXiv, Apr. 14, 2022.
- J. Yuan and Y. Weng, “Support Matrix Regression for Learning Power Flow in Distribution Grid With Unobservability,” IEEE Transactions on Power Systems, vol. 37, no. 2, pp. 1151–1161, Mar. 2022.
- P. Pareek and H. D. Nguyen, “A Framework for Analytical Power Flow Solution Using Gaussian Process Learning,” IEEE Transactions on Sustainable Energy, vol. 13, no. 1, pp. 452–463, Jan. 2022.
- S. Berrone, F. Della Santa, A. Mastropietro, S. Pieraccini, and F. Vaccarino, “Graph-Informed Neural Networks for Regressions on Graph-Structured Data,” Mathematics, vol. 10, no. 5, Art. no. 5, Jan. 2022.
- X. Hu, H. Hu, S. Verma, and Z.-L. Zhang, “Physics-Guided Deep Neural Networks for Power Flow Analysis,” IEEE Transactions on Power Systems, vol. 36, no. 3, pp. 2082–2092, May 2021.
- H. Hagmar, L. Tong, R. Eriksson, and L. A. Tuan, “Voltage Instability Prediction Using a Deep Recurrent Neural Network,” IEEE Transactions on Power Systems, vol. 36, no. 1, pp. 17–27, Jan. 2021.
- B. Donon, R. Clément, B. Donnot, A. Marot, I. Guyon, and M. Schoenauer, “Neural networks for power flow: Graph neural solver,” Electric Power Systems Research, vol. 189, p. 106547, Dec. 2020.
- M. Xiang, J. Yu, Z. Yang, Y. Yang, H. Yu, and H. He, “Probabilistic power flow with topology changes based on deep neural network,” International Journal of Electrical Power & Energy Systems, vol. 117, p. 105650, May 2020.
- Y. Yang, Z. Yang, J. Yu, B. Zhang, Y. Zhang, and H. Yu, “Fast Calculation of Probabilistic Power Flow: A Model-Based Deep Learning Approach,” IEEE Transactions on Smart Grid, vol. 11, no. 3, pp. 2235–2244, May 2020.
- B. Donon, B. Donnot, I. Guyon, and A. Marot, “Graph Neural Solver for Power Systems,” in 2019 International Joint Conference on Neural Networks (IJCNN), Jul. 2019, pp. 1–8.
- Y. Liu, N. Zhang, Y. Wang, J. Yang, and C. Kang, “Data-Driven Power Flow Linearization: A Regression Approach,” IEEE Transactions on Smart Grid, vol. 10, no. 3, pp. 2569–2580, May 2019.
- F. Schäfer, J.-H. Menke, and M. Braun, “Contingency Analysis of Power Systems with Artificial Neural Networks,” in 2018 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), Oct. 2018, pp. 1–6.
- M. Fikri, B. Cheddadi, O. Sabri, T. Haidi, B. Abdelaziz, and M. Majdoub, “Power Flow Analysis by Numerical Techniques and Artificial Neural Networks,” in 2018 Renewable Energies, Power Systems & Green Inclusive Economy (REPS-GIE), Apr. 2018, pp. 1–5.
- V. Veerasamy, R. Ramachandran, M. Thirumeni, and B. Madasamy, “Load flow analysis using generalised Hopfield neural network,” IET Generation, Transmission & Distribution, vol. 12, no. 8, pp. 1765–1773, 2018.

# Codes

- Code for "DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems": https://github.com/Mzhou-cityu/DeepOPF-Codes
- Code for "DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow": https://github.com/Mzhou-cityu/DeepOPF-Codes
- Code for "Ensuring DNN Solution Feasibility for Optimization Problems with Linear Constraints": https://github.com/Mzhou-cityu/DeepOPF-Codes
- Code for "DeepOPF-FT: One Deep Neural Network for Multiple AC-OPF Problems with Flexible Topology": https://github.com/Mzhou-cityu/DeepOPF-FT
- Code for "DeepOPF-V: Solving AC-OPF Problems Efficiently": https://github.com/wanjunhuang/hwjcode