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# 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

- 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

- 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.* - J. Wang, and P. Srikantha, "Data-driven AC Optimal Power Flow with Physics-informed Learning and Calibrations.
*arXiv preprint arXiv:2404.09128, 2024.* - 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.* - Z. A. Wubale, and M. G. Yenealem, "Predicting Ac Optimal Power Flow Solutions Using Artificial Neural Network",
*Available at SSRN 4816310*. - 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*. - 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. - 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. 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*,*153*, p.109369, 2023. - G. Chen and J. Qin, "On the Choice of Loss Function in Learning-based Optimal Power Flow",
*arXiv preprint arXiv:2402.00773, 2024.* - T. Pham and X. Li, "N-1 Reduced Optimal Power Flow Using Augmented Hierarchical Graph Neural Network",
*arXiv preprint arXiv:2402.06226, 2024.* - A. Rosemberg, M. Tanneau, B. Fanzeres, J. Garcia and P. Van Hentenryck, "Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks",
*arXiv preprint arXiv:2310.04605, 2023.* - 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. - 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.* - M. H. Dinh, F. Fioretto, M. Mohammadian and K. Baker, "An Analysis of the Reliability of AC Optimal Power Flow Deep Learning Proxies", In
*2023 IEEE PES Innovative Smart Grid Technologies Latin America (ISGT-LA)*(pp. 170-174). IEEE. - J. Mitra, and N. Nguyen, "Deatnet: Learning Model from the Combination of Convolutional Deep Neural Network and Self-Attention Mechanism for Ac Optimal Power Flow".
- 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, 2024 (early access)* - A. Unlu and M. Peña, "Combined MIMO Deep Learning Method for ACOPF with High Wind Power Integration"
*Energies*,*17*(4), p.796, 2024. - C. Dawson and C. Fan, "Adversarial optimization leads to over-optimistic security-constrained dispatch, but sampling can help"
*arXiv preprint arXiv:2310.06956 ,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
*Proceedings of the International Conference on Machine Learning (ICML), Hawaii, USA, Jul. 23-29, 2023.* - I. Murzakhanov and S. Chatzivasileiadis, "GPU-Accelerated Verification of Machine Learning Models for Power Systems",
*arXiv preprint arXiv:2306.10617, 2023.* - 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.* - I. V. Nadal, and S. Chevalier, "Scalable Bilevel Optimization for Generating Maximally Representative OPF Datasets",
*arXiv preprint arXiv:2304.10912, 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.* - 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. - R. Nellikkath, and S. Chatzivasileiadis, "Enriching Neural Network Training Dataset to Improve Worst-Case Performance Guarantees",
*arXiv preprint arXiv:2303.13228*. - A. Stratigakos, S. Pineda, J. M. Morales, and G. Kariniotakis, "Interpretable Machine Learning for DC Optimal Power Flow with Feasibility Guarantees", 2023.
- N. Popli, E. Davoodi, F. Capitanescu, and L. Wehenkel, "On the robustness of machine-learnt proxies for security constrained optimal power flow solvers", 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, H. Kim, "Self-supervised Equality Embedded Deep Lagrange Dual for Approximate Constrained Optimization",
*arXiv preprint arXiv:2306.06674, 2023.* - 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. - 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. - T. Wu, A. Scaglione, and D. Arnold, "Constrained Reinforcement Learning for Stochastic Dynamic Optimal Power Flow Control",
*arXiv preprint arXiv:2302.10382*. - 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.* - A. P. Surani and R. Sahetiya, "Graph Convolutional Neural Networks for Optimal Power Flow Locational Marginal Price",
*arXiv preprint arXiv:2301.09038, 2023.* - T. Zhao, X. Pan, M. Chen and S. H. Low, "Ensuring DNN Solution Feasibility for Optimization Problems with Linear Constraints", in Proceedings of the 11th International Conference on Learning Representations (ICLR), accepted for publication. [final version to be available ]
- 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. - 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. - 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. - R. Nellikkath, and S. Chatzivasileiadis, "Minimizing Worst-Case Violations of Neural Networks",
*arXiv preprint arXiv:2212.10930, 2022.* - 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. - R. Nellikkath and S. Chatzivasileiadis, "Minimizing Worst-Case Violations of Neural Networks",
*arXiv preprint arXiv:2212.10930, 2022.* - 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. - 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. - 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. - 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.* - M. Mostafa, K. Baker, M. H. Dinh and F. Fioretto, "Learning Solutions for Intertemporal Power Systems Optimization with Recurrent Neural Networks", in Proceedings of the 17th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS), pp. 1-6. IEEE, 2022.
- M. Li, S. Kolouri and J. Mohammadi, "Learning to Solve Optimization Problems with Hard Linear Constraints", arXiv preprint arXiv:2208.10611, 2022.
- M. Klamkin, M. Tanneau, M, T. W. Mak and P. V. Hentenryck, "Active Bucketized Learning for ACOPF Optimization Proxies", arXiv preprint arXiv:2208.07497, 2022.
- K. Baker, "Emulating AC OPF Solvers With Neural Networks," accepted for publication in IEEE Transactions on Power Systems (early access), 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- E. Lu, N. Wang, W. Zheng, X. Wang, X. Lei, Z. Zhu and Z. Gong, "Data-Driven Electricity Price Risk Assessment for Spot Market", International Transactions on Electrical Energy Systems, vol. 2022, 11 pages, 2022.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- R. Nellikkath and S. Chatzivasileiadis, "Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow", arXiv preprint arXiv:2107.00465, 2021.
- S. Liu, C. Wu and H. Zhu, "Graph Neural Networks for Learning Real-Time Prices in Electricity Market", arXiv preprint arXiv:2106.10529, 2021.
- J. Kotary, F. Fioretto and P. V. Hentenryck, "Learning Hard Optimization Problems: A Data Generation Perspective", arXiv preprint arXiv:2106.02601.
- 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.
- 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.
- S. Gupta, V. Kekatos and M. Jin, "Controlling Smart Inverters using Proxies: A Chance-Constrained DNN-based Approach", arXiv preprint arXiv:2105.00429, 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. 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.
- 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.
- 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.
- T. W. Mak, F. Fioretto and P. V. Hentenryck, "Load Embeddings for Scalable AC-OPF Learning", arXiv preprint arXiv:2101.03973, 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.
- 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. 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. 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.
- K. Baker K, "Emulating AC OPF solvers for Obtaining Sub-second Feasible, Near-Optimal Solutions", arXiv preprint arXiv:2012.10031, 2020.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- X. Pan, T. Zhao and M. Chen, "DeepOPF: Deep Neural Network for DC Optimal Power Flow", arXiv:1905.04479, May 11th, 2019.
- 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.
- 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.

#### Unsupervised Learning-based Schemes

- 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.
- 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.* - 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

- 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.* - 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.
- 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.
- 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.

## The Hybrid Framework

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

- 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.* - R, Sambharya, G. Hall, B. Amos, and B. Stellato, "Learning to Warm-Start Fixed-Point Optimization Algorithms",
*arXiv preprint arXiv:2309.07835, 2023.* - 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.
- 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. 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. - 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.
- 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.* - 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.
- 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.
- 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.
- 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.
- T. Pham, T and X. Li, "Reduced Optimal Power Flow Using Graph Neural Network," arXiv preprint arXiv:2206.13591, 2022.
- Y. Zhang, J. Liu, F. Qiu, T. Hong and R. Yao, "Deep Active Learning for Solvability Prediction in Power Systems," accepted for publication in Journal of Modern Power Systems and Clean Energy (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.
- 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.
- 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.
- O. Akdag, "A Improved Archimedes Optimization Algorithm for multi/single-objective Optimal Power Flow", Electric Power Systems Research, vol. 206, pp. 107796, Jan. 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.
- 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. 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.
- 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.
- D. Lee, K. Turitsyn, D. K. Molzahn, and L. A. Roald, "Robust AC optimal power flow with robust convex restriction", in IEEE Transactions on Power Systems, vol. 36, no. 6, pp. 4953-4966, Apr 2021.
- 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.
- 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.
- 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.
- 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.
- A. Pena-Ordieres, D. K. Molzahn, L. A. Roald, and A. Wächter A, "DC optimal power flow with joint chance constraints", in IEEE Transactions on Power Systems., vol. 36, no. 1, pp. 147-158, Jun 2020.
- T. Liu, Y. Liu, J. Liu, J. Wang, L. Xu, G. Qiu and H. Cao, "A Bayesian Learning based Scheme for Online Dynamic Security Assessment and Preventive Control", in IEEE Transactions on Power Systems, vol 35, no. 5, pp. 4088 - 4099, Sep. 2020.
- 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.
- 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.
- K. Baker, "A Learning-boosted Quasi-Newton Method for AC Optimal Power Flow", arXiv preprint arXiv:2007.06074, 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.
- 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.
- L. Chen and J.E. Tate, "Hot-Starting the AC Power Flow with Convolutional Neural Networks", arXiv preprint arXiv:2004.09342, 2020.
- Y. Chen and B. Zhang, "Learning to Solve Network Flow Problems via Neural Decoding", arXiv preprint arXiv:2002.04091, 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.
- 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.
- 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. 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.
- 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.
- D. Deka and S. Misra, "Learning for DC-OPF: Classifying Active Sets Using Neural Nets", Milan, Italy, Jun. 23 - 27, IEEE Milan PowerTech, 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.
- 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.
- P. Aristidou and G. Hug, "Optimized local control for active distribution grids using machine learning techniques", in Proceedings of 2018 IEEE Power & Energy Society General Meeting (PESGM), Portland, OR, USA, Aug. 5 - 10, 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.
- F. Thams, S. Chatzivasileiadis, P. Pinson and R. Eriksson, "Data-driven security-constrained OPF", in Proceedings of the 10th Bulk Power Systems Dynamics and Control Symposium, Espinho, Portugal, Aug. 27 - Sep. 1, 2017.
- R. Canyasse, G. Dalal and S. Mannor, "Supervised learning for optimal power flow as a real-time proxy", in Proceedings of IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT), Washington, DC, USA, Apr. 23 - 26, 2017.
- R. T. F. Ah. King, X. Tu, Louis-A. Dessaint and I Kamwa, "Multi-contingency transient stability-constrained optimal power flow using multilayer feedforward neural networks", in Proceedings pf 2016 IEEE Canadian Conference on Electrical and Computer Engineering (CCECE), Vancouver, BC, Canada, May 15 - 18, 2016.
- V. J. Gutierrez-Martinez, C. A. Canizares, C. R. Fuerte-Esquivel, A. Pizano-Martinez and X. Gu, "Neural-Network Security-Boundary Constrained Optimal Power Flow", in IEEE Transactions on Power Systems, vol. 26, no. 1, pp. 63 - 72, Feb. 2011.

## 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.
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# 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