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Large-Scale Grid Optimization: the Workhorse of Future Grid Computations

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Abstract

Purpose of Review

The computation methods for modeling, controlling, and optimizing the transforming grid are evolving rapidly. We review and systemize knowledge for a special class of computation methods that solve large-scale power grid optimization problems.

Recent Findings

We find that while mechanistic physics-based methods are leading the science in solving large-scale grid optimizations, data-driven techniques, especially physics constrained ones, are emerging as an alternative to solve otherwise intractable problems. We also find observable gaps in the field and ascertain these gaps from the paper’s literature review and by collecting and synthesizing feedback from industry experts.

Summary

Large-scale grid optimizations are pertinent for, among other things, hedging against risk due to resource stochasticity, evaluating aggregated DERs’ impact on grid operation and design, and improving the overall efficiency of grid operation in terms of cost, reliability, and carbon footprint. We attribute the continual growth in scale and complexity of grid optimizations to a large influx of new spatial and temporal features in both transmission (T) and distribution (D) networks. Therefore, to systemize knowledge in the field, we discuss the recent advancements in T and D systems from the viewpoint of mechanistic physics-based and emerging data-driven methods.

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Notes

  1. Every inequality constraint, even if inactive, introduces a new dual variable into an optimization formulation, thus increasing problem complexity for primal-dual solvers.

References

Papers of particular interest, published recently, have been highlighted as: • Of importance •• Of major importance

  1. Pan F. HIPPO - A software platform for electricity market research and development - CRADA 485. 2021. https://doi.org/10.2172/1899574. Available: https://www.osti.gov/biblio/1899574.

  2. Chen Y, Wang F, Ma Y, Yao YIEEE. IEEE transactions on power systems. 2019;35(1):711–720.

  3. Gong N, Luo X, Chen D. The Journal of Engineering. Bi-level two-stage stochastic SCUC for ISO day-ahead scheduling considering uncertain wind power and demand response. 2017;13:2549–54. https://doi.org/10.1049/joe.2017.0787. Available: https://ietresearch.onlinelibrary.wiley.com/doi/abs/10.1049/joe.2017.0787.

  4. Huang S, Dinavahi V. IEEE Systems Journal. A branch-and-cut benders decomposition algorithm for transmission expansion planning. 2017;13(1):659–669.

  5. Canizes B, Soares J, Lezama F, Silva C, Vale Z, Corchado JM. Renewable Energy. Optimal expansion planning considering storage investment and seasonal effect of demand and renewable generation. Elsevier, 2019;138;937–954.

  6. Haghighat H, Zeng B. IEEE transactions on power systems. Bilevel mixed-integer transmission expansion planning, IEEE. 2018;33(6):7309–7312.

  7. Chernyakhovskiy I, Joshi M, Rose A. Power system planning: advancements in capacity expansion modeling. National Renewable Energy Lab.(NREL), Golden, CO (United States). 2021.

  8. Klotz E, Newman AM. Practical guidelines for solving difficult linear programs. Surveys in Operations Research and Management Science. Elsevier. 2013;18:1–17.

  9. Macmillan M, Eurek K, Cole W, Bazilian MD. Solving a large energy system optimization model using an open-source solver. Energy Strategy Reviews. Elsevier. 2021;38:100755.

  10. Schweppe FC, Handschin EJ. Static state estimation in electric power systems. Proceedings of the IEEE. 1974;62(7):972–982.

  11. Abur A, Exposito AG. Power system state estimation: theory and implementation. CRC press 2004.

  12. Ghaljehei M, Ahmadian A, Golkar MA, Amraee T, Elkamel A. International Journal of Electrical Power & Energy Systems. Stochastic SCUC considering compressed air energy storage and wind power generation: a techno-economic approach with static voltage stability analysis. 2018;100:489–507. https://doi.org/10.1016/j.ijepes.2018.02.046. Available:https://www.sciencedirect.com/science/article/pii/S014206151732519X.

  13. Ye H, Wang J, Li Z. MIP reformulation for max-min problems in two-stage robust SCUC. IEEE Transactions on Power Systems. 2016;32(2):1237–1247.

  14. Jabr RA, Karaki S, Korbane JA. Robust multi-period OPF with storage and renewables. IEEE Trans Power Syst. 2014;30(5):2790–9.

    Article  Google Scholar 

  15. Gopalakrishnan A, Raghunathan AU, Nikovski D, Biegler LT, Global optimization of multi-period optimal power flow. In,. American Control Conference. IEEE. 2013;2013:1157–64.

  16. Aravena I, Molzahn DK, Zhang S, Petra CG, Curtis FE, Tu S, Wächter A, Wei E, Wong E, Gholami A. Recent developments in security-constrained AC optimal power flow: overview of challenge 1 in the ARPA-E grid optimization competition. 2022.arXiv:2206.07843.

  17. Varawala L, Dán G, Hesamzadeh MR, Baldick R. A generalised approach for efficient computation of look ahead security constrained optimal power flow European. J Oper Res. 2023. https://doi.org/10.1016/j.ejor.2023.02.018. Available: https://www.sciencedirect.com/science/article/pii/S0377221723001522.

  18. Mitrovic M, Kundacina O, Lukashevich A, Vorobev P, Terzija V, Maximov Y, Deka D. GP CC-OPF: Gaussian process based optimization tool for chance-constrained optimal power flow. 2023. arXiv:2302.08454.

  19. Scholz Y, Fuchs B, Borggrefe F, Cao KK, Wetzel M, von Krbek K, Cebulla F, Gils HC, Fiand F, Bussieck M. Speeding up energy system models-a best practice guide. 2020.

  20. Bussar C, Stöcker P, Cai Z, Moraes L Jr, Alvarez R, Chen H, Breuer C, Moser A, Leuthold M, Sauer DU. Large-scale integration of renewable energies and impact on storage demand in a European renewable power system of 2050. Energy Procedia Elsevier. 2015;73:145–53.

  21. Nalley S, LaRose A, Diefenderfer J, Staub J, Turnure J, Westfall L. The national energy modeling system: an overview 2018. Washington DC: US Department of Energy, Tech; 2019.

    Google Scholar 

  22. Diakov V, Cole W, Sullivan P, Brinkman G, Margolis R. Improving power system modeling. A tool to link capacity expansion and production cost models. Golden, CO (United States). National Renewable Energy Lab.(NREL),2015.

  23. Barrows C, McBennett B, Novacheck J, Sigler D, Lau J, Bloom A. Multi-operator production cost modeling. IEEE Trans Power Syst. 2019;34(6):4429:4437.

  24. David J, Gisin B, Gu Q, Thomas B. Extending ISO operational software to long-term production cost models. Proc. FERC Tech. Conf., pp. 1-28, Jun. 26, 2019 p 1–28.

  25. • Tsai CH, Figueroa-Acevedo A, Boese M, Li Y, Mohan N, Okullo J, Heath B, Bakke J. Challenges of planning for high renewable futures: experience in the US midcontinent electricity market. Renewable and Sustainable Energy Reviews. 2020;131:109992. MISO developed the Renewable Integration Impact Assessment (RIIA) framework to study high renewable scenarios (up to 50%) in their footprint. To assess system impact in this study, MISO ran a suite of large-scale grid optimizations, ranging from production cost modeling to ACOPF.

  26. Johnston J, Henriquez-Auba R, Maluenda B, Fripp M. Switch 2.0: a modern platform for planning high-renewable power systems. SoftwareX. 2019;10:100251. https://doi.org/10.1016/j.softx.2019.100251. (https://www.sciencedirect.com/science/article/pii/S2352711018301547)

  27. Chen Y, Pan F, Qiu F, Xavier AS, Zheng T, Marwali M, Knueven B, Guan Y, Luh PB, Wu L. Security-constrained unit commitment for electricity market: modeling, solution methods and future challenges. IEEE: IEEE Trans Power Syst; 2022.

    Google Scholar 

  28. Xavier ÁS, Qiu F, Ahmed S. Learning to solve large-scale security-constrained unit commitment problems INFORMS. J Comput. 2021;33(2):739–56.

    MathSciNet  MATH  Google Scholar 

  29. • Chen Y, Pan F, Holzer J, Rothberg E, Ma Y, Veeramany A. A high performance computing based market economics driven neighborhood search and polishing algorithm for security constrained unit commitment IEEE Trans Power Syst. 2021;36(1):292–302 https://doi.org/10.1109/TPWRS.2020.3005407. This paper is from an ARPA-E awarded HIPPO project that built parallel and distributed computing capabilities for real-world SCUC market algorithms. This particular paper develops a neighborhood search and polishing algorithm that adaptively fixes binary and continuous variables and chooses lazy constraints based on hints from an initial solution and its associated neighborhood.

  30. Shi X, Zuluaga LF. Revenue adequate prices for chance-constrained electricity markets with variable renewable energy sources. 2021. arXiv:2105.01233.

  31. Dvorkin V. Stochastic and private energy system optimization. Technical University of Denmark. 2020.

  32. Nazir N, Racherla P, Almassalkhi M. Optimal multi-period dispatch of distributed energy resources in unbalanced distribution feeders. IEEE Trans Power Syst. 2020;35(4):2683–92. https://doi.org/10.1109/TPWRS.2019.2963249.

    Article  Google Scholar 

  33. Agarwal A, Pileggi L. Large scale multi-period optimal power flow with energy storage systems using differential dynamic programming. IEEE Trans Power Syst. 2022;37(3):1750–9. https://doi.org/10.1109/TPWRS.2021.3115636.

    Article  Google Scholar 

  34. Vasylius V, Jonaitis A, Gudžius S, Kopustinskas V. Multi-period optimal power flow for identification of critical elements in a country scale high voltage power grid. Reliab Eng Syst Saf. 2021;246:107959. https://doi.org/10.1016/j.ress.2021.107959. Available https://www.sciencedirect.com/science/article/pii/S0951832021004701

  35. Kourounis D, Fuchs A, Schenk O. Toward the next generation of multiperiod optimal power flow solvers. IEEE Trans Power Syst. 2018;33(4):4005–14. https://doi.org/10.1109/TPWRS.2017.2789187.

    Article  Google Scholar 

  36. Bienstock D, Escobar M, Gentile C, Liberti L. Mathematical programming formulations for the alternating current optimal power flow problem. Ann Oper Res Springer. 2022;314(1):277–315.

    Article  MathSciNet  MATH  Google Scholar 

  37. Jereminov M, Pandey A, Pileggi L. Equivalent circuit formulation for solving AC optimal power flow. IEEE Trans Power Syst. 2018;34(3):2354–65.

    Article  Google Scholar 

  38. McNamara T, Pandey A, Agarwal A, Pileggi L. Two-stage homotopy method to incorporate discrete control variables into AC-OPF. Electr Power Syst Res Elsevier. 2012;212: 108283.

    Article  Google Scholar 

  39. Coffrin CJ. ARPA-e grid optimization competition: benchmark algorithm overview. Los Alamos National Lab.(LANL), Los Alamos, NM (United States). 2021.

  40. Crozier C, Baker K, Du Y, Mohammadi J, Li M. 2022 17th International Conference on Probabilistic Methods Applied to Power Systems (PMAPS). Data-driven contingency selection for fast security constrained optimal power flow. 2022;1–6. https://doi.org/10.1109/PMAPS53380.2022.9810574

  41. Agarwal A, Donti PL, Kolter JZ, Pileggi L. Employing adversarial robustness techniques for large-scale stochastic optimal power flow. Electr Power Syst Res. 2022;212:108497. https://doi.org/10.1016/j.epsr.2022.108497. Available: https://www.sciencedirect.com/science/article/pii/S0378779622006101

  42. Mezghani I, Misra S, Deka D. Stochastic AC optimal power flow: a data-driven approach. Electr Power Syst Res. 2020;189:106567. https://doi.org/10.1016/j.epsr.2020.106567.https://www.sciencedirect.com/science/article/pii/S0378779620303710.

  43. Roald LA, Pozo D, Papavasiliou A, Molzahn DK, Kazempour J, Conejo A. Power systems optimization under uncertainty: a review of methods and applications. Electr Power Syst Res Elsevier. 2023;214:108725.

    Article  Google Scholar 

  44. Bienstock D, Chertkov M, Harnett S. Chance-constrained optimal power flow: risk-aware network control under uncertainty. SIAM Rev SIAM. 2014;56(3):461–95.

    Article  MathSciNet  MATH  Google Scholar 

  45. Conejo AJ, Baringo L, Kazempour SJ, Siddiqui AS. Investment in electricity generation and transmission. Cham Zug, Switzerland: Springer International Publishing. vol 119. 2016.

  46. Mahdavi M, Kheirkhah AR, Macedo LH, Romero R. A genetic algorithm for transmission network expansion planning considering line maintenance. IEEE Congress on Evolutionary Computation (CEC) 2020. p 1–6.

  47. Ding T, Li C, Huang C, Yang Y, Li F, Blaabjerg F. A hierarchical modeling for reactive power optimization with joint transmission and distribution networks by curve fitting. IEEE Syst J. 2017;12(3):2739–48.

    Article  Google Scholar 

  48. Li S, Yu T, Pu T, Ming J, Fan S. Coordinated optimization control method of transmission and distribution network. IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC). 2016. p 2215–2219 https://doi.org/10.1109/APPEEC.2016.7779880.

  49. Juan Ospina, P. Towards the optimization of integrated transmission-distribution networks via the rapid prototyping of OPF formulations with PowerModelsITD.jl. In Fifth Workshop on Autonomous Energy Systems. Los Alamos National Laboratory. 2022.

  50. Zhang B. Global state estimation for whole transmission and distribution networks. Electr Power Syst Res Elsevier. 2005;74(2):187–95.

    Article  Google Scholar 

  51. Pandey A, Li S, Pileggi L. To appear in power systems operation with 100% renewable energy sources. Combined Transmission and Distribution State-Estimation for Future Electric Grids: Elsevier; 2023.

    Google Scholar 

  52. Chevalier S, Schenato L, Daniel L. Accelerated probabilistic state estimation in distribution grids via model order reduction. IEEE Power & Energy Society General Meeting (PESGM). 2021. p 1–5. https://doi.org/10.1109/PESGM46819.2021.9638151.

  53. Zamzam AS, Fu X, Sidiropoulos ND. Data-driven learning-based optimization for distribution system state estimation. IEEE Trans Power Syst. 2019;34(6):4796–805.

    Article  Google Scholar 

  54. Xie L, Choi DH, Kar S, Poor HV. Fully distributed state estimation for wide-area monitoring systems. IEEE Trans on Smart Grid. 2012;1154–1169.

  55. Guo Y, Wu W, Zhang B, Sun H. A distributed state estimation method for power systems incorporating linear and nonlinear models. Int J Electr Power & Energy Syst. Elsevier, 2015;64:608–616.

  56. Minot A, Lu YM, Li N. A distributed Gauss-Newton method for power system state estimation. IEEE Transactions on Power Systems IEEE. 2015;31(5):3804–15.

    Article  Google Scholar 

  57. Singh MK, Gupta S, Kekatos V, Cavraro G, Bernstein A. Learning to optimize power distribution grids using sensitivity-informed deep neural networks. IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm). 2020;1–6 https://doi.org/10.1109/SmartGridComm47815.2020.9302942.

  58. Paudyal S, Canizares CA, Bhattacharya K. Optimal operation of distribution feeders in smart grids. IEEE Trans Ind Electron. 2011;58(10):4495–503. https://doi.org/10.1109/TIE.2011.2112314.

    Article  Google Scholar 

  59. Bernstein A, Wang C, Dall’Anese E, Le Boudec JY, Zhao C. Load flow in multiphase distribution networks: existence, uniqueness, non-singularity and linear models. IEEE Transactions on Power Systems. 2018;33(6):5832–43. https://doi.org/10.1109/TPWRS.2018.2823277.https://ieeexplore.ieee.org/document/8332975/

  60. Stai E, Wang C, Le Boudec JY. On the solution of the optimal power flow for three-phase radial distribution networks with energy storage. IEEE Trans Control of Netw Syst. 2021;8(1):187–199. issn: 2325-5870,2372-2533. https://doi.org/10.1109/TCNS.2020.3024319.https://ieeexplore.ieee.org/document/9199091/.

  61. Dall’Anese E, Simonetto A. Optimal power flow pursuit. IEEE Trans on Smart Grid. 2018;9(2):942–52. issn: 1949-3053, 1949-3061 https://doi.org/10.1109/TSG.2016.2571982.http://ieeexplore.ieee.org/document/7480375/

  62. DallAnese E, Baker K, Summers T. Chance-constrained AC optimal power flow for distribution systems with renewables. IEEE Trans Power Syst. 2017;32(5):3427–38. https://doi.org/10.1109/TPWRS.2017.2656080. Available: https://ieeexplore.ieee.org/document/7828060/ (visited on 03/08/2023)

  63. Almassalkhi M, Brahma S, Nazir N, Ossareh H, Racherla P, Kundu S, Nandanoori SP, Ramachandran T, Singhal A, Gayme D. Hierarchical, grid-aware, and economically optimal coordination of distributed energy resources in realistic distribution systems. Energ MDPI. 2020;13(23):6399.

    Google Scholar 

  64. Yang H, Nagarajan H. Optimal power flow in distribution networks under stochastic N-1 disruptions. Electric Power Systems Research. 2020;189. https://doi.org/10.1016/j.epsr.2020.106689. https://www.sciencedirect.com/science/article/pii/S0378779620304922.

  65. Yang Q, Yang Y, Li C, Bie Z, Blaabjerg F. A data-driven stochastic reactive power optimization considering uncertainties in active distribution networks and decomposition method. IEEE Trans Smart Grid. 2017;9(50):4994–5004.

    Google Scholar 

  66. Chen X, Li N. Leveraging two-stage adaptive robust optimization for power flexibility aggregation. IEEE Trans Smart Grid. 2021;12(5):3954–65. https://doi.org/10.1109/TSG.2021.3068341.

    Article  Google Scholar 

  67. Luo X, Zhao J. Private email exchange: paper on emerging trends in large-scale optimization. (Discussions on Gaps in Industry Large-scale Optimizations) 2023. Accessed 11 Feb. 2023.

  68. Cheung K. Private email exchange: updates and a paper on large-scale grid optimization (discussions on gaps in industry large-scale optimization) 2023. Accessed 8 Feb. 2023.

  69. Ho J, Becker J, Brown M, Brown P, Chernyakhovskiy I, Cohen S, Cole W, Corcoran S, Eurek K, Frazier W. Regional Energy Deployment System (ReEDS) model documentation: version 2020. National Renewable Energy Lab.(NREL), Golden, CO (United States), Tech. Rep. 2021.

  70. Zonooz MRF, Nopiah Z, Yusof AM, Sopian K. A review of MARKAL energy modeling. Eur J Sci Res. 2009;26(3):352–61.

  71. Jereminov M, Pileggi L. Equivalent circuit programming for power flow analysis and optimization. 2021. arXiv:2112.01351.

  72. Pandey A, Jereminov M, Wagner MR, Bromberg DM, Hug G, Pileggi L. Robust power flow and three-phase power flow analyses. IEEE Trans Power Syst. 2018;34(1):616–26.

    Article  Google Scholar 

  73. Dai C, Chen Y, Wang F, Wan J, Wu L. A configuration-component-based hybrid model for combined-cycle units in MISO day-ahead market. IEEE Trans Power Syst. 2018;34(2):883–96.

    Article  Google Scholar 

  74. Wu L, Shahidehpour M, Li T. Stochastic security-constrained unit commitment. IEEE Trans Power Syst. 2007;22(2):800–811. https://doi.org/10.1109/TPWRS.2007.894843.

  75. Parvania M, Fotuhi-Firuzabad M. 1 Demand response scheduling by stochastic SCUC, IEEE Trans Smart Grid. 2010;1:89–98. https://doi.org/10.1109/TSG.2010.2046430.

  76. Osipov D, Naqvi SA, Palepu SR, Kar K, Chow JH, Gupta A. Risk-adjusted unit commitment for systems with high penetration of renewables. IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT). 2022;1–5.

  77. Cain MB, O’neill RP, Castillo A, Citeseer et al. History of optimal power flow and formulations. Federal Energy Regulatory Commission. 2012;1:1–36.

  78. Coffrin CJ. ARPA-e grid optimization competition: benchmark algorithm overview. Los Alamos National Lab (LANL). Los Alamos NM (United States) 2021.

  79. Gopinath S, Hijazi HL. Benchmarking large-scale ACOPF solutions and optimality bounds. IEEE Power & Energy Society General Meeting (PESGM). 2022;1–5. https://doi.org/10.1109/PESGM48719.2022.9916662.

  80. Petra CG, Aravena I. Solving realistic security-constrained optimal power flow problems. 2021. arXiv preprint arXiv:2110.01669.

  81. Gholami A, Sun K, Zhang S, Sun XA. Solving large-scale security constrained AC optimal power flow problems. 2022. arXiv preprint arXiv:2202.06787

  82. Bazrafshan M, Baker K, Mohammadi J. Computationally efficient solutions for large-scale security-constrained optimal power flow. 2020. arXiv preprint arXiv:2006.00585.

  83. Wächter A, Biegler LT. On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Mathematical programming Springer. 2006;106:25–57.

    Article  MathSciNet  MATH  Google Scholar 

  84. Waltz RA, Nocedal J. Knitro 2.0 user’s manual. Ziena Optimization Inc.[en ligne] disponible sur. http://www.ziena.com 2010 September 2004;7:33–34.

  85. Gholami A, Sun K, Zhang S, Sun XA. Solving large-scale security constrained AC optimal power flow problems. 2022. arXiv preprint arXiv:2202.06787.

  86. Kardoš J, Kourounis D, Schenk O, Zimmerman R. BELTISTOS: a robust interior point method for large-scale optimal power flow problems. Electr Power Syst Res Elsevier. 2022;212:108613.

    Article  Google Scholar 

  87. Almassalkhi MR, Hiskens IA. 1 Model-predictive cascade mitigation in electric power systems with storage and renewables-part I: theory and implementation. IEEE Transactions on Power Systems. 2015;30:67–77. https://doi.org/10.1109/TPWRS.2014.2320982.

    Article  Google Scholar 

  88. Amini M, Almassalkhi M. Optimal corrective dispatch of uncertain virtual energy storage systems. IEEE Transactions on Smart Grid. 2020;11(5):4155–66. https://doi.org/10.1109/TSG.2020.2979173.

    Article  Google Scholar 

  89. Warrington J, Goulart P, Mariéthoz S, Morari M. A market mechanism for solving multi-period optimal power flow exactly on AC networks with mixed participants. American Control Conference (ACC), 2012. p 3101–3107. https://doi.org/10.1109/ACC.2012.6315477.

  90. Verma S, Mukherjee V. Transmission expansion planning: a review. International Conference on Energy Efficient Technologies for Sustainability (ICEETS). 2016;350–355.

  91. Abbasi S, Abdi H, Bruno S, La Scala M. Transmission network expansion planning considering load correlation using unscented transformation. Int J Electr Power & Energy Syst. 2018;103:12–20.

  92. Abbasi S, Abdi H. Multiobjective transmission expansion planning problem based on ACOPF considering load and wind power generation uncertainties. Int Trans Electr Energy Syst. 2017;27(6):e2312.

  93. Korres GN. 1 A distributed multiarea state estimation. IEEE Trans Power Syst. 2011;26(1):73–84. https://doi.org/10.1109/TPWRS.2010.2047030.

    Article  Google Scholar 

  94. Yang T, Sun H, Bose A. Transition to a two-level linear state estimator-Part II: algorithm. IEEE Trans Power Syst. 2010;26(1):54–62.

    Article  Google Scholar 

  95. Mustafayeva D. et al. AI insights: the power sector in a post digital age. eurelectric, Tech. Rep., Nov. 2020.

  96. Donti PL, Kolter JZ. Machine learning for sustainable energy systems. Annual Review of Environment and Resources. 2021;46(1):719–47. https://doi.org/10.1146/annurev-environ-020220-061831.

    Article  Google Scholar 

  97. Duchesne L, Karangelos E, Wehenkel L. Recent developments in machine learning for energy systems reliability management. Proceedings of the IEEE. 2020;108(9):1656–76. https://doi.org/10.1109/JPROC.2020.2988715.

    Article  Google Scholar 

  98. Van Hentenryck P. Machine learning for optimal power flows. Tutorials in Operations Research: Emerging Optimization Methods and Modeling Techniques with Applications. 2021 pp 62–82 .

  99. Hasan F, Kargarian A, Mohammadi A. A survey on applications of machine learning for optimal power flow. In 2020 IEEE Texas Power and Energy Conference (TPEC). 2020;1–6. https://doi.org/10.1109/TPEC48276.2020.9042547.

  100. Zamzam AS, Baker K. Learning optimal solutions for extremely fast ac optimal power flow. In 2020 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm). 2020. pp 1–6. https://doi.org/10.1109/SmartGridComm47815.2020.9303008.

  101. Owerko D, Gama F, Ribeiro A. Optimal power flow using graph neural networks. In ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 2020. pp 5930–5934. https://doi.org/10.1109/ICASSP40776.2020.9053140.

  102. Diehl F. Warm-starting AC optimal power flow with graph neural networks. in 33rd Conference on Neural Information Processing Systems (NeurIPS). 2019;1–6.

  103. Baker K. Learning warm-start points for ac optimal power flow. in 2019 IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP). 2019;1–6. https://doi.org/10.1109/MLSP.2019.8918690.

  104. Baker K. A learning-boosted quasi-newton method for AC optimal power flow. 2020. arXiv preprint arXiv:2007.06074.

  105. Donti PL, Rolnick D, Kolter JZ. DC3: a learning method for optimization with hard constraints. 2021. arXiv preprint arXiv:2104.12225

  106. Nellikkath R, Chatzivasileiadis S. Physics-informed neural networks for ac optimal power flow. Electr Power Syst Res. 2022;212;108 412. issn: 0378-7796. https://doi.org/10.1016/j.epsr.2022.108412. Available: https://www.sciencedirect.com/science/article/pii/S0378779622005636.

  107. Fioretto F, Mak TW, Van Hentenryck P. Predicting AC optimal power flows: combining deep learning and Lagrangian dual methods. In Proceedings of the AAAI conference on artificial intelligence. 2020;34:630–7.

    Article  Google Scholar 

  108. Chatzos M, Fioretto F, Mak TW, Van Hentenryck P. Highfidelity machine learning approximations of large-scale optimal power flow. 2020. arXiv preprint arXiv:2006.16356.

  109. Mak TW, Chatzos M, Tanneau M, Van Hentenryck P. Learning regionally decentralized AC optimal power flows with admm. 2022. arXiv preprint arXiv:2205.03787

  110. Biagioni D, Graf P, Zhang X, Zamzam AS, Baker K, King J. Learning-accelerated ADMM for distributed DC optimal power flow. IEEE Control Systems Letters. 2022;6:1–6. https://doi.org/10.1109/LCSYS.2020.3044839.

    Article  MathSciNet  Google Scholar 

  111. • Park S, Chen W, Mak TW, Van Hentenryck P. Compact optimization learning for AC optimal power flow. 2023. arXiv preprint arXiv:2301.08840. This paper uses advanced statistical compression combined with neural network training to build a model which predicts ACOPF solutions to power system test cases with up to 30,000 buses. This is one of the largest known instances of end-to-end machine learning being used to predict ACOPF solutions, and it exemplifies how data-driven and learning-based innovations can help aid and accelerate large-scale grid computations.

  112. Yang Y, Wu L. Machine learning approaches to the unit commitment problem: current trends, emerging challenges, and new strategies. Electr J. 2021;34(1);106–889, , Special Issue: Machine Learning Applications To Power System Planning And Operation, issn: 1040-6190. https://doi.org/10.1016/j.tej.2020.106889. Available: https://www.sciencedirect.com/science/article/pii/S1040619020301810.

  113. Xavier AS, Qiu F. Anl-ceeesa/miplearn v0.1, version v0.1, Nov. 2020. https://doi.org/10.5281/zenodo.4287568.

  114. Pineda S, Morales JM, Jiménez-Cordero A. Data-driven screening of network constraints for unit commitment. IEEE Trans Power Syst. 2020;35(5):3695–705. https://doi.org/10.1109/TPWRS.2020.2980212.

    Article  Google Scholar 

  115. Wu J, Luh PB, Chen Y, Yan B, Bragin MA. Synergistic integration of machine learning and mathematical optimization for unit commitment. IEEE Trans Power Syst. 2023;1–10. https://doi.org/10.1109/TPWRS.2023.3240106.

  116. Kody A, Chevalier S, Chatzivasileiadis S, Molzahn D. Modeling the ac power flow equations with optimally compact neural networks: application to unit commitment. Electr Power Syst Res. 2022;213:108 282. issn: 0378–7796. https://doi.org/10.1016/j.epsr.2022.108282. Available: https://www.sciencedirect.com/science/article/pii/S0378779622004771.

  117. Crozier C, Baker K. Data-driven probabilistic constraint elimination for accelerated optimal power flow. In IEEE Power & Energy Society General Meeting (PESGM). 2022;1–5. https://doi.org/10.1109/PESGM48719.2022.9916838.

  118. Marot A, Donnot B, Romero C, et al. Learning to run a power network challenge for training topology controllers. Electr Power Syst Res. 2020;189:106–635. issn: 0378–7796. https://doi.org/10.1016/j.epsr.2020.106635. Available: https://www.sciencedirect.com/science/article/pii/S0378779620304387.

  119. Marot A, Donnot B, Dulac-Arnold G, et al. Learning to run a power network challenge: a retrospective analysis. arXiv e-prints arXiv:2103.03104. Mar. 2021. https://doi.org/10.48550/arXiv.2103.03104. cs.LG.

  120. Marot A, Donnot B, Chaouache K, et al. Learning to run a power network with trust, Electric Power Systems Research, 2022;212:108–487. issn: 0378-7796. https://doi.org/10.1016/j.epsr.2022.108487. Available: https://www.sciencedirect.com/science/article/pii/S0378779622006137.

  121. Crognier G, Tournebise P, Ruiz M, Panciatici P. Grid operationbased outage maintenance planning. Electr Power Syst Res. 2021;190:106 682. issn: 0378-7796. https://doi.org/10.1016/j.epsr.2020.106682. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0378779620304855.

  122. Clemente J. Northern Europeś energy hub looks to IBM garage and cloud PAK for data to design a green energy future, 2021. Available: https://www.ibm.com/blog/northern-europes-energy-hublooks- to-ibm-garage-and-cloud-pak-for-data-to-design-agreen-energy-future/.

  123. Lange H, Chen B, Berges M, Kar S. Learning to solve ac optimal power flow by differentiating through holomorphic embeddings. 2020. arXiv preprint arXiv:2012.09622.

  124. Amos B, Kolter JZ. OptNet: Differentiable optimization as a layer in neural networks. In Proceedings of the 34th International Conference on Machine Learning, D. Precup and Y. W. Teh, Eds., ser. Proceedings of Machine Learning Research (PMLR). 2017;70:136–145. Available: https://proceedings.mlr.press/v70/amos17a.html.

  125. Tuor A, Drgona J, Skomski M, et al. NeuroMANCER: neural modules with adaptive nonlinear constraints and efficient regularizations. 2022. Available: https://github.com/pnnl/neuromancer.

  126. Shukla SR, Paudyal S, Almassalkhi MR. Efficient distribution system optimal power flow with discrete control of load tap changers. IEEE Trans Power Syst. 2019;34(4):2970–9.

    Article  Google Scholar 

  127. Schneider KP, Mather BA, Pal BC, Ten CW, Shirek GJ, Zhu H, Fuller JC, Pereira JLR. Ochoa LF, de Araujo LR, Dugan RC, Matthias S, Paudyal S, McDermott TE, Kersting W. 1 en IEEE Transactions on Power Systems, 3, Analytic considerations and design basis for the IEEE distribution test feeders. 2018;33:3181–3188. https://doi.org/10.1109/TPWRS.2017.2760011.

  128. Bassi V, Ochoa LF, Alpcan T, Leckie C. 1 en IEEE Transactions on smart grid, electrical model-free voltage calculations using neural networks and smart meter data. 2022. p 1–1. https://doi.org/10.1109/TSG.2022.3227602. https://ieeexplore.ieee.org/document/9975837/.

  129. Sekhavatmanesh H, Ferrari-Trecate G, Mastellone S. 1 en Cancun, Mexico IEEE 61st Conference on Decision and Control (CDC), Optimal control configuration in distribution network via an exact OPF relaxation method. 2022. p 5698–5704. https://doi.org/10.1109/CDC51059.2022.9993413. https://ieeexplore.ieee.org/document/9993413/

  130. Hanif S, Sadnan R, Slay TE, Nazir N, Poudel S, Bhatti B, Reiman A, Follum J, McKinsey J, Elgindy T, Yang R. en On distribution grid optimal power flow development and integration. 2022. arXiv preprint arXiv:2212.04616.

  131. Gan L, Li N, Topcu U, Low SH. Exact convex relaxation of optimal power flow in radial networks. en IEEE Trans Autom Control 2015;60(1):72–87. https://doi.org/10.1109/TAC.2014.2332712. https://ieeexplore.ieee.org/document/6843918.

  132. Baran M, Wu F. Optimal capacitor placement on radial distribution systems, en IEEE Transactions on Power Delivery, 1989;4(1)725–734. https://doi.org/10.1109/61.19265. http://ieeexplore.ieee.org/document/19265/

  133. Jabr R. Radial distribution load flow using conic programming, en IEEE Trans Power Syst. 2006;21(3):1458–1459. https://doi.org/10.1109/TPWRS.2006.879234. http://ieeexplore.ieee.org/document/1664986/

  134. Bolognani S, Zampieri S. On the existence and linear approximation of the power flow solution in power distribution networks. en IEEE Trans Power Syst. 2016;31(1):163–172. https://doi.org/10.1109/TPWRS.2015.2395452. arXiv:1403.5031

  135. Farivar M, Low SH. Branch flow model: relaxations and convexification-Part I. IEEE Trans Power Syst. 2013;28(3):2554–64. https://doi.org/10.1109/TPWRS.2013.2255317.

    Article  Google Scholar 

  136. Farivar M, Low SH. Branch flow model: relaxations and convexification-Part I. IEEE Trans on Power Syst. 2013;28(3):2554–64. https://doi.org/10.1109/TPWRS.2013.2255317. http://ieeexplore.ieee.org/document/6507355/.

  137. Nazir N, Almassalkhi M. Co-optimization of controllable grid assets in radial networks. 2021;36(4):2761–70. https://doi.org/10.1109/TPWRS.2020.3044206.

    Article  Google Scholar 

  138. Nazir N, Almassalkhi M. Grid-aware aggregation and realtime disaggregation of distributed energy resources in radial networks. IEEE Trans Power Syst. 2021. https://doi.org/10.1109/TPWRS.2021.3121215.

    Article  Google Scholar 

  139. Nazir N, Hiskens IA, Almassalkhi MR. Exploring reactivepower limits on wind farm collector networks with convex inner approximations. In IREP Symposium - Bulk Power System Dynamics and Control. 2022.

  140. Nazir N, Almassalkhi M. Receding-horizon optimization of unbalanced distribution systems with time-scale separation for discrete and continuous control devices, in Power Systems Computation Conference. Ireland: Dublin; 2018.

  141. Arnold DB, Sankur M, Dobbe R, Brady K, Callaway DS, Von Meier A. en Optimal dispatch of reactive power for voltage regulation and balancing in unbalanced distribution systems, IEEE Power and Energy Society General Meeting (PESGM). Boston, MA, USA. 2016. p 1–5. https://doi.org/10.1109/PESGM.2016.7741261. http://ieeexplore.ieee.org/document/7741261/.

  142. Nick M, Cherkaoui R, Boudec JYL, Paolone M. An exact convex formulation of the optimal power flow in radial distribution networks including transverse components. IEEE Trans Autom Control. 2018;63(3):682–97. https://doi.org/10.1109/TAC.2017.2722100. http://ieeexplore.ieee.org/document/7964797/

  143. Franco JF, Ochoa LF, Romero R. AC OPF for smart distribution networks: an efficient and robust quadratic approach. IEEE Trans Smart Grid. 2018;9(5):4613–23. https://doi.org/10.1109/TSG.2017.2665559. https://ieeexplore.ieee.org/document/7847442/.

  144. Nazir N, Racherla P, Almassalkhi M. Optimal multi-period dispatch of distributed energy resources in unbalanced distribution feeders. IEEE Trans Power Syst. 2020;35(4):2683–92.

    Article  Google Scholar 

  145. Jha RR, Dubey A. Network-level optimization for unbalanced power distribution system: approximation and relaxation. IEEE Transactions on Power Systems. 2021;36(5):4126–39. https://doi.org/10.1109/TPWRS.2021.3066146. https://ieeexplore.ieee.org/document/9380497/.

  146. Bernstein A, Dall’Anese E. Real-time feedback-based optimization of distribution grids: a unified approach. IEEE Trans Control Netw Syst. 2019;6(3):1197–209. https://doi.org/10.1109/TCNS.2019.2929648. https://ieeexplore.ieee.org/document/8767939/.

  147. Chen Y, Shi Y, Zhang B. Data-driven optimal voltage regulation using input convex neural networks. Electr Power Syst Res. 2020;189:106741. https://doi.org/10.1016/j.epsr.2020.106741.

    Article  Google Scholar 

  148. Gupta S, Chatzivasileiadis S, Kekatos V. Deep learning for optimal volt/VAR control using distributed energy resources. 2022. arXiv preprint arXiv:2211.09557.

  149. Deka D, Kekatos V, Cavraro G. Learning distribution grid topologies: a tutorial. 2022. arXiv preprint arXiv:2206.10837.

  150. Deka D, Backhaus S, Chertkov M. Estimating distribution grid topologies: a graphical learning based approach. IEEE Power Systems Computation Conference (PSCC) 2016. p 1–7.

  151. Yu J, Weng Y, Rajagopal R. PaToPa: a data-driven parameter and topology joint estimation framework in distribution grids. IEEE Trans Power Syst. 2017;33(4):4335–47.

    Article  Google Scholar 

  152. Li H, Wert JL, Birchfield AB, Overbye TJ, San Roman TG, Domingo CM, Marcos FEP, Martinez PD, Elgindy T, Palmintier B. Building highly detailed synthetic electric grid data sets for combined transmission and distribution systems. IEEE Open Access J Power Energy. 2020;7:478–88.

    Article  Google Scholar 

  153. Pandey A, Pileggi L. Steady-state simulation for combined transmission and distribution systems. IEEE Trans Smart Grid. 2019;11(2):1124–35.

    Article  Google Scholar 

  154. Ciraci S, Daily J, Fuller J, Fisher A, Marinovici L, Agarwal K. Proceedings of the symposium on theory of modeling & simulation-DEVS integrative, FNCS: A framework for power system and communication networks co-simulation. 2014;1–8.

  155. Palmintier B, Krishnamurthy D, Top P, Smith S, Daily J, Fuller J. Workshop on modeling and simulation of cyber-physical energy systems (MSCPES), Design of the HELICS high-performance transmission-distribution-communication-market co-simulation framework. 2017;1–6.

  156. Palmintier B, Hale E, Hansen TM, Jones W, Biagioni D, Sorensen H, Wu H, Hodge BM. IGMS: an integrated ISO-to-appliance scale grid modeling system. IEEE Trans Smart Grid. 2016;8(3):1525–34.

    Article  Google Scholar 

  157. Sarstedt M, Garske S, Blaufuß C, Hofmann L. Modelling of integrated transmission and distribution grids based on synthetic distribution grid models. IEEE Milan PowerTech. 2019;1–6.

  158. Huang Q, Vittal V. Integrated transmission and distribution system power flow and dynamic simulation using mixed three-sequence/three-phase modeling. IEEE Transactions on Power Systems. 2016;32(5):3704–14.

    Article  Google Scholar 

  159. Jain H, Bhatti BA, Wu T, Mather B, Broadwater R. Integrated transmission-and-distribution system modeling of power systems: state-of-the-art and future research directions. MDPI, Energies. 2020;14(1):12.

    Article  Google Scholar 

  160. Zhou X, Chang CY, Bernstein A, Zhao C, Chen L. Economic dispatch with distributed energy resources: co-optimization of transmission and distribution systems. IEEE Control Systems Letters. 2021;5(6):1994–9. https://doi.org/10.1109/LCSYS.2020.3044542.

  161. Samaan N, Elizondo MA, Vyakaranam B, Vallem MR, Ke X, Huang R, Holzer JT, Sridhar S, Nguyen Q, Makarov YV. Combined transmission and distribution test system to study high penetration of distributed solar generation, IEEE/PES Transmission and Distribution Conference and Exposition (T &D) 2018;1–9.

  162. Jereminov M. Private email exchange: paper on emerging trends in large-scale optimization (Discussions on Gaps in Industry Large-scale Optimizations). 3rd Mar 2023.

  163. Brunner C. Private email exchange: RE: Grid optimization and industry needs/interests. 13 Mar 2023.

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Acknowledgements

The authors like to thank industry members who helped shape the direction of this paper and provided expert feedback on observable gaps in the field of large-scale optimization from the industry’s viewpoint. These include Kwok Cheung from GE Grid Solutions, Xiaochuan Luo and Jinye Zhao from ISO New England, Dan Kopin from VELCO, Cyril Brunner from Vermont Electric Cooperative, and Marko Jereminov from Pearl Street Technologies, Inc.

Funding

M. Almassalkhi gratefully acknowledges support from National Science Foundation awards ECCS-2047306.

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All authors contributed to the study conception and design. A.P. led the work on mechanistic physics-based methods for transmission and combined T &D networks, S.C. led the work on data-driven methods for both T and D networks, and M.A. led the work on physics-based methods for distribution grids. All authors read and approved the final manuscript.

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Correspondence to Amritanshu Pandey.

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A. Pandey owns equity and consults for clean-tech startup Pearl Street Technologies, Inc.

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Pandey, A., Almassalkhi, M.R. & Chevalier, S. Large-Scale Grid Optimization: the Workhorse of Future Grid Computations. Curr Sustainable Renewable Energy Rep 10, 139–153 (2023). https://doi.org/10.1007/s40518-023-00213-6

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