Despite significant research efforts to develop scalable algorithms, no existing methods have successfully solved real-world SC ACOPF problems in a truly scalable manner. For example, ARPA-E recently held 3 Grid Optimization (GO) competitions to develop such scalable algorithms for SC ACOPF problems. For the base case of the SC ACOPF, implemented in GO competition 1, the most successful solver was implemented by team gollnlp, using state-of-the-art nonlinear programming algorithms, a decomposition method using sparse approximations for recourse terms, nonconvex relaxations of complementarity constraints, and special pretreatment of the problem [4]. Despite gollnlp’s success, their method only achieved the best-known solution for 58% of cases [3], suggesting that the relaxations made to the problem lead to substantial suboptimality. Another recent work implemented a smoothing technique to approximate complementarity constraints, which, when paired with another state-of-the-art solution algorithm, also demonstrated scalable solution times [5]. However, the relaxations made again suggest that true optimal solutions may not have been fully achieved. Another approach using approximate methods is to use machine learning. CANOS relies on graph neural networks to solve the SC ACOPF problem with sublinear scaling. While CANOS was able to outperform solving the SC DCOPF both in time and accuracy [6], there were still substantial infeasibilities when compared against the solutions obtained from constrained optimization solvers.
Another practically important variant of the OPF problems is the multi-period OPF (MP OPF) problems. These problems arise when the system has to be operated along with battery energy storage systems (BESS). In the past 10 years in the US, BESS capacity has gone from nearly negligible to 26 GW of operating capacity in 2024, with an expected growth of 75% in 2025 alone [7]. In order to properly account for the change in state of charge that would occur in systems with growing utilization of BESS, the OPF needs to be expanded to include multi-period changes in demand and available resources. Solving the MP OPF with storage is thus another priority to be addressed for the near future. Several works in the literature have studied formulations of MP OPF problems. Agarwal and Pileggi have implemented the MP OPF with storage into the SUGAR engine and demonstrated using dynamic programming they could achieve scalable solution time for up to a 70,000 bus case without relaxing any of the constraints [8]. Geth and Coffrin have developed a standardized version of storage constraints which can be added to MPOPF with the flexibility of representing a wide range of energy storage modes and undergoing some of the more common convex and linear relaxations [9].
Recent advances in GPU-accelerated optimization methods have demonstrated that GPUs, implemented in ExaModels.jl and MadNLP.jl, have the potential to substantially enhance the solution speed of solving large-scale AC OPF instances [10]. While several modeling frameworks are currently available, each has limitations that necessitate the development of a more advanced platform. PowerModels.jl is a widely-used, open source tool that relies on JuMP to model several forms of the ACOPF formulation [11]. While its base package was initially restricted to static cases, it has expanded to deal with more complex formulations such as in PowerModelsSecurityConstrained.jl [12]. As a result, PowerModels has the ability to be used for a number of ACOPF problems, and has been an effective tool for modeling medium-scale problems. Implementation of the ACOPF is also present in other languages such as MATPOWER [13] for Matlab, or PyPSA [14] for Python. PyOptInterface [15] has also been recently proposed as a new modeling language for mathematical optimization, outperforming existing interfaces such as JuMP and Pyomo. Despite a number of strong options being available for modeling ACOPF, one clear missing facet is the ability to perform computations such as model derivative evaluations and application of nonlinear optimization procedures on GPUs.
The success of GPU-based solutions motivates the implementation of ACOPF problems and their variants based on scalable modeling platforms, such as ExaModels. We expand the modeling capabilities of ExaModels for the SC ACOPF and MP ACOPF with storage models in the open-source repository ExaModelsPower.jl. This work situates ExaModelsPower as the premier, open-source, standard modeling library for large-scale ACOPF problems. As the only modeling framework which supports GPU capability, ExaModels is uniquely positioned to be used as the standard for large-scale ACOPF problems. ExaModels is able to exploit the repeated patterns within objective function and constraints, which are widely prevalent in ACOPF, in a manner that preserves their parallelizable structure in order to later evaluate the model derivatives on GPUs [10]. The capability to evaluate derivatives on GPUs is crucial for the effective use of GPU-accelerated nonlinear optimization algorithms.
We will present comprehensive benchmark results comparing various solution approaches for large-scale SCOPF and MPOPF instances. This comparison will include several established solvers, such as MadNLP, MadNCL, and Ipopt. By utilizing extensive datasets from the power grid library and the GO Competition 3, we aim to assess the solution performance of these methods on large-scale models. Our preliminary results indicate that a multi-period ACOPF instance with 10 million variables can be solved in a reasonable timeframe on GPUs, surpassing CPU performance by over an order of magnitude [10,16]. While GPU-based methods can achieve moderate solution accuracy, reaching high accuracy levels remains a challenge [10]. We will provide a detailed benchmark analysis to compare the trade-offs between solution accuracy and solution time on both CPUs and GPUs, enabling a thorough assessment of the advantages and disadvantages of GPU-based solutions.
References
[1] Intergovernmental Panel On Climate Change (Ipcc), Climate Change 2022 – Impacts, Adaptation and Vulnerability: Working Group II Contribution to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change, 1st ed. Cambridge University Press, 2023. doi: 10.1017/9781009325844.
[2] J. T. Holzer, S. Elbert, H. Mittelmann, R. O’Neill, and H. Oh, “GO Competition Challenge 3: Problem, Solvers, and Solution Analysis,” Nov. 18, 2024, arXiv: arXiv:2411.12033. doi: 10.48550/arXiv.2411.12033.
[3] I. Aravena et al., “Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition,” Operations Research, vol. 71, no. 6, pp. 1997–2014, Nov. 2023, doi: 10.1287/opre.2022.0315.
[4] C. G. Petra and I. Aravena, “Solving realistic security-constrained optimal power flow problems,” Oct. 04, 2021, arXiv: arXiv:2110.01669. doi: 10.48550/arXiv.2110.01669.
[5] A. Gholami, K. Sun, S. Zhang, and X. A. Sun, “An ADMM-Based Distributed Optimization Method for Solving Security-Constrained Alternating Current Optimal Power Flow,” Operations Research, vol. 71, no. 6, pp. 2045–2060, Nov. 2023, doi: 10.1287/opre.2023.2486.
[6] L. Piloto et al., “CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbations,” Mar. 26, 2024, arXiv: arXiv:2403.17660. doi: 10.48550/arXiv.2403.17660.
[7] EIA staff, “U.S. battery capacity increased 66% in 2024,” U.S. Energy Information Administration, Mar. 2025. [Online]. Available: https://www.eia.gov/todayinenergy/detail.php?id=64705
[8] A. Agarwal and L. Pileggi, “Large Scale Multi-Period Optimal Power Flow With Energy Storage Systems Using Differential Dynamic Programming,” IEEE Trans. Power Syst., vol. 37, no. 3, pp. 1750–1759, May 2022, doi: 10.1109/TPWRS.2021.3115636.
[9] F. Geth, C. Coffrin, and D. M. Fobes, “A Flexible Storage Model for Power Network Optimization,” Apr. 29, 2020, arXiv: arXiv:2004.14768. doi: 10.48550/arXiv.2004.14768.
[10] S. Shin, F. Pacaud, and M. Anitescu, “Accelerating Optimal Power Flow with GPUs: SIMD Abstraction of Nonlinear Programs and Condensed-Space Interior-Point Methods,” Feb. 26, 2024, arXiv: arXiv:2307.16830. doi: 10.48550/arXiv.2307.16830.
[11] C. Coffrin, R. Bent, K. Sundar, Y. Ng, and M. Lubin, “PowerModels. JL: An Open-Source Framework for Exploring Power Flow Formulations,” in 2018 Power Systems Computation Conference (PSCC), Dublin, Ireland: IEEE, Jun. 2018, pp. 1–8. doi: 10.23919/PSCC.2018.8442948.
[12] PowerModelsSecurityConstrained. (Oct. 2019). [Online]. Available: https://lanl-ansi.github.io/PowerModelsSecurityConstrained.jl/stable/
[13] R. D. Zimmerman, C. E. Murillo-Sanchez, and R. J. Thomas, “MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education,” IEEE Trans. Power Syst., vol. 26, no. 1, pp. 12–19, Feb. 2011, doi: 10.1109/TPWRS.2010.2051168.
[14] T. Brown, J. Hörsch, and D. Schlachtberger, “PyPSA: Python for Power System Analysis,” JORS, vol. 6, no. 1, p. 4, Jan. 2018, doi: 10.5334/jors.188.
[15] Y. Yang, C. Lin, L. Xu, and W. Wu, “PyOptInterface: Design and implementation of an efficient modeling language for mathematical optimization,” May 16, 2024, arXiv: arXiv:2405.10130. doi: 10.48550/arXiv.2405.10130.
[16] S. Shin, V. Rao, M. Schanen, D. A. Maldonado, and M. Anitescu, “Scalable Multi-Period AC Optimal Power Flow Utilizing GPUs with High Memory Capacities,” May 22, 2024, arXiv: arXiv:2405.14032. doi: 10.48550/arXiv.2405.14032.