Developing Deep Neural Network Schemes for Solving Optimal Power Flow Problems: Solution Feasibility and Multiple Load-Solution Mappings

Project BackgroundThe optimal power flow (OPF) problem determines the least-cost generator dispatch to meet the load in a power network, subject to physical and operational constraints. It is central to power grid operations and underpins various applications, including real-time market clearing, unit commitment, demand response, reliability assessment, and grid modernization endeavors for pursuing carbon neutrality and mitigating climate change [1, 2]. Due to increasing uncertainty from renewable generation and flexible load, OPF problems need to be solved fast and accurately for reliable and economic grid operation. However, the OPF problem with a full AC power flow formulation (AC-OPF) is non-convex and NP-hard, making it difficult to solve efficiently by iterative solvers, especially for large-scale instances. Recently, there has been growing interest in employing DNN todirectlysolve OPF problems, in a fraction of the time used by iterative solvers; see some earliest works in [3, 4]. The idea is to leverage the approximation capability of DNNs [5–7] to learn the load-solution mapping of the OPF problem. Then one can feed the load to the DNN to instantly obtain a solution. To date, various studies have applied DNNs to generate quality solutions for popular OPF formulations with a few orders of magnitude speedup as compared to iterative solvers [4, 8–13]. Despite the exciting developments, two fundamental challenges remain largely open. They need to be addressed before DNN can be used to solve OPF problems efficiently and reliably. •Ensuring DNN solution feasibility. Guaranteeing solution feasibility is challenging for designing DNN schemes for constrained optimization problems, due to inherent DNN prediction errors. Failing to respect the physical and operational constraints in OPF problems can be fatal and lead to power grid instability or incur excessive operating cost [14]. •Learning one legitimate mapping. As AC-OPF problems are non-convex, there may exist multiple optimal solutions for a load input. Then the training dataset may contain “mixed” data points corresponding to multiple load-solution mappings. As a result, the trained DNN may fail to learn a legitimate mapping and generate inferior solutions. Project Aim and DescriptionWe will tackle the two critical challenges and further develop DNN schemes for solving OPF problems efficiently and reliably. Our plan is four-fold. First, we will develop apredict-and-reconstructdesign to guarantee equality constraints and reduce the number of variables to be predicted by DNNs. Second, we will develop apreventive-learningframework for guaranteeing inequality constraints. Specifically, we will systematically calibrate inequality constraints used in DNN training, thereby anticipating prediction errors and ensuring the resulting solutions remain feasible. Third, we will develop anaugmented-learningapproach to learn a unique mapping between an augmented input and the AC-OPF solution. We will then use the augmented mapping to solve AC-OPF problems. Finally, teaming up with a power system R&D center of a top-3 Fortune 500 conglomerate, we plan to carry out simulations based on real-world data and trials on actual testbed to evaluate the performance of our DNN schemes. Preliminary Result and Significance of ProjectWe have developed DNN schemes with provable feasibility guarantees for DC-OPF problems. The three proposed approaches, once successfully established, can be applied to design DNNs for solving general constrained optimization problems. We will build upon the initial success to fully develop theoretical foundation and DNN schemes for solving OPF problems efficiently and reliably, so as to facilitate the development of carbon-neutral power systems.