Data-driven Bi-level Optimization of Thermal Power Systems with embedded Artificial Neural Networks

Industrial thermal power systems have hierarchically coupled performance variables, making simultaneous optimization computationally challenging and limiting their scalable and integrated operational optimization. To address this issue for large-scale power systems, we present a machine learning-powered bi-level framework for the data-driven optimization of thermal power systems. Artificial neural network (ANN) models approximate the upper and lower-level objective functions, while the lower-level problem is analytically embedded via Karush–Kuhn–Tucker (KKT) optimality conditions. This reformulated single-level framework (ANN-KKT) is validated on three benchmark problems, achieving near-exact solutions with <0.5\% error. Scaling to 660 MW coal and 395 MW gas plants, the framework computes local optimal solutions (583 MW/7337 kJ/kWh for coal; 402 MW/8159 kJ/kWh for gas) in 0.052–0.168 s, supporting computationally efficient set-point computation for control purposes. Additionally, ANN-KKT delineates a surrogate-supported domain-consistent robust operating envelope that accounts for variable uncertainty while maintaining thermal efficiency targets (38–43\%) for the gas turbine system. The developed ANN-KKT framework offers a scalable, data-driven route for bi-level optimization, achieving energy-efficient operations of thermal power systems and contributing to Industry 5.0.