Hybrid discrete–continuous optimisation of material and energy flows in steel enterprises for flexible grid interaction

The strategic exploitation of demand-side flexibility in energy-intensive industries such as steel enterprises, is critical for advancing decarbonisation efforts. However, a fundamental challenge arises from the operational conflict between continuous-time material flow scheduling and discrete-time energy management. This study resolves this challenge with a hybrid framework for co-optimising material and energy flows in steel enterprises. The framework incorporates an improved material flow model that adjusts production makespan in continuous time domain, integrates refining furnace power regulation, and accounts for the nonlinear energy consumption of reheating furnaces relative to waiting time and temperature drops. Wherein, a novel bridging mechanism is introduced that translates the Lagrangian trajectories of individual discrete material entity into a Eulerian perspective for plant-wide, discrete-time energy consumption profiles. Synchronisation of material and energy flows enables co-optimised production and energy scheduling responding to electricity tariffs. The method shows superior computational performance, cutting solution time by 88% compared to conventional resource-task network models. Validated by a case study, this framework enabled a 4.3% reduction in total system cost, and a 7.85 MW improvement in demand response capability, accounting for 44.38% of the maximum load, thereby providing a practical paradigm for evolving steel industry into a flexible, grid-interactive virtual power plant.