A stackelberg game-based programming approach for industrial steam systems incorporating renewable energy considering demand response

Fossil fuels account for 37 % of industrial combustion, primarily used for steam production. Given the significant role of steam in industrial processes, industrial steam systems (ISS) offer a critical opportunity to accelerate the transition from fossil fuels to renewable energy by integrating renewable sources. Currently, ISS optimization focuses mainly on internal improvements, often neglecting stakeholder interactions and the inherent unpredictability of renewable energy sources. This paper introduces a novel bi-level programming approach based on Stackelberg game theory to address the balance between ISS and user interests. A new ISS model is proposed that integrates multiple renewable energy sources while accounting for their intermittency. Revenue models for energy servers (ES) and consumers (EC) are developed, and demand response mechanisms and real-time pricing are incorporated into the bi-level programming model. In the designed bi-level ISS (B-L-ISS) model, the upper level optimizes energy conversion equipment and pricing, while the lower level aims to minimize users' energy costs. The Karush-Kuhn-Tucker (KKT) conditions are used to reformulate the bi-level problem into a single-level programming problem with equilibrium constraints. Validation on a real coastal industrial steam system shows that the proposed method integrates renewable energy four times more effectively than traditional methods, reducing CO2 emissions by 15,790 tons annually, while balancing the interests of both the steam system and its users.