Graph-EXTRA enabled distributed optimal dispatch for integrated energy system in steel industry under uncertainties

The optimal dispatch for integrated energy system (IES) is vital to achieve low-carbon economic operation in steel industry, yet significant challenges arise from uncertainties such as source-load forecasting errors and equipment efficiency variations. To address these issues, a systematic dispatch method is proposed that synergizes a hybrid stochastic-robust model with a novel distributed algorithm termed Graph-EXTRA First, the hybrid stochastic-robust model is established through two stages. The deterministic modeling stage constructs the objective function and constraints to minimize operational cost and control carbon emissions. The uncertainty extension stage introduces differentiated quantification mechanisms to precisely characterize the heterogeneous nature of uncertainties. Source-load forecasting errors with observable statistical laws are represented by probability distributions, while equipment efficiency variations lacking precise distributional data are constrained within bounded intervals. Then, Graph-EXTRA improves the communication matrix of exact first-order algorithm to accommodate the unidirectional energy transmission characteristics of IES, and incorporates graph attention network to achieve adaptive step-size, thereby enhancing the iteration speed and convergence. Ultimately, the proposed method is validated through case study, demonstrating a 12.36% reduction in carbon emissions and an 8.23% reduction in operational cost compared to the traditional operation mode, providing a robust dispatch scheme for IES under uncertainties.