Source-load temporal balance entropy driven demand response for optimal scheduling of a hydrogen-methanol integrated energy system

To mitigate grid instability and peak-shaving challenges caused by the high penetration of renewable energy, this paper proposes an optimal scheduling strategy for a Hydrogen-Methanol Integrated Energy System (HMIES). First, to accurately handle the uncertainty of renewable sources, a time-varying Copula-K-means method is employed for scenario reduction to generate expected boundary conditions. Subsequently, addressing the “synchronization disorder” between stochastic renewable generation and load demand that traditional variance-based indicators often fail to capture, a novel “Source-Load Temporal Balance Entropy” metric is introduced. Unlike static statistical measures, this metric leverages information theory to quantify disorder, triggering an optimization-driven time-partitioning mechanism that replaces rigid time-of-use tariffs with dynamic Demand Response (DR) strategies. Crucially, to formulate the scheduling optimization, the aforementioned uncertainty boundaries and entropy-driven DR strategies are directly integrated as operational inputs into a refined HMIES framework. This framework features a multi-condition electrolyzer array model and carbon-captured methanol synthesis, which not only facilitates hydrogen-electricity synergy but also creates a closed loop for carbon recycling. Furthermore, to solve the high-dimensional nonlinearity of the scheduling problem, an improved Boundary-Reflective Differential Evolutionary Moss Growth Optimization (BDMGO) algorithm is proposed, which effectively mitigates premature convergence. Case studies verify that the proposed strategy reduces total operating costs by 32.16% and the peak-to-valley ratio by 15.42%. These results conclusively demonstrate the synergistic efficacy of coupling the flexible HMIES architecture with entropy-driven regulation in effectively overcoming static source-load matching limitations and optimizing both economic efficiency and grid stability.