New distributionally robust optimization framework and algorithm for energy hub scheduling integrating demand response programs under ambiguous prices and loads

With the continuous rising of global energy demand, the highly efficient energy hub scheduling (EHS) is extremely crucial to enhance system resilience and improve energy efficiency. This paper studies an EHS problem with multi-energy inputs and multi-energy outputs. The energy hub combines storage solutions for electricity and hydrogen, while also integrating demand response programs (DRPs) for both electricity and heat consumption. In reality, energy prices and loads fluctuate in real time, and the estimation of accurate probability distributions is a huge challenge. Thus, we model the partial availability of distribution information for electricity, hydrogen, and natural gas prices, as well as electricity, natural gas, and heat loads. A globalized distributionally robust energy hub scheduling (GDR-EHS) model is introduced to enhance the stability and adaptability of energy supply by creating outer and inner ambiguity sets. Lagrange duality and strong duality theory are used to obtain a computationally tractable formulation, then the proposed model is reformulated into a mixed integer linear programming (MILP) model. To enhance computational efficiency, we design an accelerated Branch and Cut (B&C) algorithm with Gomory cuts. Finally, the numerical results indicate that incorporating energy storage systems leads to a 4.39 % reduction in costs, while the addition of DRPs further lowers costs by 4.35 %. Furthermore, compared to Gurobi and the standard B&C algorithm, the accelerated B&C algorithm enhances computational efficiency by 50.1 % and 57.5 %.