Two-layer coordinated operation of multi-energy system considering carbon-oriented collaborative pricing mechanism via two-stage stochastic programming approach

To achieve low-carbon goals in a multi-energy system, coupled with an Electricity-Hydrogen-Transportation (E-H-T) system with a high penetration level of renewables, this paper proposes a dual-layer two-stage Stochastic Programming (SP) method based on the Carbon-Oriented Collaborative Pricing Mechanism (COCPM). Firstly, a dual-layer scheduling model is formulated, integrating dynamic conversions and interactive coupling of multi-energy flows. This model leverages a carbon flow tracking feedback mechanism to accurately characterize the dynamic carbon flow feedback within both layers. Using the pricing criteria derived from the dynamic carbon flow, the COCPM is employed to promote low-carbon energy consumption decisions, thereby achieving coordinated source-load interaction. Secondly, a two-stage SP approach, enhanced with a decision-making method based on confidence intervals, is employed to robustly handle uncertainties from renewable generation and demand fluctuations. Then, KKT optimality conditions, synergistically integrated with adaptive piecewise linearization techniques and a rigorous Big-M complementarity enforcement scheme, are applied to reformulate the original bi-level nonlinear optimization problem into an equivalent single-layer Mixed-Integer Linear Programming (MILP) model, ensuring computationally tractable and provably near-optimal solutions. Finally, a test system based on the E33-H6-T14 system is applied, and simulation results validate that our method can achieve low-carbon, economical, and robust operation under uncertainties.