Coordinated Optimization of Carbon-Electricity-Gas Trading in Multi-Vector Energy Systems across Buildings

High building power demand contributes significantly to carbon emissions and places considerable stress on power grid energy supply. While control and optimization methods in buildings can effectively reduce energy consumption and reshape load profiles, existing approaches often overlook the strong coupling between energy and carbon, and lack real-time, incentive-compatible mechanisms to coordinate operations across buildings and distributed energy resources. To address these limitations, this study develops a synergistic carbon–electricity–gas trading mechanism to optimize the operation of multiple buildings integrated with multi-vector energy systems, targeting improved energy efficiency, cost reduction, and emission mitigation. An enhanced Lyapunov optimization approach is proposed to transform the long-term stochastic optimization problem into a series of online-solvable subproblems, maximizing the benefits of energy storage systems and enabling efficient real-time decision-making at each operational time slot. Additionally, a dynamic storage-based pricing mechanism is introduced to reflect true trading demands, complemented by an auction-based matching strategy to facilitate inter-building energy trading. Case studies conducted on five UK campus buildings demonstrate that the proposed mechanism enhances energy efficiency and battery performance, and asymptotically approaches optimal cost performance through calibrated weighting and auxiliary parameters.