Distributed optimization for electricity–carbon coupling transactions in multiple microgrids under network constraints

The coupling of carbon transactions and electricity transactions is inevitable for microgrids (MGs), as people's awareness of carbon reduction is awakened. However, the lack of clear guidance on electricity–carbon transactions will not only increase the complexity of MGs operation, but also lead to risks of power flow exceeding limits. This paper proposes a bi-level distributed optimization framework for electricity–carbon coupled transactions in multiple MGs under network constraints. In the upper level, an carbon-enhanced distribution locational marginal price (DLMP) based on carbon emission flow models is presented to optimize power flows and guide electricity transactions in MGs. The lower level establishes a convex minimization operation model for MGs combining peer-to-peer electricity transactions and ladder carbon transactions. The prediction–correction-based alternating direction method of multipliers is employed to solve the proposed model in a distributed manner. Results of all subproblems are corrected using convex combinations to ensure convergence. Finally, different cases are discussed to verify the effectiveness of the proposed framework. The results show that DLMP may reduce the electricity interaction between MGs and other entities to a certain extent, while improving the carbon trading benefits of MGs.