Carbon emission rights (CER) are a market mechanism adopted to reduce carbon dioxide emissions. In this paper, a decentralized market model integrating electricity and CER trading is established for a microgrid. The proposed trading model not only satisfies the demand for transactions but also ensures the constraint of total carbon emissions for the microgrid. Energy storage (ES) is introduced to balance loads more economically, and the constraint specifying that the ES cannot be simultaneously charged and discharged is proven to be satisfied automatically, ensuring the convexity of the model. Furthermore, by inserting local trackers to global constraints for each node, a scalable fully distributed algorithm is designed to solve the model locally for both global equality and inequality constraints. The proposed algorithm decomposes the arithmetic demand to each user without intermediate agents, which can effectively reduce the cost and ensure the transparency of trading. The algorithm is also proven to be convergent. Numerical results verify the effectiveness of the proposed market model.
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