In light of the inherent unpredictability of wind power and other clean energy sources within each MG, a multi MG s electricity-carbon joint optimization operation method that considers robust market clearing is proposed. This method ensures the economic viability of the multi- MG s alliance while adhering to the principles of low-carbon operations and security. The constructed model comprises two layers. The upper layer establishes a robust clearing model of the upper-level electricity-carbon joint market with optimal accruals and benefits based on the marginal pricing theory. The lower layer considers the coupling of electricity-carbon joint trading, establishes a multi- MG s low-carbon joint optimization model based on the Nash negotiation theory, and proposes an electricity-carbon revenue allocation method based on the contribution degree of the interaction products to realize the reasonable allocation of the revenue of each MG. In conclusion, the accelerated-adaptive alternating direction multiplier method (AA-ADMM) is put forth as a means of solving the model. The results of the illustrative example serve to corroborate the efficacy of the methodology proposed in this paper.