To achieve low-carbon operation and protect privacy when a multi-microgrid (MMG) interacts with the distribution network (DN)

this paper proposes a hierarchical distributed dispatch model for the multi-microgrid distribution system (MMDS) that considers multidimensional

linked carbon-emission reduction strategies. Firstly

the microgrid (MG) implements the carbon capture system (CCS) and its coupling equipment to establish a CCS-power to gas (P2G) cycle carbon reduction model under the conversion mechanism of energy flow and carbon flow. Furthermore

the load energy-use curve is optimized by an incentive demand response (DR) mechanism to enhance the energy efficiency of CCS

thereby facilitating low-carbon operation. Secondly

the carbon emission flow (CEF) theory is introduced at the DN level. It utilizes the node carbon potential as a signal for reducing carbon emission

which facilitates the equal sharing of carbon responsibility to quantify the interactive power and enhances the carbon reduction benefits of synergistic and complementary relationships between MMG and DN. Finally

under the optimal operation mechanism of carbon quota and carbon trading

a low-carbon operation strategy with a multi-dimensional linkage mode is formed through the above diversified measures. A hierarchical distributed approach based on analytical target cascading (ATC) is employed to decouple interaction variables and enable a distributed solution for each operating entity. The numerical results show that the proposed strategy can significantly improve carbon economic performance

and the distributed algorithm can deliver an accurate and effective solution with limited information. Furthermore

it can be effectively applied to large-scale

complex systems and typical day-to-day cases across different seasons

with a certain degree of general applicability.