Against the backdrop of carbon neutrality goals and new power system development

hierarchical distribution-microgrid systems with three-port converters (TPCs) have drawn extensive attention. However

existing research on such systems faces three challenges: the ambiguity of carbon potential (CP) at hybrid nodes within TPCs

the intractability of nonlinear nonconvex models and insufficient coordination between distribution networks and microgrids. To address these challenges

this paper proposes a real-time carbon tracking and carbon-aware optimal coordinated dispatch framework for hierarchical distribution-microgrid systems with TPCs. First

by explicitly modelling the interport carbon emission flow interactions within TPCs

the CP of each hybrid node inside the TPCs is quantified

improving calculation accuracy by up to 89% over conventional empirical methods. Second

McCormick envelope relaxation and SOCP relaxation are introduced to convexify the bilinear carbon-flow terms and power-flow constraints

whereas binary variables are retained for ESS charging/discharging states. Accordingly

the proposed carbon-aware optimal dispatch model is formulated as a mixed-integer second-order cone programming (MISOCP) problem

reducing the objective value by 4.29% compared with the nonconvex model while avoiding initial-value sensitivity and local optima. Finally

a distribution-microgrid coordinated low-carbon dispatch strategy is proposed

which increases photovoltaic penetration to 84.11%

reduces curtailment to 11.89% and decreases carbon emission and electricity costs by 10.22% and 6.94%

respectively. These results provide a modelling and optimisation basis for low-carbon operation of future hierarchical interconnected systems with high renewable penetration.