Under the background of the new power system,it is important to make full use of the distributed generation in the distribution network to achieve carbon peaking and carbon neutrality goals. With the wide access of distributed power sources,there is bi-directional power flow between the transmission and distribution networks. If the transmission and distribution networks still follow the traditional equivalence method for optimal power calculation,accurate results will not be obtained. Therefore,a transmission-distribution-network-coordinated optimal power flow model is established. The node tearing method is used to decouple the coupling variables of the transmission network and distribution networks. On this basis,the iterative form of the model with immobile points is obtained by mathematical derivation. The traditional heterogeneous decomposition algorithm only uses the latest calculation results for iterative computation. Hence,combining with the Anderson acceleration idea in mathematics,the heterogeneous decomposition algorithm based on Anderson acceleration is proposed by using the historical iteration values to optimize the iterations of immobile points. It is demonstrated by numerical experiments that,the established model can fully utilize the initiative of the distribution networks and reduce carbon emissions. The proposed algorithm has high accuracy. In addition,compared with the heterogeneous decomposition algorithm,its convergence performance is significantly improved.