To strengthen the bidirectional supply-demand support capability at the distribution network level and achieve more refined planning under the “dual-carbon” target, this paper proposes a source-network-load-storage collaborative planning model of distribution networks, considering both low carbon and economy. First, the sequential characteristics of source and load output and load demand response are described. Second, a three-layer planning operation model of source-network-load-storage is established by combining multiple flexible resources and active management measures. The upper planning layer selects the location and capacity of the source, network and storage based on the principle of low comprehensive cost and low carbon emission. The middle scheduling layer optimizes the output scheduling of the main body of the source, network, load and storage, guided by the “dual-carbon” policy, economic operation and voltage quality. The lower reconfiguration layer reconstructs the network topology to minimize active power loss on the network side. Then, according to the characteristics of the model, the upper and middle layers are solved by the improved non-dominated sorting genetic algorithm-II (INSGA2) and the fuzzy membership degree method, while the lower layer is solved by an improved genetic algorithm (IGA). Finally, a case study is conducted using real data from a northwestern region of China. Simulation results show that the proposed method can adapt to the “dual-carbon” target, improve the economy of planning and dispatching, determine optimal active management strategies, provide effective peak shaving and valley filling, and optimize grid structure.