The linearization model is the basis of stability analysis, interface coupling mechanism research and controller design for DC power system. A radial hybrid AC and DC power distribution system with multiple DC micro-grids is divided into 4 parts, including rectifier interface and the AC main network, inverter interface and the passive AC system, the grid-connected interface and DC micro-grids, and the DC network. The transient mathematical models of each part of the system under small perturbations are respectively deduced through establishing a flexible d-q synchronous reference frame. In order to improve the universality of the model in different application scenarios, a linearized modeling method of the interface controller with control identification bits and the phase locked loop control are introduced to establish a global linear system model. By comparing with the electromagnetic transient model, the correctness and validity of the global linear model of the hybrid AC and DC distribution power system are verified. This work is supported by National Natural Science Foundation of China (No. 51677023).