Abstract: The transmission capacity of a DC distribution system is limited by the network topology, line impedance, and voltage level. When the load demand exceeds the maximum transmission power of the distribution network, the system will lose its balance point, resulting in voltage collapse. Therefore,studying the existence of the power flow solution is essential to ensure the stable and reliable operation of the DC power distribution system. Firstly, the mathematical model of the power flow of the DC power distribution system was established. The sufficient conditions for the feasible solution of the power flow were obtained by the closed interval theorem.The uniqueness of the feasible solution of the power flow was proved by the uniqueness of the limit. And a large-scale convergence power flow iterative algorithm was proposed,which provided a new and effective way for the stability study of DC power distribution system. In addition, this paper obtained analytical and numerical-based equilibrium point existence conditions. According to the analysis conditions, the existence of the power flow feasible solution of the system after load access and voltage abrupt change can be quickly evaluated, and the calculation amount is greatly reduced.According to the numerical conditions, the upper limit of the load of the feasible solution of the power flow can be calculated more accurately, and the conservativeness of the existence condition was reduced. Finally, an example was given to verify the correctness of the obtained conclusions and the effectiveness of the proposed iterative algorithm.