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In this study, a novel island partition model of distribution system with distributed generations (DGs) is presented and a two-stage method based on branch and bound algorithm is designed to solve this model. In the first stage, an initial island partition scheme is acquired through an island isolating process composed of a serial of tree knapsack problems (TKPs) and island combination process; in the second stage, an optimal island partition scheme is obtained after the feasibility checking and adjustment of the initial scheme to mitigate the constraint violations. Each TKP is solved by branch and bound algorithm with three improved measures. The proposed model meets the requirements of practical engineering application because it takes account of key factors as the load priorities, load controllability, power balance, voltage and equipment transmission capability. Moreover, the computational complexity of the method is relatively low, which makes it be acceptable for engineering application. The proposed method is verified with a 69-bus test system with six integrated DGs. Comparison with other methods demonstrates that the new model and method is feasible and valid.