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This paper discusses a new mixed numerical integral algorithm for unified dynamic simulations of power systems in which the electro-mechanical transient, medium-term and long-term dynamic phenomena are united. The main problems were analyzed using the existing Gear integral algorithm for the dynamic simulation of power systems. The new mixed integral algorithm integrates the advantages of the implicit trapezoidal integration algorithm with a fixed time step and the Gear algorithm with a variable time step. The proposed algorithm was found to achieve a great computational efficiency in the transient stability stage of unified dynamic simulation and can easily deal with discontinuous equations in control system models. The simulation results of two actual large-scale power systems show that the proposed algorithm is effective and feasible.