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This paper develops the time-periodic explicit error correction (TP-EEC) method for the convergence acceleration to a steady state in transient analysis of synchronous machines. The methods to deal with the movement of the rotor and different time-periodicity in the fixed and moving parts of the mesh are investigated. Furthermore, we propose the novel TP-EEC method based on the polyphase time periodic condition. Numerical results verify the effectiveness of the developed methods.