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Three decomposition algorithms are presented in this paper, by investigating the topological structures of special multi-area overlapping interconnected power systems. The power system is decomposed from a longitudinal, a loop or a radial overlapping interconnected structure to a group of pair-wise areas and/or subsystems. Therefore, automatic generation control (AGC) of the system can establish its own overlapping decentralized control. Overlapping decomposition factor, chosen by a rating load ratio between areas or subsystems, can improve decentralized control quality of AGC against the disturbances of load-frequency and tie-line power exchange, so as to meet the need of AGC economic operation for the power system.