Wind and solar power generators cause electric power fluctuation, batteries are combined with such the renewable energy system to absorb power fluctuations, so called, wind turbine and photovoltaic power generators and battery hybrid system (WPBHS). Such the system mainly focuses on the decentralized operation in which a large number of system devices are managed decentrally. On the other hand, its stable generating capability and fault tolerance performance depends on how to group devices into small groups in which components are managed centrally (We call it grouping). That is, the grouping itself can improve the decentralized operation performance. This paper considers overlapping grouping of WPBHS in which one device belongs to multiple groups and proposes a new decentralized operation. To verify the validity of the proposed method, this paper shows numerical experiments in terms of stable generation and fault tolerance.