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The accurate prediction of renewable energy consumption (REC) is of great significance to ensure energy security, reduce dependence on fossil energy, and promote sustainable economic and social development. In this paper, a novel grey model with conformable fractional opposite-direction accumulation (CFOA), abbreviated as the CFOGM (1,1) model, is proposed to forecast REC in Australia. The new model is discussed in detail with a new CFOA operation and the GM (1,1) model and can take full advantage of the information carried by the original data. The CFOGM (1,1) model has lower modeling error and better fitting and forecasting accuracy than other grey, Holt, and ARM models and can better capture the change trend of REC and achieve accurate prediction. The forecasting results present that the REC in Australia is 497–581 petajoules in 2021, 596–728 petajoules in 2022, and 715–912 petajoules in 2023, indicating that the REC in Australia is still accelerating. [ABSTRACT FROM AUTHOR]