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The objective and accurate prediction of energy consumption can supply an important reference and advance indicator for government to implement economic policies and energy development strategy. On account of the complexity and uncertainty of the energy system, this paper establishes a novel flexible grey multivariable model by introducing a power exponential term, a linear correct term and a random disturbance term. The novel model has the advantages in capturing the dynamic characteristics of the energy system, also it can be compatible with eight existing grey models when some parameters are assigned certain values. Additionally, to further promote the prediction performance of the novel model, the grey wolf optimizer is employed to determine the power indexes of the model. To demonstrate its performance, the proposed model is utilized to predict the energy consumption of three major provinces in China, and the fitting and prediction results of the novel model are compared with those provided by diversified competing models. The results illustrated that the novel model is superior to other competing models, offering more accurate and better performance. Finally, based on the results, several proposals for energy development are put forward for decision-makers. • The flexible multivariable grey model can adapt to more energy system structures. • The novel model can be flexibly compatible with the eight existing grey models. • A specific solution algorithm for the novel model's power indexes is discussed. • The novel model can be easily used to energy system with higher prediction accuracy. [ABSTRACT FROM AUTHOR]