Abstract The hydroelectricity consumption of China is increasing, and hydropower exerts a crucial influence on sustained economic growth. A new method for estimating the hydroelectricity consumption of China is developed through the grey modeling technique. Taking into account the inherent error occurring in the leap from differential to difference in most existing grey serial models, this study constructs an unbiased NGBM(1,1) model based on the nonlinear grey Bernoulli model (NGBM(1,1)), which outperforms other grey benchmark models by adjusting the nonlinear parameter. The structural parameters of the model are deduced from the differential equation directly and therefore, the inherent error is eliminated. Moreover, the nonlinear parameter for the novel model is determined by Particle Swarm Optimization (PSO). Based on hydroelectricity consumption from 2010 to 2018, the novel model is built to predict its volume in the later one-quarter phase of the 13th Five Year Plan of China (2019–2020). The results show that hydroelectricity consumption maintains a continuous increase, exceeding 270 million tonnes oil equivalent (Mtoe) in 2020, while the growth rate decreases to 0.77%. In accordance with these forecasts, suggestions on associated hydropower are provided for policy-makers.

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