Abstract: Accurately predicting hydropower consumption makes great sense to many countries, especially for the developing ones who have insufficient electricity supply. Thus, on one hand, accurate forecasts are conducive to the subsequent development and planning of hydropower resources. On the other hand, they can also provide solid references for the transformation and upgrading of the energy structure. To this end, a fractional grey time power model is introduced in this paper and its hyper-parameters r and a are determined by using the Cultural Algorithm, which presents strong adaptability to the characteristics of the hydropower consumption sequence. Subsequently, the property of this proposed model has been discussed, referring to the relationships with several prevailing grey prediction models. By doing this analysis, it is found that the proposed model can unify the GM(1,1),FGM(1,1),GM(1,1,t), and GM(1,1,t2) models. It means that this new model obtains high adaptability to various time series. However, just like most intelligent algorithms to optimize the hyper-parameters in the grey models, the simulation prediction results of the original sequence lack repeatability as the randomness in operation search. It means that the forecasted results differ when conducting the calculating operation for each time. In order to deal with such issues, the Monte Carlo simulation averaging method is initially used to construct a repeatable FGM(1,1,tα) model (namely RFGM(1,1,tα)). This new model can improve the reproducibility of prediction results. Compared with the benchmark models, the modeling accuracy of the proposed model is verified in terms of predicting the hydropower consumption sequence. Finally, the robustness of the number of optimal searches to the results is tested. Results show that the proposed model is the most robust and effective. Therefore, the proposed model can be considered as a promising tool for hydropower consumption forecasting because it has strong robustness and wide practicability.

Key words: RFGM(1,1,tα) model; repeatability; kernel density; benchmark models