## 5 Conclusions  
In this study, a fuel cell model was firstly constructed for commercial fuel cell vehicles, with the lithium electronic battery as an auxiliary power source and forming an electric-electric hybrid power system with the fuel cell. Power of the vehicle is provided by the fuel cell and the power battery. Fuel cell durability, output characteristics of fuel cells and pulse discharge time of the power battery were considered to determine the variable load period of the fuel cell (i.e., 15 s in this study) to optimize fuel cell and power battery collaboration on the fuel cell commercial vehicles. In order to obtain the power demand of fuel cell, the GM (1,1) model was used based on the grey system method, which is an effective predicting tool to deal with small samples and uncertain information and is suitable for fuel cell systems with incomplete data information. Three different grey predicting strategies were proposed and tested in this study: single-step prediction, multi-step prediction and multiple prediction. In the single-step grey prediction strategy, the whole power series was obtained by sampling cover data of the current moment and previous moments and then was used to predict the power demand based on a step size of one. In multi-step grey prediction, the GM (1,1) model samples the power on a 5 s cycle and predicts the power demand based on a prediction step size of three. In the multiple grey prediction, the input model sequence of this strategy covers the power demand data of six time points and expands the prediction number to three times with a step-moved prediction time window. Each strategy was simulated under CHTC-HT conditions to evaluate its effectiveness. The simulation results show that the grey multiple prediction strategy has the highest prediction accuracy when dealing with continuously changing dynamic conditions, indicated by the lowest error value of 16.944% when compared to the single-step prediction of 31.14% and multi-step prediction of 35.36%. In order to further verify the adaptability of the grey multiple prediction strategy in field testing, two different working conditions of fuel cell vehicles with more and less variable load conditions were selected (Working Condition A and Working Condition B). Results show that the multiple strategy showed the best prediction performance under stable conditions with less variable load (with the lowest error value of 2.169% compared to the single-step prediction of 2.262% and multi-step prediction of 2.502%) and dynamic conditions with frequent load changes (with the lowest error value of 1.930% compared to the single-step prediction of 2.719% and multi-stepprediction of 3.151%), which can adjust the predicting model according to the real-time data and respond to the changes in external conditions in time. In summary, the grey prediction model is an effective predicting tool in the power management of a fuel cell system, which enhances the adaptability and durability of the system. The power demand and supply of the fuel cell can be effectively predicted and managed based on the proposed multiple grey prediction model considering a dynamic time window. The system performance can further be optimized to improve the fuel efficiency and reliability of the overall operation of the vehicle. Conceptualization, J.L. ; Methodology, Y.W. ; Software, Y.L. ; Validation, Y.W. and Y.L. ; Formal analysis, Y.L. ; Investigation, Y.L. and H.Z. ; Resources, J.L. and H.Z. ; Writing--original draft, Y.W. and Y.L. ; Writing--review & editing, Y.W. ; Supervision, J.L. and H.Z. ; Funding acquisition, Y.W. and J.L. All authors have read and agreed to the published version of the manuscript. This work was funded by [National Natural Science Foundation of China] grant number [52402434], [Zhejiang Provincial Nature Science Foundation of China] grant number [LY22E050018], and [Zhejiang Department of Transportation Science and Technology Plan] grant number [2024017]. And The APC was funded by [52402434]. Not applicable.