Journal of Jilin University(Engineering and Technology Edition) ›› 2020, Vol. 50 ›› Issue (1): 36-43.doi: 10.13229/j.cnki.jdxbgxb20180966

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Energy management strategy of fuel cell bus based on Pontryagin′s minimum principle

Zhe WANG1,2(),Yi XIE1,2,Peng-fei ZANG1,2,Yao WANG1,2   

  1. 1. School of Automotive Studies, Tongji University, Shanghai 201804, China
    2. Clean Energy Automotive Engineering Center, Tongji University, Shanghai 201804, China
  • Received:2018-09-21 Online:2020-01-01 Published:2020-02-06

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Abstract:

An energy management strategy for fuel cell bus is designed based on the Pontryagin’s minimum principle, in which the fuel cell power is set as the control variable, minimal fuel consumption is taken as the objective function, and the durability of fuel cell is considered as the constraint. An on-line energy management strategy is designed with improving the Pontryagin’s minimum principle in order to adapting to different operating conditions. A fuel cell bus simulation model is built. The simulation results show that the energy management strategy can adapt to different operating conditions well, and it is better than the traditional on/off energy management strategy in terms of fuel economy and fuel cell durability.

Key words: vehicle engineering, fuel cell bus, on-line energy management strategy, Pontryagin′s minimum principle, fuel economy, durability of fuel cell

CLC Number: 

  • U461.8

Fig.1

Powertrain system structure of fuel cell bus"

Fig.2

Power?efficiency curve of fuel cell"

Fig.3

Rint equivalent circuit"

Fig.4

Solution process of Pontryagin’s minimum principle"

Fig.5

Relationship betweenλ(0) and |?SOC|"

Fig.6

Fuel cell bus forward simulation model"

Table 1

Parameters of powertrain system"

参数数值参数数值
整车整备质量/kg14 000主减速比7.72
燃料电池额定功率/kW60风阻系数0.65
燃料电池怠速功率/kW3.3迎风面积/m27.00
电机峰值功率/kW220车轮半径/m0.478
电机最高转速/(r·min-1)3 700滚阻系数0.015
电机最大转矩/(N·m)2 100电池容量/(A?h)120
电池峰值功率/kW187.2电池电压/V520

Fig.7

Simulation results of China City"

Fig.8

Simulation results of Shanghai City"

Fig.9

Simulation results of Nuremberg bus"

Table 2

Simulation results of China City"

统计结果开关模式极小值原理离线最优策略
|?SOC|0.0050.0040.000 5
大幅变载时间/s7.160.660.79
燃料电池功率变化率最大值/(kW?s-1)285.495.005.08
怠速时间/s372.580.90.9
启停次数500
燃料电池平均工作效率/%44.4653.0553.05
动力电池平均工作效率/%97.7798.3298.28

Table 3

Simulation results of Shanghai City"

统计结果开关模式极小值原理离线最优策略
|?SOC|0.0030.0080.000 7
大幅变载时间/s5.192.512.83
燃料电池功率变化率最大值/(kW?s-1)285.495.805.80
怠速时间/s289.010.90.9
启停次数300
燃料电池平均工作效率/%45.1652.7452.95
动力电池平均工作效率/%97.6198.1098.10

Table 4

Simulation results of Nuremberg bus"

统计结果开关模式极小值原理离线最优策略
|?SOC|0.00050.00030.00002
大幅变载时间/s4.4127.3722.16
燃料电池功率变化率最大值/(kW?s-1)285.495.805.80
怠速时间/s348.740.90.9
启停次数200
燃料电池平均工作效率/%43.4352.9753.03
动力电池平均工作效率/%97.1197.5297.54

Fig.10

Correction of terminal SOC value"

Fig.11

Fuel economy under different strategies"

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