Adaptive optimal energy management strategy of fuel cell vehicle by considering fuel cell performance degradation
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摘要: 为了提高系统效率与降低因不利运行条件导致的燃料电池使用寿命缩短风险，提出了考虑燃料电池性能衰退的自适应庞特里亚金极小值原理(PMP)能量管理策略，用于城市公交车燃料电池/超级电容混合动力系统；分析了离线式PMP燃料电池/超级电容混合动力系统在5种不同循环工况下的能量分配结果，获取了在3种典型城市公交循环工况下初始协态变量随能量管理系统的状态量，即超级电容荷电状态始、末时刻差值的变化关系，插值出在线式PMP初始协态变量与荷电状态的对应关系，结合PMP正则方程计算每一时刻的协态变量，形成具有维持荷电状态稳定的在线PMP协态变量自适应更新方法；将影响燃料电池性能衰退的功率变化率、启停次数和最大功率作为约束条件，并在自适应PMP的成本函数中引入燃料电池功率变化率，获取满足约束条件且混合动力系统燃料经济性较好的能量管理策略；开展控制器硬件在环(HIL)仿真测试，验证该能量管理策略的实际应用效果。研究结果表明：在不同于确定协态变量的公交工况SC03和纽约城市循环(NYCC)工况下，自适应PMP末态荷电状态稳定在目标值附近，且与离线PMP相比，燃料经济性损失分别仅为1.27%和0.93%；在不同于确定协态变量和成本函数权重系数的运行工况即中国公交行驶循环(CBDC)综合测试工况下，该自适应优化能量管理策略可实现满足约束条件的能量分配，且燃料经济性保持为离线最优经济性的90.76%；在CBDC和纽伦堡公共汽车(NurembergR36)测试工况下，HIL仿真结果与数值仿真结果平均误差均小于5%。综上，该自适应优化能量管理策略考虑了燃料电池性能衰退，可实现混合动力系统的高效运行，具有长寿命使用潜力。Abstract: To improve system efficiency and reduce the risk of working life reduction caused by the adverse operation conditions of fuel cell, an adaptive Pontryagin's minimum principle (PMP) energy management strategy with the fuel cell performance degradation consideration was proposed for the fuel cell/supercapacitor hybrid power system in the city bus. The off-line PMP energy distributions of the fuel cell/supercapacitor hybrid power system in five different driving conditions were analyzed, and the relation between the initial value of the costate variable and the difference of state variable of the energy management system, i.e., the state-of-charge difference of the supercapacitor, between the beginning and the end, was obtained. The corresponding relation between the initial value of the costate for online PMP and state-of-charge could be interpolated. Integrating with the normal equation of the PMP, the instant costate variable was obtained, and thus the adaptively updating costate variable in the online PMP leading to keep up state-of-charge could be formulated. Choosing the fuel cell performance degradation, the power change rate, number of start-stop, and maximal power of the fuel cell as the constraints of the energy management system, the fuel cell power change rate was further formulated as a penalty term in the cost function of the adaptive PMP to meet the energy management constraints as well as achieve better fuel economy. The controller hardware-in-the-loop (HIL) simulation test was carried out to validate the practical efficacy of the proposed energy management strategy.Research results show that, under the bus condition SC03 and New York City cycle condition (NYCC) that are different from the costate variable formulation used typical operation conditions, the adaptive PMP energy management can make the terminal state-of-charge approach the target value, and compared with the off-line PMP, the losses of fuel economy are only 1.27% and 0.94%, respectively. Under the China bus driving cycle (CBDC) comprehensive test condition that is different from the operation conditions used for the costate determination and cost function weighting adjustment, the proposed adaptive optimal energy management strategy can implement the energy distributions of fuel cell and supercapacitor under the provided constraints, and the fuel economy can keep up 90.76% compared with the off-line optimization. Under the CBDC and NurembergR36 test conditions, the average errors between HIL and numerical simulations are less than 5%. Consequently, the proposed adaptive optimal energy management strategy considering the performance degradation of fuel cell can implement the high operation of the hybrid power system with the potential of a long working life. 9 tabs, 13 figs, 29 refs.
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图 2 不同循环工况下λ0和ΔS关系
Figure 2. Relationships between λ0 and ΔS under different driving cycles
图 3 三种典型循环工况下车速和加速度信息
Figure 3. Vehicle speed and acceleration information under three typical driving cycles
图 4 三种典型循环工况λ0和ΔS关系
Figure 4. Relationships between λ0 and ΔS under three typical driving cycles
图 6 燃料电池/超级电容混合动力系统自适应PMP能量管理策略
Figure 6. Adaptive PMP energy management strategy of fuel cell/supercapacitor hybrid power system
图 7 CBDBUS工况下燃料电池功率和功率变化率
Figure 7. Output power and power change rate of fuel cell under CBDBUS driving cycle
图 8 NewYorkBus工况下未考虑和考虑燃料电池性能衰退能量管理结果
Figure 8. Energy management results without and with fuel cell performance degradation under NewYorkBus driving cycle
图 9 NurembergR36工况下未考虑和考虑燃料电池性能衰退能量管理结果
Figure 9. Energy management results without and with fuel cell performance degradation under NurembergR36 driving cycle
图 11 NurembergR36工况下能量管理结果
Figure 11. Energy management result under NurembergR36 driving cycle
图 12 基于DSP控制器硬件在环仿真测试验证平台
Figure 12. Simulation test verification platform based on DSP-based controller hardware-in-the-loop
图 13 CBDC和NurembergR36工况下基于DSP控制器的HIL仿真与数值仿真结果对比
Figure 13. Comparison of HIL and numerical simulation results based on DSP-based controller under CBDC and NurembergR36 driving cycles
表 1 燃料电池城市公交车主要参数
Table 1. Main parameters of fuel cell city bus
整车整备质量/kg 12 000 载客人数 33 迎风面积/m2 6.06 传动系统效率/% 90 旋转质量换算系数 1.1 空气阻力系数 0.7 车轮半径/m 0.54 滚动阻力系数 0.012 最高车速/(km·h-1) 70 
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表 2 三种典型循环工况的特征参数
Table 2. Characteristic parameters of three typical driving cycles
典型循环工况 总时间/s 平均车速/(km·h-1) 平均加速度/(m·s-2) 停车次数 CBDBUS 574 12.55 0.28 14 NewYorkBus 600 3.68 0.19 11 NurembergR36 1 089 8.91 0.25 23
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表 3 自适应式和离线式PMP仿真条件
Table 3. Adaptive and offline PMP simulation conditions
S(t0) ε Smax Smin PFC_maxlimit/kW 0.700 0.05 0.950 0.500 90.0
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表 4 燃料电池/超级电容混合动力系统自适应式与离线式PMP能量分配结果
Table 4. Adaptive and offline PMP energy distribution results of fuel cell/supercapacitor hybrid power system
工况 能量管理策略 混合动力系统等效氢耗/g 末态荷电状态 最大荷电状态 最小荷电状态 最高运行功率/kW SC03 在线式PMP 71.63 0.713 0.801 0.688 90.0 离线式PMP 70.53 0.704 0.793 0.685 90.0 NYCC 在线式PMP 29.22 0.730 0.730 0.703 90.0 离线式PMP 28.95 0.684 0.704 0.652 90.0
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表 5 考虑燃料电池性能衰退的能量管理约束
Table 5. Energy management constraints by considering fuel cell performance degradation
参数名称 运行条件描述 数值 功率变化率Δ PFC/(kW·s-1) 剧烈的动态加载工况下，易造成氧饥饿，导致质子交换膜受损，加速燃料电池性能衰退[26]，通常限制功率变化率在最大净功率的2%~20%之间[24]。 7.50 每小时启停次数nos 燃料电池启动和停机过程所形成的氧气空气界面是引起性能衰减和耐久性恶化的重要因素[27]。燃料电池在实际车况下寿命须达到5 000 h，在这期间能承受30 000次启停循环和300 000次负载周期循环[28]。计燃料电池有输出功率和0之间切换为一次启停，燃料电池冷启动不作为启停次数考虑范围内。 6 最高运行功率PFC_maxlimit/kW 燃料电池处于深功率放电状态时会导致大电流超载输出，易造成质子交换膜破损和性能衰退，降低质子传导能力[29]。 90.0
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表 6 CBDBUS工况下能量管理结果
Table 6. Energy management result under CBDBUS driving cycle
参数 α=0 α=1.0×10-11 α=7.0×10-9 nos 84 144 6 ΔPFC/(kW·s-1) [-36.25, 28.46] [18.63, 20.17] [-0.37, 0.48] PFC_max/kW 46.8 56.7 20.7 Meq/g 40.27 42.61 43.49
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表 7 NewYorkBus工况下能量管理结果
Table 7. Energy management result under NewYorkBus driving cycle
参数 α=0 α=7.0×10-9 α=5.0×10-8 nos 66 18 6 ΔPFC/(kW·s-1) [-82.23, 72.02] [-0.63, 1.19] [-0.08, 0.26] PFC_max/kW 90.0 26.4 11.9 Meq/g 19.83 21.38 21.42
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表 8 NurembergR36工况下能量管理结果
Table 8. Energy management result under NurembergR36 driving cycle
参数 α=0 α=9.5×10-9 nos 138 6 ΔPFC/(kW·s-1) [-80.42, 55.06] [-0.40, 0.63] PFC_max/kW 80.4 25.0 Meq/g 53.41 57.61
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表 9 自适应优化能量管理策略仿真结果
Table 9. Simulation results of adaptive optimization energy management strategy
工况 启停次数/(次·h-1) 功率变化率/(kW·s-1) 最高运行功率/kW 混合动力系统等效氢耗/g 始末荷电状态差值 CBDBUS 0 [-0.100, 0.180] 19.1 43.66 -0.023 NewYorkBus 6 [-0.078, 0.260] 11.9 21.42 -0.005 NurembergR36 0 [-0.085, 0.150] 12.4 57.71 0.007
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