Parameters Optimization for Hybrid Energy Storage System of Electric Vehicles Based on Cross-Entropy Algorithm
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摘要: 为了提升电动汽车动力性能、降低车辆成本，以复合电源成本和车辆电耗最小为目标，通过交叉熵（cross- entropy，CE）算法对车载复合电源的参数优化进行了研究. 首先，以某款纯电动汽车为研究对象，根据能量与功率性能指标确定锂离子电池和超级电容的容量范围；其次，选取复合电源成本和车辆电耗建立多目标优化函数，并在ADVISOR环境中搭建车辆仿真模型；接着，采用CE算法，通过种群的不断迭代，更新高斯概率密度函数的均值和方差，找到复合电源参数的Pareto最优解集；最后，从最优Pareto解集中选取典型的匹配参数，分析复合电源成本、车辆电耗和整车性能. 研究结果表明：在满足基本约束的前提下，得到了由100个解组成的Pareto最优解集. 与第二代非劣排序遗传算法（non-dominated sorting genetic algorithm-Ⅱ，NSGA-Ⅱ）比较，CE算法有更好的收敛性与分布性；复合电源成本平均降低了9.49%，车辆电耗平均降低了22.81%； 此外，城市道路循环工况（urban dynamometer driving schedule，UDDS）下车速误差最大值降低16.15%，整车动力性也有显著提升，百公里加速时间缩短7.81%，最高车速提升1.98%.Abstract: In order to improve the dynamic performance of electric vehicles and reduce costs, a parameter optimization method for vehicle-mounted hybrid power supply based on cross-entropy (CE) algorithm is explored with the intent of minimizing the hybrid power supply cost and power consumption. Firstly, a hybrid electric vehicle is used as the object, and the capacity ranges of its lithium-ion batteries and super-capacitors are determined according to the energy and power performance indexes. Secondly, the multi-objective optimization function of minimizing power supply cost and power consumption and the vehicle simulation model are established in ADVISOR. Subsequently, with CE algorithm, the mean and variance of the Gaussian probability density function are updated by the continuous iterations of populations to find out the optimal Pareto solution set. Finally, the typical solutions are selected to analyze the cost, power consumption and vehicle performance. The results show that under the basic requirements, 100 optimal solutions are found, which constitute an optimal Pareto solution set. Compared with the results of (non-dominated sorting genetic algorithm-Ⅱ) NSGA-Ⅱ, the convergence and distribution of CE algorithm are better, the cost of hybrid power supply is reduced by 9.49% and the vehicle power consumption by 22.81% on average. Furthermore, the maximum error of vehicle speed is reduced by 16.15% under UDDS cycle condition, and the vehicle dynamic performance is improved significantly with the acceleration time of 100 km reduced by 7.81% and the maximum speed increased by 1.98%.
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图 5 不同算法的锂离子电池SOC、温度及超级电容SOC
Figure 5. Lithium-ion battery SOC, supercapacitor SOC and temperature curve of different algorithms
表 1 整车参数
Table 1. Vehicle parameters
部件 参数 数值 整车 总质量/kg 1 191 长，宽，高/mm 4 410，1 750，1 000 轴距/mm 2 600 电机 最大功率/kW 75 电压等级/V 320 最大转速/（r•min−1） 10 000 最大转矩/（N•m） 200 锂离子电池 单体电池额定电压/V 3.2 单体电池额定容量/（A•h） 10～60 能量密度/（W•h•kg−1） 120 超级电容 额定电压/V 2.5 额定容量/F 1 000～3 500 能量密度/（W•h•kg−1） 6 
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表 2 整车循环工况功率需求
Table 2. Power requirements in driving cycle
项目 正（驱动）需求 负（制动）需求 总能量需求/kJ 6 799 −440.2 循环中所占时间/h 21.50 2.683 平均功率需求/kW 5.270 −2.734 峰值功率需求/kW 39.70 −8.942
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表 3 不同算法优化结果比较
Table 3. Comparison of different algorithm optimization results
项目 CE NSGA-II 优化前 最小车辆电耗/（kW•h） 2.241 8 2.125 1 7.140 1 平均车辆电耗/（kW•h） 3.254 0 3.562 8 7.140 1 最低电源成本/万元 8.311 1 9.432 8 16.080 平均电源成本/万元 10.937 1 14.169 2 16.080 锂离子电池DOD 0.061 0 0.086 0 0.154 0 超级电容DOD 0.426 1 0.465 2 制动能量回收/kJ −6 198.6 −5 469.1 −5 331.2 放电效率 0.995 2 0.989 5 0.922 0
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表 4 整车动力性能比较
Table 4. Comparison of vehicle dynamic performance
项目 CE 算法优化 NSGA-II 算法优化 未优化 最高车速/（km•h−1） 157.55 （提高 14.64%） 154.49 （提高 12.41%） 137.43 15 km/h 最大爬坡度/% 35（提高 25.00%） 33（提高 17.85%） 28 5 s 能达到的最远距离/m 195.8 （提高 3.87%） 188.9 （提高 0.21%） 188.5 0～50 km/h 加速时间/s 5.0 （提高 5.66%） 5.2 （提高 1.88%） 5.3 50～80 km/h 加速时间/s 5.8 （提高 48.67%） 6.0 （提高 46.9%） 11.3 0～100 km/h 加速时间/s 17.7 （提高 11.94%） 19.2 （提高 4.47%） 20.1
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