Stochastic dynamic user equilibrium assignment model considering penetration of electric vehicles
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摘要: 为分析电动汽车动态充电需求对公共充电设施服务水平的影响, 给充电设施网络规划与运营提供参考, 在考虑燃油汽车和电动汽车出行者行为差异、路段拥堵状态、车辆能源消耗、充电设施布局与服务水平等因素的基础上, 采用巢式Logit模型描述了包含充电需求判断、充电设施和路径选择的电动汽车出行联合选择行为; 建立了考虑用户在途快速充电行为的动态交通流分配模型, 提出了混合交通下随机动态用户均衡条件及等价的变分不等式模型, 并设计了融合电动汽车充电排队仿真的动态交通流迭代算法; 通过算例验证了模型与算法的有效性, 并进一步探究了在电动汽车推广的不同阶段, 需求和供给关键因素对充电设施服务水平的影响。研究结果表明: 受路网交通流量分布和充电设施布局的影响, 充电设施利用率在时间和空间上具有明显的非均衡性; 电动汽车混入率的提高会增加平均充电等待时间, 并改变充电高峰期的时间分布; 电动汽车电池初始电量和充电设施处的排队长度均对用户的充电需求判断呈负效应; 当路网中充电设施数量与需求规模不匹配时, 会导致服务水平急剧下降, 同时极易诱发局部拥堵; 用户在充电设施处的逗留时间以15~20 min居多, 约90%用户的等待时间在9 min以内, 因此, 提出的模型符合实际, 能够充分反映混合交通网络中电动汽车充电行为引发的一系列影响。Abstract: To analyze the impact of dynamic charging demand of electric vehicles(EVs) on the service level of public charging facilities(CFs), and provide guidances for the planning and operation of public charging network, a nested Logit model was employed to describe the joint choice behavior of EV travel including charging demand judgment, charging facility and path choices under considering the behavioral differences between EV and gasoline vehicle travelers, congestion state of road section, energy consumption of vehicle, location and service level of charing station. A dynamic traffic flow assignment model considering users' en-route fast charging behavior was developed. The stochastic dynamic user equilibrium condition under the hybrid traffic conditions and an equivalent variational inequality model were proposed, and a dynamic traffic flow iterative algorithm containing the charing queuing simulation on EVs was designed. The effectivenesses of the model and algorithm were verified through a numerical example, and the influences of some key indicators regarding charging demand and supply on the service level of CFs in different promotion phases of EVs were further discussed. Research result shows that affected by the distributions of traffic flow and CFs, the utilization ratios of CFs are unevenly distributed from both space and time perspectives. The average charging waiting time tends to increase with the rise of EV penetration rate(PR). The rise of PR also affects the temporal distribution during the charging peak. The initial state of EV battery charge and queuing length at CF have significant negative effects on users' charging demand judgement. The mismatch between the number of CFs and the demand scale in the road network may lead to a sharp decline in the service level and can easily induce local congestion. For most users, the dwell time at CF is within 15-20 min, and the waiting times of approximate 90% users are less than 9 min. Therefore, the proposed model is consistent with the reality and can fully reflect a series of influences caused by the charging behavior in the hybrid traffic network.
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图 12 用户在充电站逗留时间频数分布
Figure 12. Frequency distributions of uses' dwell times at charging stations
图 13 用户在充电站等待时间频数分布
Figure 13. Frequency distributions of uses' waiting times at charging stations
图 14 不同初始SOC下完成充电服务的车辆数
Figure 14. Numbers of vehicles completed charging service under different initial SOCs
表 1 不同电动汽车混入率下充电服务耗时
Table 1. Time consumptions of charging service under different penetration rates of EV
充电站编号 不同电动汽车混入率(%)下用户的平均等待时间/min 不同电动汽车混入率(%)下用户的平均逗留时间/min 40 60 80 40 60 80 7 0 3.04 9.28 17.21 20.36 26.79 10 0 3.66 13.07 16.87 20.72 30.51 
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表 2 不同规模下充电设施利用情况
Table 2. Utilization conditions of charging facilities under different scales
充电站编号 指标 10台充电桩 15台充电桩 20台充电桩 25台充电桩 30台充电桩 7 平均利用率/% 93 92 76 68 54 累计服务数/pcu 136 195 234 249 251 10 平均利用率/% 87 84 63 48 41 累计服务数/pcu 125 176 187 187 184
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表 3 不同布局方案下的指标统计结果
Table 3. Statistical results of indicators under different location schemes
充电站布局 节点7、10 节点7、9 节点6、11 节点6、9 节点5、11 节点5、10 总费用/103元 275.468 276.107 275.351 276.429 276.192 276.712 总能耗/kJ 6.893×108 6.917×108 6.902×108 6.911×108 6.907×108 6.891×108 均衡系数 0.115 0.361 0.204 0.719 0.448 0.393
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