考虑排放约束的电动汽车混行交通路网均衡模型

Mixed Traffic Network Equilibrium with Battery Electric Vehicles Considering Emission Constraints

随着电动汽车的推广和使用,电动汽车与燃油汽车在路网中交互运行,形成了混行交通环境。本文构建考虑排放约束和途中充电的电动汽车混行交通路网均衡模型。首先,分别定义了电动汽车用户与燃油汽车用户的出行成本函数,其中电动汽车用户出行成本包含行驶时间、充电排队时间及充电时长。其次,构建了考虑排放约束的混行交通路网均衡模型,证明了解的唯一性,推导了模型对应的KKT条件,且与Wardrop第一原理等价。然后,将均衡模型表述为包括用户均衡条件、排放约束、守恒约束的互补性条件形式,通过引入间隙函数,进一步将其转化为等价的无约束最优化问题,并利用基于梯度的算法进行求解。最后,通过算例验证了均衡模型及算法的有效性,结果表明:(1)考虑路网排放约束将影响混行交通量和充电站充电流量空间分布;(2)总需求和电动汽车渗透率不变的条件下,提高减排力度会导致路网总行程时间的增加;(3)给定减排力度时,可以确定路网总行程时间最小时对应的电动汽车最优渗透率。

With the promotion and use of electric vehicles,electric and fuel vehicles operate in a road network interactively,thus forming a mixed traffic environment.In this study,a mixed traffic network model that considers emission constraints is developed.First,the utility functions of users of battery electric and fuel vehicles are defined,with travel time,charging queuing time,and charging time taken as utility components for users of battery electric vehicles.A corresponding mixed traffic network equilibrium model is then established.We prove the uniqueness of the model solution and derive Karush-Kuhn-Tucker conditions corresponding to the mixed traffic network model,which is proven to be equivalent to Wardrop’s first principle.Third,the equilibrium model is transformed into complementary conditions that include user equilibrium conditions as well as emission and conservation constraints.A gap function is introduced and reformulated into an equivalent unconstrained optimization problem,which is then solved by a gradient-based algorithm.Finally,the effectiveness of both the model and algorithm are verified through an example network application.The results are as follows.①Road network emission constraints influence the spatial distribution of mixed traffic flows and charging demands;②An increase in emission reductions leads to an increase in total network travel time;③Given emission reductions,the optimal penetration rate of battery electric vehicles corresponding to the minimum total network travel time can be determined.