基于非线性混合充电策略的电动车物流配送路径规划模型

经典的车辆路径规划问题（VRP）通常只考虑载重约束和节点约束。随着电动物流车和充电站的增多，考虑充电时间与充电量成非线性关系的电动车路径规划问题（EVRP-NL）的研究在物流配送中也有着非常重要的意义。通过分段计算充电速率简化了以往对充电时间和充电量的非线性充电函数拟合方法，并对拟合函数进行了线性化处理。针对电动车物流配送的特性，构建了以最小化车辆固定成本、行驶成本、快充成本和换电成本之和为目标函数，考虑节点约束、载重约束、电量约束、时间窗约束及充电函数线性化约束的EVRP-NL模型，提出了由换电和非线性快充构成的非线性混合充电策略，其中非线性快充是考虑充电时间与充电量的非线性关系的快充方式。针对模拟算例的计算结果验证了模型的可行性和普适性。针对实际物流算例的计算结果表明，考虑充电时间和充电量非线性关系的混合充电模型可减少35%的充电时间和69%的充电成本，非线性混合充电策略具有显著优越性。对快充电价和换电电价进行控制变量的灵敏度分析后发现, 使用非线性混合充电策略时，随着电价升高，充电方式从电价升高的充电方式转变为电价稳定的充电方式，且电价升高至一定程度，充电方式和充电成本均不再变化。 

Routing of Electronic Automobileswith Hybrid Nonlinear Charging Strategy for Logistics Distribution

The classical vehicle routing problems (VRP) usually only consider load constraints and node constraints. As theshare of electric automobileswithin the road transportation fleet increases, the routing problem of suchelectric automobilesshowing anonlinear charging property (EVRP-NL) is of great implication to urban logistics distribution. The existing nonlinear charging functionsof charging time and charging amountarelinearized, and fitting methods are simplified by calculating charging rate sectionally.According to the characteristics of logistics distribution served by electric automobiles, an extended model of EVRP-NL with load, node, power and time window constraints and linearizedconditions of charging functionsisdeveloped, which aims to minimize the summation of fixed cost, operating cost, fast charging cost, and battery replacement cost.The extend modelachieves the nonlinear hybrid charging strategy consisting of power replacement and a fast charge method considering the nonlinear relationship between charging time and charging amount, named nonlinear fast charge.Theresults of simulationshow that the model is feasible and universal in different types of data.The results of actual logisticsdatashow that nonlinear hybrid charge can reduce 35% of charging time and 69% of charging cost, and therefore prove that nonlinear hybrid charge strategy has much more significant advantages than the othermethods.The sensitivity analysesagainstdifferent prices of fast charging and battery swapping show that the hybrid charging strategy is more inclined to the mode with a cheaper price.When the price of electricity rises to a certain level, neither charging mode nor its cost changes anymore.