# Electric-Vehicle Routing Planning Based on the Law of Electric Energy Consumption
## 3 Driving-Cycle-Based Energy Consumption Model  
### Constructing Driving Cycles of EVs  
The battery level of EVs is directly impacted by their energy consumption behavior, which further influences the necessity to visit a recharging station and the recharging time at the station. Researchers have found out that various factors affect EVs' energy consumption behavior, mainly including the load, speed, temperature, and road conditions. Thus, the driving states and resistance of EVs directly affects their energy consumption.  
Like that of CVs, the typical driving state of an EV consists of starting, accelerating, constant speed, decelerating, and stopping, and the driving state transforms from one to another during travel. Previous work either assumed a constant speed of EVs, or a linear coefficient between energy consumption and distance, which ignores the changes in driving states. Therefore, in this work, we use a more realistic model based on the driving cycles with consideration of the factors of load, travel distance, and speed. The driving cycle of a vehicle presents the change in speed with the change in driving states. The New European Driving Cycle (NEDC), which is widely used to estimate EVs' maximum driving range in China, includes two test cycles: that of the Economic Commission for Europe (ECE) and the Extra Urban Driving Cycle (EUDC). The driving cycles of ECE and EUDC are shown in Figure 1.  
ECE tests an EV operating within a city for the first four cycles, whereas EUDC tests it in a suburban area for the last cycle. The EV in EUDC operates at a higher speed than that in ECE. The driving cycle shows the change in speed over time. During ECE, the vehicle first accelerates from rest before it reaches a constant speed and runs for a period, after which it decelerates to stop and then starts to repeat similar movements. By comparison, during EUDC, the vehicle accelerates from a standstill, then undergoes an acceleration and deceleration process with different change rates, before it finally stops.  
When using EVs in urban distribution, there are three types of nodes in the network: (1) distribution center \(N_{D}\); (2) customers \(N_{C}\); and (3) recharging stations \(N_{R}\). EVs depart from \(N_{D}\) in suburban areas and visit \(N_{C}\) in the city for delivery. They visit the recharging stations when necessary, and return to \(N_{D}\) after completing the task. By comparison, the driving cycle of EVs driving from and returning to \(N_{D}\) is similar to that of EUDC, whereas driving between \(N_{C}\) and \(N_{R}\) is similar to that of ECE. Therefore, we present the following driving conditions of EVs to further describe their driving cycles.  
**Condition A: EVs depart from a distribution center to the first customer, or EVs return to the distribution center from the last customer.**  
Under this condition, an EV first starts from a stationary position and accelerates at a uniform rate \(a_{a1}\) until its speed reaches \(v_{a1}\), then it decelerates to \(v_{a2}\) at rate \(a_{a2}\). Then, it accelerates again at rate \(a_{a3}\) to speed \(v_{a3}\), then travels at a constant speed \(v_{a3}\) for some  
Figure 1: The driving cycles of ECE and EUDC.  
time, and finally decelerates to a full stop at rate \(a_{a4}\). This driving cycle is named cycle A, as shown in Figure 2.  
**Condition B: During delivery, EVs travel between customer and customer, or between customer and recharging station.**  
Under condition B, the driving cycle of an EV is as follows: an EV starts from a stationary position at a customer or recharging station, then accelerates at a uniform rate \(a_{b1}\) to speed \(v_{b1}\) and maintains \(v_{b1}\) for a period, after which it decelerates at rate \(a_{b2}\) to a complete stop when it reaches the next customer or recharging station. This driving cycle B is shown in Figure 3.