## 3 Measurement of Negative Effects of Energy Supply System
### Measurement of Negative Path Effect of Energy-Supplementing Vehicles  
The negative effects of vehicle energy replenishment mainly include vehicle energy consumption, delay time and driver psychological anxiety. The additional driving mileage is converted into the total driving mileage of the driver, and the driving cost of the driver is calculated together with the energy consumption to quantify the negative effect of the driver's path. Therefore, urban paths are considered as a large transportation network \(G(N,A,S)\), in which \(N\), \(A\) and \(S\) are the sets of nodes, links, and energy supply stations, respectively. Any entrance to any exit of the network is set as a starting and ending point (OD). After vehicles with energy supplement requirements enter this area, they are divided into the power supplement stations supported by the vehicles according to their remaining mileage and driving direction. In the network, for all OD pairs \(w\in W\) of daily travel vehicles, the traffic flow on the path \(p\in P\) is mainly composed of three types of vehicles, namely, vehicles requiring no energy supplement, electric vehicles requiring energy supplement and fuel vehicles requiring energy supplement. The path that the vehicle passes between the starting and ending pairs is \(P^{w}\), and the vehicle returns to its OD path \(p^{w}\) after generating the energy supplement demand and completing the energy supplement; when there are no alternative stations on the OD path of the vehicle, path deviation will occur, and extra mileage \(\omega_{0}\) will be generated; then the new driving path \(\overline{P^{w}}\) of the vehicle will be updated, where \(p^{w}\in\overline{P^{w}}\) and the path length is \(L(\overline{p^{w}})\geq L(p^{w})\). Therefore, the extra mileage generated by path deviation is \(\omega_{0}=L(\overline{p^{w}})-L(p^{w})\), where \(L(\overline{p^{w}})=L(p^{w})\), \(\omega_{0}=0\) means that the vehicle is supported and located on the original OD path of the vehicle after generating energy supplement demand. Assuming that vehicles recharge at most once during travel and that the recharge demand of different types of vehicles is related to their flow, the ratio between electric vehicles and fuel vehicles is set as r, where the charging ratio of electric vehicles is related to the remaining mileage \(\xi_{0}\) of vehicles and the psychological anxiety degree \(\psi\) of drivers is set as \(\alpha_{e}^{w}\), and the formula is:  
\[\alpha_{e}^{w}=\frac{2L_{e}^{w}}{\xi_{0}\psi}, \tag{10}\]  
where \(L_{e}^{w}\) is the weighted average travel distance of electric vehicles between OD pairs, and the charging distance of daily travel vehicles should be less than the remaining mileage of vehicles. \[L_{e}^{w}=\frac{\sum\limits_{p\in P^{w}}f_{p,e}^{w}L(\overline{p^{w}})}{\sum \limits_{p\in P^{w}}f_{p,e}^{w}} \tag{11}\]  
According to the change of negative effect in different time periods \(t\in T\) of energy supply stations on the path \(p\in P\), each time period will be allocated iteratively based on the previous time period. If the vehicles that need energy replenishment in the previous time period \(\Delta t\) fail to arrive at the station for energy replenishment after the end of the time period, they will be allocated together with the vehicles that need energy replenishment in the next time period \(\Delta t+1\). The link flow of each time period can be obtained, and the negative effect of the vehicle driving path can be calculated. The mileage energy consumption needs to be calculated separately according to different vehicle types.