# Economic Routing of Electric Vehicles using Dynamic Pricing in Consideration of System Voltage
## 4 Simulation Results
### Case 2  
In Case 2, the results were obtained when the base system applied price fluctuations rather than fixed price plans. Figure 10 shows the CS selected by the route of the EV when the price was changed by applying dynamic pricing. Compared to Figure 7, there is a clear difference. Most of the consequences of the concentration on CS 2 were alleviated, and the electric vehicle could be charged at CS 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Charging Station (CS)** & **CS 1** & **CS 2** \\ \hline Maximum Charging Power [kW] & 457 & 1537.5 \\ Minimum Charging Power [kW] & 0 & 225 \\ Highest Charging Price [KRW/kW] & 500 & 500 \\ Lowest Charging Price [KRW/kW] & 150 & 150 \\ Lowest Voltage [p.u.] & 0.9724 & 0.9255 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Summary of simulation results in Case 1.  
Figure 9: Voltage of CSs in Case 1.  
Figure 10 shows the charging schedule for the CS, with different results. Previously, as there was concentration on CS 2, its charging schedule showed a high demand for power. However, as a result of applying the control strategy, the charging energy demand for CS 1 was higher than that for CS 2 in the afternoon. As the price fluctuated due to dynamic pricing, the route of the EV that was about to go to CS 2 changed so that it passed through CS 1. During the dawn hours from 1:00 to 6:00 a.m., the number of EVs was relatively small, so the EV route was designated as EV 2. However, as the number of EVs increased from the afternoon on, the system operator confirmed the charging schedule of the CS and sent the dynamic pricing signal to the CSs according to the voltage. If the voltage of the CS was lowered to 0.95 p.u., the system operator reset each EV's route with the price signal to the CS according this voltage. Therefore, the EV reset the price of the CS and recalibrated the route. The change in the route of the EV helped to distribute the charging energy between CS 1 and 2 appropriately.  
Figure 11 is a graph showing the appropriately distributed voltage of the CSs. As the demand for charging energy was distributed, so was the voltage of the CSs. The voltage for CS 2 did not fall below 0.95 p.u. The voltage of CS 1 was lowered, but it did not drop below 0.95 p.u.  
Figure 11: Voltage of CSs in Case 2.  
Figure 10: EV’s CS selection rate in Case 2.  
Figure 12 shows the charging price for CS 1 and 2. From the system operator's point of view, if the voltage became lower than 0.95 p.u., the charging schedule of the CS was checked and It can provide a price change in a dynamic pricing, depending on the control strategy of the CS. Unlike the conventional TOU price, the prices of CS 1 and 2 varied in real time. In general, the price of CS 2 was higher than that of both CS 1 and the TOU price. The reason for this is that the system operator confirmed the voltage and could predict that the voltage of CS 2 would be lower than the set value, so the charging price of CS 2 was set high. The price of CS 1 fluctuated and became less than the TOU price at a time when EVs charge up. This change caused the EV to charge at CS 1 rather than at CS 2, because the EV sets the route according to the charging price at the route setup time. To designate the EV route as CS 1, the charging rate was under about KRW 100, and in the opposite situation, the charging rate of CS 2 was about KRW 800. Table 3 shows a summary of the simulation results.