# Smart Electric Vehicle Charging via Adjustable Real-Time Charging Rates
## 3 Results and Discussion
MTR performs very well because it is completely reliant on the forecasted load, and in this situation, the actual load is the forecasted load. In each subplot in Figure 8, there are 2250 green curves; each curve represents the total load observed by one transformer. In Subplot A, vehicles are charging without any scheduling protocol (uncontrolled charging), meaning as soon as each vehicle arrives home, it immediately begins charging. This creates a lot of variation between the 2250 green  
Figure 8: Charging profiles created from (**a**) uncontrolled charging, (**b**) ARVF and (**c**) MTR on the 0 percent variation baseload. curves, generating little overlap between the curves and appearing as if a lot of charging is occurring because there is a lot of visible green shading. On the contrary, in subplots B and C, vehicles are charging using a valley-filling algorithm. Most of the vehicles begin charging in Subplots B and C are generally shifted to similar times, despite when each vehicle arrives at their perspective home. This creates very little variation between the 2250 green curves, generating a significantly large overlap between the curves and appearing as if very little charging is occurring because there is a small amount of visible green shading. If each curve from every transformer in Subplot A is compared to the curve produced by the same transformer in Subplot B or C, the area under both curves would be the same. The shape of the curves in Subplots B and C are generally much flatter and wider than in Subplot A but represent the same amount of charging. As the variation begins to increase and the actual and forecasted demand deviate (i.e., a day with more homes using an air conditioner than expected), ARVF's performance increases, and MTR's performance decreases. ARVF determines how much charge a vehicle receives in a real-time, per-minute fashion based on the load the transformer is observing in that time interval. This attribute allows ARVF to adapt to unforeseen changes; if the baseload suddenly increases, the algorithm will respond to the change and adjust the amount of charge being delivered to vehicles. In this same instance, the Modified Timeslot Rejection strategy is unable to adapt to changes in the forecasted baseload and therefore uses the same charging profile for a now different baseload. When the actual baseload has approximately 20% variation from the forecasted baseload, the algorithms generally perform the same. The charging distributions are displayed in Figure 9.  
Figure 9: Charging profiles created from (**a**) uncontrolled charging, (**b**) ARVF and (**c**) MTR on the 20 percent variation baseload. Figure 10 depicts when 30% variation is present between the actual and forecasted curves. Despite the large change in the two curves, MTR does not respond to this change, maintaining the original charging sequence and scheduling vehicles in the same timeslots from the decision on the outdated forecasted curve. In contrast, ARVF reacts to the change by delivering lower rates to the charging vehicles and extending the duration of the charge. In the 0% variation example, the actual and forecasted baseload match perfectly, making the time MTR scheduled to charge vehicles ideal and outperforming ARVF. However, Table 4 shows that when the actual and forecasted baseload differs by 20% or more, ARVF's produces better results due to its real-time robustness. Table 4 shows that as variation is introduced to the forecasted and actual baseload, MTR's advantage steadily diminishes. In addition, Table 4 shows that ARVF can achieve similar results to MTR and allows for variation between the forecasted and actual baseload, making this algorithm well suited for real-world applications. In real-world applications, the forecasted load will rarely match the baseload, thereby highlighting the efficacy of this method. Figure 10: Charging profiles created from (**a**) uncontrolled charging (**b**) ARVF and (**c**) MTR on the 30 percent variation baseload.