# Smart Electric Vehicle Charging via Adjustable Real-Time Charging Rates
## 3 Results and Discussion  
ARVF utilizes a load limit to determine appropriate times to charge each vehicle and to compute the optimal rate each vehicle should receive. An analysis is conducted to explore 7 load limit cases and determine which is the best for ARVF. Stated previously in Section 2, the load limit that satisfies the primary objective (1) ensuring all vehicles charge greater than or equal to 90% of the total amount of energy that the vehicle requested, and minimizes the second objective (2) reducing the average transformer load during charging will be the finalized load limit for ARVF. After the load limit is validated, proving that it satisfies both objectives, ARVF will inherent this limit and operates by charging vehicles when the baseload is lower than the load limit. In case 1, the load limit is equal to the rated limit, meaning that ARVF fills to 75 kW. In cases 2-7, the load limit is equal to the average baseload plus a multiple its standard deviation. In cases 2, 3, 4, 5, 6, and 7, the multiple of the standard deviation is equal to 0, 0.5, 0.75, 1, 1.5, and 2, respectively. Cases 1, 2, and 3 do not charge all vehicles greater than or equal to 90% of the total amount of energy that the vehicle requested, shown in Table 2, and are eliminated from plausible load limits. Further analyzing cases 4, 5, 6, and 7, Table 3 shows each case's ability to reduce the average load during charging. Moreover, this table proves that case 4, equating the limit load to the average baseload plus 0.75 of its standard deviation performs best, reducing the average load during charging by 16.53%. Case 4 is selected as the limit load for ARVF because it performs optimally amongst the 7 cases, successfully charging all vehicles greater than or equal to 90% of the total amount of energy that the vehicle requested and reducing the average load while charging the most. This investigation shows that the rated limit is not an adequate load limit, case 1, as not all cars are able to charge greater than or equal to 90% when ARVF is applied  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & **0–40\%** & **40–50\%** & **50–60\%** & **60–70\%** & **70–80\%** & **80–90\%** & **90–100\%** \\ \hline Uncontrolled & 0 & 0 & 0 & 0 & 0 & 0 & 20,295 \\ \hline
1 & 0 & 0 & 0 & 0 & 0 & 0 & 20,295 \\ \hline
2 & 76 & 51 & 56 & 64 & 51  
to the baseload load limit. Superior results are obtained by equating the load limit to a value that is relative to the baseload. A load limit that can adjust to the baseload allows the algorithm to scale accordingly, preventing (1) small-scaled uncontrolled charging from occuring when the baseload is significantly below the rated limit and (2) low amounts of vehicles reaching full charge when the baseload is significantly above the rated limit. Based on the results in Table 3, the load limit in case 4 will be used to assess this algorithm because case 4 performs the best amongst the 7 presented cases. [PERSON] et al. [47] evaluated six algorithms, including Grid Valley filling by [PERSON] et al. [19] and Time-Of-Use (TOU) Charging from Southern California Edison (SCE) [54]. This study determined that the Grid Valley Filling with Modified Timeslot Rejection strategy produces the best results, preventing all local transformers from experiencing significant overloading. Grid Valley Filling with Modified Timeslot Rejection will hereby be referred to as MTR and will be used to evaluate the effectiveness of ARVF. When ARVF and MTR are applied to the forecasted baseload (0% variation), shown in Figure 8, the absolute maximum peak power reached amongst all transformers, the average maximum peak power reached by each transformer, and maximum peak power from the baseload are all 86.58 kW. This signifies that the maximum peaks are produced by the baseload rather than PEV charging from the algorithms. The average load during charging when ARVF and MTR are applied is 63.13 and 54.81 kW, respectively.