*5.1. Assumptions*

KS test p-values are greater than 0.05 for each hour of the day, as plotted in Figure 4. This validates that the inter-arrival times of EV sessions are exponentially distributed (Section 2.1), and thus supports our chosen models *AM* of the arrival times.

#### *5.2. Distribution of Arrival Rates λ*

To understand how the SDG parameters change with inputs, we have plotted the profiles of *λ* for weekend and weekdays for 2015 in Figure 5. We see a similar pattern for all months. Arrival models were fitted to approximate this behavior of *λ*. On weekdays, we see two peaks in the profile of *λ* that represent high frequencies of EV arrivals.

**Figure 4.** KS test p-values: For each (*<sup>m</sup>*, *dt*) combination, 24 KS tests were performed for each timeslot (*ts*). High p-values indicate that null hypotheses (IATs are exponentially distributed) could not be rejected.

**Figure 5.** Daily *λ* profiles for 2015: For each (*<sup>m</sup>*, *dt*) combination, we calculated the average arrival rate *λ*. The dotted line represents the average over those 12 months; the shaded areas indicate the percentile range.

#### *5.3. Arrival Models (AM)*

We generated 10 samples of arrivals of EVs for 2015 for both inter-arrival time (IAT) and arrival count (AC) models. The total number of arrivals per day was calculated and plotted in Figure 6. Similarly, Figure 7 shows the aggregated hourly EV arrivals. Both these plots are for weekdays, and similar results were observed in case of weekends. We can clearly see that the generated data are very similar to the actual data. We further quantitatively compared the values of the actual EV arrivals with the generated EV arrivals using a Wilcoxon test. The null hypothesis was that the means of these are equal. High *p*-values (> 0.05) indicate that the daily generated arrivals are statistically similar to the actual data. This is represented by *ns* in the figure, implying that the difference between the two samples is not significant. The results presented are for comparisons between one month of actual data to 10 samples of the same month of generated data. We go<sup>t</sup> similar results when we compare the real-world data to a single sample.

**Figure 6.** Daily aggregated EV arrivals (2015, weekdays). Significance was calculated based on Wilcoxon tests (ns: not significant, *p*-value > 0.05; \* *p*-value ≤ 0.05; \*\* *p*-value ≤ 0.01; \*\*\* *p*-value ≤ 0.001; \*\*\*\* *p*-value ≤ 0.0001).

**Figure 7.** Hourly aggregated EV arrivals (2015, weekdays). Significance was calculated based on Wilcoxon tests (ns: not significant, *p*-value > 0.05; \* *p*-value ≤ 0.05; \*\* *p*-value ≤ 0.01; \*\*\* *p*-value ≤ 0.001; \*\*\*\* *p*-value ≤ 0.0001).

#### *5.4. Mixture Models (MMc*, *MMe)*

Conditional distributions for connection times (hours) and energy required (kWh) are plotted in Figures 8 and 9 respectively. The plots on the left were created from the real-world data, and those on the right were created from the data generated from mixture models (*MMc*, *MMe*). These figures are for weekdays, and similar plots were generated for weekends. Connection times (and energy required) were generated using GMM and real-world EV arrivals. Vertical divisions in the generated data for each times slot can be seen, because we use one GMM per {*<sup>m</sup>*, *dt*, *ts*} combination.

**Figure 8.** Density plots for connection times (2015, weekdays). Generated data represent sampled connection times for real-world EV arrivals. Each point represents a bin (10 min by 10 min), and is colored based on the number of EV sessions in the bin (bins with less than 5 arrivals were not plotted to keep the graph readable).

**Figure 9.** Density plots for required energy (2015, weekdays). Generated data represent sampled energy requirements for real-world EV arrivals. Each point represents a bin (10 min by 0.16 kWh), and is colored based the number of EV sessions in the bin (bins with less than 5 arrivals were not plotted to keep the graph readable).

#### *5.5. Synthetic Data Generator (SDG)*

We generated full session samples including generated arrival times, connection times and required energy for all the models. These generated samples were compared with the real-world session data for 2015. To compare the models' synthetic samples with real-world data, 2-sample KDE tests were performed. In Figure 10a, we show the KDE test for (*ta*, *tc*), and Figure 10b shows the KDE test results on (*ta*, *E*). As we can see, the mean model for the IAT, and both models for AC have average *p*-values > 0.05, indicating that the generated data are similar to the real-world EV session data. We observed similar results in the multidimensional KS test. These results conclude that the generated samples are statistically similar to real-world data.

**Figure 10.** KDE test p-values: Daily 2 sample 2 dimensional KDE tests to compare real-world and generated data. Total of 365 tests performed for each model. *p*-value > 0.05 means datasets are similar. (**a**) Results for (arrival times *ta*, connection times *tc*). (**b**) Results for (arrival times *ta*, energy required *E*).
