*3.3. Data Aggregation*

Once optimal charging schedules and flexibility have been calculated for more than 15,000 vehicle availabilities for 5 operating strategies and 3 maximal charging powers, the results are aggregated.

First, all available vehicles, charging schedules, flexible power and energies are summed up for every time step of the field trial periods. The result is a data set that shows the total number of available vehicles at home, charging powers, flexible power and energy for every time step of the field trial.

In a final step, the summed data is clustered into weekly time steps (e.g., "Monday, 09:00"), and weekdays and weekends. The clusters are then averaged over the field trial duration.

#### **4. Results**

This chapter visualizes and describes the results of the case study in detail. The cost-optimal charging schedules are shown in the top two rows of plots, whereas the flexibility potential is shown in the bottom two rows of plots (Figure 7). The first section describes the cost-optimal charging schedules, and the second section the flexibility potentials of the vehicle availabilities from both data sets for the five operating strategies.

#### *4.1. Cost-Optimal Charging Schedules*

In the top two rows of plots, Figure 7 shows the cost-optimal power demand per vehicle for weekdays in the first row and for weekends in the second row. The curves of the *Con* and the *ToU* operating strategy are almost identical and can only be distinguished by their behavior between 3 p.m. and 9 p.m. At 4 p.m., the *ToU* curves show a smaller second peak compared to the early morning hours. This behavior can be explained by the optimizer logic and mid/on-peak tariffs. The optimizer implemented charges the vehicles as late as possible and as cheaply as possible. Considering the mid/on-peak tariffs starting at 4 p.m., the optimizer schedules all vehicles that depart between 4 and 9 PM to charge right before 4 p.m. Therefore, this trend is consistent with the implemented optimizer logic. Besides the difference mentioned in the early afternoon, the power curves for the *ToU* and *Con* operating strategy show the same trend as visualized by the histogram of the departure times in Figure 6. The amplitude ranges from 0 to 2.5 kW/EV for both data sets. On weekends, the power ranges from 0 to 1.9 kW/EV and is more spread out throughout the day. Generally, the results indicate that the Californian vehicles require greater power per vehicle compared to the German vehicles.

The *RTP* operating strategy causes charging peaks that are spread out from 11 p.m. to 8 a.m. The peaks are more irregular than the ones for the *Con* and *ToU* operating strategies. While the power curves for the *Con* and *ToU* operating strategy indicate similar trends for the US CHTS and the GER MP data set, the cost-optimal charging power differ significantly between the German and the Californian data set in the *RTP* operating strategy. The charging power for the Californian data set looks rather smooth, whereas the results of the German vehicles look much spikier. Since the German data set was collected over a period of three months, a single drop in the real-time prices and the corresponding peak of charging power have a greater impact on the average charging power than those that occurred during the 12-month Californian field trial with only a few vehicles. However, the amplitude ranges also from 0 to 2.5 kW/EV for both data sets. Since real-time prices are much more difficult to forecast and exhibit erratic short-term changes, the demand peaks are most probably overestimated in these results.

The cost-optimal charging power for the operating strategy *Con* + *MI* indicates a shifted charging behavior. Whereas the *Con* operating strategy schedules vehicle charging right before their departure in the morning hours, the minimal price increments force the optimizer to charge the vehicles right after they arrive home. Therefore, the charging power curve for the *Con* + *MI* follows the almost Gaussian distribution of the arrival times shown in Figure 6. The amplitude ranges from 0 to 2 kW/EV, which is comparable to the curves of the *Con* and *ToU* operating strategies.

Nevertheless, *ToU* + *MI* cause the greatest charging power peaks (see Figure 7). Every day at 9 p.m., the optimizer schedules the vehicles that arrived between 4 and 9 p.m. to start charging at the same time. This leads to power peaks of more than 6 kW/EV for both data sets.

Overall, the US CHTS and the GER MP results show similar trends for the cost-optimal charging power for the five operating strategies simulated.

#### *4.2. Flexibility*

#### 4.2.1. Operating Strategies

In the bottom two plots of Figure 7 the ranges of flexibility for the five operating strategies simulated are visualized.

For EVs, positive flexibility is equivalent to a pause or postponement of the charging process. Therefore, the upper boundary of the flexibility is equal to the optimal charging power.

According to the definition in Section 1, negative flexibility is the ability to consume electricity ahead of its schedule. Considering the operating strategy *Con* + *MI* and a cost optimization, no negative flexibility can be offered. Therefore, the lower boundary of the simulation results is congruent with the zero line (see Figure 7).

Similar to the aforementioned operating strategy, *ToU* + *MI* result in no negative flexibility between 9 p.m. and 4 p.m. From 4 p.m. to 9 p.m., the negative flexibility increases linearly as vehicles arrive home, and their charging process is scheduled from 9 p.m. onwards owing to lower electricity prices. At 9 p.m., negative flexibility drops back to zero.

The operating strategy *Con* and *ToU* result in almost identical negative flexibility results. Furthermore, the negative flexibility that can be offered follows the vehicle availability curves discussed in Section 3.1.3). Periodically, at night time, negative flexibility increases and reaches its maximum around 1 to 3 a.m. During the morning hours before 12 a.m., the flexibility decreases. Negative flexibility ranges from −5 kW/EV to −7.5 kW/EV with the *Con* and *ToU* operating strategies. On weekends, the ranges are smaller since vehicle fluctuations also decrease. At 4 p.m., the *ToU* operating strategy causes a minor drop in negative flexibility due to the charging of vehicles that depart between 4 and 9 p.m.

The *RTP* operating strategy also follows the vehicle availability described in Section 3.1.3). However, in contrast to the results of the *ToU* and *Con* operating strategies, the maximum negative flexibility is available right before midnight. After midnight, when electricity prices are the lowest, the vehicles are charged and the available negative flexibility decreases. On weekends, the range of negative flexibility that can be offered decreases slightly as the fluctuations in vehicle availabilities also decrease. The negative flexibility that can be offered ranges between −2 kW/EV and −7 kW/EV for both data sets. Therefore, *RTP* prices lead to less offerable negative flexibility than a *Con* or *ToU* operating strategy.

Having described the impact of the five operating strategies, the next subsections describe the impact of the maximal charging power on the offerable flexibility of EVs.
