4.2.2. Maximal Charging Power

To analyze the impact of the maximum charging power level, the optimization and flexibility calculation for all vehicle availabilities are repeated for three maximum charging power levels: 3.7 kW, 11 kW, and 22 kW. Figure 8 shows the positive and negative flexible power that can be offered for the GER MP data set. Each operating strategy corresponds to a row and each maximum charging power level to a column of heat maps. Tables 5 and 6 summarize the maximal flexible power and average flexible power for all five operating strategies. Generally, the positive flexibility is also representative of the cost-optimal charging power.


**Table 5.** Maximum and average positive flexible power for five operating strategies and three maximum charging powers.

**Table 6.** Maximum and average negative flexible power for five operating strategies and three maximum charging powers.


The results of the *ToU* and *Con* operating strategy show similar behavior. As described in Section 4.1, the optimizer schedules EV chargings at the latest possible time. This leads to higher charging powers and a high level of positive flexibility from 3 a.m. to 8 a.m. on weekdays. A higher maximum charging power increases the maximal and average positive flexible power that can be offered (see Figure 8). However, the duration of positive flexibility seems to decrease with increasing maximum charging power in Figure 8. With a higher charging power level, the energy required is charged over a shorter time period, and therefore leads to a compressed availability of positive flexibility. The increase of maximal and average positive flexible power with an increasing maximum charging power can be explained by assuming that with a low charging power, e.g., 3.7 kW, not all vehicles are completely charged. In this case, the vehicle cannot offer any flexibility. With a higher maximum charging power, the charging station charges the EV over a shorter period and can therefore offer more flexibility. However, this relation is not linear, since the average positive flexible power seems to only change insignificantly from 11 to 22 kW. Therefore, the two observations described complement each other.

Considering the cost optimization described in IV.A, the results for positive flexible power for the *ToU* + *MI*, *Con* + *MI*, and *RTP* operating strategies indicate a similar behavior. With an increasing charging power, the positive flexible power that can be offered is compressed in time whereas the maximal power increases. Furthermore, the average quantity of positive flexibility increases (see Table 5). Both effects are explained in the previous paragraph.

Nevertheless, the *ToU* + *MI* and *RTP* operating strategies cause such high charging peaks at 9 p.m. (*ToU* + *MI*) and overnight (*RTP*) that the average maximal positive flexible power is three and two times higher than in the remaining operating strategies. Whereas the impact of the *RTP* might be overestimated since in a real-world scenario prices cannot be predicted as easily, the *ToU* + *MI* operating strategy can pose a major threat to grid stability.

Considering *ToU* and *Con* operating strategies, most negative flexibility can be offered at night and on weekends, when most vehicles are at home. Operating strategies with minimal price increments result in no flexibility (*Con* + *MI*) or only for short durations from 4 to 9 p.m. (*ToU* + *MI*). The causes have been discussed in the previous section. An *RTP* operating strategy shows similar trends as the *ToU* and *Con* operating strategies for weekdays. Most negative flexibility is offered at nighttime, from 5 p.m. to 3 p.m. On weekends, negative flexibility is at a high level and homogenously distributed for the *Con* and *ToU* operating strategy, whereas *RTP* results indicate a similar behavior as during the week. Such behavior can be explained by the time-varying electricity prices that are lower at nighttime throughout the entire week.

As discussed in the previous subsection the *ToU*, *Con*, and *RTP* operating strategies show similar trends in offerable negative flexibility. Table 6 displays the absolute differences between the operating strategies and the maximal charging power.

A variation in charging power results in an increase in maximal and average negative flexibility for all five simulated pricing scenarios. In order to identify a mathematical relationship between the maximum charging power and the amount of negative flexibility further simulations are required.

With all results summarize, the next chapter discusses the validity and limitations of the applied method.

## **5. Discussion**

This paper presents a thorough analysis of cost-optimal charging schedules and flexibility potential of more than 15,000 vehicle availabilities at home for five operating strategies, and three maximal charging power levels. While the calculation of cost-optimal charging schedules is state of the art, the quantification and analysis of the available flexibility of EV complements and enhances existing literature.

In this analysis, perfect price forecasts have been used to analyze the flexibility of EVs. For the first four operating strategies, which were based on *Con* and *ToU* tariffs, the consideration of perfect price forecasts would not have led to any other results. However, in the case of *RTP* the effect of the perfect price forecast is not negligible. Since *RTP* cannot be forecasted precisely and multiple methods lead to a range of results, the absolute impact of *RTP* is expected to be smaller in reality. Therefore, future research will investigate the impact of the uncertainty of price forecasts on the flexibility that can be offered.

Overall, the *ToU* + *MI* operating strategy leads to the least favorable charging behavior and flexibility offers. The average charging power indicates major peaks at 9 p.m. and a smaller peak at 3:45 p.m. Both peaks are caused by the mid- and on-peak prices between 4 and 9 p.m. These peaks occur every weekday with similar power levels and therefore represent a significant stress for grid operation. The original assumption that the network could be relieved by time-varying discrete tariffs will become obsolete in the near future, when charging processes will be optimized and automated. This conclusion is in line with the existing literature [13,17]. Nevertheless, *ToU* operating strategies lead to the overall minimum charging costs compared to the other operating strategies (see Figure 9). Despite the seemingly cheaper *ToU* tariffs, regulators should omit operating strategies that offer pre-known price differences in the future for the sake of grid stability and security of supply.

**Figure 9.** Cumulated charging costs in € for five operating strategies and three maximum charging power levels. For this analysis, the 11,103 vehicle availabilities of the GER MP field trial were used.

In order to achieve grid-friendly user behavior and not to create further grid congestions, we will investigate the integration of local energy markets (LEM). LEM enable participants to trade and exchange their electricity locally. Market agents within HEMS predict the vehicle availability, post bids on the LEM, and adjust their bids automatically based on market results. With this approach, different prices are calculated locally, and users are motivated to consume electricity in times of high generation and to generate electricity in times of high demand.

For this case study, the most recent publicly available data sets with all required parameters were chosen. Since the field trial data was collected from a wide variety of households with different types of vehicles and only contain information about the distances traveled, departure and arrival times, the results can only be representative for realistic user behavior but not for specific types of vehicles. The energy demands of the vehicles were calculated based on the distances traveled. Even though the two data sets are not from the same year (2012/2013 and 2017), the results do not indicate any major differences. Furthermore, the report on the GER MP state that the trends in transportation and individual mobility have remained almost constant over the last 10 years [21]. Therefore, the effect of the different survey periods is considered insignificant. Nevertheless, the continuation of the coronavirus pandemic may mean that employees will be able to work from home to a greater extent, and that vehicle availability may therefore change in the long term. This effect has not yet been taken into account in this study but would be an interesting new aspect.

The gathered flexibility results of this case study are based on availabilities of vehicles at home. However, the method described is neither limited to those two regions nor to quantify flexibility based on EVs at home. This method is applicable to any region/data set that contains information about trip start and end times, purpose or start and end location of the trip, means of transport and distance travelled. Further investigations will investigate differences from other world regions and the quantification of flexibility at other locations, such as workplaces.
