Model Input

In order to assess the potential of an EV fleet to adapt its demand according to an available renewable power source a centralized optimization approach, map-ping the decision problem of an EV aggregator, is employed. For the analysis it is assumed that the generation patterns and the individual trips are known for the period of the optimization horizon. This makes the following model a benchmark assessment of the charging flexibility of an EV fleet in the given con-figuration. The optimization objective of the aggregator is to minimize the usage of conventional generation capacity by adapting EV charging to the given gen-eration, but always under the condition that all trips are fulfilled, and hence the mobility needs of the drivers met. The technical implementation of the model builds on Java and the IBM ILOG CPLEX 12.4 optimization suite.

Driving Patterns

The driving behavior for the benchmark assessment is based on the previously employed profiles and sociodemographic groups, in particular the behavior of full-time employees and retired persons is modeled. The data set builds on the German Mobility Panel (MOP), as presented in Chapter 3. The profiles have a time resolution of 15 minutes which is also chosen as the time interval for the optimization process. The profiles have a time-horizon of one week. For the analysis the same most recent 1000 driving profiles for each group as in the analysis in Chapter 4 are utilized. Due to range restrictions of the specified EV some of the profiles can not be fulfilled. In addition, the restriction of charging only at the home location with the standard connection power of 3.6 kW also reduces the number of viable profiles. This represents a conservative approach to the assumption of charging infrastructure availability and will be addressed in more detail in the result section. When a profile is referred to as viable, this means that the profile can be fulfilled when charging takes place at the specified power level without delay after arriving at a location. This charging strategy thus corresponds to AFAP as introduced earlier. Any other controlled charging

Mon−Emp Mon−Ret Tue−Emp Tue−Ret Wed−Emp Wed−Ret Thu−Emp Thu−Ret Fri−Emp Fri−Ret Sat−Emp Sat−Ret Sun−Emp Sun−Ret

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Employees and Retired − km per Day

km per Day

Figure 5.2: Weekly trip variation for employees and retired driving profiles.

strategy will likely encompass some delays, and will thus not charge the vehicle as fast, but instead will employ the flexibility for the given objective.

Because of the restrictions in battery capacity and charging power the follow-ing analyses are conducted with a sample of 846 vehicles of employees and 946 vehicles for retired persons in order to have the same data set in every scenario for comparison. This already shows that a vehicle with 31.5 kWh, even though it has quite a large battery can not cover all of the driving demand that occurs.

Nevertheless, it can be observed that for employees still 846 out of 1000 initial profiles are viable, showing that for most purposes EVs are suitable. The di-rect comparison between retirees and employees shows that employees have very distinct driving needs, in particular on weekdays where most trips occur to work and back in the morning and in the evening respectively. Profiles of retired persons in turn have different patterns and beside their overall lower driving distance during a week also have their travel maxima during the day (cf. Sec-tion 4.3.2).

Figure 5.2 shows the range of variation of daily driving distances in km for both profile groups. It can be observed that the median of the daily driving dis-tances of employees is 20.0 km on average over the whole week. On weekdays the median is 28.0 km whereas on weekends the median is only 6.0 km. This is a distinct drop in driving distance on the weekend. The mean values for em-ployees are similar in their relation, on weekdays the mean distance per day is

36.8 km whereas on the weekend the mean distance is 20.5 km. There is a con-siderable amount of variation in the daily driving requirements for employees but 75% of the profiles travel less than 54.0 km a day demonstrating that EVs are very well applicable even to more demanding mobility requirements.

For the retired profile group similar general patterns can be observed for weekdays and weekends. The travel distances are considerably lower. The me-dian for weekdays is only 8.05 km whereas the mean travel distance per week-day is 17.8 km. On weekends the variation is even higher, the median is 1.8 km and the mean 15.7 km. The 75% quantile with a value of only 22.0 km indicates, that the distance requirements of retired persons are less demanding than the ones of employees.

EV Specification

The EV specification builds on the values already presented in Section 4. The specifications are chosen such that they accurately represent current and near future vehicle technology. In particular the specifications similar to the BMW Mini E are (cf. Table 4.1) employed to characterize a generic EV. The usable bat-tery capacity is 31.5 kWh and the consumption per km is 0.15 kWh, as specified in Table 5.3. This also enables a better comparison of the results obtained with respect to the required charging times and the applicability to the given empir-ical driving profiles. The charging powers that are assumed correspond to the basic capabilities of nearly every German household which allow charging in the range between 3.6 - 11 kW, following the specifications for EU Standard and EU Semi-Fast given in Table 2.6.

Generation Data

The renewable generation data was obtained from the 50 Hertz TSO in 15 minute resolution for the respective regulation zone consisting of eastern Germany and the city of Hamburg. This data was chosen in order to represent the already high share of volatile generation as compared to total load. For the utilized data set of the complete year of 2009 this means that the average minimum load of 4 -5 GW during the night, could already be surpassed by wind generation with a generation maximum of 9 GW, (50-Hertz, 2010). The installed wind generation capacity of the 50 Hertz TSO-zone was 10,571 MW at the end of 2009, whereas photovoltaic (PV) generation only had an installed capacity of 975.1 MW. These two intermittent renewable energy sources represent the largest share of renew-able generation capacity in Germany, are highly varirenew-able, and only to a minor

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Figure 5.3: Monthly variation of the employed generation profiles for wind and PV in 2009.

Table 5.1: Summary statistics of the employed generation data.

Gen. Source Min. 1st Qu. Median Mean CV 3rd Qu. Max.

Wind [MW] 1.2 555.4 1326.0 1789.0 0.91 2431.0 9081.0 Percent of Max. [%] 0.01 6.12 14.60 19.70 - 26.77

Solar [MW] 1.0 22.8 80.3 111.5 0.92 182.8 460.5

Percent of Max. [%] 0.22 4.95 17.44 24.21 - 39.70

extent controllable. Therefore, as argued before it is important to employ avail-able demand flexibility for balancing purposes. Figure 5.3 shows the range of monthly generation variation for the complete year of 2009 for wind and solar generation.

It can be observed that wind generation has a typical higher overall produc-tion level in the winter and particular late autumn months. The variaproduc-tion level of wind generation is higher than the one of PV, even in relative terms. Table 5.1 presents the summary statistics of the generation time series for 2009. The minimal values are similarly low for both generation technologies, nevertheless, the difference between the generation maximum and the quantile and mean val-ues is considerably higher for wind power than for PV. In particular, PV has a mean generation value (for the times with generation during the day) that is 4.13 times lower than the generation maximum. Both generation technologies show seasonal generation characteristics, e.g., wind is more prevalent in the winter and autumn months whereas PV has a clear overall maximum in the summer months.

Figure 5.4 shows weekly generation patterns of the data employed for the

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Time Slot in Week 4, (Jan.)

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Time Slot in Week 28, (July)

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Time Slot in Week 37, (Sept.)

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Figure 5.4: Exemplary weekly generation profiles for wind (left) and solar (right) gener-ation for winter, summer and intermediate weeks.

analysis for winter, summer and intermediate periods. PV has as a clear diurnal cycle which makes it more predictable (on a large scale) than wind power gen-eration, which in turn has no such clear cycles. The example of week 4 at the top of Figure 5.4 indicates that there can be periods in which wind and PV both do not generate sufficient energy for the projected energy needs of EVs for several consecutive days. Other examples in turn show that wind can be to some extent complementary to PV generation as in the case of week 37, where the generation peak occurs during a dip in the PV generation output. In order to still guar-antee that the mobility requirements of the EV-owners are met, an additional controllable generator with minimum run time requirements is further assumed to cover this mandatory demand.

The renewable generation data presented above is rescaled in this analysis in order to map a hypothetical plant which is producing exactly as much electric-ity over the whole year as required by the respective EV fleet. This way the volatile characteristics of intermittent generation are represented by empirical

Table 5.2: Benchmark Model Parameters

Parameter Description Symbol Unit/Domain Charge amount of vehicle v in time slot[t−1, t] ϕ^b (kWh) Conventional generation in time slot[t−1, t] g_t,C (kWh) Maximum generation in time slot[t−1, t] gt,C (kWh) Renewable generation in time slot[t−1, t] gt,I (kWh)

Number of time slots T 15 min.

Number of vehicles V #

Consumption of vehicle v in time slot[t−1, t] dt,v (kWh) Battery state of vehicle v at time t SOCt,v (kWh) Usable capacity of the storage device C (kWh) Maximum charge amount in one time slot ϕ (kWh)

Charging efficiency η^c (%)

Charging availability vehicle v at time t zt,v {0,1}

b please observe that in contrast to sections 4.2 and 5.3 ϕ is not only in the range [0..1] but characterizes an energy amount in kWh.

inputs and can be balanced by the coordinated demand of flexible EVs. The formal scheduling model that is important for the EV-fleet of an aggregator (cf.

section 3.2) is therefore described in the next section.