Parameters definition

This section defines the parameters needed for the description of the model.

3.3.1.1 Average distance driven per number of cars: group

The initial idea is to split the vehicles into 10 groups with different travelled distance per day. In figure 3.4, the owners of a car living in Bornholm are divided into 30 groups depending on the driven km/day. In this model the 30 groups are clustered into 10 groups, as shown in Figure 3.5. In Figure 3.4, from 0 to 10 km there are two groups, 0-5 km and 5-10 km, in the new configuration the two groups are summed up into one (G1), as in Figure 3.5. Same procedure is applied to the following groups.

Figure 3.5: Daily average driven distance per share of cars in Bornholm clustered into 10 groups.

Clustering the 30 groups into 10 groups is an important simplification when the considered fleet of EVs is in the hundreds. If 30 groups are considered, few EVs per group would be present and it would be difficult to observe differences between them. On the contrary, if the EVs fleet is in the thousands, the model can be built with 30 groups to observe more variety between the groups. With 30 groups the procedure would be the same described below for the 10 groups, but with different steps of km.

The 10 groups are characterized as follows:

• Groups 1-5: each group contains the cars driven in a certain range of kilometres with steps of 10 km:

G1: driven distance x: 0 < x ≤ 10 km;

G2: driven distance x: 10 < x ≤ 20 km;

G3: driven distance x: 20 < x ≤ 30 km;

G4: driven distance x: 30 < x ≤ 40 km;

G5: driven distance x: 40 < x ≤ 50 km;

• Groups 6-10: each group contains the cars driven in a certain range of kilometres with steps of 20 km:

G6: driven distance x: 50 < x ≤ 70 km;

G7: driven distance x: 70 < x ≤ 90 km;

G8: driven distance x: 90 < x ≤ 110 km;

G9: driven distance x: 110 < x ≤ 130 km;

G10: driven distance x: 130 < x ≤ 150 km;

The difference between the steps, 10 and 20 km, is reasonable considering that 80% of the vehicles drive less than 50 km/day, as observed in Figure 3.4.

The group number of a vehicle does never change during the simulation and the share of cars per each group can be seen in Figure 3.5.

3.3.1.2 Accumulated kilometres: class

The classes are defined from 1 to 10 and they represent the kilometres accumulated by the vehicle at the end of the day. The class number of a vehicle can be equal or higher than the group number. It can never be lower, since the accumulated km by a vehicle after one or more days can never be lower than the driven kilometres in a day.

The classes are characterized as in Table 3.3.

Table 3.3: Class characterization.

The SOC is used in this model to determine the amount of hours that the EVs need to charge, also called charge or charging time. To determine the SOC of the EV at the plug-in time, the maximum kilometres of each class is considered. This may seem an overestimation of the SOC, since not all the EVs of a group drive the maximum number of km of their group. Nevertheless, the SOC depends on the driven km/day, but also on driving behaviour, outside temperature etc., therefore the approximation includes the worst case scenario. The SOC is defined as the remaining capacity of the battery and it can be evaluated in per unit (p.u.), as ratio between the capacity of the battery at time t (Q(t)) and the nominal capacity (Qn), see equation 3.1:

SOC(t) = Q(t)

Qn (3.1)

Q(t) is influenced by the operating conditions, such as load current and temperature. Qn

is given by the manufacturer and it represents the maximum amount of charge that can be stored in the battery (40 kWh for the considered Nissan LEAF). Q(t) is determined considering the average range distance equal to 200 km (dmax). In accordance with the average energy consumption of 0.214 kWh/km estimated for a Nissan LEAF 30 kWh in [55], the ratio between 40 kWh and 200 km is 0.2 kWh/km. Therefore the average range distance is chosen of 200 km, even though lower than the 240 km (150 miles) from EPA shown in Table 2.3.

The difference between Qn and Q(t) is the used capacity at time t (Qu(t)). In this analysis SOC and used capacity are calculated only once per day, when the car has travelled its expected distance (defined by the group number) and it is not driven anymore. For this reason time t is from now named day d. The used capacity at day d (Qu(d)) for the EVs of each group is evaluated with equation 3.2.

The EVs of each group are driven and if they are not charged they accumulate kilometres.

If a car did not charge on day ’d − 1’, the used capacity on day d (Qu(d)) is higher:

Qu(d) = kmdriven(d) ∗ 0.2kW h

km + Qu(d − 1) (3.2)

km_driven(d) is the distance driven on day d, 0.2 is the consumed energy per km. Knowing the used capacity on day d and the battery capacity, the SOC is determined with equation 3.1. The group characteristics are shown in Table 3.4.

Table 3.4: Groups of EVs characterized by driven km/day and SOC at the end of the drive,

A confidential Japanese statistics conducted by Nissan on 10000 Nissan LEAF 24 kWh derived the probability of charging at home of the commuters, based on the SOC of the daily driven distance.

The human behaviour influences the charging pattern of the EVs. For instance, equal driven kilometres but different driving behaviours cause different SOC at the end of the day. Another factor is the range anxiety, which highly influences the decision of the owners to charge the vehicle. Considering an individual user the range anxiety is difficult to predict, because the users tend to charge their vehicles even when it is not necessary [65].

Differently, considering large groups of EVs, as done by Nissan, it is possible to derive a relation between the plug-in rate and the SOC.

The Japanese research analyzed the level of SOC of the EVs battery when the consumers use to recharge their vehicle at home. It showed that the plug-in rate increases with lower SOC at the end of the day, and at the same SOC, the plug-in rate increases with longer trip distance per day.

Figure 3.6 illustrates a re-representation of the Japanese analysis. As in section 3.3.1.1, in Figure 3.6 ten groups with the same subdivision of km/day are represented: six different lines for the first six groups and a single red line for the last four groups. The last four groups have the same behaviour, because the plug-in rate in the Japanese analysis was very close to 1, therefore the author simplified the model considering the value constantly 1, meaning that the EVs of these groups charge every day. Furthermore, the line "plug-in limit" represents the relation between the accumulated kilometres and SOC.

Starting from the right y-axis, knowing the driven km/day it is possible to determine the SOC of the EVs at the plug-in time with the "plug-in limit" line. Afterwards, for each group of EVs, using the SOC and the left y-axis, the plug-in rate of cars is determined following the respective line of driven km/day of the group.

As aforementioned, G1-G5 have steps of 10 km and G6-G10 have steps of 20 km. Another explanation for this hypothesis is shown in Figure 3.6: lower is the SOC at the end of the day, higher is the plug-in rate. This means that, when driving 90 km or 130 km, the human decision of charging or not is the same: due to the range anxiety, the owner would

charge in both cases. With the Nissan LEAF 24 kWh considered in the Japanese study, consumers that drive above 70 km/day charge their vehicle every day, owing to the range anxiety factor. In this thesis the Nissan LEAF 40 kWh is considered. Nevertheless, due to lack of data about EVs with similar capacities, as conservative estimate it is assumed that the EVs charge when they are driven more than 70 km/day (>70). With 70 km the SOC is 0.65 p.u., as shown in Figure 3.6. EVs of G1-G6 drive less than 70 km/day, but they are forced to charge when they accumulate more than 70 km. Their plug-in rate curves are variable from SOC = 0.65 p.u. to SOC = 1 p.u., when SOC is lower than 0.65 p.u.

all the EVs of the groups are charged. EVs of G7-G10 are instead charged every evening, therefore the plug-in rate is constantly 1.

Figure 3.6: Plug-in rate - SOC relation for the 10 defined groups.

3.3.2 Model description