Model description .1 General model overview

The model generates individual charging patterns for the EVs, where the sum of the charging patterns fit the analyzed distribution of Figures 3.5 and 3.6. The input of the model are the numbers of EVs and days that want to be simulated. The EVs are then divided into 10 groups, as shown in Figure 3.5. The groups characterize the EVs with their average driven km per day (group). Using Figure 3.6 the plug-in rate at home of the EVs is determined: a part of the EVs charge and the rest does not charge. The share of charging EVs differs depending on the travelled km per day: higher is the group number, higher is the probability of charging. The no charging share accumulates kilometres. To create more variance between the no charging EVs, the no charging share is split into 2 or 3 subgroups depending on their group number. It is important to remember that the vehicles are always part of the same group (km/day), but they change class (accumulated

km end-day). The model takes track of each individual EV and its accumulated km, so the output of the model is characterized by one number and one letter for every considered day: the number indicates how many km are accumulated, the letter says if the EV has to charge ("Y" as yes) or not ("N" as no). Knowing these two information, the charging pattern of each EV can be designed, as it will be detailed in Section 3.3.3.

3.3.2.2 Description of the process

The model is described with a flow chart in Figure 3.7.

The input of the model is the number of EVs and the number of days that want to be simulated. Each EV is characterized by its group number. On day d, the group number of each EV is checked: if the group number is larger than 6 the EV charges, if the group number is lower or equal than 6, the class number is also checked. As for the group number, if the class is larger than 6 the EV charges, if the class is lower or equal than 6 the EV goes on with the loop. At the beginning of the simulation all the EVs are considered fully charged (SOC = 1), meaning that on day 1 the class number matches the group number of the EV.

An EV of G1 can have classes 1-6, but it never has classes 7-10, since at 70 km accumulated it is forced to charge. An EV of G2 cannot be part of class 1, because it never accumulates less than 10 km, since it never drives less than 10 km/day. For the same reason of an EV of G1, the EV of G2 cannot be part of classes 7-10. Similar approach is applied to the other groups.

All the EVs that do not have group or class number higher than 6 are clustered into categories (f): all EVs with same group and class on day d. EVs part of the same category f enter in "loop b" of Figure 3.7. Using the curves in Figure 3.6, knowing the group and the class number the rate of charging EVs is determined as the "share of charged EVs"

(%Y ). The rest EVs do not charge (%N). The share %Y charges, therefore the SOC at the beginning of day ’d+1’ is 1 and the km accumulated are reset to 0. The share %N does not charge, therefore the accumulated km by those EVs increases with the steps shown in Table 3.5 to create more variety between the groups and to avoid over-estimation of the driven km. To better understand how the accumulated steps are increased, an example with EVs from G1 is analysed. The EVs of G1 are driven 0-10 km every day. The first day, at the plug-in time the plug-in rate is determined by line "0 < x ≤ 10 km per day"

in Figure 3.6: the plug-in rate indicates the share of charging EVs (%Y ), the rest is not charging (%N). The %N share starts the second day with a lower SOC than the %Y share.

EVs of G1 daily drive from 0 to 10 km, but on day 1 the %Y share charges with charging time that corresponds to cars driven for 10 km. On day 2 EVs of %N share are driven other 0-10 km. If they are driven 0-5 km, then the accumulated km is lower than 10 km;

if they are driven 5-10 km, then the accumulated km is between 10 and 20 km. In this situation, charging all the EVs as they would have driven 10 or 20 km is excessive, therefore the EVs are split into 2 groups, 50% are assumed as driven 0-5 km and 50% 5-10 km. The first group becomes part of class 1, the second becomes part of class 2. EVs in class 1 accumulate maximum 10 km, whereas EVs in class 2 accumulate maximum 20 km. The following days the procedure is the same. If not charged, the EVs continue to accumulate

Figure 3.7: Flow chart of the plug-in pattern model.

km and they become part of higher classes, doing steps as shown in Table 3.5. To sum up, the EVs of G1 follow the curve in Figure 3.6, doing steps of 5 or 10 km, being part always of the same group, but changing class which represents the km accumulated.

The same procedure is applied to groups G2-G6: the steps and the percentage of the EVs of each group are shown in Table 3.5.

EVs of groups G7-G10 do never enter in loop b since their group number is larger than 6.

Table 3.5: Steps of accumulated km per day d by EVs that do not charge on day d.

Group Steps accumulated km per day Group Steps accumulated km per day G1 - 50 % EVs: 0-5 km step When all the categories f are entered in loop b, day d is completed and the simulation loop starts again with d = d + 1.

3.3.2.3 Model output

The output of the model is characterized by a number and a letter for each EV and day:

• the number represents the class of the EV at the end of the day, saying the number of accumulated km;

• the letter says if the EV is charging or not: "Y" if charging, "N" if not.

Reconsidering the example in the previous section, at the end of day 1, EVs of G1 have the same class number, because there are no accumulated km from previous days (at the beginning of the simulation all EVs have SOC = 1), therefore they are all part of the same category f. During loop b the EVs of this category are split in 2 shares: %Y are the EVs charging the first evening (1Y), %N are the EVs not charging the first evening, with accumulated km 0 < x ≤ 10 (1N). See Figure 3.8 for graphical representation. At the end of day 2, the two shares become:

• 1Y is split into 2 other shares: 1Y, 1N. As for day 1, the share of EVs 1Y is determined using Figure 3.6, the rest is not charged 1N.

• 1N is split into 3 shares: EVs that charge (1Y); EVs that do not charge and have accumulated maximum 10 km during the 2 days (1N); EVs that do not charge and have accumulated from 10 to 20 km (2N).

At the end of day 2 there are 5 shares of EVs of G1, but some of them have the same characteristics (number and letter). Thus the EVs with same characteristics are summed up into three shares: 1Y, 1N, 2N. The procedure is the same in the following days, but with creation of more shares, since the accumulated km increase when the EVs are not charged.

Figure 3.8: Example of share subdivision of EVs.

When an EV is charged, the number of km accumulated is reset and the following day the count starts again from zero for the individual EV. Therefore, the EV is grouped with the EVs with the same class characteristics to evaluate the plug-in rate using the curves in Figure 3.6.

The same procedure is applied to groups G2-G5 using the kilometres distribution of Table 3.5 to determine the new class of the EVs. EVs of groups 2, 3, 4 and 5, if not charged on day 1, they are split into two shares: EVs of G2 do steps of 10-15 or 15-20 km, becoming part of classes 3 and 4; EVs of G3 do steps of 20-25 or 25-30 km, becoming part of classes 5 and 6; EVs of G4 do steps of 30-35 or 35-40 km, becoming part of classes 5 and 7; EVs of G5 do steps of 40-45 or 45-50 km, becoming part of classes 7 and 8. G6 is slightly different from the previous ones, due to the fact that the EVs of this group can drive from 50 to 70 km per day (gap of 20 km). When the EVs are not charged, they are divided into 3 classes: 8, 9, 10, each one with 33% EVs, see Table 3.5. EVs of G6 cannot accumulate kilometres for more than 2 days in a row, since the classes 8-10 represent an amount of accumulated kilometres larger than 70 km, meaning that the second day they need to charge anyway. The difference between these three classes is given by the charging time as it will be explained in Section 3.3.3.

Finally, EVs of G7-G10 are driven more than 70 km per day, concluding that these EVs charge every evening. The difference between the four groups is given as well by the charging time.