*5.2. Case\_2—Partially-Flexible*

In this case study, the aggregator has power over the behavior of electric vehicle owners in a more extended period. By agreement, the behavior of vehicle owners is less uncertain, and part of the energy is consumed in fewer hours. With the extended period of control over the behavior of vehicles, the aggregator can make better decisions, since periods of better market prices are available to inject energy into the grid and thus improve profit. In this case study, the scenarios of driving requirements and the availabilities of electric vehicles are in accordance with the data in Appendix A, Table A2. The driving hours are just 5 hours per day, giving the aggregator the possibility to implement more profitable decisions without significantly interfering in the routines of vehicle owners. It is worth noting that hours 10, 13, 21, and 22 are flexible hours with high day-ahead market prices. Purchase offering and sale curves are in Figures 4 and 5, respectively.

**Figure 4.** Purchase offering curves: **left**, hour 6; **right**, hour 11.

**Figure 5.** Sale offering curves: **left**, hour 12; **right**, hour 22.

Figure 4 shows that at hour 6, the aggregator is only available to buy energy below 43 €/MWh. Above this value, the offer is 0 MWh. The aggregator is available to buy 4.5 MWh for values between €34 and €43. To buy 10 MWh, the aggregator only accepts at a value of around €31. The offer values for hour 6 of Case 2 are very similar to the values for hour 6 of Case 1. The difference is in the offer of 4.5 MWh, which in Case 1 is 4.9 MWh. At hour 11, the aggregator is only available to buy energy below 56 €/MWh. Above this value, the offer is 0 MWh. The aggregator is available to buy 3.6 MWh for values between €51 and €56. To buy 7.7 MWh and 9.8 MWh, the aggregator only accepts at a value of around €48 and €44, respectively. Compared to hour 11 in Case 1, the aggregator is more demanding, since the aggregator only accepts to trade below €56, while in Case 1 the trade starts from €64. Figure 5 shows that at hour 12, the aggregator is only available to sell energy above 61 €/MWh. Below this value, the offer is 0 MWh. The aggregator is available to sell 5.5 MWh for values between €61 and €66. To sell 8.8 MWh, the aggregator only accepts at a value of around €69. Compared to hour 12 in Case 1, the aggregator starts to trade from €61, while, in Case 1, the aggregator starts to trade from €69. However, for Case 2, starting at €69, the aggregator only negotiates an amount of energy equal to 8.8 MWh. A convenient consent of the owners of vehicles allows the aggregator, by implementing the strategy that yields a higher profit, to consider rewarding the owners in order to encourage further flexibility.
