*4.1. ULTRA Mode*

In this mode, the charging power (*PU*,*EVU* ) is set to be the vehicle nominal power (*Pnom*,*EVU* ), whenever possible. If the microgrid reaches its contracted demand at the same *tm*, the power is proportionally reduced to each vehicle in this mode, using the index *f <sup>U</sup>*(*tm*) < 1 determined by:

$$\overline{f}\_{lI}(t\_m) = \frac{P\_{lim} - P\_{net}(t\_m)}{\sum P\_{nom, EV\_{lI}}(t\_m)}\tag{18}$$

wherein *Plim* is the demand contracted by the microgrid and *Pnom*,*EVU* is the nominal power charging of each vehicle in this mode. If the microgrid has already reached the contracted demand before the charging power calculation, *PU* is set to zero, and all vehicles in this mode are idle. Briefly, the charging power of ULTRA mode is proposed to be:

$$P\_{L,EV\_{l\bar{l}}} = \begin{cases} P\_{nom\prime} & \text{if } P\_{net}(t\_m) + P\_{l\bar{l}}(t\_m) \leqslant P\_{lim} \\ \overline{P}\_{l\bar{l}}(t\_m), & \text{otherwise,} \end{cases} \tag{19}$$

wherein *PU*(*tm*) = *f <sup>U</sup>*(*tm*)*Pnom*.

## *4.2. FAST Mode*

This mode follows the same strategy applied in ULTRA mode, providing the maximum charging power, taking into account that the previous mode is already achieved. Whenever a microgrid power limitation occurs, FAST mode power dispatch is limited by the index *f <sup>F</sup>*(*tm*) < 1, given by:

$$\overline{f}\_F(t\_m) = \frac{P\_{lim} - P\_{net}(t\_m) - P\_{lI}(t\_m)}{\sum P\_{nom, EV\_F}(t\_m)},\tag{20}$$

wherein *PU*(*tm*) indicates the sum of all vehicles in ULTRA mode. Like the previous mode, the limitation strategy is applied to this case; if the microgrid demand has already reached its limit, then *PF* is set to zero. Thereby, the resultant charging power of the FAST mode may be written as:

$$P\_{F,EV\_F} = \begin{cases} P\_{nom\_f} & \text{if } P\_{net}(t\_m) + P\_{U}(t\_m) + P\_F(t\_m) \leqslant P\_{lim} \\ P\_F(t\_m)\_{\prime} & \text{otherwise,} \end{cases} \tag{21}$$

Herein, *PF*(*tm*) = *f <sup>F</sup>*(*tm*)*Pnom*.
