*3.5. Power Variation Limitation*

The cost function of V2G mode also includes the charging power variation limitation, in order to avoid sudden changes in the control law. The limitation normalized by the maximum charger power is given by:

$$E\_{0, \Delta PE} = \beta\_0 \left( \frac{P\_{EV\_{2G}}^\*(t\_m)}{P\_{nom}} \right)^2 \tag{15}$$

Herein, the gain *β*<sup>0</sup> establishes the maximum variation, and *Pnom* is the maximum charging power.
