Electricity grids worldwide are experiencing increased peak demands and decreasing simultaneity due to higher shares of Renewable Energy Sources (RES). It is expected that many grids will soon reach their limits. One solution to mitigate these issues is exploiting flexibility in e.g. electric vehicles. In this work, a shrinking horizon model predictive controller is constructed to optimally charge and discharge EVs with respect to the day ahead electricity price or grid carbon intensity. The model takes into account that users with a dual rate electricity plan only want to charge during their off-peak hours. A feature to implement a household PV setup in the optimization is included. The possible consequences in terms of associated carbon emissions, utility costs and user costs are analysed using a simulation based on data from 4279 charging sessions that took place between June 23, 2021 and June 23, 2022. The sessions are split in 2855 weekday sessions (duration between 4 and 24 hours) and 1424 weekend sessions (duration between 4 and 60 hours). It is found that using current circumstances, minimizing the carbon emissions using bidirectional charging results in a higher price (5.5 %) for the utility than using the current state of the art, unidirectional charging minimizing the wholesale electricity cost. Bidirectional charging minimizing the wholesale electricity cost results in higher emissions compared to unidirectional charging (2.8 %), and even compared to uncontrolled charging (0.9 – 3.6 %). The reason for this seems to be a negative correlation between carbon intensity and wholesale price during the times that vehicles are typically connected although this needs further investigation to be confirmed.