A smart integration of electric vehicles (EVs) in the future energy system will be crucial in decarbonizing the energy sector. Bidirectional EVs can provide flexibility for the system and generate revenues for the user through multiple use cases. We model both exclusive photovoltaic (PV) self-consumption optimization and the combined usage of PV self-consumption optimization and arbitrage trading for a household with an unmanaged, smart, and bidirectional charging EV in a linear (LP) and mixed-integer linear programming (MILP). Since power flows in a typical household are low, varying non-linear charging and discharging efficiencies of the bidirectional EV in the MILP result in more realistic revenues that are 30% lower than in the LP with fixed efficiencies. For a typical German household using a bidirectional EV for optimizing PV self-consumption, these revenues are about 310 €/a, mostly generated during the summer. Arbitrage trading well complements this vehicle-to-home use case in the winter months, resulting in revenues up to 530 €/a. These significant revenue potentials can lead to more profitable and interactive EVs incentivizing users to change from internal combustion vehicles to electric mobility.