Smart girds security is raising a lot of concerns to governments, energy industries, and consumers. Due to the vulnerability of smart grids and their critical nature, they can be a prime target for cyberattacks. False data injections in targeted buses can manipulate the power system measurements in such a way that the power flow in the system's lines are altered. If those attacks are not observed, the attacker is able to overflow some lines with minimal unobserved false data injections which might cause power outages and even system blackouts. This paper proposes a bi-level mixed integer linear programming (BMILP) optimization model for false data injection on targeted buses to cause an overflow in transmission lines of a power system. The upper level problem of the model finds the minimum false data injections in targeted buses that can bypass DC state estimation and cause an overflow in selected lines by the attacker. The lower level problem runs the optimal power flow problem taking into account the false data injections to find a new optimal solution that satisfies the optimal power flow constraints and prevent lines overflow. The paper validates the results of such an attack considering IEEE 30 bus test system with several possible cases for the attack.