The electric power grid has evolved immensely with time and the modern power grid is dependent on communication networks for efficient transmission and distribution. Since communication networks are vulnerable to various kinds of cyber attacks it is important to detect them and prevent an important machinery like the power grid to get affected from cyber attacks. False data injection attacks (FDIA) are one of the most common attack strategies where an attacker tries to trick the underlying control system of the grid, by injecting false data in sensor measurements to cause disruptions. Our work has focused towards Least Effort attacks of two types i.e., Random and Target Attacks. Further, we propose a data augmented deep learning based solution to detect such attacks in real time. We aim at generating realistic attack simulations on standard IEEE 14 architectures and train neural networks to detect such attacks.