False Data Injection (FDI) attacks are a common form of Cyber-attack targetting smart grids. Detection of stealthy FDI attacks is impossible by the current bad data detection systems. Machine learning is one of the alternative methods proposed to detect FDI attacks. This paper analyzes three various supervised learning techniques, each to be used with three different feature selection (FS) techniques. These methods are tested on the IEEE 14-bus, 57-bus, and 118-bus systems for evaluation of versatility. Accuracy of the classification is used as the main evaluation method for each detection technique. Simulation study clarify the supervised learning combined with heuristic FS methods result in an improved performance of the classification algorithms for FDI attack detection.