The Convolutional Neural Network (CNN) methodologies have been a fundamental deep learning solution to smart grid applications. It is essential to investigate and evaluate the progress of this method in the smart grid. Consequently, a comprehensive investigation with the aid of PRISMA had been conducted. The PRISMA standard queries including the CNNs and its abbreviation forms of ConvNet or CNN reveal a significant increase in the popularity of this deep learning method in smart grid applications. This research identifies 2200 pieces of literature in the field. After considering the PRISMA guideline the most relevant and fundamental application had been reduced to 46 documents where the single and hybrid methods had been identified. The investigation showed that hybrid methods delivered a better performance with higher accuracy. It is expected that more hybrid methods will have emerged in the smart grid application.