The distinctive fault characteristics of battery energy storage stations (BESSs) significantly affect the reliability of conventional protection methods for transmission lines. In this paper, the three-dimensional (3D) data scattergrams are constructed using current data from both sides of the transmission line and their sum. Following a comprehensive analysis of the varying characteristics of 3D data scattergrams under different conditions, a 3D data scattergram image classification based protection method is developed. The depth-wise separable convolution is used to ensure a lightweight convolutional neural network (CNN) structure without compromising performance. In addition, a Bayesian hyperparameter optimization algorithm is used to achieve a hyperparametric search to simplify the training process. Compared with artificial neural networks and CNNs, the depth-wise separable convolution based CNN (DPCNN) achieves a higher recognition accuracy. The 3D data scattergram image classification based protection method using DPCNN can accurately separate internal faults from other disturbances and identify fault phases under different operating states and fault conditions. The proposed protection method also shows first-class tolerability against current transformer (CT) saturation and CT measurement errors.