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• The vulnerable branches which affect the transient voltage security are identified. • Image-form samples combine grid structure and power flow information visually. • Knowledge visualization makes CNN-based transient voltage stability assessment model more understandable and reliable. • A comprehensive vulnerability indicator integrates the knowledge in CNN, grid topology and branch state. • The proposed method is demonstrated on a real-life provincial grid with renewable energy integration. Because of the increasing proportion of grid-connected converters, the transient voltage problem has increased the risk of the secure and stable operation of power systems. As the extension of transient voltage stability assessment (TVSA), transient voltage vulnerability assessment is the key technique to detect the crucial elements which can cause the insecurity risk of power system transient voltage. Although deep learning-based TVSA models have demonstrated the high accuracy, it is more important to display the knowledge learnt by the models and utilize it to recognize the weakness of transient voltage. This paper presents a transient voltage vulnerability assessment method by knowledge visualization of convolutional neural network (CNN). First, the image-form sample construction method is proposed to characterize the power system operating condition, which prepares for training CNN-based TVSA model. Then, the knowledge in TVSA model is visualized based on Gradient-weighted Class Activation Mapping (Grad-CAM) and Activation Maximization (AM) algorithms, which is analyzed from the perspective of power system stability. Finally, a comprehensive vulnerability indicator is proposed for identify the weakness of transient voltage, which combines the knowledge inside the TVSA model and the indicators with clear physical meaning. Simulation results of the New England 39-bus test system and the real Shandong provincial power grid in China demonstrate that the visualization makes the model more reliable and the proposed method can accurately identify the vulnerable branches. [ABSTRACT FROM AUTHOR]