We propose the joint graph attention neural network (GAT), clustering with adaptive neighbors (CAN) and probabilistic graphical model for dynamic power flow analysis and fault characteristics. In fact, computational efficiency is the main focus to enhance, whilst we ensure the performance accuracy at the accepted level. Note that Machine Learning (ML) based schemes have a requirement of sufficient labeled data during training, which is not easily satisfied in practical applications. Also, there are unknown data due to new arrived measurements or incompatible smart devices in complex smart grid systems. These problems would be resolved by our proposed GAT based framework, which models the label dependency between the network data and learns object representations such that it could achieve the semi-supervised fault diagnosis. To create the joint label dependency, we develop the graph construction from the raw acquired signals by using CAN. Next, we develop the probabilistic graphical model of Markov random field for graph representation, which supports for the GAT based framework. We then evaluate the proposed framework in the use-case application in smart grid and make a fair comparison to the existing methods.