A Cyber-Physical System (CPS) incorporates communication dynamics and software into phsical processes, providing abstractions, modeling, design, and analytical techniques for the system. Based on spatial temporal graph neural networks (STGNNs), anomaly detection technology has been presented to detect anomaly data in smart grids with good performance. However, since topological changes of power networks in smart grids often already predict the occurrence of anomalies, traditional models based on STGNNs to portray network evolution cannot be directly utilized in smart grids. Our research proposed a smart grid anomaly detection method on the grounds of STGNNs, which used evolution in the information of several attributes that affected the power network to represent the evolution of the power network, subsequently used STGNNs to obtain the time-space dependencies of nodes in several information networks, and used a cross-domain method to help the anomaly detection of the power network through anomaly information of other related networks. Laboratory findings reveal that the abnormal data detection rate of our scheme reaches 90% in the initial stage of data transmission and outperforms other comparative methods, and as time goes by, the detection rate becomes higher and higher.