In the process of the operation and construction of the smart grid, the development of science and technology and the improvement of social productive forces have put forward higher requirements for the development of the power system. In this process, the scale and form of the power system have also changed to a certain extent, and power security has also become the most concerned issue. In the information society, through the application of the Internet of things and big data technology in power security management and control. It can simplify the operation process of the staff and reduce the occurrence of accidents. Distributed smart grid is a new technology proposed for power networks with elastic nodes, which can realize dynamic electricity price demand response without large-scale transformation of infrastructure. In order to analyze the system stability of DSG, six representative machine learning classification models are applied to analyze the stability data of 10000 samples of 4-node system. Combined with the requirements of power system security, stability and economy, the effect of each classification model on the prediction of DSG system stability is tested.