As the number of distributed power supplies increases on the user side, smart grids are becoming larger and more complex. These changes bring new security challenges, especially with the widespread adoption of data-driven control methods. This paper introduces a novel black-box false data injection attack (FDIA) method that exploits the measurement modules of distributed power supplies within smart grids, highlighting its effectiveness in bypassing conventional security measures. Unlike traditional methods that focus on data manipulation within communication networks, this approach directly injects false data at the point of measurement, using a generative adversarial network (GAN) to generate stealthy attack vectors. This method requires no detailed knowledge of the target system, making it practical for real-world attacks. The attack’s impact on power system stability is demonstrated through experiments, highlighting the significant cybersecurity risks introduced by data-driven algorithms in smart grids.