False data injection attacks (FDIAs) targeting AC state estimation pose significant challenges, especially when only power measurements are available, and voltage measurements are absent. Current machine learning-based approaches struggle to effectively control state estimation errors and are confined to the data distribution of training sets. To address these limitations, we propose the physics-informed extrapolative adversarial variational autoencoder (PI-ExAVAE) for generating controllable and stealthy false data injections. By incorporating physically consistent priors derived from the AC power flow equations, which enforce both the physical laws of power systems and the stealth requirements to evade bad data detection mechanisms, the model learns to generate attack vectors that are physically plausible and stealthy while inducing significant and controllable deviations in state estimation. Experimental results on IEEE-14 and IEEE-118 systems show that the model achieves a 90% success rate in bypassing detection tests for most attack configurations and outperforms methods like SAGAN by generating smoother, more realistic deviations. Furthermore, the use of physical priors enables the model to extrapolate beyond the training data distribution, effectively targeting unseen operational scenarios. This highlights the importance of integrating physics knowledge into data-driven approaches to enhance adaptability and robustness against evolving detection mechanisms.