Modern power systems face significant challenges in state estimation and real-time monitoring, particularly regarding response speed and accuracy under faulty conditions or cyber-attacks. This article proposes a hybrid approach using physics-informed neural networks (PINNs) to enhance the accuracy and robustness of power system state estimation. By embedding physical laws into the neural network architecture, PINNs improve estimation accuracy for transmission grid applications under both normal and faulty conditions, while also showing potential in addressing security concerns, such as data manipulation attacks. Experimental results show that the proposed approach outperforms traditional machine learning models, achieving up to <inline-formula><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula>83% higher accuracy on unseen subsets of the training dataset and <inline-formula><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula>65% better performance on entirely new, unrelated datasets. Experiments also show that during a data manipulation attack against a critical bus in a system, the PINN can be up to <inline-formula><tex-math notation="LaTeX">$\sim$</tex-math></inline-formula>93% more accurate than an equivalent neural network.