We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and accuracy and also implement several other recently proposed ideas. We successfully apply these PINNs to study the transient dynamics of synchronous generators. We also make progress towards applying PINNs for inverter models. Such enhanced PINNs can allow us to accelerate high-fidelity simulations needed to ensure a stable and reliable renewables-rich grid of the future.