Real time or faster than real time simulation can enable system operators to foresee the effect of crucial contingencies on the power system dynamics and take timely actions to prevent system instability. Parareal in time method uses concurrent computations on different segments of the time domain of interest to speed up the dynamic simulations. This paper describes the application of an adaptive nonlinear model reduction method in improving computational speed of the Parareal solver. The proposed method adaptively switches between a hybrid system with selective linearization and a completely linear system based on the size of a disturbance. The functions in the hybrid system are linearized based on the electrical distance between specific generators and the area where disturbances originated. The proposed method is tested on the 327-machine 2383-bus Polish system.