As the proportion of nuclear power in the power grid continues to increase, for the safe, stable, and economical operation of the power system, nuclear power plants must participate in the peak shaving operation of the power system. Therefore, it is very important to study the impact of the power system on nuclear power plants. In this paper, a nonlinear dynamic model of a pressurized water reactor (PWR) is built on the MATLAB/Simulink simulation platform. The model includes the point kinetics reactor core model, the thermal-hydraulics model, the piping & plenum model, the steam generator module, the reactivity module, the sensor model and the turbine module, in addition to the governor module and the simulation model of the power system. Based on the established dynamic model of nuclear power plant and an island power system module, the response of the model was tested under load variations. There are often some short circuit faults in the power system. To verify the stability of the model, the impact of the single-phase-to-ground fault in the power system on the nuclear power plant is analyzed. In this paper, the nuclear power plant can maintain stable operation in the event of a transient failure in the power system.