To build a large-scale renewable energy integrated system in the power system, power fluctuation mitigation and damping measures must be implemented during grid connection. PID damping controllers and traditional intelligent controllers with pole configuration are usually used for improving damping. Integration of large wind power plants and photovoltaic power plants into the power system faces transient power oscillation and fault ride-through (FRT) capability under fault conditions. Therefore, this paper proposes a static synchronous compensator (STATCOM) damper based on a recurrent Petri fuzzy probabilistic neural network (RPFPNN) to improve the transient stability of the power system when large offshore wind farms and photovoltaic power plants are integrated into the power system, suppress power fluctuation, and increase FRT capability. To verify the effectiveness of the proposed control scheme, a three-phase short circuit fault at the connected busbar is modeled in the time domain as part of a nonlinear model. From the comparison of simulation results, the proposed control scheme can effectively slow down the transient fluctuation of power supply to the grid-connected point when the grid is faulty, reach steady-state stability within 1–1.5 s, and reduce overshoot by more than 50%. It can also provide system voltage support at an 80% voltage drop and assist in stabilizing the system voltage to increase FRT capability. It also improves stability more than PID controllers when disturbances are present. Therefore, it maximizes the stability and safety of the power grid system.