Virtual Inertia Deficiency and Control Optimization in High Renewable Penetration Power Systems

High penetration of wind and photovoltaic generation is changing the frequency dynamic characteristics of modern power systems. When synchronous generators are replaced by inverter based resources, the equivalent system inertia decreases. After disturbances, frequency changes more rapidly, RoCoF increases, frequency nadir becomes lower, and recovery time becomes longer. This study focuses on virtual inertia deficiency and control optimization in high renewable penetration power systems. The IEEE 39 bus standard system is used to construct 0 percent, 30 percent, 50 percent, and 70 percent renewable penetration scenarios. MATPOWER, Python, and MATLAB/Simulink are combined for power flow calculation, controller parameter optimization, and time domain simulation. Three control strategies are compared, including no virtual inertia control, fixed parameter VSG control, and MPC optimized VSG control. The results show that when renewable penetration increases from 0 percent to 70 percent, equivalent inertia decreases from 4.85 s to 1.76 s, the maximum RoCoF increases from 0.31 Hz/s to 0.91 Hz/s, and the frequency nadir drops from 49.72 Hz to 49.43 Hz. MPC optimized control improves the frequency nadir to 49.61 Hz in the 70 percent renewable scenario and reduces storage power stress. These results indicate that virtual inertia allocation should be jointly optimized with renewable penetration, critical buses, and storage constraints. The framework provides a reproducible technical path for frequency security control in high renewable power systems.