In recent years, power systems have encountered numerous challenges, particularly with the growing integration of renewable energy sources. Among these, wind energy has emerged as a clean and cost-effective option, but its impact on power system stability has become a critical concern. This impact largely depends on the type of induction generators used in wind turbines, which are primarily categorized into two types: fixed-speed wind turbines, which typically use squirrel cage induction generators (SCIG), and variable-speed wind turbines, which rely on doubly-fed induction generators (DFIG). A combined wind farm (CWF) leverages the advantages of both generator types. To enhance the dynamic performance of such a wind farm, the integration of compensators is essential. Among these, the Static Synchronous Compensator (STATCOM), a third-generation FACTS (Flexible AC Transmission Systems) device, has gained considerable attention for its effectiveness. In this study, a power system connected to a combined wind farm is designed, with a STATCOM installed at one of its buses. To further improve the damping of system oscillations during faults, a supplementary PID controller is incorporated into the STATCOM structure. The Particle Swarm Optimization (PSO) algorithm is employed to determine the optimal PID controller coefficients. However, as the PSO process can be computationally intensive, an Artificial Neural Network (ANN) is introduced to estimate the PID parameters in real time when system operating conditions change. Simulation results, conducted using MATLAB/Simulink software, demonstrate the effectiveness of the proposed approach, validating its potential to enhance power system stability in the presence of combined wind farms.