Introduction In modern power systems, maintaining voltage stability, optimizing power transfer, and enhancing grid reliability are critical challenges. Thyristor Controlled Series Capacitors (TCSC) have emerged as an effective FACTS (Flexible AC Transmission System) controller that dynamically regulates transmission line reactance . However, for optimal implementation, precise mathematical modeling and simulation techniques are essential. Engineers use steady-state analysis, dynamic simulations, and AI-driven models to predict TCSC performance under real-world conditions . In this article, we will explore: ✅ The importance of TCSC modeling in power systems ✅ Mathematical representations and equations used for TCSC analysis ✅ Different modeling techniques: steady-state, dynamic, and real-time AI-driven models ✅ How simulations help in power system stability and fault recovery Keywords: TCSC Simulation Models for Power Systems, Voltage Stability with FACTS Controllers,...