## 1 Introduction  
Demands from the environment and the economy have driven power networks to become much more heavily laden and inadequately dampened. With the rise in electric power consumption and the need to regulate the system quickly and adaptably in a competitive context, current power systems can now survive challenging conditions. However, unanticipated disturbances cause poorly damped oscillations that eventually lead to instability, which have become more common in electrical power networks all over the world. A power system must be able to sustain operational stability under typical operating conditions and return to a suitable equilibrium following disturbances. Proper system modelling and damping controller devices are required to reduce oscillations and improve and maintain the angle stability of a power system. Coordination control, flexible alternating current transmission system (FACTS), and PSS are the three categories of dampening techniques that have been used. FACTS may provide damping for inter-area modes and for local-area oscillation modes [1; 2; 3; 4; 5]. High-power electronic technology-based superior control in high-voltage power transmission systems is used to reinforce power systems via FACTS technology, which has been deployed in a significant number of real power systems. The following describes the active power delivered to the load via the transmission line:  
\[P_{ab}=\frac{V_{a}V_{b}}{x_{t}}\sin\theta \tag{1}\]  
where the \(\theta\) is the phase angle between a transmission line's sending \(V_{a}\) and receiving \(V_{b}\) end voltages. Through the adjustment of line parameters, including line voltage, phase angle, and line impedance \(x_{t}\), a FACTS device controller can manage the flow of electricity down a transmission line. Thyristor-based and convertor-based FACTS controllers can be distinguished by their base. The three main categories of thyristor-based controllers are static var compensators (SVCs), which regulate line voltage magnitude; thyristor-controlled series compensators (TCSCs), which regulate line impedance to regulate power flow; and thyristor-controlled phase shifters (TCPSs), which regulate the line voltage phase angle to regulate power flow. Two different types of converter-based FACTS controllers exist, namely, the voltage source converter (VSC), which is built on synchronous voltage sources that act as an ideal machine with no rotation and inertia, and the current source converter. Both devices generate and regulate reactive power flow independently of line voltages and currents. The static synchronous compensator (STATCOM), static synchronous series compensator (SSSC), and unified power flow controller (UPFC) are the three primary types of VSC-based FACTS controllers [2]. Using a FACTS has advantages such as power flow control, increased transmission and loading capacity, improved stability of the power system, secure tie line connections, voltage control and flicker mitigation, reactive power compensation, reduced reactive power flows, improved power quality and power conditioning, and flexibility in connecting new renewable and distributed generation [6]. The fundamental TCSC module, which consists of a series of fixed capacitor and a thyristor-controlled reactor (TCR), is a capacitive reactance controller in the power transmission system that ensures that reactive power is exchanged continuously and effectively to control the parameters of power lines. The TCSC uses an open-loop control system to adjust its series reactance and control the flow of power. By varying its reactance, the TCSC controls the line current through a closed loop. When functioning in an open or a closed loop, the TCSC provides power flow control or line current control by varying its reactance. By quickly changing the reactance of a transmission line, TCSC increases the system's capacity for power transfer, dampening, mitigation of sub-synchronous resonance, and voltage stability [2].