## 1 Introduction
### Literature Review  
The significance of a power system lies in its essential role of delivering secure and cost-efficient energy to consumers. To accomplish this goal, meticulous planning and the efficient management of the power system are imperative. Of particular importance is the precise control of power transmission lines, as it has a direct impact on the dependability and economic performance of the entire power grid. This article explores key facets of optimal power control, with a specific emphasis on mitigating low-frequency electromechanical oscillations that have the potential to jeopardize the stability and functionality of the power system [2]. Low-frequency electromechanical oscillations, characterized by local (0.7-2.0 Hz) and interarea (0.1-0.8 Hz) modes, pose a significant risk to the stability of power systems. It is imperative to effectively suppress these oscillations to ensure the safe operation of the grid. Groundbreaking research conducted by [PERSON] and [PERSON] in 1969 [3] initiated inquiries into the synchronization and damping of torques in power systems with weak damping characteristics. Their work underscored the pivotal role of Automatic Voltage Regulators (AVRs) that exhibit fast response times, low time constants, and high gains in augmenting the stability boundaries of power systems during disruptive events. While AVRs with swift response times prove effective under normal circumstances, they exhibit limitations under high-load conditions, particularly in weak transmission systems. To address these constraints and mitigate their detrimental effects on power system stability, power system stabilizers (PSSs) are integrated into the excitation systems of synchronous machines. PSSs are engineered to introduce electric torque that is synchronized with changes in the rotor's angular velocity, thereby supplying damping torque [4]. Properly tuned PSSs have demonstrated remarkable efficacy, especially in managing local oscillatory patterns [4]. However, there are instances where PSSs may encounter challenges in damping interarea oscillations [5]. To confront the issue of interarea oscillations, FACTS emerges as a promising alternative. FACTS not only enhances the overall performance of power systems but also possesses the ability to dampen interarea oscillations when coupled with a Power Oscillation Damping (POD) controller [6]. This amalgamation offers a comprehensive solution to the intricate problem of power system stability, ensuring effective control of interarea oscillations. Recently, many scholars have conducted research on LFO damping. In [7], the authors investigated the design of damping and internal controllers for UPFCs concerning LFO damping. In [8], the enhancement of a power system's dynamic stability was discussed, utilizing a STATCOM and an FLC-based stabilizer. Researchers examined the coordinated design of a PSO-based multi-machine power system stabilizer and TCSC damping controller in [2; 9]. The authors of [10] explored the utilization of a unified power flow controller to manage power flow and increase bus voltage in a power transmission system. In [3; 11], the authors scrutinized the impact of UPFC settings on power flow within a power system. The authors of [12] described the utilization of a unified power flow controller to augment the capacity of active power flow in a power system employing an IEEE 14-bus system. The mitigation of low-frequency oscillations in a connected power system was outlined in [13]. The authors of [14] provided a comprehensive analysis of the role of unified power flow regulation in voltage power transfer. In [3; 15], the authors detailed how the performance of power system stability was enhanced by employing multiple damping controllers based on PSS and UPFC. The improvement of power system damping through TCSC and controller design based on genetic algorithms was explored in [16]. In [17], the authors presented the damping function of a unified power flow controller.