## 1 Introduction
Comparing the performance of algorithms when authors utilise a single convergence curve to test the performance of damping controllers in some instances is inappropriate. These issues are clear indicators that a thorough analysis was not performed before designing the damping controller for the power system. Designing a damping controller is a multimodal optimisation issue, and when the optimisation parameters in large power systems are increased, so are the complexity levels. These are intricate and challenging issues. Therefore, the performance of heuristic algorithms is negatively impacted by their ability to be trapped in the local minima. Heuristic algorithms thus become stuck in the local minima and perform worse as the issue dimension grows. As a result, developing a robust damping controller using an optimal damping scheme is challenging. To find the best damping controller solution, exploration and exploitation processes must be balanced. Numerous metaheuristic optimisation algorithms have used stochastic techniques; yet these techniques have poor solution convergence. Several suggested approaches offer good search space exploration but have limited exploitation, or vice versa [22]. To locate the maxima or minima, metaheuristic optimisation techniques are employed. These methods either use algorithms based on swarms or evolution. Particle swarm optimisation (PSO), firefly, ant colony, gravitational search algorithm (GSA), and immunity algorithm (IA) are examples of swarm-based algorithms. The evolutionary programming (EP) differential algorithm, EP, and genetic algorithm (GA) are examples of evolution-based algorithms. Premature convergence is a constraint of GA and PSO brought on by the local minimum stagnation issue. GSA is limited in its ability to solve challenging optimisation issues. To find the best options for a damping controller, IA performs better during the exploration phase than during the exploitation phase. EP functions more effectively during the exploitation phase than during the exploration phase. Other optimisation methods, such as tabu search and simulated annealing methods, have poor convergence rates and cannot handle multimodal issues [5; 22]. Recently, a wide variety of indicators has been applied in the construction of controllers that inject or absorb reactive power to reduce oscillations in power networks. To reduce overshoots and settling times in power system oscillations, the following parameters are used: damping factor, damping ratio, eigenvalues, integral absolute error (IAE), integral squared error (ISE), integral of the time-weighted absolute error (ITAE), and integral of time multiplied by the squared error (ITSE). Damping ratio eigenvalue analysis provides the small-signal stability analysis for the two-area interconnected power system with load frequency controller in collaboration with FACTS and energy storage device [33]. ISE, ITSE, and power system stabilisers for improving dynamic stability [34; 35] are used to more accurately assess the system performance for compensating reactive power [36]. In a deregulated environment, ITAE is used as the objective function for improving the stability of the power system based on a conventional UPFC and multi-source power system [28; 37]. When evaluating the system's effectiveness for reactive power adjustment, the ITSE and damping ratio are used [38]. Overshoots of oscillations are mitigated by the damping ratio indicator. However, it performs poorly in terms of settling time, and conversely for the indicator of damping factor. Therefore, a single indicator cannot perform better in terms of both settling time and oscillation overshoots. The key contributions of the paper are as follows:  
* Novel mathematical modelling of a PIDF controller and its power stability aspect was used as a damping controller. This controller has never been applied to the stability of a power system. * To build a reliable damping controller design for an SMIB system, the evolutionary programming sine cosine algorithm (EPSCA) technique was developed.