## 3 Design of the Proposed Controller for the Power System
### Developed Owl Search Algorithm (DOSA)  
The DOSA is a state-of-the-art meta-heuristic algorithm that offers several advantages over other algorithms such as GTO, MSA, PSO, and ABC. These advantages include: (1) Efficient Search: The DOSA utilizes the owl search behavior, enabling efficient exploration of the search space. The algorithm is designed to strike a balance between exploration  
Figure 4: Inside structure of the FOPD-FOPID controller. and exploitation, facilitating fast convergence towards optimal solutions. (2) Global Optimization: The DOSA is a global optimization algorithm, capable of seeking the global optimum without getting trapped in local optima. This characteristic makes it well-suited for tackling complex optimization problems with multiple solution vertices. (3) Robustness: The DOSA exhibits robustness against noise and uncertainty in the objective function. It adapts effectively to noisy and dynamic environments, making it suitable for real-world applications where the objective function may change over time. (4) Minimal Control Parameters: Compared to other optimization algorithms, the DOSA requires a reduced number of control parameters. This simplifies the tuning process, reduces computational load, and facilitates implementation across various domains. (5) Fast Convergence Speed: The DOSA demonstrates fast convergence in a wide range of optimization problems. It efficiently converges towards near-optimal solutions, significantly reducing the computational time required for finding high-quality solutions. These advantages have been documented in various studies [47; 48; 49], highlighting the effectiveness and versatility of the DOSA algorithm. Similar to the application of other meta-heuristic algorithms in electrical engineering [50; 51; 52], its execution is initiated by fortuitously selecting a population. Within this algorithm, said population symbolizes the owls' positioning amidst the forest trees exemplifying the search space. Given that the number of random populations is represented as \"n\" and the forest is considered as a d-dimensional search space in this algorithm, visually expressing the chance placements of these nocturnal creatures within an n \(\times\) d matrix can be encapsulated with Equation (13) [47]:  
\[x= \begin{bmatrix}x_{1,1}&\dots&x_{1,d}\\.&&.\\.&&.\\ x_{n,1}&\dots&x_{n,d}\end{bmatrix} _{n\times d} \tag{13}\]  
where the component \(x_{i,j}\) in the matrix defines the \(j\)th variable (dimension) of \(i\)th owl. In the owl search algorithm, the term \"\(i\)th owl\" refers to the owl that is being considered or processed in the \(i\)th iteration or step of the algorithm. The owl search algorithm is a heuristic search algorithm inspired by the behavior of owls when hunting prey. It uses a combination of local search and global exploration to find an optimal solution. In each iteration, the algorithm evaluates the current owl (\(i\)th owl) and updates its position based on certain rules and heuristics. The process continues until a satisfactory solution is found or the search space has been fully explored. To make an introductory state of uniform dissemination, Equation (14) is utilized [47; 48; 49]:  
\[x_{i}=x_{l}+(x_{l}+x_{u})Z(0,1) \tag{14}\]  
In Equation (14), \(X_{i}\) could be irregular and uniform numbers between [0, 1], and \(x_{u}\) and \(x_{\mathrm{l}}\) are the upper and lower bounds of the \(i\)th owl within the \(j\)th measurement. In the realm of mathematical equations, specifically Equation (14), \(Z\)(0,1) stands as an intriguing integer that embraces both randomness and uniformity within its numerical essence, constrained between the ethereal boundaries [0,1]. Furthermore, the mysterious confines of \(x_{u}\) and \(x_{\mathrm{l}}\) possess a duality and significance in defining not just any owl's position within this enigmatic forest, but rather the profound location it assumes in the \(j\)th dimension.