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Multi-Dimensional Optimal Power Flow (MDOPF) is a fundamental task in power systems engineering aimed at optimizing the operation of electrical networks while considering various constraints such as power generation, transmission, and distribution. The mathematical model of MDOPF involves formulating it as a non-linear, non-convex optimization problem aimed at minimizing specific objective functions while adhering to equality and inequality constraints. The objective function typically includes terms representing the Fuel Cost (FC), Entire Network Losses (ENL), and Entire Emissions (EE), while the constraints encompass power balance equations, generator operating limits, and network constraints, such as line flow limits and voltage limits. This paper presents an innovative Improved Kepler Optimization Technique (IKOT) for solving MDOPF problems. The IKOT builds upon the traditional KOT and incorporates enhanced local escaping mechanisms to overcome local optima traps and improve convergence speed. The mathematical model of the IKOT algorithm involves defining a population of candidate solutions (individuals) represented as vectors in a high-dimensional search space. Each individual corresponds to a potential solution to the MDOPF problem, and the algorithm iteratively refines these solutions to converge towards the optimal solution. The key innovation of the IKOT lies in its enhanced local escaping mechanisms, which enable it to explore the search space more effectively and avoid premature convergence to suboptimal solutions. Experimental results on standard IEEE test systems demonstrate the effectiveness of the proposed IKOT in solving MDOPF problems. The proposed IKOT obtained the FC, EE, and ENL of USD 41,666.963/h, 1.039 Ton/h, and 9.087 MW, respectively, in comparison with the KOT, which achieved USD 41,677.349/h, 1.048 Ton/h, 11.277 MW, respectively. In comparison to the base scenario, the IKOT achieved a reduction percentage of 18.85%, 58.89%, and 64.13%, respectively, for the three scenarios. The IKOT consistently outperformed the original KOT and other state-of-the-art metaheuristic optimization algorithms in terms of solution quality, convergence speed, and robustness. [ABSTRACT FROM AUTHOR]

Multi-area power systems (MAPSs) are highly complex non-linear systems facing a fundamental issue in real-world engineering problems called frequency stability problems (FSP). This paper develops an enhanced slime mold optimization algorithm (ESMOA) to optimize the tuning parameters for a cascaded proportional derivative-proportional integral (PD-PI) controller. The novel ESMOA proposal includes a new system that combines basic SMO, chaotic dynamics, and an elite group. The motion update incorporates the chaotic technique, and the exploitation procedure is enhanced by searching for a select group rather than merely the best solution overall. The proposed cascaded PD-PI controller based on the ESMOA is employed for solving the FSP in MAPSs with two area non-reheat thermal systems to keep the balance between the electrical power load and the generation and provide power system security, reliability, and quality. The proposed cascaded PD-PI controller based on the ESMOA is evaluated using time domain simulation to minimize the integral time-multiplied absolute error (ITAE). It is evaluated in four different test situations with various sets of perturbations. For tuning the cascaded PD-PI controller, the proposed ESMOA is compared to the golden search optimizer (GSO) and circle optimizer (CO), where the proposed ESMOA provides the best performance. Furthermore, the findings of the proposed cascaded PD-PI controller based on the ESMOA outperform previous published PID and PI controllers adjusted using numerous contemporary techniques. [ABSTRACT FROM AUTHOR]