Enhanced Kepler Optimization Method for Nonlinear Multi-Dimensional Optimal Power Flow

Abstract

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.