The transmission line is the main component in the power system consisting of inductance, capacitance, and resistance. These parameters are important during the transmission line design. This research work applies a novel optimisation technique, grey wolf optimisation (GWO), to calculate the overhead transmission line parameter. The best optimal value is estimated with the control variables. Furthermore, the effect of different bundle conductors, that is, two, three, and four bundle conductors, radius, and spacing between the conductors on the transmission line is also analysed. GWO is a recently developed nature‐inspired meta‐heuristic algorithm. Single‐phase and three‐phase transmission line test systems have been adopted for testing purposes. The proposed algorithm is inspired by the command hierarchy and hunting system of grey wolves. The algorithm is applied to 14 benchmark optimisation functions with dimension and number of search agents. The results of the GWO algorithms are optimised and are superior as compared to previously applied algorithms. The proposed algorithm achieved the best optimal solutions for most of these functions that have been validated statistically. From the results, it is identified that the proposed algorithm is computationally efficient and performs significantly better in terms of accuracy, robustness, and convergence speed.

Metaheuristic algorithms (MAs) are powerful tools for solving complex optimization problems across diverse domains. This comprehensive study analyzes 162 MAs through a unified multi-criteria taxonomy classifying algorithms by control parameters (parameter-free, low-parameter, high-parameter), inspiration sources (biological, physical, human-based), search space scope, and exploration–exploitation balance—alongside bibliometric assessment of publications from 2000 to 2024 (including articles, reviews, books, and conference papers). We evaluate the time complexity of 24 highly cited MAs and their real-world applications in engineering, healthcare, and energy systems. Results demonstrate that different MAs exhibit algorithmic simplicity, often requiring only a small number of control parameters, and are capable of efficient global search. Additionally, several algorithms demonstrate strong adaptability for hybridization with other techniques. However, certain methods are prone to premature convergence, primarily due to unbalanced exploration and exploitation dynamics. The proposed work also critically examines metaphor-inspired algorithms, whose contributions are critically evaluated in light of their conceptual complexity. The rise of such methods has led to redundancy and fragmentation in the field, as many reframe familiar optimization principles using superficial metaphors rather than advancing core algorithmic mechanisms. Bibliometric analysis reveals accelerated growth in MA research (64% journal articles, 31% conference papers, 3% from reviews, 1% from conference reviews, and 1% from book chapters). Similarly, in terms of classification, human-inspired methods constitute the largest category (45%), followed by evaluation-inspired (33%), swarm-inspired (14%), and game-inspired and physics-based algorithms (4%). This work consolidates two decades of advancements, identifies critical performance limitations, and provides practical guidelines for algorithm selection and hybridization to enhance optimization efficiency.

Nowadays Distribution generation (DG) has achieved to further precious awareness, especially inside the power system fields, so the strength and dependability specifically in the distribution system. Optimum scheduling of DG not only focuses on the size of DG only too puts a load on the optimal location of generators. Install for DG at the optimum location along with optimal size into the distribution system would improve the system performance and also give price effectual solved to the planning of the distribution network. The positive impact of optimum DG position into the distribution system would improve system voltage profile, reduction in line losses, improved power standard, make better reliability and strength of the distribution network. GWO is modeled based on the unique hunt, searching for a target, encircling target, and attacking prey, are executing to perform the optimization. The GWO is determined to the IEEE-16, 30, 57 and 118-bus test systems radial distribution network as well as considering multiplier DG units in the system. The better study outcome of the attained to without DG, with DG, type 1 DG, type 2 DG, with type 3 DG at 0.9 pf and with type DG at unity pf. Moreover, the obtained is compared as well as the net outcome of the proposed procedure for the sequence to see the efficiency and effectual and the distribution systems.

The transmission line is the backbone of the power system. A transmission-line working principle is based on its components: inductance, capacitance, and resistance. These components are important in operation, and designing transmission lines as the voltage drop in the power transmission lines depends on these components. In this research work, the flux linkage technique has been proposed to calculate the transmission line's parameters. The transmission-line conductor's resistance has a vital role in calculating power losses in the transmission line. The capacitance and inductance are formed in the transmission line due to the magnetic field of the conductor. For the precise calculation of transmission-line parameters, the temperature correction resistance will improve power-flow efficiency in the power system using power-flow equations. This research work aims to identify the transmission-line parameters and analyze the effect of different bundle conductors, such as two, three, and four bundle conductors. It is observed that when the conductor area is increased in square millimeters (mm ² ), the inductance is decreased, and the capacitance is increased in both single- and three-phase transmission lines, the average percent difference of capacitance and inductance is 99.55% and 55.49%, respectively. The simulation results are provided to show how the proposed techniques can work successfully under various bundle conductors.