article · Mathematics
An advanced meta-heuristic technique combines a gradient-based optimiser with a crossover operator to improve solution diversity during computational searches. Named GBOC, the method maintains search direction and local optima avoidance rules while introducing greater randomness into generational solutions. It is designed to identify the optimal sizing and placement of distribution static VAR compensators within electrical distribution networks. The primary objective is to maximise annual energy savings by mitigating power losses across light, average, and peak loading conditions. Evaluated on IEEE 33, 69, and 118-node benchmark systems, the approach incorporates financial constraints represented by reactive power compensation limits of 50% and 75%. Computational results show substantial economic savings from reduced yearly energy losses, with the algorithm outperforming several established techniques, including the baseline gradient-based optimiser, differential evolution, and the salp swarm algorithm.
Electrical distribution networks experience significant financial and operational losses as power demands fluctuate. By identifying the most effective locations and capacities for reactive power compensation devices, this approach helps grid planners curb costly power dissipation. It ensures that investments in grid-stabilising hardware yield maximum efficiency and financial savings across varying consumer demand cycles.
This work applies to power distribution planning, directly targeting distribution network operators and utility engineers seeking to reduce operational expenditure from line losses. The technology sits at the early-stage simulation level, having been validated on standard IEEE benchmark models rather than operational utility grids. Transition towards commercial application would require embedding the algorithm into commercial power-flow software tools and validating performance against actual grid infrastructure.
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A gradient-based optimizer (GBO) is a recently inspired meta-heuristic technique centered on Newton’s gradient-based approach. In this paper, an advanced developed version of the GBO is merged with a crossover operator (GBOC) to enhance the diversity of the created solutions. The merged crossover operator causes the solutions in the next generation to be more random. The proposed GBOC maintains the original Gradient Search Rule (GSR) and Local Escaping Operator (LEO). The GSR directs the search to potential areas and aids in its convergence to the optimal answer, while the LEO aids the searching process in avoiding local optima. The proposed GBOC technique is employed to optimally place and size the distribution static VAR compensator (D-SVC), one of the distribution flexible AC transmission devices (D-FACTS). It is developed to maximize the yearly energy savings via power losses concerning simultaneously different levels of the peak, average, and light loadings. Its relevance is tested on three distribution systems of IEEE 33, 69, and 118 nodes. Based on the proposed GBOC, the outputs of the D-SVCs are optimally varying with the loading level. Furthermore, their installed ratings are handled as an additional constraint relating to two compensation levels of 50% and 75% of the total reactive power load to reflect a financial installation limit. The simulation applications of the proposed GBOC declare great economic savings in yearly energy losses for the three distribution systems with increasing compensation levels and iterations compared to the initial case. In addition, the effectiveness of the proposed GBOC is demonstrated compared to several techniques, such as the original GBO, the salp swarm algorithm, the dwarf mongoose algorithm, differential evolution, and honey badger optimization.
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DOI: 10.3390/math11051077
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