Simultaneous Allocation of PV Systems and Shunt Capacitors in Medium Voltage Feeders Using Quadratic Interpolation Optimization-Based Gaussian Mutation Operator

This study introduces an enhanced version of quadratic interpolation optimization (QIO) merged with Gaussian mutation (GM) operator for optimizing photovoltaic (PV) units and capacitors within distribution systems, addressing practical considerations and discrete nature of capacitors. In this regard, the variations in power loading and power productions from PV sources are taken into consideration. The QIO is inspired by the generalized quadratic interpolation (GQI) method in mathematics and is enhanced with GM operator that introduces randomness into the solution to explore the search space and avoid premature convergence. The proposed QIO-GM is tested on practical Egyptian and standard IEEE distribution systems, demonstrating its effectiveness in minimizing energy losses. Comparative studies against standard QIO, northern goshawk optimization (NGO), and optical microscope algorithm (OMA), as well as other reported algorithms, validate QIO-GM’s superior performance. Numerically, in the first system, the designed QIO-GM algorithm achieves 2.5% improvement over QIO, a 4.4% improvement over NGO, and a 9.2% improvement over OMA, leading to a substantial reduction in carbon dioxide (Co₂) emissions from 110,823.886 to 79,402.82 kg, reflecting a commendable 28.35% decrease. Similarly, in the second system, QIO demonstrates a significant reduction in Co₂ emissions from 72,283.328 to 54,627.65 kg, with a commendable 28.3% decrease. These results underscore QIO-GM’s effectiveness in not only optimizing energy losses but also contributing to substantial environmental benefits through reduced emissions.