Quadratic interpolation manta ray foraging optimization: a meta-heuristic approach for simultaneous DG allocation and distribution system reconfiguration

Abstract This paper introduces a meta-heuristic algorithm called Quadratic Interpolation Manta Ray Foraging Optimization (QIMRFO) for simultaneous distributed generation (DG) unit allocation and distribution system reconfiguration (DSR) within distribution systems (DS). The main objectives of this study are to minimize real power loss (RPL), reduce voltage deviation (VD), and maximize the voltage stability index (VSI). The QIMRFO algorithm enhances the original Manta Ray Foraging Optimization (MRFO) by integrating a quadratic interpolation strategy to improve the foraging performance. The numerical results demonstrate that the QIMRFO algorithm exhibits excellent performance in terms of accuracy and robustness across seven benchmark functions and 15 CEC2017 benchmark functions. Furthermore, the QIMRFO method is applied and assessed on the standard IEEE 33 and 69-bus DSs using load flow calculations based on the backward/forward sweep technique. Consequently, optimal simultaneous DSR and DG allocation, combined with an optimal power factor (PF), leads to significant reductions in RPL and VD while enhancing VSI. Comparative analyses against MRFO and other state-of-the-art methods from the literature reveal that QIMRFO consistently delivers superior solution quality. For the 33-bus system, QIMRFO achieves RPL reductions of 33.8622%, 65.50%, 94.32%, 71.30%, 94.322%, 83.92%, 89.12%, and 92.11% across various scenarios, including: DSR alone; integration of three photovoltaic (PV) units; three wind turbines (WT); simultaneous integration of three PV units with DSR; simultaneous DSR with three WT units; simultaneous DSR with one PV and one WT unit; simultaneous DSR with two PV and one WT unit; and simultaneous DSR with one PV and two WT units in the DS. Similarly, for the 69-bus system under the same scenarios, the RPL reductions are 56.18%, 69.14%, 98.13%, 83.66%, 98.25%, 94.59%, 95.89%, and 97.43%, respectively. These results establish QIMRFO as an effective approach for addressing the simultaneous DG allocation with the DSR problem in radial DS, offering substantial improvements in system performance and efficiency.