Enhancement of power system steady-state stability through allocation of quantum-inspired grey wolf optimization algorithm-based multiple D-STATCOM Units

Modern distribution networks suffer from power losses and voltage instability under various loading conditions. Mitigating these operational issues requires optimal allocation of custom power devices, such as Distribution Static Compensators (D-STATCOMs). To address this challenge, this study develops a quantum-inspired grey wolf optimization (QGWO) algorithm for allocating D-STATCOMs to ensure steady-state stability, improve bus voltage profiles, and reduce power losses. Distinct from existing variants, QGWO models search agents as probabilistic quantum state vectors, utilizing a fitness-driven amplitude scaling and dynamic phase angle adaptation. Using the backward-forward sweep (BFS) load-flow method, the performance is evaluated across base-load, load-increment, and single-phase fault scenarios on practical 44- and IEEE 69-bus test systems. The voltage stability margin (VSM) is utilized to determine maximum loading factors. For the 44-bus system, buses 22, 29, and 41 with capacities of 637.69 kVAR, 503.75 kVAR, and 351.01 kVAR are found as the optimal locations and sizes. With these units, power losses are reduced by 50.894% under the base-load scenario. For the IEEE 69-bus system, buses 11, 17 and 61 with capacities of 358.69kVAR, 254.02kVAR and 1206.75kVAR reduce power losses by 42.76% under the base-load scenario. Using VSM, the maximum loading factor is found as 1.53 and 2.65 for 44- and 69-bus systems. Statistically, the proposed QGWO achieves the lowest mean power loss, with Wilcoxon rank-sum tests confirming its advantage over PSO, APSO, GWO, and CGWO. Weight sensitivity analysis demonstrates that the optimal solution remains invariant to changes in objective-function weights. Economically, cost-benefit sensitivity analyses confirm the financial viability of the project.