Hybrid LSF–FPA Optimization for Optimal Capacitor Placement and Sizing in Radial Distribution Systems

Increasing demand in radial distribution systems intensifies active power losses, voltage drops, and power factor deterioration, leading to reduced network efficiency and increased annual operating costs. Shunt capacitor banks can mitigate these effects by supplying reactive power locally; however, determining their locations and discrete ratings constitutes a nonlinear optimization problem governed by the radial network structure, nonlinear load flow equations, reactive power compensation limits, power factor requirements, and commercially available capacitor sizes. This paper presents a hybrid methodology that combines Loss Sensitivity Factors (LSFs) for candidate-bus screening with the Flower Pollination Algorithm (FPA) for discrete capacitor sizing. The LSF stage ranks buses according to the local sensitivity of active power losses to reactive power variations and applies a voltage-based screening criterion to reduce the number of decision variables. The FPA subsequently explores the reduced search space through global and local pollination, while a projection-and-repair procedure maps every continuous trial vector onto admissible capacitor ratings in 50 kVAr increments. The objective function minimizes the annual cost of active power losses, capacitor bank installation, and installed reactive power capacity. The method is evaluated on the IEEE 33-bus, 69-bus, and 141-bus radial distribution systems. For the IEEE 33-bus system, active power losses decrease from 202.7 to 133.5 kW and the power factor increases from 0.8502 to 0.9827. For the IEEE 69-bus system, losses decrease from 225.0 to 145.9 kW and the power factor increases from 0.8159 to 0.9705. For the IEEE 141-bus system, losses decrease from 632.7 to 453.7 kW and the power factor increases from 0.8500 to 0.9876. The corresponding cost savings in terms of annual loss are USD 36,371.52, USD 41,574.96, and USD 94,082.40. The compensation configurations improve the voltage profiles in all three systems; nevertheless, the resulting minimum voltages of 0.939, 0.932, and 0.948 p.u. remain below the 0.95 p.u. lower reference because voltage deviation is evaluated as a performance indicator rather than enforced through a hard constraint or penalty term. The results demonstrate that the proposed LSF–FPA framework provides effective loss reduction, power factor correction, and voltage profile improvement, while the economic comparison shows that the solution with the greatest loss reduction benefit does not necessarily produce the lowest total annual cost.