Optimal sizing and placement of capacitors using an improved particle swarm optimization to enhance networks reliability and voltage profile in distribution systems

Abstract

Enhancing radial distribution systems’ reliability and power quality is essential for ensuring efficient and standard-compliant electricity delivery under growing load demands. This study proposes an improved particle swarm optimization (IPSO) based on the nonlinearly decreasing inertia weight ($w)$ that uses the feature of the cosine function. This proposed method helps to optimize capacitor placement and sizing, while minimizing power losses and voltage deviation, improving reliability and voltage profiles. The proposed method was also compared with three other inertia weights and tested on IEEE 33 and 69 bus systems for sizing and the best location of capacitors under three load scenarios. The backward/forward sweep load flow method was employed for load flow analysis in the distribution systems. The real power loss obtained for the normal load of the 33-bus system was 122.62 kW compared to the base case of 202. 68 kW, this shows a 39.50 % reduction. The voltage deviation obtained with IPSO was 0.0015p.u compared to the base case of 0.0035p.u. The reliability was enhanced with percentage increases of 14.74 %, 23.95 %, 10.79 %, 29.39 %, and 29.42 %, respectively, for SAIFI, SAIDI, CAIDI, EENS, and AENS. The power loss for the IPSO for the light load condition was 33.498 kW, the voltage deviation of IPSO was 0.000506p.u., and the reliability indices were 2.1202, 1.6744, 0.78975, 377.5616, and 0.02075 for SAIFI, SAIDI, CAIDI, EENS, and AENS, respectively. The heavy load condition for power loss reduction for IPSO was 239.485 kW, and the voltage deviation was 0.001826p.u. The assessment of reliability indices gives SAIFI (2.2057), SAIDI (1.735), CAIDI (0.78657), EENS (4330.0819), and AENS (0.23792). This underscores the efficacy of IPSO in improving reliability and voltage profile while reducing power loss. The power loss for the 69 bus system was 113.8047 kW at normal load compared to other PSO-$w1$, PSO-$w2$, and PSO-$w3$ with the values of 116.7882, 115.7898, and 115.0942 kW, respectively, resulting in a 49.56 % reduction for IPSO. The voltage deviation of IPSO was 0.0000665p.u., compared to the base case of 0.001443p.u. The reliability metrics were SAIFI, SAIDI, CAIDI, EENS, and AENS, demonstrating improvements with percentage increases of 12.28 %, 19.10 %, 7.78 %, 39.60 %, and 39.60 %, respectively. At the light load, the power loss is 34.5488 kW with a 33.06 % reduction; at the heavy load, the power loss is 217.752 kW with a 66.63 % reduction. This underscores the efficacy of IPSO in reducing energy waste and deferring infrastructure upgrades, and the results outperformed those of other methods in the literature. The superiority and effectiveness of the IPSO were further verified on the Wilcoxon and Friedman signed-rank test. The findings offer policymakers and utilities a decision-support tool for capacitor placement that strengthens reliability standards, reduces losses, enhances voltage stability, and improves service continuity.