Time Varying Multi-Unit Placement of PV and D STATCOM in Radial Distribution Networks: A Particle Swarm Optimization Study with Convergence Analysis

Abstract

Optimal placement and sizing of photovoltaic (PV) and D-STATCOM units is a well-studied approach for reducing active power losses and improving voltage profiles in radial distribution networks. However, most published studies, including a recent joint PV+D-STATCOM optimization on the IEEE 33-bus system reporting a 69.18% loss reduction, evaluate the network under a single static load/generation snapshot, and place only one unit of each device. This paper extends that formulation in two directions: simultaneous multi-unit placement of two PV units and two D-STATCOM units (an 8- dimensional decision space), and evaluation under a time-varying daily load profile represented as four duration-weighted blocks spanning a full 24-hour cycle. The load profile is not assumed: it uses a real time-block consumption pattern for industrial and commercial consumers published by the Maharashtra Electricity Regulatory Commission (MERC) in MSEDCL's Multi-Year Tariff Order (Case No. 217 of 2024), based on MSEDCL's own observed feeder demand data; solar irradiance factors remain an illustrative assumption pending site-specific data. A backward/forward sweep power-flow solver was implemented and validated against the source study's published base-case results (202.68 kW active losses, 0.9131 p.u. minimum voltage). Under the static, single-snapshot assumption, multi-unit placement via standard particle swarm optimization (PSO) achieves a mean 82.3% active loss reduction (N=40 runs). Under the time-varying formulation with the real MERC load pattern, mean daily energy loss reduction is 49.3% (N=60 runs) - lower than the static estimate, but higher than an earlier illustrative-profile estimate, because the real industrial/commercial demand pattern peaks during the 9am-5pm block, which coincides with PV availability, rather than in the evening as commonly assumed for residential-dominated feeders; loss reduction reaches 83.0% during this solar-coincident peak block versus 36.0% during the evening block. An Adaptive Chaotic PSO (ACPSO) variant was benchmarked against standard PSO across all three formulations using paired statistical tests; standard PSO matched or modestly outperformed ACPSO in mean solution quality in every case, though the gap was not statistically significant under the real load data (paired Wilcoxon p=0.44). These results indicate that static snapshot analysis overstates the achievable benefit of PV+D-STATCOM compensation, that the size of this gap depends materially on the coincidence between a feeder's actual demand pattern and solar availability, and that for this class of placement problem, temporal load modeling had a larger effect on realistic performance estimates than algorithmic sophistication in the optimizer.

KEYWORDS: D-STATCOM, Distribution Networks, Loss Minimization, Multi-Unit Optimization, Particle Swarm Optimization, Photovoltaic Placement, Time-Varying Load