3rd TAGRA

Transformer overloading in densely populated urban distribution networks is a critical challenge during peak consumption hours. While traditional Flexible AC Transmission Systems (FACTS) are cost-prohibitive, Continuously Variable Series Reactors (CVSRs) offer a highly economical alternative (approximately $10/kVAr) by regulating transformer reactance—up to a maximum of 3 Ohm—via magnetic core saturation. To maximize economic benefits, it is crucial to minimize the number of CVSR devices deployed. This study investigates the optimal placement of CVSR devices across the 48 secondary network transformers of the highly meshed IEEE 342-Node Low Voltage Networked Test System (LVNTS). Four distinct analytical approaches are compared: the Shortest Path, Loading-Based, Transformer Sensitivity-Based, and Piecewise Optimization (MILP) algorithms. A co-simulation framework coupling MATLAB and OpenDSS was utilized to evaluate these algorithms under severe conditions, including a system-wide load increment and area-based load surges. The findings reveal that while graph-theory and loading-based methods offer rapid computational times, they often fail to capture the localized, non-linear dynamics of overloaded nodes accurately. Conversely, the Piecewise Optimization-Based method—formulated as a Mixed-Integer Linear Program (MILP)—demonstrated superior accuracy. By approximating non-linear power flow curves into multiple linear segments, this algorithm successfully identified the exact transformers requiring intervention and maintained all power flows strictly below the 1 MVA limit. The results indicate that utilizing piecewise sensitivity matrices for CVSR allocation provides distribution system operators with a highly precise and cost-effective strategy to alleviate congestion and defer grid upgrades.