# Optimizing Phase Allocation in Unbalanced Power Distribution Networks using a Linearized DistFlow Formulation Source: [Optimizing Phase Allocation in Unbalanced Power Distribution Networks using a Linearized DistFlow Formulation]() Collection index: [llms.txt]() Data updated: 2025-10-26T03:56:26.552Z Authors: Rahul K. Gupta, Daniel K. Molzahn Published: 2025-01-12T19:59:34.000Z ## Abstract Power distribution networks, especially in North America, are often unbalanced but are designed to keep unbalance levels within the limits specified by IEEE, IEC, and NEMA standards. However, rapid integration of unbalanced devices, such as electric vehicle (EV) chargers and single-phase solar plants, can exacerbate these imbalances. This increase can trigger protection devices, increase losses, and potentially damage devices. To address this issue, phase swapping (or phase allocation) has been proposed. Existing approaches predominantly rely on heuristic methods. In this work, we develop a mixed integer linear programming (MILP) approach for phase allocation. Our approach uses linearized DistFlow equations to represent the distribution network and incorporates a phase consistency constraint, enforced with binary variables, to ensure that downstream phase configurations align with upstream configurations. We validate the proposed approach on multiple benchmark test cases and demonstrate that it effectively improves network balance, as quantified by various metrics. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()