Optimizing Phase Allocation in Unbalanced Power Distribution Networks using a Linearized DistFlow Formulation

TL;DR

This work addresses voltage unbalance in unbalanced distribution networks caused by single-phase devices by proposing a MILP-based phase allocation method. It leverages a linearized DistFlow model (Lin3DistFlow) and a phase-consistency constraint to represent the grid and enforce downstream-upstream phase alignment, enabling global optimization. The approach is validated on IEEE-13, -37, and -123 networks under varying per-phase capacity scenarios, showing reduced voltage unbalance when capacity is increased. The results indicate fast solve times and reproducible, globally optimal phase allocations with potential for practical deployment in distribution networks.

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.

Figures (5)

• Figure 1: Branch flow model in radial grids.
• Figure 2: Example of a phase-consistent assignment problem.
• Figure 3: IEEE 13-bus benchmark network (base case). For the equivalent representation, the nodes are color-coded as follows: Red, Green, and Blue represent phases A, B, and C, respectively. Combinations of two or more colors indicate multiple phases; for example, Red + Blue = Purple means the presence of phases A and C, Blue + Green = Cyan means phases B and C, and Red + Green + Blue = White indicates the presence of all phases.
• Figure 4: Optimized phase allocation is evaluated across three cases: Case 1, Case 2, and Case 3 correspond to the per-phase capacity to be equal to, double, and triple the per-phase spot load, respectively.
• Figure 5: Voltage magnitudes for Cases 1, 2 and 3.