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Abstract-Optimization of distributed power assets is a powerful tool that has the potential to assist utility efforts to ensure customer voltages are within pre-defined tolerances and to improve distribution system operations. While convex relaxations of Optimal Power Flow (OPF) problems have been proposed for both balanced and unbalanced networks, these approaches do not provide universal convexity guarantees and scale inefficiently as network size and the number of constraints increase. In balanced networks, a linearized model of power flow, the LinDistFlow model, has been successfully employed to solve approximate OPF problems quickly and with high degrees of accuracy. In this work, an extension of the LinDistFlow model is proposed for unbalanced distribution systems, and is subsequently used to formulate an approximate unbalanced OPF problem that uses VAR assets for voltage balancing and regulation. Simulation results on the IEEE 13 node test feeder demonstrate the ability of the unbalanced LinDistFlow model to perform voltage regulation and balance system voltages.

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