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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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The proliferation of phasor measurement units (PMUs) into electric power distribution grids presents new opportunities for utility operators to manage distribution systems more effectively. One potential application of PMU measurements is to facilitate distribution grid re-configuration. Given the increasing amount of Distributed Energy Resource (DER) penetration into distribution grids, in this work we formulate an Optimal Power Flow (OPF) approach that manages DER power injections to minimize the voltage phasor difference between two nodes on a distribution network to enable efficient network reconfiguration. In order to accomplish this, we develop a linear model that relates voltage phase angles to real and reactive power flows in unbalanced distribution systems. Used in conjunction with existing linearizations relating voltage magnitude differences to power flows, we formulate an OPF capable of minimizing voltage phasor differences across different points in the network. In simulations, we explore the use of the developed approach to minimize the phasor difference across switches to be opened or closed, thereby providing an opportunity to automate and increase the speed of reconfigurations in unbalanced distribution grids.

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