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# Geometry of Power Flows and Optimization in Distribution Networks

@article{Lavaei2014GeometryOP, title={Geometry of Power Flows and Optimization in Distribution Networks}, author={Javad Lavaei and David N. Tse and Baosen Zhang}, journal={IEEE Transactions on Power Systems}, year={2014}, volume={29}, pages={572-583} }

- Published 2014 in IEEE Transactions on Power Systems
DOI:10.1109/TPWRS.2013.2282086

We investigate the geometry of injection regions and its relationship to optimization of power flows in tree networks. The injection region is the set of all vectors of bus power injections that satisfy the network and operation constraints. The geometrical object of interest is the set of Pareto-optimal points of the injection region. If the voltage magnitudes are fixed, the injection region of a tree network can be written as a linear transformation of the product of two-bus injection regions… CONTINUE READING

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