16,508 research outputs found
Convex Relaxations and Linear Approximation for Optimal Power Flow in Multiphase Radial Networks
Distribution networks are usually multiphase and radial. To facilitate power
flow computation and optimization, two semidefinite programming (SDP)
relaxations of the optimal power flow problem and a linear approximation of the
power flow are proposed. We prove that the first SDP relaxation is exact if and
only if the second one is exact. Case studies show that the second SDP
relaxation is numerically exact and that the linear approximation obtains
voltages within 0.0016 per unit of their true values for the IEEE 13, 34, 37,
123-bus networks and a real-world 2065-bus network.Comment: 9 pages, 2 figures, 3 tables, accepted by Power System Computational
Conferenc
Stein factors for negative binomial approximation in Wasserstein distance
The paper gives the bounds on the solutions to a Stein equation for the
negative binomial distribution that are needed for approximation in terms of
the Wasserstein metric. The proofs are probabilistic, and follow the approach
introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are
used to quantify the accuracy of negative binomial approximation to parasite
counts in hosts. Since the infectivity of a population can be expected to be
proportional to its total parasite burden, the Wasserstein metric is the
appropriate choice.Comment: Published at http://dx.doi.org/10.3150/14-BEJ595 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Exact Convex Relaxation of Optimal Power Flow in Tree Networks
The optimal power flow (OPF) problem seeks to control power generation/demand
to optimize certain objectives such as minimizing the generation cost or power
loss in the network. It is becoming increasingly important for distribution
networks, which are tree networks, due to the emergence of distributed
generation and controllable loads. In this paper, we study the OPF problem in
tree networks. The OPF problem is nonconvex. We prove that after a "small"
modification to the OPF problem, its global optimum can be recovered via a
second-order cone programming (SOCP) relaxation, under a "mild" condition that
can be checked apriori. Empirical studies justify that the modification to OPF
is "small" and that the "mild" condition holds for the IEEE 13-bus distribution
network and two real-world networks with high penetration of distributed
generation.Comment: 22 pages, 7 figure
Exact Convex Relaxation of Optimal Power Flow in Radial Networks
The optimal power flow (OPF) problem determines power generation/demand that
minimize a certain objective such as generation cost or power loss. It is
nonconvex. We prove that, for radial networks, after shrinking its feasible set
slightly, the global optimum of OPF can be recovered via a second-order cone
programming (SOCP) relaxation under a condition that can be checked a priori.
The condition holds for the IEEE 13-, 34-, 37-, 123-bus networks and two
real-world networks, and has a physical interpretation.Comment: 32 pages, 10 figures, submitted to IEEE Transaction on Automatic
Control. arXiv admin note: text overlap with arXiv:1208.407
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