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

Nuclear reactions in astrophysical plasmas

In the process of slow neutron capture nucleosynthesis, one often has to take into account that nuclei undergoing neutron capture and beta decay may not be only in their ground states, but also in long-lived excited states, known as nuclear isomers. Such isomers might not be thermally equilibrated with the nuclear ground states. In this thesis, we theoretically investigate the efficiency of nuclear excitation by electron capture (NEEC) to deplete such isomeric states in dense stellar plasmas under the sprocess conditions. Due to the high charge states available in such plasmas, NEEC is not always accompanied by its detailed-balance counterpart, the inverse process internal conversion, and reaction rates can be considered separately. We investigate the cases of 58m Co, 99mTc, 121mSn, 121mSb and 152mEu and compare the NEEC depletion rates with relevant beta and gamma decay rates of the isomeric states. The results for 58mCo, 121mSb and 152mEu show that NEEC should be considered as relevant isomer depletion channel in astrophysical plasmas

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