2,090 research outputs found
New Formulation and Strong MISOCP Relaxations for AC Optimal Transmission Switching Problem
As the modern transmission control and relay technologies evolve,
transmission line switching has become an important option in power system
operators' toolkits to reduce operational cost and improve system reliability.
Most recent research has relied on the DC approximation of the power flow model
in the optimal transmission switching problem. However, it is known that DC
approximation may lead to inaccurate flow solutions and also overlook stability
issues. In this paper, we focus on the optimal transmission switching problem
with the full AC power flow model, abbreviated as AC OTS. We propose a new
exact formulation for AC OTS and its mixed-integer second-order conic
programming (MISOCP) relaxation. We improve this relaxation via several types
of strong valid inequalities inspired by the recent development for the closely
related AC Optimal Power Flow (AC OPF) problem. We also propose a practical
algorithm to obtain high quality feasible solutions for the AC OTS problem.
Extensive computational experiments show that the proposed formulation and
algorithms efficiently solve IEEE standard and congested instances and lead to
significant cost benefits with provably tight bounds
Matrix Minor Reformulation and SOCP-based Spatial Branch-and-Cut Method for the AC Optimal Power Flow Problem
Alternating current optimal power flow (AC OPF) is one of the most
fundamental optimization problems in electrical power systems. It can be
formulated as a semidefinite program (SDP) with rank constraints. Solving AC
OPF, that is, obtaining near optimal primal solutions as well as high quality
dual bounds for this non-convex program, presents a major computational
challenge to today's power industry for the real-time operation of large-scale
power grids. In this paper, we propose a new technique for reformulation of the
rank constraints using both principal and non-principal 2-by-2 minors of the
involved Hermitian matrix variable and characterize all such minors into three
types. We show the equivalence of these minor constraints to the physical
constraints of voltage angle differences summing to zero over three- and
four-cycles in the power network. We study second-order conic programming
(SOCP) relaxations of this minor reformulation and propose strong cutting
planes, convex envelopes, and bound tightening techniques to strengthen the
resulting SOCP relaxations. We then propose an SOCP-based spatial
branch-and-cut method to obtain the global optimum of AC OPF. Extensive
computational experiments show that the proposed algorithm significantly
outperforms the state-of-the-art SDP-based OPF solver and on a simple personal
computer is able to obtain on average a 0.71% optimality gap in no more than
720 seconds for the most challenging power system instances in the literature
Manning condensation in two dimensions
We consider a macroion confined to a cylindrical cell and neutralized by
oppositely charged counterions. Exact results are obtained for the
two-dimensional version of this problem, in which ion-ion and ion-macroion
interactions are logarithmic. In particular, the threshold for counterion
condensation is found to be the same as predicted by mean-field theory. With
further increase of the macroion charge, a series of single-ion condensation
transitions takes place. Our analytical results are expected to be exact in the
vicinity of these transitions and are in very good agreement with recent
Monte-Carlo simulation data.Comment: 4 pages, 4 figure
A Cycle-Based Formulation and Valid Inequalities for DC Power Transmission Problems with Switching
It is well-known that optimizing network topology by switching on and off
transmission lines improves the efficiency of power delivery in electrical
networks. In fact, the USA Energy Policy Act of 2005 (Section 1223) states that
the U.S. should "encourage, as appropriate, the deployment of advanced
transmission technologies" including "optimized transmission line
configurations". As such, many authors have studied the problem of determining
an optimal set of transmission lines to switch off to minimize the cost of
meeting a given power demand under the direct current (DC) model of power flow.
This problem is known in the literature as the Direct-Current Optimal
Transmission Switching Problem (DC-OTS). Most research on DC-OTS has focused on
heuristic algorithms for generating quality solutions or on the application of
DC-OTS to crucial operational and strategic problems such as contingency
correction, real-time dispatch, and transmission expansion. The mathematical
theory of the DC-OTS problem is less well-developed. In this work, we formally
establish that DC-OTS is NP-Hard, even if the power network is a
series-parallel graph with at most one load/demand pair. Inspired by Kirchoff's
Voltage Law, we give a cycle-based formulation for DC-OTS, and we use the new
formulation to build a cycle-induced relaxation. We characterize the convex
hull of the cycle-induced relaxation, and the characterization provides strong
valid inequalities that can be used in a cutting-plane approach to solve the
DC-OTS. We give details of a practical implementation, and we show promising
computational results on standard benchmark instances
Discrete aqueous solvent effects and possible attractive forces
We study discrete solvent effects on the interaction of two parallel charged
surfaces in ionic aqueous solution. These effects are taken into account by
adding a bilinear non-local term to the free energy of Poisson-Boltzmann
theory. We study numerically the density profile of ions between the two
plates, and the resulting inter-plate pressure. At large plate separations the
two plates are decoupled and the ion distribution can be characterized by an
effective Poisson-Boltzmann charge that is smaller than the nominal charge. The
pressure is thus reduced relative to Poisson-Boltzmann predictions. At plate
separations below ~2 nm the pressure is modified considerably, due to the
solvent mediated short-range attraction between ions in the the system. For
high surface charges this contribution can overcome the mean-field repulsion
giving rise to a net attraction between the plates.Comment: 12 figures in 16 files. 19 pages. Submitted to J. Chem. Phys., July
200
Dispersion control for matter waves and gap solitons in optical superlattices
We present a numerical study of dispersion manipulation and formation of
matter-wave gap solitons in a Bose-Einstein condensate trapped in an optical
superlattice. We demonstrate a method for controlled generation of matter-wave
gap solitons in a stationary lattice by using an interference pattern of two
condensate wavepackets, which mimics the structure of the gap soliton near the
edge of a spectral band. The efficiency of this method is compared with that of
gap soliton generation in a moving lattice recently demonstrated experimentally
by Eiermann et al. [Phys. Rev. Lett. 92, 230401 (2004)]. We show that, by
changing the relative depths of the superlattice wells, one can fine-tune the
effective dispersion of the matter waves at the edges of the mini-gaps of the
superlattice Bloch-wave spectrum and therefore effectively control both the
peak density and the spatial width of the emerging gap solitons.Comment: 8 pages, 9 figures; modified references in Section 2; minor content
changes in Sections 1 and 2 and Fig. 9 captio
Symbol calculus and zeta--function regularized determinants
In this work, we use semigroup integral to evaluate zeta-function regularized
determinants. This is especially powerful for non--positive operators such as
the Dirac operator. In order to understand fully the quantum effective action
one should know not only the potential term but also the leading kinetic term.
In this purpose we use the Weyl type of symbol calculus to evaluate the
determinant as a derivative expansion. The technique is applied both to a
spin--0 bosonic operator and to the Dirac operator coupled to a scalar field.Comment: Added references, some typos corrected, published versio
Electrostatic Interactions of Asymmetrically Charged Membranes
We predict the nature (attractive or repulsive) and range (exponentially
screened or long-range power law) of the electrostatic interactions of
oppositely charged and planar plates as a function of the salt concentration
and surface charge densities (whose absolute magnitudes are not necessarily
equal). An analytical expression for the crossover between attractive and
repulsive pressure is obtained as a function of the salt concentration. This
condition reduces to the high-salt limit of Parsegian and Gingell where the
interaction is exponentially screened and to the zero salt limit of Lau and
Pincus in which the important length scales are the inter-plate separation and
the Gouy-Chapman length. In the regime of low salt and high surface charges we
predict - for any ratio of the charges on the surfaces - that the attractive
pressure is long-ranged as a function of the spacing. The attractive pressure
is related to the decrease in counter-ion concentration as the inter-plate
distance is decreased. Our theory predicts several scaling regimes with
different scaling expressions for the pressure as function of salinity and
surface charge densities. The pressure predictions can be related to surface
force experiments of oppositely charged surfaces that are prepared by coating
one of the mica surfaces with an oppositely charged polyelectrolyte
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