363 research outputs found
On Stability of a Distributed Averaging PI Frequency and Active Power Controlled Differential-Algebraic Power System Model
We consider the problems of stability, frequency restoration and optimal steady-state resource allocation in a heterogeneous and structure-preserving differential-algebraic equation (DAE) power system model. Thereby, we include constant-power-controlled loads (CPCLs) and constant-power-controlled sources (CPCSs) explicitly in the analysis and network control design. This results in a power system model with mixed algebraic as well as first- and second-order differential dynamics. We show that the abovementioned control objectives can be achieved via a distributed averaging proportional integral (DAPI) control and, in particular, extend the stability proof in [1] to the resulting closed-loop DAE system
Comparison of an h- and hp-Adaptive Finite Element Solver for Chemo-Mechanically Coupled Battery Electrode Particles
Numerical investigations of mechanical stresses for phase transforming battery electrode materials on the particle scale are computationally highly demanding. The limitations are mainly induced by the strongly varying spatial and temporal scales of the underlying phase field model, which require an ultra fine mesh and time resolution, however, solely at specific stages in space and time. To overcome these numerical difficulties we present a general-purpose space and time adaptive solution algorithm based on an hp-adaptive finite element method and a variable-step, variable-order time integrator. At the example of a chemo-mechanical electrode particle model we demonstrate the computational savings gained by the hp-adaptivity. In particular, we compare the results to an h-adaptive finite element method and show the reduction of computational complexity
Simulation of the Deformation for Cycling Chemo-Mechanically Coupled Battery Active Particles with Mechanical Constraints
Next-generation lithium-ion batteries with silicon anodes have positive characteristics due to higher energy densities compared to state-of-the-art graphite anodes. However, the large volume expansion of silicon anodes can cause high mechanical stresses, especially if the battery active particle cannot expand freely. In this article, a thermodynamically consistent continuum model for coupling chemical and mechanical effects of electrode particles is extended by a change in the boundary condition for the displacement via a variational inequality. This switch represents a limited enlargement of the particle swelling or shrinking due to lithium intercalation or deintercalation in the host material, respectively. For inequality constraints as boundary condition a smaller time step size is need as well as a locally finer mesh. The combination of a primal-dual active set algorithm, interpreted as semismooth Newton method, and a spatial and temporal adaptive algorithm allows the efficient numerical investigation based on a finite element method. Using the example of silicon, the chemical and mechanical behavior of one- and two-dimensional representative geometries for a charge-discharge cycle is investigated. Furthermore, the efficiency of the adaptive algorithm is demonstrated. It turns out that the size of the gap has an significant influence on the maximal stress value and the slope of the increase. Especially in two dimension, the obstacle can cause an additional region with a lithium-poor phase
Simulation of the Deformation for Cycling Chemo-Mechanically Coupled Battery Active Particles with Mechanical Constraints
Next-generation lithium-ion batteries with silicon anodes have positive
characteristics due to higher energy densities compared to state-of-the-art
graphite anodes. However, the large volume expansion of silicon anodes can
cause high mechanical stresses, especially if the battery active particle
cannot expand freely. In this article, a thermodynamically consistent continuum
model for coupling chemical and mechanical effects of electrode particles is
extended by a change in the boundary condition for the displacement via a
variational inequality. This switch represents a limited enlargement of the
particle swelling or shrinking due to lithium intercalation or deintercalation
in the host material, respectively. For inequality constraints as boundary
condition a smaller time step size is need as well as a locally finer mesh. The
combination of a primal-dual active set algorithm, interpreted as semismooth
Newton method, and a spatial and temporal adaptive algorithm allows the
efficient numerical investigation based on a finite element method. Using the
example of silicon, the chemical and mechanical behavior of one- and
two-dimensional representative geometries for a charge-discharge cycle is
investigated. Furthermore, the efficiency of the adaptive algorithm is
demonstrated. It turns out that the size of the gap has an significant
influence on the maximal stress value and the slope of the increase. Especially
in two dimension, the obstacle can cause an additional region with a
lithium-poor phase
Convergence of simple adaptive Galerkin schemes based on h − h/2 error estimators
We discuss several adaptive mesh-refinement strategies based on (h − h/2)-error estimation. This class of adaptivemethods is particularly popular in practise since it is problem independent and requires virtually no implementational overhead. We prove that, under the saturation assumption, these adaptive algorithms are convergent. Our framework applies not only to finite element methods, but also yields a first convergence proof for adaptive boundary element schemes. For a finite element model problem, we extend the proposed adaptive scheme and prove convergence even if the saturation assumption fails to hold in general
Rotational state-changing collisions between N and Rb at low energies
We present a theoretical study of rotationally elastic and inelastic
collisions between molecular nitrogen ions and Rb atoms in the sub-Kelvin
temperature regime prevalent in ion-atom hybrid trapping experiments. The cross
sections for rotational excitation and de-excitation collisions were calculated
using quantum-scattering methods on ab-initio potential energy surfaces for the
energetically lowest singlet electronic channel of the system. We find that the
rotationally inelastic collision rates are at least an order of magnitude
smaller than the charge-exchange rates found in this system, rendering
inelastic processes a minor channel under the conditions of typical hybrid
trapping experiments.Comment: 6 pages, 5 figures, Computational study of rotational state changing
collision
On Metric Dimension of Functigraphs
The \emph{metric dimension} of a graph , denoted by , is the
minimum number of vertices such that each vertex is uniquely determined by its
distances to the chosen vertices. Let and be disjoint copies of a
graph and let be a function. Then a
\emph{functigraph} has the vertex set
and the edge set . We study how
metric dimension behaves in passing from to by first showing that
, if is a connected graph of order
and is any function. We further investigate the metric dimension of
functigraphs on complete graphs and on cycles.Comment: 10 pages, 7 figure
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In situ Raman spectroscopy on silicon nanowire anodes integrated in lithium ion batteries
Rapid decay of silicon anodes during lithiation poses a significant challenge in application of silicon as an anode material in lithium ion batteries. In situ Raman spectroscopy is a powerful method to study the relationship between structural and electrochemical data during electrode cycling and to allow the observation of amorphous as well as liquid and transient species in a battery cell. Herein, we present in situ Raman spectroscopy on high capacity electrode using uncoated and carbon-coated silicon nanowires during first lithiation and delithiation cycle in an optimized lithium ion battery setup and complement the results with operando X-ray reflection diffraction measurements. During lithiation, we were able to detect a new Raman signal at 1859 cm−1 especially on uncoated silicon nanowires. The detailed in situ Raman measurement of the first lithiation/delithiation cycle allowed to differentiate between morphology changes of the electrode as well as interphase formation from electrolyte components
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