Direct stability evaluation of power systems with detailed generator models using structure-preserving energy functions

Energy-based direct methods for transient stability analysis are potentially useful both as offline tools for planning purposes as well as for online security assessment. In this paper, a novel structure-preserving energy function (SPEF) is developed using the philosophy of structure-preserving model for the system and detailed generator model including flux decay, transient saliency, automatic voltage regulator (AVR), exciter and damper winding. A simpler and yet general expression for the SPEF is also derived which can simplify the computation of the energy function. The system equations and the energy function are derived using the centre-of-inertia (COI) formulation and the system loads are modelled as arbitrary functions of the respective bus voltages. Application of the proposed SPEF to transient stability evaluation of power systems is illustrated with numerical examples.

Dynamic security assessment of power systems using structure-preserving energy functions

An application of direct methods to dynamic security assessment of power systems using structure-preserving energy functions (SPEF) is presented. The transient energy margin (TEM) is used as an index for checking the stability of the system as well as ranking the contigencies based on their severity. The computation of the TEM requires the evaluation of the critical energy and the energy at fault clearing. Usually this is done by simulating the faulted trajectory, which is time-consuming. In this paper, a new algorithm which eliminates the faulted trajectory estimation is presented to calculate the TEM. The system equations and the SPEF are developed using the centre-of-inertia (COI) formulation and the loads are modelled as arbitrary functions of the respective bus voltages. The critical energy is evaluated using the potential energy boundary surface (PEBS) method. The method is illustrated by considering two realistic power system examples.

Energy Functions And Basic Equations For Ferroelectrics

Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

Potential energy functions for ground state surfaces of HCO and HNO

Analytical potential functions are reported for the ground state surfaces of HCO and HNO, the functions being derived from spectroscopic and ab initio data. Harmonized force fields have been deduced for the stable configurations of both molecules and vibration frequencies predicted for the metastable species COH and NOH.

A New Structure Preserving Energy Function Incorporating Transmission Line Resistances

A novel method to account for the transmission line resistances in structure preserving energy functions (SPEF) is presented in this paper. The method exploits the equivalence of a lossy network having the same conductance to susceptance ratio for all its elements to a lossless network with a new set of power injections. The system equations and the energy function are developed using centre of inertia (COI) variables and the loads are modelled as arbitrary functions of respective bus voltages. The application of SPEF to direct transient stability evaluation is presented considering a realistic power system example.

Energy demands of diverse spiking cells from the neocortex, hippocampus, and thalamus

It has long been known that neurons in the brain are not physiologically homogeneous. In response to current stimulus, they can fire several distinct patterns of action potentials that are associated with different physiological classes ranging from regular-spiking cells, fast-spiking cells, intrinsically bursting cells, and low-threshold cells. In this work we show that the high degree of variability in firing characteristics of action potentials among these cells is accompanied with a significant variability in the energy demands required to restore the concentration gradients after an action potential. The values of the metabolic energy were calculated for a wide range of cell temperatures and stimulus intensities following two different approaches. The first one is based on the amount of Na+ load crossing the membrane during a single action potential, while the second one focuses on the electrochemical energy functions deduced from the dynamics of the computational neuron models. The results show that the thalamocortical relay neuron is the most energy-efficient cell consuming between 7 and 18 nJ/cm(2) for each spike generated, while both the regular and fast spiking cells from somatosensory cortex and the intrinsically-bursting cell from a cat visual cortex are the least energy-efficient, and can consume up to 100 nJ/cm(2) per spike. The lowest values of these energy demands were achieved at higher temperatures and high external stimuli.

Analytical potential energy function and spectroscopic parameters for the ground and excited states of NaH

set of energies at different internuclear distances for the ground electronic state and two excited electronic states of NaH molecule have been calculated using valence internally contracted multireference configuration interaction(MRCI) including Davidson correction and three basis sets. Then, a potential energy curve (PEC) for each state was determined by extrapolating MRCI energies to the complete basis sets limit. Based on the PECs, accurate vibrational energy levels and rotational constants were determined. The computational PECs are were fitted to analytical potential energy functions using the Murrell-Sorbie potential function. Then, accurate spectroscopic parameters were calculated. Compared with experimental results, values obtained with the basis set extrapolation yield a potential energy curve that gives accurate vibrational energy levels, rotational constants and spectroscopic parameters for the NaH molecule. (C) 2004 Elsevier B.V. All rights reserved.

Protein Docking by the Underestimation of Free Energy Funnels in the Space of Encounter Complexes

Similarly to protein folding, the association of two proteins is driven by a free energy funnel, determined by favorable interactions in some neighborhood of the native state. We describe a docking method based on stochastic global minimization of funnel-shaped energy functions in the space of rigid body motions (SE(3)) while accounting for flexibility of the interface side chains. The method, called semi-definite programming-based underestimation (SDU), employs a general quadratic function to underestimate a set of local energy minima and uses the resulting underestimator to bias further sampling. While SDU effectively minimizes functions with funnel-shaped basins, its application to docking in the rotational and translational space SE(3) is not straightforward due to the geometry of that space. We introduce a strategy that uses separate independent variables for side-chain optimization, center-to-center distance of the two proteins, and five angular descriptors of the relative orientations of the molecules. The removal of the center-to-center distance turns out to vastly improve the efficiency of the search, because the five-dimensional space now exhibits a well-behaved energy surface suitable for underestimation. This algorithm explores the free energy surface spanned by encounter complexes that correspond to local free energy minima and shows similarity to the model of macromolecular association that proceeds through a series of collisions. Results for standard protein docking benchmarks establish that in this space the free energy landscape is a funnel in a reasonably broad neighborhood of the native state and that the SDU strategy can generate docking predictions with less than 5 � ligand interface Ca root-mean-square deviation while achieving an approximately 20-fold efficiency gain compared to Monte Carlo methods.

Analytical potentials for triatomic molecules IX. The prediction of anharmonic force constants from potential energy surfaces based on harmonic force fields and dissociation energies for SO2 and O3

Analytical potential energy functions which are valid at all dissociation limits have been derived for the ground states of SO2 and O3. The procedure involves minimizing the errors between the observed vibrational spectra and spectra calculated by a variational procedure. Good agreement is obtained between the observed and calculated spectra for both molecules. Comparisons are made between anharmonic force fields, previously determined from the spectral data, and the force fields obtained by differentiating the derived analytical functions at the equilibrium configurations.

Analytical potentials for triatomic molecules from spectroscopic data VI. On choosing internal coordinates to describe triatomic potential energy surfaces with more than one minimum

Orthogonal internal coordinates are defined which have useful properties for constructing the potential energy functions of triatomic molecules with two or three minima on the surface. The coordinates are used to obtain ground state potentials of ClOO and HOF, both of which have three minima.

Parameterizing a Simple Potential Energy Function Appropriate for Vibrational Frequencies Using Molecular Dynamics

A Maple scheme for quickly parameterizing vibrational potential energy functions is presented. As an example, the potential energy function's parameters for the vibrational motions in H_2O_2 are obtained assuming the simplest potential energy function. This paper was originally written as a research paper, but rejected by the referees. It is therefore being edited into an ``educational'' paper for student usage.

Correlations between designability and various structural characteristics of protein lattice models

Using six kinds of lattice types (4×4 ,5×5 , and6×6 square lattices;3×3×3 cubic lattice; and2+3+4+3+2 and4+5+6+5+4 triangular lattices), three different size alphabets (HP ,HNUP , and 20 letters), and two energy functions, the designability of proteinstructures is calculated based on random samplings of structures and common biased sampling (CBS) of proteinsequence space. Then three quantities stability (average energy gap),foldability, and partnum of the structure, which are defined to elucidate the designability, are calculated. The authors find that whatever the type of lattice, alphabet size, and energy function used, there will be an emergence of highly designable (preferred) structure. For all cases considered, the local interactions reduce degeneracy and make the designability higher. The designability is sensitive to the lattice type, alphabet size, energy function, and sampling method of the sequence space. Compared with the random sampling method, both the CBS and the Metropolis Monte Carlo sampling methods make the designability higher. The correlation coefficients between the designability, stability, and foldability are mostly larger than 0.5, which demonstrate that they have strong correlation relationship. But the correlation relationship between the designability and the partnum is not so strong because the partnum is independent of the energy. The results are useful in practical use of the designability principle, such as to predict the proteintertiary structure.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.