State estimation in power systems using linear model infinity norm-based trust region approach

State estimation is one of the most important functions in an energy control centre. An computationally efficient state estimator which is free from numerical instability/ill-conditioning is essential for security assessment of electric power grid. Whereas approaches to successfully overcome the numerical ill-conditioning issues have been proposed, an efficient algorithm for addressing the convergence issues in the presence of topological errors is yet to be evolved. Trust region (TR) methods have been successfully employed to overcome the divergence problem to certain extent. In this study, case studies are presented where the conventional algorithms including the existing TR methods would fail to converge. A linearised model-based TR method for successfully overcoming the convergence issues is proposed. On the computational front, unlike the existing TR methods for state estimation which employ quadratic models, the proposed linear model-based estimator is computationally efficient because the model minimiser can be computed in a single step. The model minimiser at each step is computed by minimising the linearised model in the presence of TR and measurement mismatch constraints. The infinity norm is used to define the geometry of the TR. Measurement mismatch constraints are employed to improve the accuracy. The proposed algorithm is compared with the quadratic model-based TR algorithm with case studies on the IEEE 30-bus system, 205-bus and 514-bus equivalent systems of part of Indian grid.

Application of the random eigenvalue problem in forced response analysis of a linear stochastic structure

The random eigenvalue problem arises in frequency and mode shape determination for a linear system with uncertainties in structural properties. Among several methods of characterizing this random eigenvalue problem, one computationally fast method that gives good accuracy is a weak formulation using polynomial chaos expansion (PCE). In this method, the eigenvalues and eigenvectors are expanded in PCE, and the residual is minimized by a Galerkin projection. The goals of the current work are (i) to implement this PCE-characterized random eigenvalue problem in the dynamic response calculation under random loading and (ii) to explore the computational advantages and challenges. In the proposed method, the response quantities are also expressed in PCE followed by a Galerkin projection. A numerical comparison with a perturbation method and the Monte Carlo simulation shows that when the loading has a random amplitude but deterministic frequency content, the proposed method gives more accurate results than a first-order perturbation method and a comparable accuracy as the Monte Carlo simulation in a lower computational time. However, as the frequency content of the loading becomes random, or for general random process loadings, the method loses its accuracy and computational efficiency. Issues in implementation, limitations, and further challenges are also addressed.

Linear and nonlinear optical properties of expanded porphyrins: a DMRG study

We study absorption spectra and two photon absorption coefficient of expanded porphyrins (EPs) by the density matrix renormalization group (DMRG) technique. We employ the Pariser-Parr-Pople (PPP) Hamiltonian which includes long-range electron-electron interactions. We find that, in the 4n+2 EPs, there are two prominent low-lying one-photon excitations, while in 4n EPs, there is only one such excitation. We also find that 4n+2 EPs have large two-photon absorption cross sections compared to 4n EPs. The charge density rearrangement in the one-photon excited state is mostly at the pyrrole nitrogen site and at the meso carbon sites. In the two-photon states, the charge density rearrangement occurs mostly at the aza-ring sites. In the one-photon state, the C-C bond length in aza rings shows a tendency to become uniform. In the two-photon state, the bond distortions are on C-N bonds of the pyrrole ring and the adjoining C-C bonds which connect the pyrrole ring to the aza or meso carbon sites.

Closed-form solutions for non-uniform Euler-Bernoulli free-free beams

In this paper, the free vibration of a non-uniform free-free Euler-Bernoulli beam is studied using an inverse problem approach. It is found that the fourth-order governing differential equation for such beams possess a fundamental closed-form solution for certain polynomial variations of the mass and stiffness. An infinite number of non-uniform free-free beams exist, with different mass and stiffness variations, but sharing the same fundamental frequency. A detailed study is conducted for linear, quadratic and cubic variations of mass, and on how to pre-select the internal nodes such that the closed-form solutions exist for the three cases. A special case is also considered where, at the internal nodes, external elastic constraints are present. The derived results are provided as benchmark solutions for the validation of non-uniform free-free beam numerical codes. (C) 2013 Elsevier Ltd. All rights reserved.

A transform approach to linear network coding for acyclic networks with delay

The algebraic formulation for linear network coding in acyclic networks with each link having an integer delay is well known. Based on this formulation, for a given set of connections over an arbitrary acyclic network with integer delay assumed for the links, the output symbols at the sink nodes at any given time instant is a Fq-linear combination of the input symbols across different generations, where Fq denotes the field over which the network operates. We use finite-field discrete Fourier transform (DFT) to convert the output symbols at the sink nodes at any given time instant into a Fq-linear combination of the input symbols generated during the same generation. We call this as transforming the acyclic network with delay into n-instantaneous networks (n is sufficiently large). We show that under certain conditions, there exists a network code satisfying sink demands in the usual (non-transform) approach if and only if there exists a network code satisfying sink demands in the transform approach. Furthermore, assuming time invariant local encoding kernels, we show that the transform method can be employed to achieve half the rate corresponding to the individual source-destination mincut (which are assumed to be equal to 1) for some classes of three-source three-destination multiple unicast network with delays using alignment strategies when the zero-interference condition is not satisfied.

Does linear separability really matter? Complex visual search is explained by simple search

Visual search in real life involves complex displays with a target among multiple types of distracters, but in the laboratory, it is often tested using simple displays with identical distracters. Can complex search be understood in terms of simple searches? This link may not be straightforward if complex search has emergent properties. One such property is linear separability, whereby search is hard when a target cannot be separated from its distracters using a single linear boundary. However, evidence in favor of linear separability is based on testing stimulus configurations in an external parametric space that need not be related to their true perceptual representation. We therefore set out to assess whether linear separability influences complex search at all. Our null hypothesis was that complex search performance depends only on classical factors such as target-distracter similarity and distracter homogeneity, which we measured using simple searches. Across three experiments involving a variety of artificial and natural objects, differences between linearly separable and nonseparable searches were explained using target-distracter similarity and distracter heterogeneity. Further, simple searches accurately predicted complex search regardless of linear separability (r = 0.91). Our results show that complex search is explained by simple search, refuting the widely held belief that linear separability influences visual search.

Generalization of deviated linear cyclic pursuit

Earlier work on cyclic pursuit systems has shown that using heterogeneous gains for agents in linear cyclic pursuit, the point of convergence (rendezvous point) can be chosen arbitrarily. But there are some restrictions on this set of reachable points. The use of deviated cyclic pursuit, as discussed in this paper, expands this set of reachable points to include points which are not reachable by any known linear cyclic pursuit scheme. The limits on the deviations are determined by stability considerations. Such limits have been analytically obtained in this paper along with results on the expansion in reachable set and the latter has also been verified through simulations.

Codes for solving three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces

Three codes, that can solve three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces, are provided here. The file 'bemconst.m' contains a MATLAB code for solving three dimensional linear elastostatic problems using constant boundary elements while ignoring body forces. The file 'bemconst.f90' is a Fortran translation of the MATLAB code contained in the file 'bemconst.m'. The file 'bemconstp.f90' is a parallelized version of the Fortran code contained in the file 'bemconst.f90'. The file 'inbem96.txt' is the input file for the Fortran codes contained in the files 'bemconst.f90' and 'bemconstp.f90'. Author hereby declares that the present codes are the original works of the author. Further, author hereby declares that any of the present codes, in full or in part, is not a translation or a copy of any of the existing codes written by someone else. Author's institution (Indian Institute of Science) has informed the author in writing that the institution is not interested in claiming any copyright on the present codes. Author is hereby distributing the present codes under the MIT License; full text of the license is included in each of the files that contain the codes.

Elastic-plastic contact conditions for frictionally constrained bodies under cyclic tangential loading

A Frictionally constrained condition implies dependence of friction force on tangential displacement amplitude. The condition may occur due to chemical, physical, and/or mechanical interaction between the contacting surfaces. The condition, sometimes also referred to as the presliding condition or partial slip condition, is characterized under fretting. Under such conditions, various experimental studies indicate the existence of two distinguishable regions, that is, stick region and slip region. In the present study, frictionally constrained conditions are identified and the evolutions of stick-slip regions are investigated in detail. Investigations have been performed on self-mated stainless steel and chromium carbide coated surfaces mated against stainless steel, under both vacuum and ambient conditions. Contact conditions prevailing at the contact interface were identified based on the mechanical responses and were correlated with the surface damage observed. Surface degradation has been observed in the form of microcracks and material transfer. Detailed numerical analysis has also been performed in order to understand the energy dissipation and the damage mode involved in the surface or subsurface damage. It has been observed that under frictionally constrained conditions, the occurrence of annular slip features are mainly due to the junction growth, resulting from elastic-plastic deformation at the contact interface. Ratcheting has been observed as the governing damage mode under cyclic tangential loading condition.

Elastic thickness structure of the Andaman subduction zone: Implications for convergence of the Ninetyeast Ridge

We use the Bouguer coherence (Morlet isostatic response function) technique to compute the spatial variation of effective elastic thickness (T-e) of the Andaman subduction zone. The recovered T-e map resolves regional-scale features that correlate well with known surface structures of the subducting Indian plate and the overriding Burma plate. The major structure on the India plate, the Ninetyeast Ridge (NER), exhibits a weak mechanical strength, which is consistent with the expected signature of an oceanic ridge of hotspot origin. However, a markedly low strength (0< T-e <3 km) in that region, where the NER is close to the Andaman trench (north of 10 N), receives our main attention in this study. The subduction geometry derived from the Bouguer gravity forward modeling suggests that the NER has indented beneath the Andaman arc. We infer that the bending stresses of the viscous plate, which were reinforced within the subducting oceanic plate as a result of the partial subduction of the NER buoyant load, have reduced the lithospheric strength. The correlation, T-e < T-s (seismogenic thickness) reveals that the upper crust is actively deforming beneath the frontal arc Andaman region. The occurrence of normal-fault earthquakes in the frontal arc, low Te zone, is indicative of structural heterogeneities within the subducting plate. The fact that the NER along with its buoyant root is subducting under the Andaman region is inhibiting the subduction processes, as suggested by the changes in trench line, interrupted back-arc volcanism, variation in seismicity mechanism, slow subduction, etc. The low T-e and thinned crustal structure of the Andaman back-arc basin are attributed to a thermomechanically weakened lithosphere. The present study reveals that the ongoing back-arc spreading and strike-slip motion along the West Andaman Fault coupled with the ridge subduction exerts an important control on the frequency and magnitude of seismicity in the Andaman region. (C) 2013 Elsevier Ltd. All rights reserved.

Epoch extraction based on integrated linear prediction residual using plosion index

Epoch is defined as the instant of significant excitation within a pitch period of voiced speech. Epoch extraction continues to attract the interest of researchers because of its significance in speech analysis. Existing high performance epoch extraction algorithms require either dynamic programming techniques or a priori information of the average pitch period. An algorithm without such requirements is proposed based on integrated linear prediction residual (ILPR) which resembles the voice source signal. Half wave rectified and negated ILPR (or Hilbert transform of ILPR) is used as the pre-processed signal. A new non-linear temporal measure named the plosion index (PI) has been proposed for detecting `transients' in speech signal. An extension of PI, called the dynamic plosion index (DPI) is applied on pre-processed signal to estimate the epochs. The proposed DPI algorithm is validated using six large databases which provide simultaneous EGG recordings. Creaky and singing voice samples are also analyzed. The algorithm has been tested for its robustness in the presence of additive white and babble noise and on simulated telephone quality speech. The performance of the DPI algorithm is found to be comparable or better than five state-of-the-art techniques for the experiments considered.

Linear and nonlinear optical studies on 3,6-bis (2 pyridyl) pyridazine

3,6-Bis (2 pyridyl) pyridazine has been synthesized and characterized by NMR, XRD and elemental analyses. The vibrational studies were carried out by using FTIR and Raman spectroscopy and the modes of vibrations were analysed and compared with the theoretically calculated values. The nonlinear optical property of the title compound was examined by Kurtz-Perry method and Hyper Raleigh scattering with the fundamental wavelength of 1064nm. This compound possesses less SHG efficiency but large first hyperpolarizability. (C) 2013 Elsevier GmbH. All rights reserved.

Effects of initial height on the steady-state persistence probability of linear growth models

The effects of the initial height on the temporal persistence probability of steady-state height fluctuations in up-down symmetric linear models of surface growth are investigated. We study the (1 + 1)-dimensional Family model and the (1 + 1)-and (2 + 1)-dimensional larger curvature (LC) model. Both the Family and LC models have up-down symmetry, so the positive and negative persistence probabilities in the steady state, averaged over all values of the initial height h(0), are equal to each other. However, these two probabilities are not equal if one considers a fixed nonzero value of h(0). Plots of the positive persistence probability for negative initial height versus time exhibit power-law behavior if the magnitude of the initial height is larger than the interface width at saturation. By symmetry, the negative persistence probability for positive initial height also exhibits the same behavior. The persistence exponent that describes this power-law decay decreases as the magnitude of the initial height is increased. The dependence of the persistence probability on the initial height, the system size, and the discrete sampling time is found to exhibit scaling behavior.

Transverse elastic response of bundled coated cylinders

The overall elastic response of a bundle of coated cylinders is a major aspect of thermal, nuclear and automotive engineering designs. This paper extends the previous work on tubular bundles to assess the effect of coating material and thickness. A major contribution from this paper is determining the overall transverse elastic response of coated thick cylinders by extending the Michell stress function approach in conjunction with contact mechanics. Finite element results using contact elements pave the way for applying the contact stress boundary conditions for Michell analysis. Theoretical and finite element analyses overall give results consistent with the previous work, and the results also fall within the well-established Voigt-Reuss bounds. (C) 2013 Elsevier Ltd. All rights reserved.