Lyapunov Stability Analysis of Power Systems

Over the past ten years, a vast outflow of research and publications has resulted from the use of Lyapunov\u27s second or direct method of stability analysis. This research trend stems from the appearance of the original work of Lyapunov in 1892, more than three quarters of a century ago; but only recently has this concept been appreciated to the point where researchers in the area of stability of dynamic systems are aware of its potentialities. La Salle and Lefschetz wrote the first comprehensive book in English about Lyapunov stability theory. In most cases describing a physical system, the energy stored in the system appears to be a natural candidate. This is neither a necessary nor a sufficient criterion for choosing a function and many examples of stable systems are known where the energy is not a suitable Lyapunov function. The extension of this abstract theory to the analysis of real-world problems has posed yet another problem; the conflict between the theorist and the practitioner. This treatise envisages the study of large power system stability with the aid of Lyapunov functions. The primary purpose of the investigation is an extensive study of Willems\u27 conjecture (discussed in Chapter III) for the derivation of Lyapunov functions for multimachine power systems. The study extends the Lyapunov method to analyze operations of practical significance such as automatic circuit reclosing. An investigation is made into the effects of parameter variation on the extent of stability. New methods of generating Lyapunov functions have also been attempted. Wall\u27s energy metric algorithm is shown to yield a suitable function for the analysis of a second-order system. Two systems have been studied using Lyapunov stability analysis. The advantages and disadvantages of Lyapunov\u27s method are discussed and some suggestions are offered for further research

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Cosmic acceleration in a model of scalar-tensor gravitation

In this paper we consider a model of scalar-tensor theory of gravitation in which the scalar field, $\phi$ determines the gravitational coupling G and has a Lagrangian of the form, $\mathcal{L}_{\phi} =-V(\phi)\sqrt{1 - \partial_{\mu}\phi\partial^{\mu}\phi}$. We study the cosmological consequence of this theory in the matter dominated era and show that this leads to a transition from an initial decelerated expansion to an accelerated expansion phase at the present epoch. Using observational constraints, we see that the effective equation of state today for the scalar field turns out to be $p_{\phi}=w_{\phi}{\rho}_{\phi}$, with $w_{\phi}=-0.88$ and that the transition to an accelerated phase happened at a redshift of about 0.3.Comment: 12 pages, 2 figures, matches published versio

Sonoluminescence as Quantum Vaccum Radiation

We argue that the available experimental data is not compatible with models of sonoluminescence which invoke dynamical properties of the interface without regard to the compositional properties of the trapped gas inside the bubble.Comment: 2 pages,Revtex,No figures,Submitted to PRL(comments

Unexpected and Abnormally Low Hdl Cholesterol Levels on Combination Hypolipidemic Therapy

Abstract In general, Indians have low HDL cholesterol levels. Fenofibrate, a drug widely used in the treatment of hypertriglyceridemia, usually also increases HDL cholesterol. There have been a few reports in the literature of a paradoxical decrease in serum HDL-cholesterol in patients treated with fenofibrate, either alone or in combination with a statin. We report three cases of paradoxical decrease in serum HDL- cholesterol in type 2 diabetic patients treated with a statin-fenofibrate combination

A comparative study of night-time enhancement of TEC at a low latitude station on storm and quiet nights including the local time, seasonal and solar activity dependence

International audienceThe main characteristics of night-time enhancements in TEC during magnetic storms are compared with those during quiet nights for different seasons and solar activity conditions at Palehua, a low latitude station during the period 1980?1989. We find that the mean amplitude has both a seasonal and solar activity dependence: in winter, the values are higher for weak storms as compared to those during quiet nights and increase with an increase in solar activity. In summer, the mean amplitude values during weak storms and quiet nights are almost equal. But during equinox, the mean amplitude values for quiet nights are greater than those during weak storms. The mean half-amplitude duration is higher during weak storms as compared to that during quiet nights in summer. However, during winter and equinox, the durations are almost equal for both quiet and weak storm nights. For the mean half-amplitude duration, the quiet night values for all the seasons and equinoctial weak storm values increase with an increase in solar activity. The occurrence frequency (in percent) of TEC enhancement during weak storms is greater than during quiet nights for all seasons. The mean amplitude, the mean half-amplitude duration and the occurrence frequency (in percent) of TEC enhancement values are higher during major storms as compared to those during quiet nights. The above parameters have their highest values during pre-midnight hours. From the data analysed, this behaviour is true in the case of major storms also

Macroscopic synthesis and characterization of giant fullerenes

Thermal treatment of carbon soot produced by arc evaporation of nickel-filled graphite rods in 500 Torr of helium gives giant fullerenes showing characteristic IR, Raman, NMR and powder XRD signatures. Transmission electron micrographs show faceted structures with pentagonal, hexagonal and spherical shapes. The simplicity and similarity of the IR spectrum with those of smaller fullerenes suggest that the material is a form of large fullerenes. Chemical treatment of the material gives carbon onions

A note on perfect scalar fields

We derive a condition on the Lagrangian density describing a generic, single, non-canonical scalar field, by demanding that the intrinsic, non-adiabatic pressure perturbation associated with the scalar field vanishes identically. Based on the analogy with perfect fluids, we refer to such fields as perfect scalar fields. It is common knowledge that models that depend only on the kinetic energy of the scalar field (often referred to as pure kinetic models) possess no non-adiabatic pressure perturbation. While we are able to construct models that seemingly depend on the scalar field and also do not contain any non-adiabatic pressure perturbation, we find that all such models that we construct allow a redefinition of the field under which they reduce to pure kinetic models. We show that, if a perfect scalar field drives inflation, then, in such situations, the first slow roll parameter will always be a monotonically decreasing function of time. We point out that this behavior implies that these scalar fields can not lead to features in the inflationary, scalar perturbation spectrum.Comment: v1: 11 pages; v2: 11 pages, minor changes, journal versio