A structure-preserving energy function for stability analysis of AC/DC systems

Direct stability analysis ofAC/DC power systems using a structure-preserving energy function (SPEF) is proposed in this paper. The system model considered retains the load buses thereby enabling the representation of nonlinear voltage dependent loads. TheHVDC system is represented with the same degree of detail as is normally done in transient stability simulation. The converter controllers can be represented by simplified or detailed models. Two or multi-terminalDC systems can be considered. The stability analysis is illustrated with a 3-machine system example and encouraging results have been obtained.

Stability of the viscous flow of a fluid through a flexible tube

The stability of Hagen-Poiseuille flow of a Newtonian fluid of viscosity eta in a tube of radius R surrounded by a viscoelastic medium of elasticity G and viscosity eta(s) occupying the annulus R < r < HR is determined using a linear stability analysis. The inertia of the fluid and the medium are neglected, and the mass and momentum conservation equations for the fluid and wall are linear. The only coupling between the mean flow and fluctuations enters via an additional term in the boundary condition for the tangential velocity at the interface, due to the discontinuity in the strain rate in the mean flow at the surface. This additional term is responsible for destabilizing the surface when the mean velocity increases beyond a transition value, and the physical mechanism driving the instability is the transfer of energy from the mean flow to the fluctuations due to the work done by the mean flow at the interface. The transition velocity Gamma(t) for the presence of surface instabilities depends on the wavenumber k and three dimensionless parameters: the ratio of the solid and fluid viscosities eta(r) = (eta(s)/eta), the capillary number Lambda = (T/GR) and the ratio of radii H, where T is the surface tension of the interface. For eta(r) = 0 and Lambda = 0, the transition velocity Gamma(t) diverges in the limits k much less than 1 and k much greater than 1, and has a minimum for finite k. The qualitative behaviour of the transition velocity is the same for Lambda > 0 and eta(r) = 0, though there is an increase in Gamma(t) in the limit k much greater than 1. When the viscosity of the surface is non-zero (eta(r) > 0), however, there is a qualitative change in the Gamma(t) vs. k curves. For eta(r) < 1, the transition velocity Gamma(t) is finite only when k is greater than a minimum value k(min), while perturbations with wavenumber k < k(min) are stable even for Gamma--> infinity. For eta(r) > 1, Gamma(t) is finite only for k(min) < k < k(max), while perturbations with wavenumber k < k(min) or k > k(max) are stable in the limit Gamma--> infinity. As H decreases or eta(r) increases, the difference k(max)- k(min) decreases. At minimum value H = H-min, which is a function of eta(r), the difference k(max)-k(min) = 0, and for H < H-min, perturbations of all wavenumbers are stable even in the limit Gamma--> infinity. The calculations indicate that H-min shows a strong divergence proportional to exp (0.0832 eta(r)(2)) for eta(r) much greater than 1.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear flow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear how of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

The effect of boundaries on the plane Couette flow of granular materials: a bifurcation analysis

The tendency of granular materials in rapid shear ow to form non-uniform structures is well documented in the literature. Through a linear stability analysis of the solution of continuum equations for rapid shear flow of a uniform granular material, performed by Savage (1992) and others subsequently, it has been shown that an infinite plane shearing motion may be unstable in the Lyapunov sense, provided the mean volume fraction of particles is above a critical value. This instability leads to the formation of alternating layers of high and low particle concentrations oriented parallel to the plane of shear. Computer simulations, on the other hand, reveal that non-uniform structures are possible even when the mean volume fraction of particles is small. In the present study, we have examined the structure of fully developed layered solutions, by making use of numerical continuation techniques and bifurcation theory. It is shown that the continuum equations do predict the existence of layered solutions of high amplitude even when the uniform state is linearly stable. An analysis of the effect of bounding walls on the bifurcation structure reveals that the nature of the wall boundary conditions plays a pivotal role in selecting that branch of non-uniform solutions which emerges as the primary branch. This demonstrates unequivocally that the results on the stability of bounded shear flow of granular materials presented previously by Wang et al. (1996) are, in general, based on erroneous base states.

Appraisal of Bishop's method of slope stability analysis

The stability of slopes is a major problem in geotechnical engineering. Of the methods available for the analysis of soil slopes such as limit equilibrium methods, limit analysis and numerical methods such as FEM and FDM, limit equilibrium methods are popular and generally used, owing to their simplicity in formulation and in evaluating the overall factor of safety of slope. However limit equilibrium methods possess certain disadvantages. They do not consider whether the slope is an embankment or natural slope or an excavation and ignore the effect of incremental construction, initial stress, stress strain behavior etc. In the work reported in this paper, a comparative study of actual state of stress and actual factor of safety and Bishop's factor of safety is performed. The actual factor of safety is obtained by consideration of contours of mobilised shear strains. Using Bishop's method of slices, the critical slip surfaces of a number of soil slopes with different geometries are determined and both the factors of safety are obtained. The actual normal stresses and shear stresses are determined from finite difference formulation using FLAG (Fast Lagrangian Analysis of Continuaa) with Mohr-Coulomb model. The comparative study is performed in terms of parameter lambda(c phi) (= gamma H tan phi/c). I is shown that actual factor of safety is higher than Bishop's factor of safety depending on slope angle and lambda(c phi).

Pseudo-Static and Pseudo-Dynamic Stability Analysis of Tailings Dam Under Seismic Conditions

In this paper the seismic slope stability analyses are performed for a typical section of 44 m high water retention type tailings earthen dam located in the eastern part of India, using both the conventional pseudo-static and recent pseudo-dynamic methods. The tailings earthen dam is analyzed for different upstream conditions of reservoir like filled up with compacted and non-compacted dumped waste materials with different water levels of the pond tailings portion. Phreatic surface is generated using seepage analysis in geotechnical software SEEP/W and that same is used in the pseudo-static and pseudo-dynamic analyses to make the approach more realistic. The minimum values of factor of safety using pseudo-static and pseudo-dynamic method are obtained as 1.18 and 1.09 respectively for the chosen seismic zone in India. These values of factor of safety show clearly the demerits of conventional pseudo-static analysis compared to recent pseudo-dynamic analysis, where in addition to the seismic accelerations, duration, frequency of earthquake, body waves traveling during earthquake and amplification effects are considered.

Analytical theory and stability analysis of an elongated nanoscale object under external torque

We consider the rotational motion of an elongated nanoscale object in a fluid under an external torque. The experimentally observed dynamics could be understood from analytical solutions of the Stokes equation, with explicit formulae derived for the dynamical states as a function of the object dimensions and the parameters defining the external torque. Under certain conditions, multiple analytical solutions to the Stokes equations exist, which have been investigated through numerical analysis of their stability against small perturbations and their sensitivity towards initial conditions. These experimental results and analytical formulae are general enough to be applicable to the rotational motion of any isolated elongated object at low Reynolds numbers, and could be useful in the design of non-spherical nanostructures for diverse applications pertaining to microfluidics and nanoscale propulsion technologies.

Stability analysis of aperiodic messages scheduled in the dynamic segment of flex ray protocol

In a cyber physical system like vehicles number of signals to be communicated in a network system has an increasing trend. More and more mechanical and hydraulic parts are replaced by electronic control units and infotainment and multimedia applications has increased in vehicles. Safety critical hard real time messages and aperiodic messages communicated between electronic control units have been increased in recent times. Flexray is a high bandwidth protocol consisting of static segment for supporting hard real time messages and a dynamic segment for transmitting soft and non real time messages. In this paper, a method to obtain the stability region for the random arrival of messages in each electronic control units which is scheduled in the dynamic segment of Flexray protocol is presented. Number of mini slots available in the dynamic segment of Flexray restricts the arrival rate of tasks to the micro controllers or the number of micro controllers connected to the Flexray bus. Stability region of mathematical model of the system is compared with the Flexray protocol simulation results.

Exponential compact higher order scheme and their stability analysis for unsteady convection-diffusion equations

Exponential compact higher-order schemes have been developed for unsteady convection-diffusion equation (CDE). One of the developed scheme is sixth-order accurate which is conditionally stable for the Peclet number 0 <= Pe <= 2.8 and the other is fourth-order accurate which is unconditionally stable. Schemes for two-dimensional (2D) problems are made to use alternate direction implicit (ADI) algorithm. Example problems are solved and the numerical solutions are compared with the analytical solutions for each case.

Design and development of Fiber Bragg Grating sensing plate for plantar strain measurement and postural stability analysis

This paper describes an ab initio design and development of a novel Fiber Bragg Grating (FBG) sensor based strain sensing plate for the measurement of plantar strain distribution in human foot. The primary aim of this work is to study the feasibility of usage of FBG sensors in the measurement of plantar strain in the foot; in particular, to spatially resolve the strain distribution in the foot at different regions such as fore-foot, mid-foot and hind-foot. This study also provides a method to quantify and compare relative postural stability of different subjects under test; in addition, traditional accelerometers have been used to record the movements of center of gravity (second lumbar vertebra) of the subject and the results obtained have been compared against the outcome of the postural stability studies undertaken using the developed FBG plantar strain sensing plate. (C) 2013 Elsevier Ltd. All rights reserved.

Small-Signal Stability Analysis of an Open-loop Induction Motor Drive Including the Effect of Inverter Dead-Time

This paper demonstrates light-load instability in open-loop induction motor drives on account of inverter dead-time. The dynamic equations of an inverter fed induction motor, incorporating the effect of dead-time, are considered. A procedure to derive the small-signal model of the motor, including the effect of inverter dead-time, is presented. Further, stability analysis is carried out on a 100-kW, 415V, 3-phase induction motor considering no-load. For voltage to frequency (i.e. V/f) ratios between 0.5 and 1 pu, the analysis brings out regions of instability on the V-f plane, in the frequency range between 5Hz and 20Hz. Simulation and experimental results show sub-harmonic oscillations in the motor current in this region, confirming instability as predicted by the analysis.

Stability of the flow in a soft tube deformed due to an applied pressure gradient

A linear stability analysis is carried out for the flow through a tube with a soft wall in order to resolve the discrepancy of a factor of 10 for the transition Reynolds number between theoretical predictions in a cylindrical tube and the experiments of Verma and Kumaran J. Fluid Mech. 705, 322 (2012)]. Here the effect of tube deformation (due to the applied pressure difference) on the mean velocity profile and pressure gradient is incorporated in the stability analysis. The tube geometry and dimensions are reconstructed from experimental images, where it is found that there is an expansion and then a contraction of the tube in the streamwise direction. The mean velocity profiles at different downstream locations and the pressure gradient, determined using computational fluid dynamics, are found to be substantially modified by the tube deformation. The velocity profiles are then used in a linear stability analysis, where the growth rates of perturbations are calculated for the flow through a tube with the wall modeled as a neo-Hookean elastic solid. The linear stability analysis is carried out for the mean velocity profiles at different downstream locations using the parallel flow approximation. The analysis indicates that the flow first becomes unstable in the downstream converging section of the tube where the flow profile is more pluglike when compared to the parabolic flow in a cylindrical tube. The flow is stable in the upstream diverging section where the deformation is maximum. The prediction for the transition Reynolds number is in good agreement with experiments, indicating that the downstream tube convergence and the consequent modification in the mean velocity profile and pressure gradient could reduce the transition Reynolds number by an order of magnitude.

Stability of Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous layer

We present the linear stability analysis of horizontal Poiseuille flow in a fluid overlying a porous medium with anisotropic and inhomogeneous permeability. The generalized Darcy model is used to describe the flow in the porous medium with the Beavers-Joseph condition at the interface of the two layers and the eigenvalue problem is solved numerically. The effect of major system parameters on the stability characteristics is addressed in detail. It is shown that the anisotropic and inhomogeneous modulation of the permeability of the underlying porous layer provides an effective means for passive control of the flow stability.