Stability and convergence of implicit numerical methods for a class of fractional advection-dispersion models

In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 < γ < 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with damping with index 1 < γ < 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for example, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.

Practical stability of approximating discrete-time filters with respect to model mismatch

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Practical stability is established in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Improving stability of a DFIG-based wind power system with tuned damping controller

This paper focuses on the implementation of a damping controller for the doubly fed induction generator (DFIG) system. Coordinated tuning of the damping controller to enhance the damping of the oscillatory modes is presented using bacterial foraging technique. The effect of the tuned damping controller on converter ratings of the DFIG system is also investigated. The results of both eigenvalue analysis and the time-domain simulation studies are presented to elucidate the effectiveness of the tuned damping controller in the DFIG system. The improvement of the fault ride-through capability of the system is also demonstrated.

Rough fuzzy control of SVC for power system stability enhancement

This paper presents a new approach to the design of a rough fuzzy controller for the control loop of the SVC (static VAR system) in a two area power system for stability enhancement with particular emphasis on providing effective damping for oscillatory instabilities. The performances of the rough fuzzy and the conventional fuzzy controller are compared with that of the conventional PI controller for a variety of transient disturbances, highlighting the effectiveness of the rough fuzzy controller in damping the inter-area oscillations. The effect of the rough fuzzy controller in improving the CCT (critical clearing time) of the two area system is elaborated in this paper as well.

Sufficiently informative measurements for stability of approximate conditional mean estimates

This paper establishes sufficient conditions to bound the error in perturbed conditional mean estimates derived from a perturbed model (only the scalar case is shown in this paper but a similar result is expected to hold for the vector case). The results established here extend recent stability results on approximating information state filter recursions to stability results on the approximate conditional mean estimates. The presented filter stability results provide bounds for a wide variety of model error situations.

Probability analysis of machine angle stability with non-gaussian wind power input

The security of power transfer across a given transmission link is typically a steady state assessment. This paper develops tools to assess machine angle stability as affected by a combination of faults and uncertainty of wind power using probability analysis. The paper elaborates on the development of the theoretical assessment tool and demonstrates its efficacy using single machine infinite bus system.

Stability studies of HIV-1 Pr55gag virus-like particles made in insect cells after storage in various formulation media

Background: HIV-1 Pr55gag virus-like particles (VLPs) expressed by baculovirus in insect cells are considered to be a very promising HIV-1 vaccine candidate, as they have been shown to elicit broad cellular immune responses when tested in animals, particularly when used as a boost to DNA or BCG vaccines. However, it is important for the VLPs to retain their structure for them to be fully functional and effective. The medium in which the VLPs are formulated and the temperature at which they are stored are two important factors affecting their stability. FINDINGS We describe the screening of 3 different readily available formulation media (sorbitol, sucrose and trehalose) for their ability to stabilise HIV-1 Pr55gag VLPs during prolonged storage. Transmission electron microscopy (TEM) was done on VLPs stored at two different concentrations of the media at three different temperatures (4[degree sign]C, --20[degree sign]C and -70[degree sign]C) over different time periods, and the appearance of the VLPs was compared. VLPs stored in 15% trehalose at -70[degree sign]C retained their original appearance the most effectively over a period of 12 months. VLPs stored in 5% trehalose, sorbitol or sucrose were not all intact even after 1 month storage at the temperatures tested. In addition, we showed that VLPs stored under these conditions were able to be frozen and re-thawed twice before showing changes in their appearance. Conclusions Although the inclusion of other analytical tools are essential to validate these preliminary findings, storage in 15% trehalose at -70[degree sign]C for 12 months is most effective in retaining VLP stability.

Pulse dynamics in a three-component system : stability and bifurcations

In this article, we analyze the stability and the associated bifurcations of several types of pulse solutions in a singularly perturbed three-component reaction-diffusion equation that has its origin as a model for gas discharge dynamics. Due to the richness and complexity of the dynamics generated by this model, it has in recent years become a paradigm model for the study of pulse interactions. A mathematical analysis of pulse interactions is based on detailed information on the existence and stability of isolated pulse solutions. The existence of these isolated pulse solutions is established in previous work. Here, the pulse solutions are studied by an Evans function associated to the linearized stability problem. Evans functions for stability problems in singularly perturbed reaction-diffusion models can be decomposed into a fast and a slow component, and their zeroes can be determined explicitly by the NLEP method. In the context of the present model, we have extended the NLEP method so that it can be applied to multi-pulse and multi-front solutions of singularly perturbed reaction-diffusion equations with more than one slow component. The brunt of this article is devoted to the analysis of the stability characteristics and the bifurcations of the pulse solutions. Our methods enable us to obtain explicit, analytical information on the various types of bifurcations, such as saddle-node bifurcations, Hopf bifurcations in which breathing pulse solutions are created, and bifurcations into travelling pulse solutions, which can be both subcritical and supercritical.

Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

Power system stability enhancement in a deregulated environment using FACTS devices

In deregulated versions of free-market electricity, producers will be free to send power along other utilities. The price of power strongly depends and fluctuates according to mutual benefit index of both supplier and consumer. In such a situation, strong interaction among utilities may cause instabilities in the system. As the frequency of market-based dispatch increases market forces tend to destabilize the stable system dynamics depending on the value of Ks/τλ(market dependent parameter) ratio. This tends to destabilize the coupled dynamics. The implementation of TCSC can effectively damp the inter area modes of oscillations of the coupled market system.

Small signal stability analysis of a DFIG based wind power system with tuned damping controller under super/sub-synchronous mode of operation

This paper focuses on the super/sub-synchronous operation of the doubly fed induction generator (DFIG) system. The impact of a damping controller on the different modes of operation for the DFIG based wind generation system is investigated. The co-ordinated tuning of the damping controller to enhance the damping of the oscillatory modes using bacteria foraging (BF) technique is presented. The results from eigenvalue analysis are presented to elucidate the effectiveness of the tuned damping controller in the DFIG system. The robustness issue of the damping controller is also investigated

Numerical solutions of stochastic differential equations – implementation and stability issues

Stochastic differential equations (SDEs) arise fi om physical systems where the parameters describing the system can only be estimated or are subject to noise. There has been much work done recently on developing numerical methods for solving SDEs. This paper will focus on stability issues and variable stepsize implementation techniques for numerically solving SDEs effectively.

Factors affecting the stability analysis of earth dam slopes subjected to reservoir drawdown

The drawdown of reservoirs can significantly affect the stability of upstream slopes of earth dams. This is due to the removal of the balancing hydraulic forces acting on the dams and the undrained condition within the upstream slope soils. In such scenarios, the stability of the slopes can be influenced by a range of factors including drawdown rates, slope inclination and soil properties. This paper investigates the effects of drawdown rate, saturated hydraulic conductivity and unsaturated shear strength of dam materials on the stability of the upstream slope of an earth dam. In this study, the analysis of pore-water pressure changes within the upstream slope during reservoir drawdown was coupled with the slope stability analysis using the general limit equilibrium method. The results of the analysis suggested that a decrease in the reservoir water level caused the stability of the upstream slope to decrease. The dam embankment constructed with highly permeable soil was found to be more stable during drawdown scenarios, compared to others. Further, lower drawdown rates resulted in a higher safety factor for the upstream slope. Also, the safety factor of the slope calculated using saturated shear strength properties of the dam materials was slightly higher than that calculated using unsaturated shear strength properties. In general, for all the scenarios analysed, the lowest safety factor was found to be at the reservoir water level of about 2/3 of drawdown regime.

Preliminary study on the stability of highly sensitive fiber Bragg grating temperature sensors [对高灵敏光纤光栅温度传感器的稳定性的初探]

As a novel sensitive element and due to its advantages of immunity to electrical interference, distributed measurement, etc., fiber Bragg grating (FBG) has been researched widely. To realize the substitution of high accurate electronic temperature sensors, high sensitive FBG temperature sensors can be made by taking advantage of its characters of being sensitive to both temperature and strain. Although there are reports about high sensitive FBG temperature sensors, however, few about their stability have been done. We manufactured a high sensitive FBG temperature sensor, and put it together with an average FBG temperature sensor and an electronic crystal temperature sensor into a stainless steel container filled by water to observe the room temperature change. By comparing their results in two weeks, we have found out that: although the high sensitive FBG temperature sensor is in much better agreement with the electronic crystal sensor than the average FBG sensor is, it has occurred some small drifts. Because the drifts appeared in the process of further pulling the FBG, it might be a result of the slip of the FBG fixing points. This contributes some good experiences to the application of FBG in high accuracy temperature measurement.