Types Of Stability Problems Research Articles

Impact of the Generation System Parameters on the Frequency Response of the Power System: A UK Grid Case Study

The operation and the development of power system networks introduce new types of stability problems. The effect of the power generation and consumption on the frequency of the power system can be described as a demand/generation imbalance resulting from a sudden increase/decrease in the demand and/or generation. This paper investigates the impact of a loss of generation on the transient behaviour of the power grid frequency. A simplified power system model is proposed to examine the impact of change of the main generation system parameters (system inertia, governor droop setting, load damping constant, and the high-pressure steam turbine power fraction), on the primary frequency response in responding to the disturbance of a 1.32 GW generation loss on the UK power grid. Various rates of primary frequency responses are simulated via adjusting system parameters of the synchronous generators to enable the controlled generators providing a fast-reliable primary frequency response within 10 s after a loss of generation. It is concluded that a generation system inertia and a governor droop setting are the most dominant parameters that effect the system frequency response after a loss of generation. Therefore, for different levels of generation loss, the recovery rate will be dependent on the changes of the governor droop setting values. The proposed model offers a fundamental basis for a further investigation to be carried on how a power system will react during a secondary frequency response.

Lower Bound Limit Analysis Using Power Cone Programming for Solving Stability Problems in Rock Mechanics for Generalized Hoek–Brown Criterion

This study introduces a methodology to solve plane strain stability problems in rock mechanics, following the generalized Hoek and Brown yield criterion, by employing the lower bound finite elements limit analysis in conjunction with the power cone programming. The efficacy of the proposed approach has been demonstrated by solving three different types of stability problems: (1) finding the bearing capacity of strip footings on rock media, (2) assessing the stability of finite rock slopes, and (3) the stability analysis of unlined rectangular tunnels in rock mass. In all the cases, the results obtained from the analysis have been compared thoroughly with that computed using (1) nonlinear programming, and (2) semi-definite programming technique. The present approach has been found to be computationally very robust and it generates very accurate solutions.

Analysis on Stability and Ultimate Bearing Capacity of Steel Truss Arch Bridge

Based on the secondary development of ANSYS, a through-type steel truss arch bridge is modeled, and the most unfavorable position of live load for each concerning location of the bridge is determined by using the influence lines program self-developed with parametric language. Linear elastic stability analysis of the whole bridge is firstly conducted, and followed by calculating the ultimate bearing capacity of the bridge with the consideration of geometrical and material nonlinearity of structure. By analyzing the buckling modes and safety coefficients of two types of stability problems, and comparing the linear elastic and nonlinear stability analysis results, the first type stability analysis, as a non-conservative method, is found to be suitable for ideal structures; the second stability analysis is found to be completely different from the first stability analysis, with different buckling mode and lower stability coefficient. Therefore, it can be concluded that the ultimate carrying capacity of structures should be determined based on the second stability analysis.

A stabilization procedure for soil-water coupled problems using the element-free Galerkin method

The development of stability problems related to classical mixed methods has recently been observed. In this study, a soil-water coupled boundary-value problem, one type of stability problem, is presented using the element-free Galerkin method (EFG method). In this soil-water coupled problem, anomalous behavior appears in the pressure field unless a stabilization technique is used. The remedy to such numerical instability has generally been to adopt a higher interpolation order for the displacements than for the pore pressure. As an alternative, however, an added stabilization term is incorporated into the equilibrium equation. The advantages of this stabilization procedure are as follows: (1) The interpolation order for the pore pressure is the same as that for the displacements. Therefore, the interpolation functions in the pore pressure field do not reduce the accuracy of the numerical results. (2) The stabilization term consists of first derivatives. The first derivatives of the interpolation functions for the EFG Method are smooth, and therefore, the solutions for pore pressure are accurate. In order to validate the above stabilization technique, some numerical results are given. It can be seen from the results that a good convergence is obtained with this stabilization term.

Bifurcation Subsystem Method Based Classification for Power System Stability Problems

A bifurcation subsystem method based classification of types and classes of bifurcation is presented in this article. The study of the types of stability problems in power systems and the identification of different classes of each type of bifurcation are required in order to prescribe cures for stabilizing a specific bifurcation. With the help of the bifurcation subsystem method, this article is trying to address the following questions which have been raised: (a) what is the relation between network and dynamic bifurcation?; (b) how and why are interarea and local modes produced?; (c) what are the classes and types of bifurcation for different load models?; and (d) how do we find the bifurcation subsystem and the behaviors when singularity induced bifurcation occurs? The bifurcation subsystem method is applied to a two-area example power system and the classification of bifurcations that occur to this example system is studied thoroughly. The complete numerical examples are shown and analyzed to verify the classes of saddle-node, Hopf, and singularity induced bifurcation hypothesized previously.

Numerical stability analysis in structural dynamics

Stability analyses play an important role in structural dynamics. To treat the occurring problems properly, basic knowledge of the stability theory is required. There are so many different solution techniques in scientific books and journals that there might be doubts whether the proposed algorithms reflect the arising task sufficiently. Therefore, the objective of the present paper is to introduce a unified stability concept based on Lyapunov Exponents. From this, suitable numerical procedures for different types of stability problems can be derived directly. The efficiency of the proposed algorithms is documented by means of an appropriate example.

Dynamische Stabilitätsanalyse eines Dreigelenkstabwerks unter Verwendung numerischer Nachweiskonzepte

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Stability, queue length, and delay of deterministic and stochastic queueing networks

We present two types of stability problems: 1) conditions for queueing networks that render bounded queue lengths and bounded delay for customers, and 2) conditions for queueing networks in which the queue length distribution of a queue has an exponential tail with rate /spl theta/. To answer these two types of stability problems, we introduce two new notions of traffic characterization: minimum envelope rate (MER) and MER with respect to /spl theta/. We also develop a set of rules for network operations such as superposition, input-output relation of a single queue, and routing. Specifically, we show that: 1) the MER of a superposition process is less than or equal to the sum of the MER of each process, 2) a queue is stable in the sense of bounded queue length if the MER of the input traffic is smaller than the capacity, 3) the MER of a departure process from a stable queue is less than or equal to that of the input process, and 4) the MER of a routed process from a departure process is less than or equal to the MER of the departure process multiplied by the MER of the routing process. Similar results hold for MER with respect to /spl theta/ under a further assumption of independence. For single class networks with nonfeedforward routing, we provide a new method to show that similar stability results hold for such networks under the first come, first served policy. Moreover, when restricting to the family of two-state Markov modulated arrival processes, the notion of MER with respect to /spl theta/ is shown to be equivalent to the recently developed notion of effective bandwidth in communication networks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability of Laminated Composites

The characteristic special feature of deformation behavior of modern laminated composite materials and structural elements fabricated from these materials, at current levels of loading and operating conditions is the occurrence of the purely three-dimensional stress-deformed state. In this process some specific mechanical phenomena and effects may occur, which is impossible to describe within the framework of applied or approximate approaches existing currently in deformable solid body mechanics. The structure of massive laminated materials may be included in this class of phenomena when the critical parameters of the problem depend only on the ratio between mechanical and geometrical characteristics of single layers and are independent of the dimensions and the form of the total laminated body as a whole. Since this phenomenon may be the beginning of the process of fracture of these materials, and the loss of the load-carrying capacity of structure elements fabricated from them, we consider below, in three-dimensional formulation, the problem of the surface and internal instability in laminated composite materials under compressive surface loads. The classification of the existing types of stability problems is presented for laminated materials and approaches for their solution presented in the literature. On the basis of three-dimensional linearized stability theory, within the framework of the piecewise-homogeneous media model, the general formulation of the most characteristic classes of stability problems of laminated materials is given in Lagrangian coordinates at small and finite, homogeneous and inhomogeneous precritical deformation. Analytic and variational methods of investigation of formulated problems are given with application to various models of laminated bodies models, in accordance with accepted stability criteria. The accuracy of these models is evaluated, based on the example of the solution of certain model problems; the range of application is given for existing applied and approximate approaches to the analysis of formulated problems. Results of solution of specific problems are given; specific mechanical effects, characteristic for the phenomenon considered, are found. Recommendations are formulated for engineering design and computational methods. New promising areas of research are pointed out for the problem of laminated composite materials stability.

On stability of probabilistic automata in environments1

Flachs [1], Rabin [7], and Paz [6] have considered topics in the stability of probabilistic automata. Here we extend these results to the more general forms, automata in deterministic environments (ADE). We shall be concerned with two types of stability problems that arise from small perturbations of the environment configurations for an ADE. By consideration of the asymptotic properties of long products of stochastic matrices whose entries are subject to small perturbations concomitant to the environment configuration perturbations, we arrive at sufficient conditions for the state distribution function to be stable (s-stability). In its acceptor formulation the behavior of an ADE is characterized by the sets T ( A, e, λ), the set of tapes accepted by A with environment sequence e and cut-point λ. Sufficient conditions are given for tape-acceptance stability (a-stability) in terms of s-stability and in terms that do not require s-stability. These stability results are pointwise results that give the size of the perturbation of the environment configuration to avoid instability.