Estimation Of Stability Region Research Articles

Stability results for delayed-recruitment models in population dynamics

This paper relates the stability properties of a class of delay-difference equations to those of an associated scalar difference equation. Simple but powerful conditions for testing global stability are presented which are independent of the length of the time delay involved. For models which do not have globally stable equilibria, estimates of stability regions are obtained. Some well known baleen whale models are used to illustrate the results.

Method of power transformations for analysis of stability of nonlinear control systems

New frequency-domain criteria for absolute stability are obtained. These criteria essentially improve the estimates of stability regions in the parameter space compared with well-known results of V.M. Popov (1961,1973) and the circle criterion of J.J. Bongiorno (1964).

On nonlinear reaction-diffusion systems

This paper presents a qualitative analysis for a coupled system of two reaction-diffusion equations under various boundary conditions which arises from a number of physical problems. The nonlinear reaction functions are classified into three basic types according to their relative quasi-monotone property. For each type of reaction functions, an existence-comparison theorem, in terms of upper and lower solutions, is established for the time-dependent system as well as some boundary value problems. Three concrete physical systems arising from epidemics, biochemistry and engineering are taken as representatives of the basic types of reacting problems. Through suitable construction of upper and lower solutions, various qualitative properties of the solution for each system are obtained. These include the existence and bounds of time-dependent solutions, asymptotic behavior of the solution, stability and instability of nontrivial steady-state solutions, estimates of stability regions, and finally the blowing-up property of the solution. Special attention is given to the homogeneous Neumann boundary condition.

Stability and stability region estimation of large-scale power systems

The model of an n-machine power system, considered to have uniform damping and transfer conductances, is decomposed into n−1 free subsystems interacting with one another. Stability analysis and stability regions are estimated by means of a vector Lyapunov function. The Lyapunov functions of the free subsystems and the corresponding aggregate matrix are formed by a special method so that maximum stability regions may be obtained both for the free subsystems and for the overall system.

Computational Aspects in Practical Application of Lyapunov Method to Power Systems

For online transient security monitoring quick determination of critical clearing time is one of the most important requirements. Repeated integration of system equations, for this purpose, is ruled out. Recent approaches have favoured Lyapunov method. However,the work on fast and accurate determination of stability region by this method is not yet complete. In this paper, available control theory for systems with single nonlinearity is extended to multi-nonlinear systems and is applied to multimachine power systems. It has been shown that a vast majority of points, searched hitherto, for computing the minimum of Lyapunov function, are not necessary. The approach drastically reduces the number of search points and gives reasonable estimates of stability regions even in those cases where other methods have not succeeded. This is illustrated by a 5 machine and a 13-machine system. It is hoped that this method will provide a basis for online transient stability programs.

Multimachine power systems: Stability, decomposition, and aggregation

A new approach is proposed for transient stability analysis of interconnected power systems, which is based upon the concept of vector Lyapunov functions and the decomposition-aggregation method. The approach results in an exact procedure for computation of stability region estimates which are expressed explicitly in terms of system parameters. More refined models of the subsystems can be readily accommodated by the new approach. In particular, the transfer conductances are included in the present study, a feature which is almost exclusively missing in transient stability analysis of multimachine systems by Lyapunov's method.

Decomposition and Stability of Multimachine Power Systems

An m-machine model with nonuniform damping and transfer conductances is pair-wise decomposed into m-1 interconnected subsystems each containing the speed of the reference machine as a common part. The overlapping decomposition leads to a Lur’e-Postnikov type of subsystem stability analysis and a vector Liapunov function application to computations of stability region estimates for the overall m-machine model. The proposed decomposition stability analysis should be judged satisfactory to the extent that the conservativeness of the obtained estimates are outweighed by their computational simplicity and the structural insight the approach can provide in transient stability analysis of multimachine power systems.

A multi-machine power system Liapunov function using the generalized Popov criterion

A certain mathematical model of a multi-machine power system, which is suitable for transient stability studies and allows for machine damping, is Bhown to satisfy the generalized Popov criterion, within a limited range. Hence it is possible to use a systematic method to construct a Lur'e-type Liapunov function for the system. The Liapunov function obtained in this paper contains damping terms whose weight can be adjusted by a variable parameter. The variation will have corresponding effects on the estimates of the system's stability region.

Determination of stability regions with the inverse Nyquist array

A new criterion for closed-loop stability and the design of linear multivariable control systems is developed using the inverse-Nyquist-array method and an Ostrowski theorem. Estimates of the gain margins in each loop and bounds on the stable-gain space are obtained using the bands of Ostrowski circles superimposed on the diagonal elements of the inverse Nyquist array. The manner of application of this new approach is similar to the way in which the bands of Gershgorin circles are used. The new criterion allows the diagonal dominance requirements to be relaxed in one row or in one column of the inverse Nyquist array at each point on the D contour, while still permitting the origin encirclements of the determinant of the inverse-transfer-function matrix to be determined from those of its diagonal elements. As a consequence the estimated stability region is larger than that obtained when strict dominance requirements are imposed.