Stability Boundary Of Systems Research Articles

A New Synchronous Generator Out-of Step Relay Scheme Part I Abbreviated Version

In the abbreviated version of the proposed generator out-of-step relay scheme, the equations solved by the powerplant computer are based on a two-machine system model in which the classical representation is used for each machine (the protected machine, or powerplant, and the interconnected system equivalent machine) and resistance is neglected. Tripping is initiated when the iteratively computed value of the Lyapunov V-function during a system disturbance exceeds the V-function's maximum value b, on the system stability boundary, computed prior to initiation of the scheme's disturbed-system high-speed computing mode, from preprogrammed and measured predisturbed system data and from preprogrammed postdisturbed system data. Nondelayed tripping prior to the time system torque angle reaches 180°is permitted provided the angle is favorable for breaker operation. If the angle is not favorable at the time instability is detected, tripping is delayed until the angle becomes favorable.

An analytical study of the thermally induced two-phase flow instabilities including the effect of thermal non-equilibrium

The problem of thermally induced flow instabilities in a uniformly heated boiling channel has been studied analytically. The effect of thermal non-equilibrium between the phases has been included by deriving a constitutive equation for the mass rate of vapor generation from steady state energy consideration. The system characteristic equation is derived by introducing a small perturbation in the inlet velocity, and the system stability boundary is determined by using the D-partition method. When compared with the equilibrium theory, the present non-equilibrium theory predicts a more stable system at low subcooling number and a more unstable system at high subcooling number. When compared with experiment, the present non-equilibrium theory agrees well with the data on the system stability boundary at low subcooling and the frequency of oscillations. However, further studies are required for better prediction of the system stability at high subcooling.

On the convexity of the stability boundary of continous elastic systems under two-parameter nonconservative loading

On the convexity of the stability boundary of continous elastic systems under two-parameter nonconservative loading

On the estimation of the stability boundary of symmetric structural systems

A perturbation method of analysis for the estimation of the stability boundary of symmetric conservative structural systems, whose loss of stability is associated with pre-buckling large deflections, is presented in completely general terms. The general formulation covers a wide class of discrete elastic structural systems, and the results produced are in the form of formulae suitable to be used directly in estimating the stability of many particular systems, without necessarily repeating the entire analysis. The proposed analysis can be performed in a relatively simple manner since the procedure adapted reduces the solution of simultaneous non-linear equations to the recursive solution of a set of linear equations, and the derivatives of the associated stability determinant are conveniently evaluated at the zero-state. A theorem concerning the shape of the stability boundary of a specialized class of system is proved. The problem of stability of a shallow arch illustrating the essential features of the theory is discussed and the results of a simple experiment performed on a model arch are compared with the theory. Quantitative as well as qualitative agreement is observed.

The stability boundary of systems with one degree of freedom (Part II)

The stability boundary of systems with one degree of freedom (Part II)

The stability boundary of systems with one degree of freedom (Part I)

It is shown that the stability boundary of a one-degree-of-freedom conservative structural system cannot have convexity towards the region of instability. An example illustrating the essential features of the theory is discussed. The results of two experiments providing qualitative verification of the theory are reported.

The convexity of the stability boundary of symmetric structural systems

The elastic stability of a discrete conservative structural system with independent loading parameters is studied. Attention is restricted to systems which satisfy certain analytical symmetry conditions and which lose their initial stability at a point of bifurcation. A theorem, concerning the convexity of the stability boundary of such systems, is established.

Efficient application of D -Decomposition techniques to determine stability boundaries for multiparameter systems, with particular reference to induction machines

It is shown that the technique of D-decomposition can be applied in a particular efficient way to synthetise parameter combinations defining stable conditions in multiparameter systems. A range of results of value in connection with the steady-state stability of induction motors on variable-frequency supplies is presented.

Approximation of the asymptotic stability boundary of discrete-time control systems using an inverse transformation approach

The objective of this paper is to describe the use of the direct method of Lyapunov together with an inverse transformation process as a basis for determining the stability domain and for estimating the stability boundary of the null solution of a set of autonomous difference equations which describe the dynamics of a class of discrete-time control systems. Two theorems are developed which give sufficient conditions for the existence of an asymptotic stability boundary, which is a hypersurface enclosing a simply-connected domain, provided that a Lyapunov function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\upsilon(x)</tex> exists in a neighborhood of the origin. The proofs of these theorems indicate that an original subdomain of asymptotic stability, obtained by using a Lyapunov function, can be enlarged by applying an inverse transformation to the boundary of the subdomain. The inverse transformation is defined from the given set of difference equations as giving the state at the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</tex> th instant in terms of the state at the ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k+1</tex> )th instant. The exact boundary of asymptotic stability is theoretically obtained in the limit by carrying out the inverse transformation an infinite number of times. Analogous to the work on stability, two theorems give sufficient conditions for the existence of an instability boundary which is a hypersurface surrounding a simply connected domain that includes the origin. It is shown that a known domain of instability found by using a Lyapunov function can be increased in size by applying the inverse transformation to its boundary. An important property of this approach is that each time the inverse transformation is applied, an enlarged region of known asymptotic stability or instability is found. In addition to giving stability information, the successive plots of the boundaries can also be used to give the settling time of the system.

Approximation of the asymptotic stability boundary of discrete-time control systems using an inverse transformation approach

Approximation of the asymptotic stability boundary of discrete-time control systems using an inverse transformation approach