Practical Stability Region Research Articles

Multi-Parameter Practical Stability Region Analysis of Wind Power System Based on Limit Cycle Amplitude Tracing

The existing division of system stability region does not fully consider the influence of nonlinear characteristics of the system. To address the challenge that it is difficult to inscribe the stability region of wind power grid-connected systems accurately and quantitatively, this paper proposes a nonlinear system multi-parameter practical stability region analysis method based on limit cycle amplitude tracking. Firstly, the nonlinear dynamic model of multi-machine system with doubly fed induction generator (DFIG) is established, and the bifurcation diagram of the system is obtained by nonlinear analysis of the model. Then, the limit cycle-parameter diagram is obtained by tracking the limit cycle of the Hopf bifurcation point of the system, and the problem of how the system oscillation evolves with the change of operating parameters is analyzed. Afterwards, the single parameter practical stability region of the nonlinear system is obtained by combining the system equilibrium manifold. Finally, the multi-parameter practical stability region of the nonlinear system is obtained by the three-dimensional bifurcation map with the system time delay, DFIG output active power and reactive load as the bifurcation parameters. The division of the stability region has important guiding significance for the parameter adjustment in the actual operation of the system.

Polynomial stochastic dynamical indicators

This paper introduces three types of dynamical indicators that capture the effect of uncertainty on the time evolution of dynamical systems. Two indicators are derived from the definition of finite-time Lyapunov exponents, while a third indicator directly exploits the property of the polynomial expansion of the dynamics with respect to the uncertain quantities. The paper presents the derivation of the indicators and a number of numerical experiments that illustrates the use of these indicators to depict a cartography of the phase space under parametric uncertainty and to identify robust initial conditions and regions of practical stability in the restricted three-body problem.

Impact of saturation nonlinearities/disturbances on the small-signal stability of power systems: An analytical approach

In this paper, a multi-objective optimization model is presented to estimate the practical stability region and maximum endurable disturbance rejection for a small-signal power system dynamic model with saturation nonlinearities and disturbance rejection. Iterative algorithms are developed to solve for Pareto optimized solutions (POS) of this optimization. Furthermore, as an application of this approach to power systems, a method to analyze the impact of saturation nonlinearities and disturbance rejection on power system small-signal stability is introduced based on the estimated stability region and maximum endurable disturbance rejection. Numerical results of a test power system with detailed saturated PSS controllers are described, indicating the reliability and simplicity of the method.

Estimating stability regions for mismatched uncertain variable structure systems with bounded controllers

We address the problem of the estimation of stability regions of a class of mismatched uncertain variable structure systems with bounded controllers. The estimation of stability regions such as the practical stability region, the asymptotic stability region, and the exponential stability region are discussed. Moreover, the state transformation used in previous paper is no longer needed so that a new estimation result is directly related to the original system states without state transformation.

Estimating stability regions for mismatched uncertain variable structure systems with bounded controllers

We address the problem of the estimation of stability regions of a class of mismatched uncertain variable structure systems with bounded controllers. The estimation of stability regions such as the practical stability region, the asymptotic stability region, and the exponential stability region are discussed. Moreover, the state transformation used in previous paper is no longer needed so that a new estimation result is directly related to the original system states without state transformation.

Stability regions estimation for mismatched uncertainvariable structure systems with bounded controllers

The problem of estimating the stability regions of mismatched uncertain variable structure systems (VSS) with bounded controllers is considered. Based on Lyapunov stability theory, the estimations of stability regions such as the practical stability region (PSR), asymptotical stability region (ASR), and exponential stability region (ESR) are discussed.

Estimation of the practical stability region of a class of robust controllers with input constraint

In this paper, new practical stability results are obtained from a class of proposed constrained robust controllers. Unlike the previous relevant work, the stability investigation is now extended to the actual control modification region. For the class of uncertain systems with an unstable nominal part, our results give a closer estimation of regions of attraction and of ultimate boundedness. The closed loop stability is shown to be maintained in a region where the modified control and its original are distinct.

Stability in the mean of solutions of difference equations

We consider the membership of solutions of stochastic difference equations in special sets. The notion of stability in the mean is introduced for nonlinear equations. Some assertions about practical stability are proved under certain restrictions. The problem of optimization of regions of practical stability is solved in a particular case.

Robust output feedback stabilization of uncertain dynamic systems with bounded controllers

AbstractWe propose a new class of infinitely many bounded output feedback controllers for uncertain dynamic systems with bounded uncertainties. No statistical information about the uncertainties is assumed. A variable structure systems approach is employed in the synthesis of the proposed output feedback controllers. The role of the system zeros in the output feedback stabilization using the variable structure approach is discussed. We show that the proposed controllers guarantee the practical stability of the closed‐loop system and give estimates of the regions of practical stability.

Robust control synthesis for uncertain/nonlinear dynamical systems

This paper addresses the problem of robust state and output-feedback controller design for uncertain and nonlinear dynamic systems. First, a robust state-feedback nonlinear control law is synthesized. This control strategy practically stabilizes the closed-loop system. Then a state estimator for the nonlinear/uncertain plant is designed and its performance analyzed. Finally, the control law and the estimator are combined and the practical stability region is estimated. The results are illustrated by their application to a benchmark problem for robust control design.

Amplitude bounds for general nonautonomous second-order systems

An extension of the tracking-function method is described which may be used to obtain bounds on the response of general nonlinear, nonstationary, forced second-order systems. Two examples illustrate the facility with which the method may be applied, and the regions of practical stability which can be achieved.

Stability of chemical reactors in the presence of sustained disturbances

AbstractA general method is developed for constructing regions of practical stability for nonlinear lumped‐parameter systems. The region of practical stability serves as a bound on the system response for a general class of magnitude‐constrained disturbances. The construction method is based on a modified Liapunov approach but is not restricted to a particular type of Liapunov function. The method is applicable to higher order systems in which several disturbance variables are present. Numerical results are presented for a CSTR with magnitude‐constrained disturbances in feed composition and feed temperature.

Computer program for obtaining regions of practical stability for second-order autonomous systems

A computer program is described for investigating the practical stability and ultimate boundedness of nonlinear 2nd-order autonomous systems. The program is based upon the `tracking function' method. The Van der Pol equation, a chemical-reactor system and a negative-resistance oscillator are analysed as examples.

Computer application of the tracking-function approach to practical stability

A computing algorithm based on the tracking-function method is presented for obtaining regions of practical stability and ultimate boundedness for second-order autonomous differential equations. It is shown that the algorithm obviates certain problems of the tracking-function method as originally formulated. The Van der Pol equation is analysed as an example.