Author
L. Fekih-Ahmed
Bio: L. Fekih-Ahmed is an academic researcher from Cornell University. The author has contributed to research in topics: Nonlinear system & Lyapunov function. The author has an hindex of 7, co-authored 11 publications receiving 630 citations.
Papers
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TL;DR: In this article, the authors use static and dynamic models to explain voltage collapse, where the static model is used before a saddle-node bifurcation and the dynamic model is employed after the bifurecation.
Abstract: Several voltage collapses have had a period of slowly decreasing voltage followed by an accelerating collapse in voltage. The authors clarify the use of static and dynamic models to explain this type of voltage collapse, where the static model is used before a saddle-node bifurcation and the dynamic model is used after the bifurcation. Before the bifurcation, a static model can be used to explain the slow voltage decrease. The closeness of the system to bifurcation can be interpreted physically in terms of the ability of transmission systems to transmit reactive power to load buses. Simulation results show how this ability varies with system parameters. It is suggested that voltage collapse could be avoided by manipulating system parameters so that the bifurcation point is outside the normal operating region. After the bifurcation, the system dynamics are modeled by the center manifold voltage collapse model. The essence of this model is that the system dynamics after bifurcation are captured by the center manifold trajectory. The behavior predicted by the model is found simply by numerically integrating the system differential equations to obtain this trajectory. >
275 citations
TL;DR: In this paper, the development of dynamic load models using the measurement approach for the Taipower system is described. But the authors focus on the use of the measured data from an online transient recording system to develop dynamic load model structures.
Abstract: Accurate dynamic load models allow more precise calculations of power system controls and stability limits, which are critical in the planning and operation of power systems. The development of dynamic load models using the measurement approach for the Taipower system are described. Two dynamic load model structures are developed. A procedure for applying a set of measured data from an online transient recording system to develop dynamic load models for the Taipower system is described. A technique based on the concept of confidence interval is used to validate the developed high-order load model structure. Case studies are also presented. >
152 citations
07 Dec 1988
TL;DR: In this article, a voltage collapse model for a simple three-bus power system model with a dynamic induction motor was proposed, showing that the model can be applied to a simple power system.
Abstract: Voltage collapse dynamics were previously modeled by the movement of the system state along a particular trajectory at a saddle node bifurcation. The authors apply this voltage collapse model to a simple three-bus power system model which includes a dynamic induction motor model. Voltage collapse dynamics are demonstrated, showing that the model can be applied to a simple power system. Approximate calculations suggest that load reactive power balance is an important factor in this collapse. >
109 citations
TL;DR: In this paper, the notion of a quasi-stability region was introduced and a comprehensive theory for it was developed, and the class of nonlinear dynamical systems whose stability regions are robust relative to small perturbations of the underlying vector fields was characterized.
Abstract: The concept of a stability region (region of attraction) of nonlinear dynamical systems is widely accepted in many fields such as engineering and the sciences. When utilizing this concept, the Lyapunov function approach has been found to give rather conservative estimations of the stability regions of many nonlinear systems. In this paper we study the notion of a quasi-stability region and develop a comprehensive theory for it. It is shown that, working on the concept of quasi-stability regions, one can greatly overcome the problem of conservative estimations of stability regions using the Lyapunov function approach. A complete characterization of quasi-stability regions is presented. Dynamical as well as topological properties of quasi-stability regions are also derived. The quasi-stability regions are shown to be robust relative to small perturbations of the underlying vector fields. The class of nonlinear dynamical systems whose stability regions equal their quasi-stability regions is characterized.
47 citations
TL;DR: In this paper, the authors developed an effective scheme to estimate stability regions by using an energy function that is a generalization of the Lyapunov functions, which can optimally estimate the stability regions.
Abstract: In this paper, we develop an effective scheme to estimate stability regions by using an energy function that is a generalization of the Lyapunov functions. It is shown that the scheme can optimally estimate stability regions. A fairly comprehensive study for the structure of the constant energy surface lying inside the quasi-stability region is presented. A topological characterization, as well as a dynamical characterization for the point on the quasi-stability boundary and the point on the stability boundary with the minimum value of an energy function are derived. These characterizations are then used in the development of a computational scheme to estimate quasi-stability regions. By utilizing an energy function approach (or Lyapunov function approach), this scheme can significantly reduce conservativeness in estimating the stability region, because the estimated stability region characterized by the corresponding energy function is the largest one within that stability region.
36 citations
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Book•
01 Jan 1994
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.
Abstract: Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.
11,085 citations
TL;DR: In this paper, the authors described the loss of stability when a stable equilibrium point disappears in a saddle node bifurcation and presented a simple model of the system dynamics after the bifurecation.
414 citations
01 Nov 1995
TL;DR: In this article, a theoretical foundation of direct methods for both network-reduction and network-preserving power system models is presented, along with numerical solution algorithms capable of supporting online applications of the direct methods.
Abstract: Stability analysis programs are a primary tool used by power system planning and operating engineers to predict the response of the system to various disturbances. Important conclusions and decisions are made based on the results of stability studies. This paper presents a theoretical foundation of direct methods for both network-reduction and network-preserving power system models. In addition to an overview, new results are offered. A systematic procedure of constructing energy functions for both network-reduction and network-preserving power system models is proposed. An advanced method, called the BCU method, of computing the controlling unstable equilibrium point is presented along with its theoretical foundation. Numerical solution algorithms capable of supporting online applications of direct methods are provided. Practical demonstrations of using direct methods and the BCU method for online transient stability assessments on two power systems are described. Further possible improvements, enhancements and other applications of direct methods are outlined.
412 citations
TL;DR: BIFurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input.
Abstract: Bifurcation control deals with modification of bifurcation characteristics of a parameterized nonlinear system by a designed control input. Typical bifurcation control objectives include delaying t...
350 citations
TL;DR: In this article, a tutorial introduction in bifurcation theory is given, and the applicability of this theory to study nonlinear dynamical phenomena in a power system network is explored.
Abstract: A tutorial introduction in bifurcation theory is given, and the applicability of this theory to study nonlinear dynamical phenomena in a power system network is explored. The predicted behavior is verified through time simulation. Systematic application of the theory revealed the existence of stable and unstable periodic solutions as well as voltage collapse. A particular response depends on the value of the parameter under consideration. It is shown that voltage collapse is a subset of the overall bifurcation phenomena that a system may experience under the influence of system parameters. A low-dimensional center manifold reduction is applied to capture the relevant dynamics involved in the voltage collapse process. The need for the consideration of nonlinearity, especially when the system is highly stressed, is emphasized. >
317 citations