On the Number and Types of Unstable Equilibria in Nonlinear Dynamical Systems With Uniformly-Bounded Stability Regions

被引：14

作者：

Chiang, Hsiao-Dong ^{[1
]}

Wang, Tao ^{[1
]}

机构：

[1] Cornell Univ, Sch Elect & Comp Engn, Ithaca, NY 14853 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2016年 / 61卷 / 02期

基金：

美国国家科学基金会;

关键词：

Existence theorem; nonlinear dynamical system; power system; stability region; unstable equilibrium point; PROGRAMMING PROBLEMS; POWER-SYSTEM; METHODOLOGY;

D O I：

10.1109/TAC.2015.2438416

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Classical theorems on the complete characterization of stability boundaries provided little information about the existence and types of unstable equilibrium points on a stability boundary. In this technical note, we derive analytical results and sufficient conditions about the existence of all types of unstable equilibrium points in a dynamical system whose stability regions are uniformly bounded. Some applications of these analytical results are illustrated using electric power systems.

引用

页码：485 / 490

页数：6

共 22 条

[1]

[Anonymous], 1978, AM MATH SOC CBMS

[2] GEOMETRIC CRITICAL-POINT ANALYSIS OF LOSSLESS POWER SYSTEM MODELS [J].

BAILLIEUL, J ;

BYRNES, CI .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1982, 29 (11) :724-727

[3]

Chiang H. D., 2014, OPTIMIZATION SCI ENG, P67

[4]

Chiang H.D., 2011, DIRECT METHODS STABI

[5] STABILITY REGIONS OF NONLINEAR AUTONOMOUS DYNAMICAL-SYSTEMS [J].

CHIANG, HD ;

HIRSCH, MW ;

WU, FF .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1988, 33 (01) :16-27

[6] PREDICTING UNSTABLE MODES IN POWER-SYSTEMS - THEORY AND COMPUTATIONS [J].

CHIANG, HD ;

TONG, JZ ;

MIU, KN .

IEEE TRANSACTIONS ON POWER SYSTEMS, 1993, 8 (04) :1429-1437

[7] STABILITY REGIONS OF NONLINEAR DYNAMICAL-SYSTEMS - A CONSTRUCTIVE METHODOLOGY [J].

CHIANG, HD ;

THORP, JS .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1989, 34 (12) :1229-1241

[8] Quasi-stability regions of nonlinear dynamical systems: Theory [J].

Chiang, HD ;

FekihAhmed, L .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 1996, 43 (08) :627-635

[9] A systematic search method for obtaining multiple local optimal solutions of nonlinear programming problems [J].

Chiang, HD ;

Chu, CC .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 1996, 43 (02) :99-109

[10] Characterization of Stability Region for General Autonomous Nonlinear Dynamical Systems [J].

Costa Alberto, Luis Fernando ;

Chiang, Hsiao-Dong .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2012, 57 (06) :1564-1569

← 1 2 3 →