An improved power system stability criterion with multiple time delays

Since there exist significant time delays in the data of phasor measurement unit (PMU) and wide-area measurement system (WAMS), to evaluate their impact is very important for power system online stability assessment and controller design in the wide-area environment. In this paper, we use Lyapunov stability theory and linear matrix inequality (LMI) method to analyze the impact of time delays on power system stability. An improved delay-dependent stability criterion for power system stability analysis with multiple time delays is presented. Based on Lyapunov-Krasovskii theory, a proper Lyapunov functional is firstly constructed. And, in deduction of its derivative function along the system trajectory, some necessary slack variables are introduced so as to reduce the method conservativeness. Then the derivative function is expressed as a set of linear matrix inequalities, which can be easily solved with LMI toolboxes in Matlab or Scilab. Finally, a typical two-dimension time-delayed system and WSCC 3-generator-9-bus system with two time delays are employed to validate the method effectiveness. It is revealed that the presented method is correct, effective and with less conservativeness. Work of this paper is helpful for power system stability assessment and control with considering time delays under wide-area environment.

[1]  D. P. Atherton,et al.  Modified Smith predictor and controller for processes with time delay , 1999 .

[2]  Hongjie Jia,et al.  A Simple Approach to Determine Power System Delay Margin , 2007, 2007 IEEE Power Engineering Society General Meeting.

[3]  PooGyeon Park,et al.  A delay-dependent stability criterion for systems with uncertain time-invariant delays , 1999, IEEE Trans. Autom. Control..

[4]  Jin-Hua She,et al.  Delay-dependent exponential stability of delayed neural networks with time-varying delay , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Yong He,et al.  Stability Analysis and Robust Control of Time-Delay Systems , 2010 .

[6]  Chyi Hwang,et al.  Use of Lambert W function to stability analysis of time-delay systems , 2005, Proceedings of the 2005, American Control Conference, 2005..

[7]  Emilia Fridman,et al.  An improved stabilization method for linear time-delay systems , 2002, IEEE Trans. Autom. Control..

[8]  Qing-Long Han,et al.  Delay-dependent H ∞ control of linear discrete-time systems with an interval-like time-varying delay , 2008, Int. J. Syst. Sci..

[9]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[10]  Chyi Hwang,et al.  A note on the use of the Lambert W function in the stability analysis of time-delay systems , 2005, Autom..

[11]  Yong He,et al.  Delay-dependent stability criteria for linear systems with multiple time delays , 2006 .

[12]  Yong He,et al.  Delay-dependent criteria for robust stability of time-varying delay systems , 2004, Autom..

[13]  Yu Xiaodan,et al.  A simple method for power system stability analysis with multiple time delays , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[14]  F. Al-Sunni,et al.  Approximation of time-delay systems , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[15]  Emilia Fridman,et al.  Stability of linear systems with time-varying delays , 2007 .

[16]  Xiaodan Yu,et al.  Power system small signal stability region with time delay , 2008 .

[17]  Pei Zhang,et al.  Study on the impact of time delay to power system small signal stability , 2006, MELECON 2006 - 2006 IEEE Mediterranean Electrotechnical Conference.

[18]  Hailin Liu,et al.  Delay-dependent stability for neural networks with time-varying delay , 2007 .

[19]  Shengyuan Xu,et al.  Improved delay-dependent stability criteria for time-delay systems , 2005, IEEE Transactions on Automatic Control.

[20]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[21]  Yuechao Wang,et al.  An LMI approach to stability of systems with severe time-delay , 2004, IEEE Transactions on Automatic Control.

[22]  J. Hale.  Theory of Functional Differential Equations , 1977 .