Robust stochastic stability of power system with time-varying delay under Gaussian random perturbations

In this paper, by taking into account the stochastic perturbations, the power system with time-varying delay under Gaussian random perturbations is formulated into the stochastic differential equation, then the robust stochastic stability is discussed in detail. Based on Lyapunov stability theory, some improved robust stability and robust stochastic stability criteria are developed, where the restrictions on the derivative of time-varying delay are removed so as to reduce the conservatism. The obtained results formulated in the form of linear matrix inequalities (LMIs) can be effectively solved by the LMI toolbox. Finally, one machine and infinite system under random perturbations is provided to demonstrate the effectiveness and usefulness of the developed results.

[1]  G.T. Heydt,et al.  Evaluation of time delay effects to wide-area power system stabilizer design , 2004, IEEE Transactions on Power Systems.

[2]  A. Bellen,et al.  Methods for linear systems of circuit delay differential equations of neutral type , 1999 .

[3]  Lihua Xie,et al.  Output feedback H∞ control of systems with parameter uncertainty , 1996 .

[4]  Federico Milano,et al.  Impact of Time Delays on Power System Stability , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[6]  Balarko Chaudhuri,et al.  Wide-area measurement-based stabilizing control of power system considering signal transmission delay , 2004 .

[7]  Peng Shi,et al.  Stochastic Synchronization of Markovian Jump Neural Networks With Time-Varying Delay Using Sampled Data , 2013, IEEE Transactions on Cybernetics.

[8]  Min Wu,et al.  Delay-dependent robust load frequency control for time delay power systems , 2013, 2013 IEEE Power & Energy Society General Meeting.

[9]  Shengyuan Xu,et al.  Relaxed passivity conditions for neural networks with time-varying delays , 2014, Neurocomputing.

[10]  Vijay Vittal,et al.  Application of the structured singular value theory for robust stability and control analysis in multimachine power systems. I. Framework development , 1998 .

[11]  Zidong Wang,et al.  On Passivity and Passification of Stochastic Fuzzy Systems With Delays: The Discrete-Time Case , 2010, IEEE Trans. Syst. Man Cybern. Part B.

[12]  D. Hill,et al.  Numerical Simulation for Stochastic Transient Stability Assessment , 2012, IEEE Transactions on Power Systems.

[13]  Ping Ju,et al.  Responses and stability of power system under small Gauss type random excitation , 2012 .

[14]  Wei Zhinong,et al.  Wavelet-based electromechanical mode shape identification from ambient data of random load excitation , 2012 .

[15]  K. Tomsovic,et al.  Application of linear matrix inequalities for load frequency control with communication delays , 2004, IEEE Transactions on Power Systems.

[16]  Zhenjiang Zhao,et al.  Passivity and passification for stochastic Takagi-Sugeno fuzzy systems with mixed time-varying delays , 2013, Neurocomputing.

[17]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[18]  Yong He,et al.  Further Results on Delay-Dependent Stability of Multi-Area Load Frequency Control , 2013, IEEE Transactions on Power Systems.

[19]  H. Bevrani,et al.  On Load–Frequency Regulation With Time Delays: Design and Real-Time Implementation , 2009, IEEE Transactions on Energy Conversion.

[20]  Lennart Söder,et al.  Modeling real-time balancing power demands in wind power systems using stochastic differential equations , 2010 .

[21]  Quanyuan Jiang,et al.  Stability analysis of time delayed power system based on Cluster Treatment of Characteristic Roots method , 2008, 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century.

[22]  F. Milano,et al.  A Systematic Method to Model Power Systems as Stochastic Differential Algebraic Equations , 2013, IEEE Transactions on Power Systems.

[23]  Zidong Wang,et al.  Quantized $H_{\infty }$ Control for Nonlinear Stochastic Time-Delay Systems With Missing Measurements , 2012, IEEE Transactions on Automatic Control.

[24]  Innocent Kamwa,et al.  Wide-area measurement based stabilizing control of large power systems-a decentralized/hierarchical approach , 2001 .

[25]  Min Wu,et al.  Stability Analysis for Neural Networks With Time-Varying Interval Delay , 2007, IEEE Transactions on Neural Networks.

[26]  Deng Feiqi.  A Numeric Method for Stochastic Transient Stability Analysis of Excitation Control System , 2011 .

[27]  Zidong Wang,et al.  Robust filtering with stochastic nonlinearities and multiple missing measurements , 2009, Autom..

[28]  Shengyuan Xu,et al.  Stability Analysis of Distributed Delay Neural Networks Based on Relaxed Lyapunov–Krasovskii Functionals , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[29]  Shengyuan Xu,et al.  Robust H∞ control for uncertain stochastic systems with state delay , 2002, IEEE Trans. Autom. Control..

[30]  I. C. Decker,et al.  Wide-Area Measurements-Based Two-Level Control Design Considering Signal Transmission Delay , 2009, IEEE Transactions on Power Systems.

[31]  Jinde Cao,et al.  Stochastic Synchronization of Complex Networks With Nonidentical Nodes Via Hybrid Adaptive and Impulsive Control , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[32]  Yu Xiaodan.  A Delay-dependent Robust Stability Criterion for Power System and Its Application , 2010 .

[33]  J. Wen,et al.  Delay-Dependent Stability Analysis of the Power System With a Wide-Area Damping Controller Embedded , 2011, IEEE Transactions on Power Systems.

[34]  J. Wen,et al.  Delay-dependent stability for load frequency control with constant and time-varying delays , 2009, 2009 IEEE Power & Energy Society General Meeting.