Model-Free MLE Estimation for Online Rotor Angle Stability Assessment With PMU Data

Recent research has demonstrated that the rotor angle stability of a power system can be assessed by identifying the sign of the system's maximal Lyapunov exponent (MLE). A positive (negative) MLE implies unstable (stable) rotor angle dynamics. However, because the MLE may fluctuate between positive and negative values for a long time after a severe disturbance, determining the system stability is difficult when observing a positive or negative MLE without knowing its further fluctuation trend. In this paper, a new approach for online rotor angle stability assessment is proposed to address this problem. The MLE is estimated by a recursive least-squares-based method from real-time rotor angle measurements, and two critical parameters, the Theiler window, and the MLE estimation initial time step are carefully chosen to make sure that the calculated MLE curves present distinct features for different stability conditions. By using the proposed stability assessment criteria, the developed approach can provide a timely and reliable assessment of rotor angle stability. Extensive tests on the New England 39-bus system and the Northeast Power Coordinating Council 140-bus system verify the effectiveness of the proposed approach.

[1]  V. I. Oseledec.  A multiplicative ergodic theorem: Lyapunov characteristic num-bers for dynamical systems , 1968 .

[2]  B. Spalding,et al.  Coherency recognition for transient stability studies using singular points , 1977, IEEE Transactions on Power Apparatus and Systems.

[3]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[4]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[5]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[6]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[7]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.

[8]  Ryouichi Tsukui,et al.  Fast generation shedding equipment based on the observation of swings of generators , 1988 .

[9]  M. Haque,et al.  Determination of first swing stability limit of multimachine power systems through Taylor series expansions , 1989 .

[10]  K. R. Padiyar,et al.  ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY , 1990 .

[11]  D. Ruelle,et al.  Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems , 1992 .

[12]  Jianbo Gao,et al.  Local exponential divergence plot and optimal embedding of a chaotic time-series , 1993 .

[13]  M. Rosenstein,et al.  A practical method for calculating largest Lyapunov exponents from small data sets , 1993 .

[14]  H. Kantz.  A robust method to estimate the maximal Lyapunov exponent of a time series , 1994 .

[15]  Chih-Wen Liu,et al.  Detection of transiently chaotic swings in power systems using real-time phasor measurements , 1994 .

[16]  Joe H. Chow,et al.  Inertial and slow coherency aggregation algorithms for power system dynamic model reduction , 1995 .

[17]  Mohammed H. Haque.  Further developments of the equal-area criterion for multimachine power systems , 1995 .

[18]  J. A. Stewart,et al.  Nonlinear Time Series Analysis , 2015 .

[19]  A.G. Phadke,et al.  An Adaptive Out-of-Step Relay , 1997, IEEE Power Engineering Review.

[20]  Chih-Wen Liu,et al.  New methods for computing power system dynamic response for real-time transient stability prediction , 2000 .

[21]  Axel Röbel.  Synthesizing Natural Sounds Using Dynamic Models of Sound Attractors , 2001, Computer Music Journal.

[22]  George G. Karady,et al.  On-line transient stability enhancement using multi-agent technique , 2002, 2002 IEEE Power Engineering Society Winter Meeting. Conference Proceedings (Cat. No.02CH37309).

[23]  Carson W. Taylor,et al.  Definition and Classification of Power System Stability , 2004 .

[24]  P. Kundur,et al.  Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions , 2004, IEEE Transactions on Power Systems.

[25]  F. Milano,et al.  An open source power system analysis toolbox , 2005, 2006 IEEE Power Engineering Society General Meeting.

[26]  Alberto Del Angel,et al.  Estimation of rotor angles of synchronous machines using artificial neural networks and local PMU-based quantities , 2007, Neurocomputing.

[27]  Kai Sun,et al.  An Online Dynamic Security Assessment Scheme Using Phasor Measurements and Decision Trees , 2007, IEEE Transactions on Power Systems.

[28]  K. Schneider,et al.  Feasibility studies of applying Kalman Filter techniques to power system dynamic state estimation , 2007, 2007 International Power Engineering Conference (IPEC 2007).

[29]  J.H. Chow,et al.  Synchronized Phasor Data Based Energy Function Analysis of Dominant Power Transfer Paths in Large Power Systems , 2007, IEEE Transactions on Power Systems.

[30]  M. McCullough.  Phase space reconstruction: Methods in applied economics and econometrics , 2008 .

[31]  Lu Fang,et al.  Transient stability analysis with equal area criterion directly used to a non-equivalent generator pair , 2009, 2009 International Conference on Power Engineering, Energy and Electrical Drives.

[32]  I Kamwa,et al.  Development of rule-based classifiers for rapid stability assessment of wide-area post disturbance records , 2009, IEEE PES General Meeting.

[33]  G. Sugihara,et al.  Generalized Theorems for Nonlinear State Space Reconstruction , 2011, PloS one.

[34]  Yun Zou,et al.  An Improved Iterative Method for Assessment of Multi-Swing Transient Stability Limit , 2011, IEEE Transactions on Power Systems.

[35]  I. Kamwa,et al.  Dynamic State Estimation in Power System by Applying the Extended Kalman Filter With Unknown Inputs to Phasor Measurements , 2011, IEEE Transactions on Power Systems.

[36]  Chen-Ching Liu,et al.  PMU-Based Monitoring of Rotor Angle Dynamics , 2011, IEEE Transactions on Power Systems.

[37]  Kit Po Wong,et al.  A Reliable Intelligent System for Real-Time Dynamic Security Assessment of Power Systems , 2012, IEEE Transactions on Power Systems.

[38]  J. McCalley,et al.  VANTAGE: A Lyapunov exponents based technique for identification of coherent groups of generators in power systems , 2013 .

[39]  Venkataramana Ajjarapu,et al.  Real-Time Monitoring of Short-Term Voltage Stability Using PMU Data , 2013, IEEE Transactions on Power Systems.

[40]  Wei Kang,et al.  Adaptive Optimal PMU Placement Based on Empirical Observability Gramian , 2014, 1411.7016.

[41]  Yuxiang Yang,et al.  Frequency Estimation of Distorted and Noisy Signals in Power Systems by FFT-Based Approach , 2014, IEEE Transactions on Power Systems.

[42]  J. R. Trapero,et al.  Recursive Estimation and Time-Series Analysis. An Introduction for the Student and Practitioner, Second edition, Peter C. Young. Springer (2011), 504 pp., Hardcover, $119.00, ISBN: 978-3-642-21980-1 , 2015 .

[43]  V. Ajjarapu,et al.  PMU-Based Model-Free Approach for Real-Time Rotor Angle Monitoring , 2015, IEEE Transactions on Power Systems.

[44]  Abhinav Singh,et al.  Estimating dynamic model parameters for adaptive protection and control in power system , 2015, 2015 IEEE Power & Energy Society General Meeting.

[45]  Greg Welch,et al.  Dynamic State Estimation of a Synchronous Machine Using PMU Data: A Comparative Study , 2015, IEEE Transactions on Smart Grid.

[46]  Kai Sun,et al.  Optimal PMU placement for power system dynamic state estimation by using empirical observability Gramian , 2015, 2015 IEEE Power & Energy Society General Meeting.

[47]  J. Laskar,et al.  Chaos detection and predictability , 2016 .

[48]  Kai Sun,et al.  Power system observability and dynamic state estimation for stability monitoring using synchrophasor measurements , 2016 .

[49]  Innocent Kamwa,et al.  Local and Wide-Area PMU-Based Decentralized Dynamic State Estimation in Multi-Machine Power Systems , 2016, IEEE Transactions on Power Systems.

[50]  Pratyasa Bhui,et al.  Real-Time Prediction and Control of Transient Stability Using Transient Energy Function , 2017, IEEE Transactions on Power Systems.

[51]  Bin Wang,et al.  Properties of the Frequency–Amplitude Curve , 2017, IEEE Transactions on Power Systems.

[52]  Kai Sun,et al.  Dynamic State Estimation for Multi-Machine Power System by Unscented Kalman Filter With Enhanced Numerical Stability , 2015, IEEE Transactions on Smart Grid.

[53]  Jitesh H. Panchal,et al.  Risk Mitigation for Dynamic State Estimation Against Cyber Attacks and Unknown Inputs , 2015, IEEE Transactions on Smart Grid.