Nonlinear Koopman modes of coupled swing dynamics and coherency identification

We report modal analysis of coupled swing dynamics of a multi-machine power system. The analysis is based on the so-called Koopman operator, a linear, infinite-dimensional operator that is defined for any nonlinear dynamical system and captures full information of the system. The modal analysis makes it possible to extract single-frequency modes, which are called Koopman modes, embedded in the coupled swing dynamics and to identify a coherent group of generators in which they swing together in frequency and phase.

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

[2]  P. Kundur,et al.  Power system stability and control , 1994 .

[3]  Felix F. Wu,et al.  Chaos in a simple power system , 1993 .

[4]  M. Mackey,et al.  Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics , 1998 .

[5]  C. Caramanis.  What is ergodic theory , 1963 .

[6]  P. Varaiya,et al.  Nonlinear oscillations in power systems , 1984 .

[7]  I. Mezić.  Spectral Properties of Dynamical Systems, Model Reduction and Decompositions , 2005 .

[8]  B. O. Koopman,et al.  Hamiltonian Systems and Transformation in Hilbert Space. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[9]  M. Hayashi,et al.  Construction of power system transient stability equivalents using the Lyapunov function , 1981 .

[10]  P. Kokotovic,et al.  Area Decomposition for Electromechanical Models of Power Systems , 1980 .

[11]  I. Mezic,et al.  Nonlinear Koopman Modes and Coherency Identification of Coupled Swing Dynamics , 2011, IEEE Transactions on Power Systems.

[12]  A.H.M.A. Rahim,et al.  Identification of coherent generators using energy function , 1990 .

[13]  Andrzej Banaszuk,et al.  Comparison of systems with complex behavior , 2004 .

[14]  B. Bowler,et al.  An Analysis of Interarea Dynamics of Multi-Machine Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[15]  I. Mezić,et al.  Spectral analysis of nonlinear flows , 2009, Journal of Fluid Mechanics.

[16]  Aurel Wintner,et al.  Harmonic Analysis and Ergodic Theory , 1941 .

[17]  George Troullinos,et al.  Coherency and Model Reduction: A State Space Point of View , 1989, IEEE Power Engineering Review.

[18]  A.G. Phadke,et al.  Synchronized phasor measurements in power systems , 1993, IEEE Computer Applications in Power.

[19]  Takashi Hikihara,et al.  Global swing instability of multimachine power systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[20]  B. Chaudhuri,et al.  Coherency identification in power systems through principal component analysis , 2005, IEEE Transactions on Power Systems.

[21]  S. Shankar Sastry,et al.  Coherency for interconnected power systems , 1981 .