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2013 | OriginalPaper | Buchkapitel

6. Krylov Subspace and Balanced Truncation Methods for Power System Model Reduction

verfasst von : Shanshan Liu, Peter W. Sauer, Dimitrios Chaniotis, M. A. Pai

Erschienen in: Power System Coherency and Model Reduction

Verlag: Springer New York

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Abstract

In this chapter, we discuss two mathematical approaches for model reduction of power systems which do not use coherency information. The advantages of these approaches lie in the ability to handle large systems. The Krylov and balanced truncation methods take into account system reachability and observability in obtaining reduced-order models of the external system, and thus would perform better than methods based simply on eigenvalues. In the case of balanced truncation approach, a sensitivity analysis is carried out. Through the eigenvalue information, we also establish a connection of these methods with the coherency- based approaches.

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Vorheriges Kapitel A Hybrid Dynamic Equivalent Using ANN-Based Boundary Matching Technique

Nächstes Kapitel Reduction of Large Power System Models: A Case Study

R. Podmore, Identification of coherent generators for dynamic equivalents. IEEE Trans. Power Apparatus Syst. PAS–97(4), 1344–1354 (1978)CrossRef

R. Podmore, A. Germond, Dynamic equivalents for transient stability studies. Systems control, Inc., final report prepared for EPRI project RP-763, April 1977

L. Wang, M. Klein, S. Yirga, P. Kundur, Dynamic reduction of large power systems for stability studies. IEEE Trans. Power Syst. 12, 889–895 (1997)CrossRef

P.V. Kokotović, B. Avramović, J.H. Chow, J.R. Winkelman, Coherency based decomposition and aggregation. Automatica 18, 47–56 (1982)MATHCrossRef

I.J. Perez-Arriaga, G.C. Verghese, F.C. Schweppe, Selective modal analysis with applications to electric power systems, part I: Heuristic introduction. IEEE Trans. Power Apparatus Syst. PAS–101(9), 3117–3125 (1982)CrossRef

M.A. Pai, R.P. Adgaonkar, Electromechanical distance measure for decomposition of power systems. Electr. Power Energy Syst. 6(4), 249–254 (1984)CrossRef

J. Lawler, R.A. Schlueter, P. Rusche, D.L. Hackett, Modal-coherent equivalents derived from an RMS coherency measure. IEEE Trans. Power Apparatus Syst. PAS–99(4), 1415–1425 (1980)CrossRef

H. You, V. Vittal, X. Wang, Slow cherency-based islanding. IEEE Trans. Power Syst. 19, 483–491 (2004)CrossRef

M.-H. Chang, H.-C. Wang, Novel clustering method for coherency identification using an artificial neural network. IEEE Trans. Power Syst. 9, 2056–2062 (1994)CrossRef

10.

D. Chaniotis, Krylov Subspace Methods in Power System Studies, Ph.D. dissertation, University of Illinois at Urbana-Champaign, 2001

11.

S. Liu, Dynamic-Data Driven Real-Time Identification for Electric Power Systems, Ph.D. dissertation, University of Illinois at Urbana-Champaign, 2009

12.

W.E. Arnoldi, The principle of minimized iteration in the solution of the matrix eigenvalue. Q. Appl. Math. 19, 17–29 (1951)MathSciNet

13.

C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators. J. Res. Natl. Bur. Stan. 45, 255–282 (1950)MathSciNetCrossRef

14.

M.R. Hestenes, E.L. Stiefel, Methods of conjugate gradients for solving linear systems. J. Res. Natl. Bur. Stan. 49, 409–436 (1952)MathSciNetMATHCrossRef

15.

C. Lanczos, Solution of systems of linear equations by minimized iterations. J. Res. Natl. Bur. Stan. 49, 33–53 (1952)MathSciNetCrossRef

16.

R. Fletcher, Conjugate gradient methods for indefinite systems, in Proceedings of the Dundee Biennal Conference on Numerical Analysis 1974, New York, 1975

17.

R.W. Freund, N.M. Nachtigal, An implementation of the look-ahead Lanczos algorithm for Non-Hermitian matrices: Part 2, NASA Ames Research Center, Technical report no. 90.46, 1990

18.

P. Sonneved, CGS: a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 10, 36–52 (1989)CrossRef

19.

H.A. van der Vorst, Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comput. 13, 631–644 (1992)MATHCrossRef

20.

Y. Saad, M.H. Schultz, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)MathSciNetMATHCrossRef

21.

Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd edn. (SIAM, Philadelphia, 2003)MATHCrossRef

22.

A.C. Antoulas, Approximation of Large-Scale Dynamical Systems (SIAM, Philadelphia, 2005)MATHCrossRef

23.

S. Gugercin, A.C. Antoulas, A survey of model reduction by balanced truncation and some new results. Int. J. Control 77(8), 748–766 (2004)MathSciNetMATHCrossRef

24.

A. Laub, M. Heath, C. Paige, R. Ward, Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Trans. Autom. Control 32, 115–122 (1987)MATHCrossRef

25.

B.C. Moore, Principal component analysis in linear systems: controllability, observability, and model reduction. IEEE Trans. Autom. Control AC–26, 17–32 (1981)CrossRef

26.

K. Glover, All optimal Hankel-norm approximations of linear multivariable systems and their \(L^\infty \) norms. Int. J. Control 39, 1115–1193 (1984)MathSciNetMATHCrossRef

27.

S. Lall, J.E. Marsden, S. Glavaski, A subspace approach to balanced truncation for model reduction of nonlinear control systems. Int. J. Robust Nonlinear Control 12(6), 519–535 (2002)MathSciNetMATHCrossRef

28.

S. Lall, C. Beck, Error bounds for balanced model reduction of linear time-varying systems. IEEE Trans. Autom. Control 48, 946–956 (2003)MathSciNetCrossRef

29.

H. Sandberg, A. Rantzer, Balanced truncation of linear time-varying systems. IEEE Trans. Autom. Control 49, 217–229 (2004)MathSciNetCrossRef

30.

P.W. Sauer, M.A. Pai, Power System Dynamics and Stability (Prentice Hall, Englewood Cliffs, 1998)

31.

G. Rogers, Power System Oscillations (Kluwer, Dordrecht, 2000)CrossRef

32.

J. Chow, G. Rogers, Power systems toolbox, Available: http://www.ecse.rpi.edu/ chowj

33.

A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, S. Tarantola, Global Sensitivity Analysis: The Primer (Wiley-Interscience, New York, 2008)

34.

D. Chaniotis, M. Pai, Model reduction in power systems using Krylov subspace methods. IEEE Trans. Power Syst. 20, 888–894 (2005)CrossRef

Titel: Krylov Subspace and Balanced Truncation Methods for Power System Model Reduction
verfasst von: Shanshan Liu
Peter W. Sauer
Dimitrios Chaniotis
M. A. Pai
Verlag: Springer New York
Buch: Power System Coherency and Model Reduction
Print ISBN: 978-1-4614-1802-3

Electronic ISBN: 978-1-4614-1803-0

Copyright-Jahr: 2013
DOI: https://doi.org/10.1007/978-1-4614-1803-0_6