• Joe H. Chow
Part of the Power Electronics and Power Systems book series (PEPS, volume 94)


This introductory chapter gives a brief overview of power system coherency and model reduction literature. This survey focuses on both the early results and some more recent developments, and organizes power system model reduction techniques into two broad categories. One category of methods is to use coherency and aggregation methods to obtain reduced models in the form of nonlinear power system models. The other category is to treat the external system or the less relevant part of the system as an input–output model and obtain a lower order linear or nonlinear model based on the input–output properties. This chapter also provides a synopsis of the remaining chapters in this monograph.


Power System Model Reduction External System Power System Stabilizer Transfer Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    R.W. deMello, R. Podmore, K.N. Stanton, Coherency-based dynamic equivalents: Applications in transient stability studies. PICA Conference Proceedings (1975) , pp. 23–31Google Scholar
  2. 2.
    R. Podmore, Identification of coherent generators for dynamic equivalents. IEEE. Trans. Power Apparatus Syst. PAS–97(4), 1344–1354 (1978)CrossRefGoogle Scholar
  3. 3.
    A.J. Germond, R. Podmore, Dynamic aggregation of generating unit models. IEEE Trans. Power Apparatus Syst. PAS–97(4), 1060–1069 (1978)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    J.H. Chow, G. Peponides, P.V. Kokotović, B. Avramović, J.R. Winkelman, Time-Scale Modeling of Dynamic Networks with Applications to Power Systems (Springer-Verlag, New York, 1982)MATHCrossRefGoogle Scholar
  6. 6.
    J.H. Chow, J.R. Winkelman, M.A. Pai, P.W. Sauer, Singular perturbation analysis of large scale power systems. J. Electr. Power Energy Syst. 12, 117–126 (1990)CrossRefGoogle Scholar
  7. 7.
    C.W. Taylor, D.C. Erickson, Recording and analyzing the July 2 cascading outage. IEEE Comput. Appl. Power. 10(1), 26–30 (1997)CrossRefGoogle Scholar
  8. 8.
    J.H. Chow, J. Cullum, R.A. Willoughby, A sparsity-based technique for identifying slow-coherent areas in large power systems. EEE Trans. Power Apparatus Syst. PAS–103, 463–473 (1983)Google Scholar
  9. 9.
    N. Martins, Efficient eigenvalue and frequency response methods applied to power system small-signal stability studies. IEEE Trans. Power Syst. 1, 217–225 (1986)CrossRefGoogle Scholar
  10. 10.
    N. Uchida, T. Nagao, A new eigen-analysis methcd of steady-state stability studies for large power systems: S matrix method. IEEE Trans. Power Syst. 2, 706–714 (1988)CrossRefGoogle Scholar
  11. 11.
    L. Wang, A. Semlyen, Applications of sparse eigenvalue techniques to the small signal stabiity analysis of large power systems. IEEE Trans. Power Syst. 5, 635–642 (1990)CrossRefGoogle Scholar
  12. 12.
    J. Zaborszky, K.-W. Whang, G.M. Huang, L.-J. Chiang, and S.-Y. Lin, A clustered dynamical model for a class of linear autonomous systems using simple enumerative sorting, IEEE Trans on Circuits and Systems, vol. CAS-29, 747–758, (1982).Google Scholar
  13. 13.
    R. Nath, S.S. Lamba, K.S.P. Rao, Coherency based system decomposition into study and external areas using weak coupling. IEEE Trans. Power Apparatus Syst. PAS–104, 1443–1449 (1985)CrossRefGoogle Scholar
  14. 14.
    P.V. Kokotović, H. Khalil, J. O’Reilly, Singular Perturbation Methods in Control: Analysis and Design (Academic Press, London, 1986)MATHGoogle Scholar
  15. 15.
    R.A. Date, J.H. Chow, Aggregation properties of linearized two-times-scale power networks. IEEE Trans. Circuits Syst. 38, 720–730 (1991)Google Scholar
  16. 16.
    J.H. Chow, New algorithms for slow coherency aggregation of large power systems, in Systems and Control Theory for Power Systems, IMA Volumes in Mathematics and its Applications, vol. 64, ed. by J.H. Chow, R.J. Thomas, P.V. Kokotović (Springer-Verlag, New York, 1994)Google Scholar
  17. 17.
    J.M. Undrill, A.E. Turner, Construction of power system electromechanical equivalents by modal analysis. IEEE Trans. Power Apparatus Syst. PAS–90, 2049–2059 (1971)Google Scholar
  18. 18.
    G. Rogers, Power System Oscillations (Kluwer Academic, Dordrecht, 2000)CrossRefGoogle Scholar
  19. 19.
    J.H. Chow, K.W. Cheung, A toolbox for power system dynamics and control engineering education. IEEE Trans. Power Syst. 7, 1559–1564 (1992)CrossRefGoogle Scholar
  20. 20.
    S.D. Dukić, A.T. Sarić, Dynamic model reduction: An overview of available techniques with application to power systems, Serbian. J. Electr. Eng. 9(2), 131–169 (2012)Google Scholar
  21. 21.
    J.M. Undrill, J.A. Casazza, E.M. Gulachenski, L.K. Kirchmayer, Electromechanical equivalents for use in power system stability studies. IEEE Trans. Power Apparatus Syst. PAS–90, 2060–2071 (1971)CrossRefGoogle Scholar
  22. 22.
    W.W. Price, E.M. Gulachenski, P. Kundur, F.J. Lange, G.C. Loehr, B.A. Roth, R.F. Silva, Testing of the modal dynamic equivalents technique. IEEE Trans. Power Apparatus Syst. PAS–97, 1366–1372 (1978)Google Scholar
  23. 23.
    W.W. Price, B.A. Roth, B.A. Roth, Large-scale implementation of modal dynamic equivalents. IEEE Trans. Power Apparatus Syst. PAS–100, 3811–3817 (1981)Google Scholar
  24. 24.
    E.J. Davison, A method for simplifying dynamic systems. IEEE Trans. Autom. Control AC–11, 93–101 (1966)MathSciNetCrossRefGoogle Scholar
  25. 25.
    I.J. Pérez-Arriaga, G.C. Verghese, F.C. Schweppe, Selective modal analysis with applications to electric power systems. part I: Heuristic introduction. part II: The dynamic stability problem. IEEE Trans. Power Apparatus Syst. PAS–101, 3117–3134 (1982)CrossRefGoogle Scholar
  26. 26.
    F.L. Pagola, L. Rouco, I.J. Pérez-Arriaga, Analysis and control of small signal stability in electric power systems by selective modal analysis, in Eigenanalysis and Frequency Domain Methods for System Dynamic Performance. (IEEE Publication 90TH0292-3-PWR, 1990) , pp. 77–96Google Scholar
  27. 27.
    B.C. Moore, Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Trans. Autom. Control AC–26, 17–32 (1981)CrossRefGoogle Scholar
  28. 28.
    K. Glover, All optimal Hankel-norm approximations of linear multivariable systems and their \(L^\infty \) norms. International Journal of Control 39, 1115–1193 (1984)Google Scholar
  29. 29.
    P. Benner, V. Mehrmann, D.C. Sorensen, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Sciences and Engineering, vol. 45 (Springer, Berlin, 2005)CrossRefGoogle Scholar
  30. 30.
    A.C. Antoulas, Approximation of Large-Scale Dynamical Systems (SIAM, Philadelphia, 2005)MATHCrossRefGoogle Scholar
  31. 31.
    J.R. Winkelman, J.H. Chow, B.C. Bowler, B. Avramovic, P.V. Kokotović, An analysis of interarea dynamics of multi-machine systems. IEEE Trans. Power Apparatus Syst. PAS–100, 754–763 (1981)Google Scholar
  32. 32.
    S. Haykin, Neural Networks and Learning Machines, 3rd edn. (Prentice Hall, Englewood Cliffs NJ, 2008)Google Scholar
  33. 33.
    A.G. Phadke, J.S. Thorp, Synchronized Phasor Measurements and their Applications (Springer, New York, 2008)MATHCrossRefGoogle Scholar
  34. 34.
    D.J. Trudnowski, Estimating electromechanical mode shape from synchrophasor measurements. IEEE Trans. Power Syst. 23(3), 1188–1195 (2008)CrossRefGoogle Scholar
  35. 35.
    J.H. Chow, A. Chakrabortty, L. Vanfretti, M. Arcak, Estimation of radial power system transfer path dynamic parameters using synchronized phasor data. IEEE Trans. Power Syst. 23(2), 564–571 (May 2008)CrossRefGoogle Scholar
  36. 36.
    A. Murdoch, G. Boukarim, Performance Criteria and Tuning Techniques, Chapter 3 in IEEE Tutorial Course - Power System Stabilization via Excitation Control (Tampa, Florida, 2007)Google Scholar
  37. 37.
    E.V. Larsen, J.H. Chow, SVC control design concepts for system dynamic performance, in IEEE Power Engineering Society Publication 87TH0187-5-PWR Application of Static Var Systems for System Dynamic Performance, 1987Google Scholar
  38. 38.
    E.V. Larsen, J.J. Sanchez-Gasca, J.H. Chow, Concepts for design of FACTS controllers to damp power swings. IEEE Trans. Power Syst. 10, 948–956 (1995)CrossRefGoogle Scholar
  39. 39.
    C. Gama, L. Änguist, G. Ingeström, M. Noroozian, Commissioning and operative experience of TCSC for damping power oscillation in the Brazilian north-south interconnection. Paper 14–104, CIGRE Session 2000Google Scholar
  40. 40.
    V. Centeno, A.G. Phadke, A. Edris, J. Benton, M. Gaugi, G. Michel, An adaptive out-of-step relay. IEEE Trans Power Syst. 26, 334–343 (1997)Google Scholar
  41. 41.
    H. You, V. Vittal, X. Wang, Slow cherency-based islanding. IEEE Trans. Power Syst. 19, 483–491 (2004)Google Scholar
  42. 42.
    G. Xu, V. Vittal, A. Anatoliy, J.E. Thalman, Controlled islanding demonstrations in WECC system. IEEE Trans. Power Deliv. 12, 61–71 (2011)Google Scholar
  43. 43.
    A.-A. Fouad, V. Vittal, Power System Transient Stability Analysis using the Transient Energy Function Method (Prentice-Hall, Englewood Cliffs NJ, 1992)Google Scholar
  44. 44.
    P. Kundur, Power System Stability and Control (McGraw-Hill, New York, 1994)Google Scholar
  45. 45.
    L. Vanfretti, Phasor measurement based state estimation of electric power systems and linearized analysis of power system network oscillations, PhD thesis, Rensselaer Polytechnic Institute, 2009Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Rensselaer Polytechnic InstituteNew YorkUSA

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