Skip to main content

Introduction

  • Chapter
  • First Online:
Power System Coherency and Model Reduction

Part of the book series: Power Electronics and Power Systems ((PEPS,volume 94))

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    This discussion can readily be extended to multiple external systems, as well as some buffer or boundary systems between the study system and the external system.

  2. 2.

    Note that (1.7) can be shown to be equivalent to the formulation in [17] using the study system boundary buses as inputs and current injected into the study system as the outputs, and maintaining a linearized model of the external system power network.

References

  1. R.W. deMello, R. Podmore, K.N. Stanton, Coherency-based dynamic equivalents: Applications in transient stability studies. PICA Conference Proceedings (1975) , pp. 23–31

    Google Scholar 

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

    Article  Google Scholar 

  3. A.J. Germond, R. Podmore, Dynamic aggregation of generating unit models. IEEE Trans. Power Apparatus Syst. PAS–97(4), 1060–1069 (1978)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Book  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  7. C.W. Taylor, D.C. Erickson, Recording and analyzing the July 2 cascading outage. IEEE Comput. Appl. Power. 10(1), 26–30 (1997)

    Article  Google Scholar 

  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. N. Martins, Efficient eigenvalue and frequency response methods applied to power system small-signal stability studies. IEEE Trans. Power Syst. 1, 217–225 (1986)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  14. P.V. Kokotović, H. Khalil, J. O’Reilly, Singular Perturbation Methods in Control: Analysis and Design (Academic Press, London, 1986)

    MATH  Google Scholar 

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

    Book  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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)

    Article  Google Scholar 

  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. 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. E.J. Davison, A method for simplifying dynamic systems. IEEE Trans. Autom. Control AC–11, 93–101 (1966)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  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. 77–96

    Google Scholar 

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

    Article  Google Scholar 

  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. 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)

    Book  Google Scholar 

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

    Book  MATH  Google Scholar 

  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. S. Haykin, Neural Networks and Learning Machines, 3rd edn. (Prentice Hall, Englewood Cliffs NJ, 2008)

    Google Scholar 

  33. A.G. Phadke, J.S. Thorp, Synchronized Phasor Measurements and their Applications (Springer, New York, 2008)

    Book  MATH  Google Scholar 

  34. D.J. Trudnowski, Estimating electromechanical mode shape from synchrophasor measurements. IEEE Trans. Power Syst. 23(3), 1188–1195 (2008)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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. 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, 1987

    Google Scholar 

  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)

    Article  Google Scholar 

  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 2000

    Google Scholar 

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

    Google Scholar 

  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. 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. P. Kundur, Power System Stability and Control (McGraw-Hill, New York, 1994)

    Google Scholar 

  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, 2009

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Joe H. Chow .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Chow, J.H. (2013). Introduction. In: Chow, J. (eds) Power System Coherency and Model Reduction. Power Electronics and Power Systems, vol 94. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1803-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-1803-0_1

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-1802-3

  • Online ISBN: 978-1-4614-1803-0

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics