Skip to main content
SpringerLink
Log in

Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment

  • Chapter
Applied Mathematics for Restructured Electric Power Systems

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

  • 2852 Accesses

Abstract

Power system dynamic performance enhancement can often be formulated as a dynamic embedded optimization problem. The associated cost function quantifies performance and involves dynamically evolving state variables. The dynamic model is embedded within the constraints. Power systems form an important example of hybrid systems, with interactions between continuous dynamics and discrete events playing a fundamental role in behavior. However, it is shown that for a large class of problems, the cost function is smooth even though the underlying dynamic response is non-smooth. Complementing this design-oriented optimization framework, techniques for assessing power system performance and vulnerability can often be expressed as boundary value problems, and solved using shooting methods. It is shown that performance limitations are closely related to grazing phenomena. Techniques are presented for determining parameter values that induce limit cycles and grazing.

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

Access this chapter

Log in via an institution
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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. U.S.-Canada Power System Outage Task Force. Final Report on the August 14, 2003 Blackout in the United States and Canada: Causes and Recommendations. April 2004.

    Google Scholar 

  2. K. Kim, H. Schättler, V. Venkatasubramanian, J. Zaborszky, and P. Hirsch. Methods for Calculating Oscillations in Large Power Systems. IEEE Transactions on Power Systems, 12:1639–1648, 1997.

    Article  Google Scholar 

  3. G. Rogers. Power System Oscillations. Kluwer Academic Publishers, Norwell, MA, 2000.

    Google Scholar 

  4. L.G. Perez, A.J. Flechsig, and V. Venkatasubramanian. Modeling the Protective System for Power System Dynamic Analysis. IEEE Transactions on Power Systems, 9:1963–1973, 1994.

    Article  Google Scholar 

  5. M.S. Ćalović. Modeling and Analysis of Under-Load Tap-Changing Transformer Control Systems. IEEE Transactions on Power Apparatus and Systems, PAS-103:1909–1915, 1984.

    Google Scholar 

  6. M.D. Lemmon, K.X. He, and I. Markovsky. Supervisory Hybrid Systems. IEEE Control Systems Magazine, 19:4:42–55, August 1999.

    Article  Google Scholar 

  7. A.F. Filippov. Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers, The Netherlands, 1988.

    Google Scholar 

  8. D. Liberzon. Switching in Systems and Control. Birkhäuser, Boston, MA, 2003.

    MATH  Google Scholar 

  9. I.A. Hiskens. Power System Modeling for Inverse Problems. IEEE Transactions on Circuits and Systems I, 51:539–551, 2004.

    Article  MathSciNet  Google Scholar 

  10. J. Stoer and R. Bulirsch. Introduction to Numerical Analysis, 2nd edition. Springer, New York, 1993.

    MATH  Google Scholar 

  11. P.M. Frank. Introduction to System Sensitivity Theory. Academic Press, New York, 1978.

    MATH  Google Scholar 

  12. I.A. Hiskens and M.A. Pai. Trajectory Sensitivity Analysis of Hybrid Systems. IEEE Transactions on Circuits and Systems I, 47:204–220, 2000.

    Article  Google Scholar 

  13. W.F. Feehery, J.E. Tolsma, and P.I. Barton. Efficient Sensitivity Analysis of Large-Scale Differential-Algebraic Systems. Applied Numerical Mathematics, 25:41–54, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  14. S. Li, L. Petzold, and W. Zhu. Sensitivity Analysis of Differential-Algebraic Equations: A Comparison of Methods on a Special Problem. Applied Numerical Mathematics, 32:161–174, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  15. I.A. Hiskens. Systematic Tuning of Nonlinear Power System Controllers. Proceedings of the 2002 IEEE International Conference on Control Applications, 19–24, Glasgow, Scotland, September 2002.

    Google Scholar 

  16. C. Moors and T. Van Cutsem. Determination of Optimal Load Shedding Against Voltage Instability. Proceedings of the 13th Power Systems Computation Conference, 2:993–1000, Trondheim, Norway, June 1999

    Google Scholar 

  17. F.L. Lewis and V.L. Syrmos. Optimal Control, 2nd edition. Wiley, New York, 1995.

    Google Scholar 

  18. M.S. Branicky, V.S. Borkar, and S.K. Mitter. A Unified Framework for Hybrid Control: Model and Optimal Control theory. IEEE Transactions on Automatic Control, 43:31–45, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Galán and P.I. Barton. Dynamic Optimization of Hybrid Systems. Computers Chemical Engineering, 22:S183–S190, 1998.

    Article  Google Scholar 

  20. B. Piccoli. Hybrid Systems and Optimal Control. Proceedings of the 37 th IEEE Conference on Decision and Control, Tampa, FL, December 1998.

    Google Scholar 

  21. J. Nocedal and S.J. Wright. Numerical Optimization. Springer-Verlag, New York, 1999.

    MATH  Google Scholar 

  22. M. Larsson. Coordinated Voltage Control in Electric Power Systems. PhD Thesis, Department of Industrial Electrical Engineering and Automation, Lund Institute of Technology, Lund, Sweden, 2000.

    Google Scholar 

  23. R. Seydel. Practical Bifurcation and Stability Analysis. Springer-Verlag, New York, 1994.

    MATH  Google Scholar 

  24. P. Gavey. Voltage Stability in the Mid North Coast: Investigation of Voltage Oscillation Occurrence on 26th March 1993. Final Year Project Report, Department of Electrical and Computer Engineering, The University of Newcastle, Australia, 1995.

    Google Scholar 

  25. T.S. Parker and L.O. Chua. Practical Numerical Algorithms for Chaotic Systems. Springer-Verlag, New York, NY, 1989.

    MATH  Google Scholar 

  26. V. Donde and I.A. Hiskens. Shooting Methods for Locating Grazing Phenomena in Hybrid Systems. International Journal of Bifurcation and Chaos, 2004, Submitted.

    Google Scholar 

  27. P.W. Sauer and M.A. Pai. Power System Dynamics and Stability. Prentice Hall, Upper Saddle River, NJ, 1998.

    Google Scholar 

  28. M.H. Fredriksson and A.B. Nordmark. Bifurcations Caused by Grazing Incidence in Many Degrees of Freedom Impact Oscillators. Proceedings of Royal Society London A, 453:1961:1261–1276, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  29. M. di Bernardo, C.J. Budd, and A.R. Champneys. Grazing and Border-Collision in Piecewise-Smooth Systems: A Unified Analytical Framework. Physical Review Letters, 86:2553–2556, 2001.

    Article  Google Scholar 

  30. R.W. Brockett. Minimum attention control. Proceedings of the 36 th IEEE Conference on Decision and Control, 2628–2632, 1997.

    Google Scholar 

  31. V. Venkatasubramanian, H. Schättler, and J. Zaborszky. Dynamics of Large Constrained Nonlinear Systems—a Taxonomy Theory. Proceedings of the IEEE, 83:1530–1561, 1995.

    Article  Google Scholar 

  32. D. Divan. Smart Wires: Demonstration of a Distributed Static Series Compensator (DSSC) Module. SoftSwitching Technologies Presentation, Middleton, WI, March 2004.

    Google Scholar 

  33. B. Ramanathan and V. Vittal. A Structured Singular Value Based Small Signal Stability Performance Boundary for Direct Load Control. Proceedings of IEEE Power Systems Conference and Exposition (PSCE), New York, October 2004 (to appear).

    Google Scholar 

  34. I.A. Hiskens and B. Gong. Voltage Stability Enhancement via Model Predictive Control of Load. Proceedings of the Symposium on Bulk Power System Dynamics and Control VI, Cortina d’Ampezzo, Italy, August 2004 (to appear).

    Google Scholar 

  35. J.R. Hockenberry and B.C. Lesieutre. Evaluation of Uncertainty in Dynamic Simulations of Power System Models I: the Probabilistic Collocation Method. IEEE Transactions on Power Systems, 19:1483–1491, 2004.

    Article  Google Scholar 

  36. I.A. Hiskens, M.A. Pai, and T.B. Nguyen. Bounding Uncertainty in Power System Dynamic Simulations. Proceedings of IEEE PES Winter Meeting, Singapore, January 2000.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Wisconsin, Madison

    Ian A. Hiskens & Jung-Wook Park

  2. University of Illinois, Urbana-Champaign

    Vaibhav Donde

Authors
  1. Ian A. Hiskens
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jung-Wook Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vaibhav Donde
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. of Electrical, Computer, & Systems Engineering, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY, 12180

    Joe H. Chow

  2. Dept. of Electrical and Electronic Engineering, Hong Kong University, Pokfulam Road, Hong Kong

    Felix F. Wu

  3. Center for Energy Systems and Control, Howard University, 2300 Sixth Street NW, Washington, DC, 20059

    James Momoh

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer Science+Business Media, Inc.

About this chapter

Cite this chapter

Hiskens, I.A., Park, JW., Donde, V. (2005). Dynamic Embedded Optimization and Shooting Methods for Power System Performance Assessment. In: Chow, J.H., Wu, F.F., Momoh, J. (eds) Applied Mathematics for Restructured Electric Power Systems. Power Electronics and Power Systems. Springer, Boston, MA. https://doi.org/10.1007/0-387-23471-3_9

Download citation

  • DOI: https://doi.org/10.1007/0-387-23471-3_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-387-23470-0

  • Online ISBN: 978-0-387-23471-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation