Skip to main content
SpringerLink
Log in

CTDAE & CTODE models and their applications to power system stability analysis with time delays

  • Published:
Science China Technological Sciences Aims and scope Submit manuscript

Abstract

In this paper, two new models suitable for power system stability analysis with considering time delays are derived. They are constraint time-delayed ordinary differential equation model (CTODE model) and constraint time-delayed differential algebraic equation model (CTDAE model). In these two models, dimension of the time-delayed equation is significantly reduced so as to speed up the calculation efficiency. Detail derivations to their nonlinear and incremental linear forms are given. And, some of their good features are discussed. Finally, a typical time-delayed system and single-machine-infinite-bus system are selected to validate the new models through Lyapunov-Krasovskii criterion and eigenvalue locus tracing procedure. It reveals that some unnecessary calculations in the algorithm can be avoided to achieve higher efficiency based on new models. The new models and new criterion given in this paper are helpful to design wide area protectors for bulk power systems.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gu K Q, Kharitonov V L, Chen J. Stability of Time Delay Systems. Boston: Birkhäuser, 2003

    Book  MATH  Google Scholar 

  2. Lakshmanan M, Senthilkumar D V. Dynamics of Nonlinear Time Delay Systems. Berlin: Springer, 2011

    Book  Google Scholar 

  3. Wu H X, Tsakalis K S, Heydt G T. Evaluation of time delay effects to wide-area power system stabilizer design. IEEE T Power Sys, 2004, 19(4): 1935–1941

    Article  Google Scholar 

  4. Jia H J, Yu X D, Wang C S. Power system small signal stability region with time delay. Int J Elect Power & Energy Syst, 2008, 30(1): 16–22

    Article  Google Scholar 

  5. Wu M, He Y, She J H. Stability Analysis and Robust Control of Time Delay Systems. Beijing: Science Press, 2009

    Google Scholar 

  6. Hale J K, Lunel S M V. Introduction to Functional Differential Equations. New York: Springer-Verlag, 1993

    MATH  Google Scholar 

  7. Wieslaw M, Trzaska Z W. Singularity-induced bifurcations in electrical power systems. IEEE T Power Syst, 2005, 20(1): 312–320

    Article  Google Scholar 

  8. Jia H J, Na G Y, Lee S T, et al.. Study on the impact of time delay to power system small signal stability. Proceedings of 13th IEEE-Melecon, Benalmádena (Málaga), Spain, 2006. 1011–1014

    Google Scholar 

  9. Saffet A. Computation of time delay margin for power system small-signal stability. Euro Trans Elect Power, 2009, 19(7): 949–968

    Article  Google Scholar 

  10. Jia H J, Cao X D, Yu X D, et al. A simple approach to determine power system delay margin, Proceedings of IEEE General Meeting, Tampa, Florida, 2007, vol 2, 799–805

    Google Scholar 

  11. Dong C, Yu X D, Jia H J. Simple method to determine power system delay margin (in Chinese). Automation of Electric Power Systems, 2008, 32(1): 6–10

    Google Scholar 

  12. Jia H J, Yu X D, Wang C S, et al. Study on power system extended small signal stability region (DE-SSSR) in time delay space. Proceedings of 15th IEEE-Melecon, Valletta, Malta, 2010, vol 1, 1569–1574

    Google Scholar 

  13. Yu X D, Jia H J, Zhao J L. A LMI based approach to power system stability analysis with time delay. Proceedinds of IEEE-Tencon 2008, Hyderabad, India, 2008. 1–6

    Google Scholar 

  14. Sun Q, An H Y, Jia H J, et al, An improved power system stability criterion with multiple time delays. Proceedings of IEEE General Meeting, Calgary, Canada, 2009, vol 1, 786–792

    Google Scholar 

  15. Liu F, Yokoyama R, Zhou Y C, et al. Free-weighting matrices-based robust wide-area FACTS control design with considering signal time delay for stability enhancement of power systems. IEEJ Trans Elect Electr Eng, 2012, 7(1): 31–39

    Article  Google Scholar 

  16. Saffet A, Nwankpa C O. Probabilistic evaluation of small signal stability of power systems with time delays. Int Rev Elect Eng, Part B, 2010, 5(1): 205–216

    Google Scholar 

  17. An H Y, Jia H J, Yu X D. An improved delay-dependent robust stability criterion and application to power system stability analysis with time delays. Proceedings of IEEE-Powercon, Hangzhou, China, 2010, Paper ID: 5666129

    Google Scholar 

  18. Hasan A M, Minwon P, In-Keun Y. Enhancement of transient stability by fuzzy logic-controlled SMES considering communication delay. Int J Elect Power & Energy Syst, 2009, 31(7–8): 402–408

    Google Scholar 

  19. Lu C, Han Y D, Wu X C. Field experiments of wide area damping controllers for multiple HVDC links. Proceedings of IEEE Asia Pacific Conference on Circuits and Systems, Macao, China, 2008. 627–630

    Google Scholar 

  20. Li P, He J B, Shi J H, et al. The theory and practice of wide-area damping control for bulk HVAC/HVDC hybrid power systems, Southern Power Syst Technol, 2008, 2(4): 13–17

    Google Scholar 

  21. Taylor C W. The future in on-line security assessment and wide-area stability control. Proceedings of IEEE PES Winter Meeting, Singapore, 2000, vol 1, 78–83

    Google Scholar 

  22. Chaudhuri B, Majumder R, Pal B. Wide area measurement based stabilizing control of power system considering signal transmission delay. Proceedings of IEEE PES General Meeting, San Francisco, 2005, vol 2, 1447–1452

    Google Scholar 

  23. Chen Y, Lv J H, Yu X H. Robust consensus of multi-agent systems with time varying delays in noisy environment. Sci China-Tech Sci, 2011, 54(8): 2014–2023

    Article  MATH  Google Scholar 

  24. Li J Y, Zhang L, Wang Z H. A simple algorithm for testing the stability of periodic solutions of some nonlinear oscillators with large time delay. Sci China Tech Sci, 2011, 54(8): 2033–2043

    Article  MATH  Google Scholar 

  25. Zhang S, Xu J. Oscillation control for n-dimensional congestion control model via time-varying delay. Sci China Tech Sci, 2011, 54(8): 2014–2023

    Article  Google Scholar 

  26. Zhang X J, Xiong C H, Ding Y,et al. Variable-step integration method for milling chatter stability prediction with multiple delay. Sci China Tech Sci, 2011, 54(12): 3137–3154

    Article  MATH  Google Scholar 

  27. Miao W W, Jia H J, Wang D, et al. Active power regulation of wind power systems through demand response. Sci China Tech Sci, 2012, 55(6): 1667–1676

    Article  Google Scholar 

  28. Qi Y, Jia H J, Mu Y F. Frequency response of autonomous microgrid based on family-friendly controllable loads. Sci China Tech Sci, 2013, 56(3): 693–702

    Article  Google Scholar 

  29. Yu X D, Jia H J, Wang C S. An eigenvalue spectrum tracing algorithm and its application in time delayed power system (in Chinese). Autom Elec Power Syst, 2012, 36(24): 10–14, 38

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Smart Grid of Ministry of Education, Tianjin University, Tianjin, 300072, China

    XiaoDan Yu, HongJie Jia & ChengShan Wang

Authors
  1. XiaoDan Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. HongJie Jia
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. ChengShan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to HongJie Jia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yu, X., Jia, H. & Wang, C. CTDAE & CTODE models and their applications to power system stability analysis with time delays. Sci. China Technol. Sci. 56, 1213–1223 (2013). https://doi.org/10.1007/s11431-013-5165-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11431-013-5165-x

Keywords

Search

Navigation