Cover
Vol. 17 No. 2 (2021)

Published: December 31, 2021

Pages: 219-225

Review Article

Chaos Phenomenon in Power Systems: A Review

Abdul-Basset A. Al-Hussein 1
1Electrical Engineering Department, University of Basrah, Basrah, Iraq
History
  • Received: October 5, 2021
  • Revised: October 25, 2021
  • Accepted: October 25, 2021
  • Available Online: November 2, 2021
DOI

https://doi.org/10.37917/ijeee.17.2.25

Abstract

This review article puts forward the phenomena of chaotic oscillation in electrical power systems. The aim is to present some short summaries written by distinguished researchers in the field of chaotic oscillation in power systems. The reviewed papers are classified according to the phenomena that cause the chaotic oscillations in electrical power systems. Modern electrical power systems are evolving day by day from small networks toward large-scale grids. Electrical power systems are constituted of multiple inter-linked together elements, such as synchronous generators, transformers, transmission lines, linear and nonlinear loads, and many other devices. Most of these components are inherently nonlinear in nature rendering the whole electrical power system as a complex nonlinear network. Nonlinear systems can evolve very complex dynamics such as static and dynamic bifurcations and may also behave chaotically. Chaos in electrical power systems is very unwanted as it can drive system bus voltage to instability and can lead to voltage collapse and ultimately cause a general blackout.

Keywords

References

  1. B. A. Carreras, J. M. Reynolds-Barredo, I. Dobson, and D. E. Newman, “Validating the OPA cascading blackout model on a 19402 bus transmission network with both mesh and tree structures,” 2019.
  2. H. H. Alhelou, M. E. Hamedani-Golshan, T. C. Njenda, and P. Siano, “A survey on power system blackout and cascading events: Research motivations and challenges,” Energies, vol. 12, no. 4, pp. 1–28, 2019.
  3. L. L. Lai, H. T. Zhang, S. Mishra, D. Ramasubramanian, C. S. Lai, and F. Y. Xu, “Lessons learned from July 2012 Indian blackout,” in 9th IET International Conference on Advances in Power System Control, Operation and Management (APSCOM 2012), 2012, pp. 1–6.
  4. Y. Wang, M. Luo, Y. Xiao, and H. Chen, “Research on chaos phenomena in power system,” PEAM 2011 - Proc. 2011 IEEE Power Eng. Autom. Conf., vol. 2, no. 2, pp. 453–456, 2011.
  5. N. Shrirao, A. Pandey, V. Chaurasia, R. Gupta, N. Modi, and R. Malpani, “A Review: Comparative Analysis of Chaotic Systems With Their Fractional Order Counterparts,” SSRN Electron. J., pp. 1–9, 2020.
  6. W. Ditto and T. Munakata, “Principles and applications of chaotic systems,” Commun. ACM, vol. 38, no. 11, pp. 96–102, 1995.
  7. X. Zhou, S. Li, and Y. Ma, “The review of chaos research in power system,” Adv. Mater. Res., vol. 542– 543, pp. 111–114, 2012.
  8. N. Kopell and R. B. Washburn, “Chaotic Motions in the Two-Degree-of-Freedom Swing Equations,” IEEE Trans. Circuits Syst., vol. 29, no. 11, pp. 738–746, 1982.
  9. F. M. A. Salam, “Chaos in the one generator system with excitation feedback,” in The 22nd IEEE Conference on Decision and Control, 1983, pp. 360–364.
  10. R.-L. Chen and P. P. Varaiya, “Degenerate Hopf bifurcations in power systems,” IEEE Trans. circuits Syst., vol. 35, no. 7, pp. 818–824, 1988.
  11. H.-D. Chiang, “Application of Bifurcation Analysis to Power Systems,” pp. 1–24, 2004.
  12. J. Li and V. Venkatasubramanian, “Study of Hopf bifurcations in a simple power system model,” Proc. IEEE Conf. Decis. Control, vol. 4, no. 4, pp. 3075–3079, 2000.
  13. D. Q. Wei and X. S. Luo, “Noise-induced chaos in single-machine infinite-bus power systems,” Epl, vol. 86, no. 5, 2009.
  14. W. Ji and V. Venkatasubramanian, “Hard-limit induced chaos in a fundamental power system model,” Int. J. Electr. Power Energy Syst., vol. 18, no. 5, pp. 279–295, 1996.
  15. A.-B. A. Al-Hussein, F. R. Tahir, and K. Rajagopal, “Chaotic Power System Stabilization Based on Novel Incommensurate Fractional-Order Linear Augmentation Controller,” Complexity, vol. 2021, 2021.
  16. V. Venkatasubramanian, “Coexistence of four different attractors in a fundamental power system model,” IEEE Trans. Circuits Syst. I Fundam. Theory Appl., vol. 46, no. 3, pp. 405–409, 1999.
  17. Y. H. Qin and J. C. Li, “Random parameters induce chaos in power systems,” Nonlinear Dyn., vol. 77, no. 4, pp. 1609–1615, 2014.
  18. Q. Ying-Hua, “Random-phase-induced chaos in power systems,” Chinese Phys. B, vol. 19, no. 6, 2010.
  19. B. V Chirikov, “A universal instability of many- dimensional oscillator systems,” Phys. Rep., vol. 52, no. 5, Al-Hussein | 225 pp. 263–379, 1979.
  20. I. Dobson, H. D. Chiang, J. S. Thorp, and L. Fekih- Ahmed, “Model of voltage collapse in electric power systems,” Proceedings of the IEEE Conference on Decision and Control. pp. 2104–2109, 1988.
  21. I. Dobson and H. D. Chiang, “Towards a theory of voltage collapse in electric power systems,” Syst. Control Lett., vol. 13, no. 3, pp. 253–262, 1989.
  22. A.-B. A. Al-Hussein, F. R. Tahir, and O. Boubaker, “Chaos Elimination in Power System Using Synergetic Control Theory,” in 2021 18th International Multi- Conference on Systems, Signals & Devices (SSD), 2021, pp. 340–345.
  23. H. D. Chiang, C. W. Liu, P. P. Varaiya, F. F. Wu, and M. G. Lauby, “Chaos in a simple power system,” IEEE Trans. Power Syst., vol. 8, no. 4, pp. 1407–1417, 1993.
  24. K. G. Rajesh and K. R. Padiyar, “Bifurcation analysis of a three node power system with detailed models,” Int. J. Electr. Power Energy Syst., vol. 21, no. 5, pp. 375–393, 1999.
  25. A.-B. A. Al-Hussein, F. R. Tahir, A. Ouannas, T.-C. Sun, H. Jahanshahi, and A. A. Aly, “Chaos suppressing in a three-buses power system using an adaptive synergetic control method,” Electronics, vol. 10, no. 13, p. 1532, 2021.
  26. Z. Jing, D. Xu, Y. Chang, and L. Chen, “Bifurcations, chaos, and system collapse in a three node power system,” Int. J. Electr. Power Energy Syst., vol. 25, no. 6, pp. 443– 461, 2003.
  27. H. Jia, N. Guangyu, S. T. Lee, and P. Zhang, “Study on the impact of time delay to power system small signal stability,” Proc. Mediterr. Electrotech. Conf. - MELECON, vol. 2006, no. 1, pp. 1011–1014, 2006.
  28. M. L. Ma and F. H. Min, “Bifurcation behavior and coexisting motions in a time-delayed power system,” Chinese Phys. B, vol. 24, no. 3, 2015.
  29. H. K. Chen, T. N. Lin, and J. H. Chen, “Dynamic analysis, controlling chaos and chaotification of a SMIB power system,” Chaos, Solitons and Fractals, vol. 24, no. 5, pp. 1307–1315, 2005.
  30. M. Bongiorno, On control of grid-connected voltage source converters: mitigation of voltage dips and subsynchronous resonances. Chalmers Tekniska Hogskola (Sweden), 2007.
  31. A. A. Fouad and K. T. Khu, “Subsychronous Resonance Zones in the IEEE" Bench Mark" Power System,” IEEE Trans. Power Appar. Syst., no. 3, pp. 754–762, 1978.
  32. A. M. Harb and M. S. Widyan, “Modern nonlinear theory as applied to SSR of the IEEE second benchmark model,” 2003 IEEE Bol. PowerTech - Conf. Proc., vol. 3, pp. 967–973, 2003.
  33. A. M. Harb and M. S. Widyan, “Chaos and bifurcation control of SSR in the IEEE second benchmark model,” Chaos, Solitons and Fractals, vol. 21, no. 3, pp. 537–552, 2004.
  34. M. S. Widyan, “Controlling chaos and bifurcations of SMIB power system experiencing SSR phenomenon using SSSC,” Int. J. Electr. Power Energy Syst., vol. 49, no. 1, pp. 66–75, 2013.
  35. A. M. Harb and M. M. Alomari, “Bifurcation and chaos theory as applied to SSR of the IEEE second benchmark model (system # 2) with the presence of the damper windings,” Proc. 2005 Int. Conf. Sci. Comput. CSC’05, vol. 6203, no. December, pp. 177–183, 2005.
  36. M. M. Alomari, M. S. Widyan, M. Abdul-Niby, and A. Gheitasi, “Hopf Bifurcation Control of Subsynchronous Resonance Utilizing UPFC,” Eng. Technol. Appl. Sci. Res., vol. 7, no. 3, pp. 1588–1594, 2017.
  37. B. A. Mork and D. L. Stuehm, “Application of nonlinear dynamics and chaos to ferroresonance in distribution systems,” IEEE Trans. Power Deliv., vol. 9, no. 2, pp. 1009–1017, 1994.
  38. S. Mozaffari, S. Henschel, and A. C. Soudack, “Chaotic ferroresonance in power transformers,” IEE Proc. Gener. Transm. Distrib., vol. 142, no. 3, pp. 247–250, 1995.
  39. H. Radmanesh and G. B. Gharehpetian, “Ferroresonance suppression in power transformers using chaos theory,” Int. J. Electr. Power Energy Syst., vol. 45, no. 1, pp. 1–9, 2013.
  40. S. Rezaei, “Power Oscillation Due to Ferroresonance and Subsynchronous Resonance,” Power Syst. Stab., 2019.
  41. P. Ferracci, “Ferroresonance–Cahier technique Schneider no. 190,” Groupe Schneider, 1998.