Skip to main content
Log in

Bifurcation analysis of a Buck DC–DC converter applied to distributed power systems

  • Original Article
  • Published:
International Journal of System Assurance Engineering and Management Aims and scope Submit manuscript

Abstract

The aim of this paper is to investigate through a detailed analysis the stability and bifurcation pattern of the nonlinear phenomena in the Buck DC–DC converter. Such a study may lead to a better explanation of the dynamics behaviours of the converter. First, a nonlinear system modelling is derived for open-loop Buck converter with state variables of the input current and the output voltage. The large-signal time-domain nonlinear averaged model is used to understand the interaction on the slow scale using nonlinear analysis techniques. The model is extended for the closed-loop system while employing a proportional-integral control solution. After the initial analysis of this converter and stability region identification, we utilize the MATCONT and MATLAB packages to analyze the detailed bifurcation scenario as important parameters are varied. The analysis shows how instabilities can occur on the slow and fast scales. The simulation was performed to explore the dynamic performance.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  • Abed EH, Wang HO, Tesi A (1995) Control of bifurcations and chaos. In: Levine WS (ed) The control handbook. CRC Press & IEEE Press, Boca Raton, pp 951–966

    Google Scholar 

  • Allag A, Hadri Hamida A et al (2006) Power loss analysis in high frequency quasi resonant DC link power conversion for induction heating application. AMSE Journals 79(2):73–84 France, Mai

    Google Scholar 

  • Deane JHB, Hamill DC (1990) Analysis, simulation and experimental study of chaos in the Buck converter. Proc IEEE Power Electron Spec Conf 491–498

  • Dhooge A, Govaerts W, Kuznetsov YA (2003) MATCONT: a matlab package for numerical bifurcation analysis of ODEs. ACM Trans Math Software 29:141–164

    Article  MATH  MathSciNet  Google Scholar 

  • Hadri Hamida A (2011) Contribution à l’analyse et à la commande des convertisseurs DC–DC parallèles à PWM. PhD thesis, University of Biskra, Algeria

  • Hadri Hamida A, Allag A et al. (2004) Efficiency considerations of Quasi resonant DC link converter. In: proceedings of conference ICEMS, international conference on electrical machines and systems. Jeju Island, Korea 361–362

  • Hadri Hamida A, Allag A et al. (2006) Application of an adaptive nonlinear control strategy to AC-DC-PWM converter feeding induction heating. IEEE conference IECON 2006, pp. 1598–1602, Paris, France

  • Hadri Hamida A, Allag A et al. (2008) Adaptive nonlinear control of AC-DC-PWM converter feeding induction heating. AMSE J, vol. 63, no. 2:40–51, France

    Google Scholar 

  • Hadri Hamida A, Zerouali S et al. (2013) Toward a nonlinear control of an AC-DC-PWM converter dedicated to induction heating. Frontiers in energy, Springer Journals, article in press

  • Hadri-Hamida A, Allag A et al. (2007) Adaptive nonlinear control of a passively clamped two switch quasi resonant DC link converter. Int J Appl Electromag Mech 25, no. 1–4:537–542, ISEM, IOS Press

    Google Scholar 

  • Hadri-Hamida A, Allag A et al. (2009) A nonlinear adaptive backstepping approach applied to a three phase PWM AC-DC converter feeding induction heating. Elsevier Journals, CNSNS vol. 14, no. 4, pp. 1515–1525

  • Lee FC (1990) Modeling, analysis, and design of PWM converter, vol 2. Virginia Power Electronic Center Publications Series, Blacksburg

    Google Scholar 

  • Mazumder SK, Nayfeh AH et al (2001) Theoretical and experimental investigation of the fast- and slow-scale instabilities of a DC–DC converter. IEEE Trans Power Electron 16(2):201–216

    Article  Google Scholar 

  • Nayfeh AH, Balachandran B (1995) Applied nonlinear dynamics. Wiley, New York

    Book  MATH  Google Scholar 

  • Prajoux R, Marpinard JC, Jalade J (1976) Etablissement de modeles mathematiques pour regulateurs de puissance a modulation de largeur d’impulsions (pwm). ESA Sci Tech Rev 2:25–42

    Google Scholar 

  • Tse CK (1994) Flip bifurcation and chaos in three-state boost switching regulators. IEEE Transact Circuits Syst 41(1):16–23

    Article  MathSciNet  Google Scholar 

  • Wang HO, Chen DS, Bushnellt LG (2000) Dynamic Feedback Control of Bifurcations. In: proceedings of IEEE decision and control conference,pp. 1619–1624

  • Wiggins S (1988) Global bifurcations and chaos. Springer, New York

    Book  MATH  Google Scholar 

  • Wiggins S (1990) Introduction to applied nonlinear dynamical systems and chaos. Springer, New York

    Book  MATH  Google Scholar 

  • Wood JR (1989) Chaos: a real phenomenon in power electronics. In: proc IEEE Appl Power Electron Conf Expo, 115–124

  • Zerouali S, Mimoune SM Allag A, Hadri Hamida A (2006) Zero voltage switching with optimal linear quadratic regulator for power supply feeding an induction heating. Asian Power Electron J vol. 1, no. 1, Mars

  • Zerouali S, Allag A, Mimoune SM, Hadri Hamida A (2007) Extended kalman filter for uninterruptible power supplies applied to non linear loads. Int J Appl Electromag Mech vol. 25, no. 1–4:565–569. ISEM Bad Gastein, IOS Press

  • Zerouali S, Allag A, Mimoune SM, Hadri Hamida A, Ayad MY, Miraoui A (2007) An adaptive linear quadratic regulator (LQR) applied to Buck-series resonant inverter for induction heating. AMSE J vol. 62, no. 1:94–104, France

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Amel Hadri-Hamida.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hadri-Hamida, A., Ghoggal, A. & Zerouali, S. Bifurcation analysis of a Buck DC–DC converter applied to distributed power systems. Int J Syst Assur Eng Manag 5, 307–312 (2014). https://doi.org/10.1007/s13198-013-0161-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13198-013-0161-x

Keywords

Navigation