In this study, the non-linear dynamics of a full bridge DC–AC inverter controlled by fixed frequency pulse-width modulation which is widely used in solar energy systems is investigated. The main results are illustrated with the aid of time domain simulations obtained from an accurate non-linear time varying model of the system derived without making any quasi-static approximation. Results reveal that for high filter time-constants, the system loses stability via Hopf bifurcation and exhibits mode-locked periodic motion and for low filter time-constants, via period-doubling bifurcation resulting in period-bubbling structures and intermittent chaos. The mode-locked instability is also theoretically verified using Jacobian matrix derived from an averaged model and that of period-bubbling instability is verified using monodromy matrix based on Filippov's method of differential inclusions. Furthermore, extensive analyses are performed to study the mechanism of the emergence of intermittency and remerging chaotic band attractors (or Feigenbaum sequences) for variation in filter parameters and to demarcate the bifurcation boundaries. Phase portraits and Poincaré sections before and after the bifurcations are shown. Experimental results are also provided to confirm the observed bifurcation scenario.

References

1. 1)
  - 23. Deivasundari, P., Uma, G., Murali, K.: ‘Chaotic dynamics of voltage-mode controlled buck converter with periodic interference signals’, Int. J. Bifurcation Chaos2013, 23, (6), pp. 1350099-1–1350099-32.
2. 2)
  - 5. Rodriguez, E., El Aroudi, A., Guinjoan, F., Alarcón, E.: ‘A ripple-based design-oriented approach for predicting fast-scale instability in DC-DC switching power supplies’, IEEE Trans. Circuits Syst. I, 2012, 59, (1), pp. 215–227 (doi: 10.1109/TCSI.2011.2161396).
3. 3)
  - 14. Giaouris, D., Banerjee, S., Zahawi, B., Pickert, V.: ‘Control of fast scale bifurcations in power-factor correction converters’, IEEE Trans. Circuits Syst. II, 2007, 54, (9), pp. 805–809 (doi: 10.1109/TCSII.2007.900350).
4. 4)
  - 9. Giaouris, D., Banerjee, S., Imrayed, O., Mandal, K., Zahawi, B., Pickert, V.: ‘Complex interaction between tori and onset of three-frequency quasi-periodicity in a current-mode controlled boost converter’, IEEE Trans. Circuits Syst. I, 2012, 59, pp. 207–214 (doi: 10.1109/TCSI.2011.2161371).
5. 5)
  - 18. Li, M., Dai, D., Ma, X., Iu, H.H.C.: ‘Fast-scale period-doubling bifurcation in voltage-mode controlled full-bridge inverter’, IEEE Int. Symp. Circuits and System, Seattle, WA, 2008, pp. 2829–2832.
6. 6)
  - 7. Wang, F.Q., Ma, X.K.: ‘Stability and bifurcation in a voltage controlled negative-output KY boost converter’, Phys. Lett. A, 2011, 375, pp. 1451–1456 (doi: 10.1016/j.physleta.2011.02.029).
7. 7)
  - 22. Tse, C.K.: ‘Complex behaviour of switching power converters’ (CRC Press, Boca Raton, NY, 2004).
8. 8)
  - 3. Giaouris, D., Banerjee, S., Zahawi, B., Pickert, V.: ‘‘Stability analysis of the continuous conduction mode buck converter via Filippov's method’’, IEEE Trans. Circuits Syst. I, 2008, 55, pp. 1084–1096 (doi: 10.1109/TCSI.2008.916443).
9. 9)
  - 13. Dai, D., Li, S., Ma, X., Tse, C.K.: ‘Slow-scale instability of single stage power-factor-correction power supplies’, IEEE Trans. Circuits Syst. I, 2007, 54, (8), pp. 1724–1735 (doi: 10.1109/TCSI.2007.902516).
10. 10)
  - 24. Lakshmanan, M., Murali, K.: ‘Chaos in nonlinear oscillators: controlling and synchronisation’ (World Scientific, Singapore, 1996).
11. 11)
  - 19. Aroudi, A., Rodriguez, E., Orabi, M., Alarcon, E.: ‘Modelling of switching frequency instabilities in buck based DC-AC H-bridge inverters’, Int. J. Circuits Theory Appl., 2011, 39, pp. 175–193 (doi: 10.1002/cta.627).
12. 12)
  - 1. Basak, B., Parui, S.: ‘Exploration of bifurcation and chaos in buck converter supplied from a rectifier’, IEEE Trans. Power Electr., 2010, 25, (6), pp. 1556–1564 (doi: 10.1109/TPEL.2009.2035500).
13. 13)
  - 11. Ma, W., Wang, M., Liu, S., Li, S., Yu, P.: ‘Stabilising the average-current-mode-controlled boost PFC converter via washout-filter-aided method’, IEEE Trans. Circuits Syst. II, 2011, 58, (9), pp. 595–599 (doi: 10.1109/TCSII.2011.2161170).
14. 14)
  - 20. Sturcken, N., O'Sulivan, E.: ‘A 2.5D integrated voltage regulator using coupled-magnetic-core inductors on silicon interposer delivering 10.8 A/mm2’. IEEE Int. Solid-state Circuits Conf., 2012, pp. 400–402.
15. 15)
  - 17. Iu, H.H.C., Robert, B.: ‘Control of chaos in PWM current-mode H-bridge inverter using time-delayed feedback’, IEEE Trans. Circuits Syst. I, 2003, 50, (8), pp. 1125–1129 (doi: 10.1109/TCSI.2003.815220).
16. 16)
  - 2. Angulo, F., Olivar, G., di Bernardo, M.: ‘Two-parameter discontinuity-induced bifurcation curves in a ZAD-strategy-controlled DC-DC buck converter’, IEEE Trans. Circuits Syst. I, 2008, 55, (8), pp. 2392–2401 (doi: 10.1109/TCSI.2008.918226).
17. 17)
  - 4. Maity, S., Tripathy, D., Bhattacharya, T.K., Banerjee, S.: ‘Bifurcation analysis of PWM-1 voltage-mode controlled buck converter using the exact discrete model’, IEEE Trans. Circuits Syst. I, 2007, 54, pp. 1120–1130 (doi: 10.1109/TCSI.2007.895526).
18. 18)
  - 25. Thamilmaran, K., Lakshmanan, M.: ‘Classification of bifurcations and routes to chaos in a variant Murali-Lakshmanan-Chua circuit’, Int. J. Bifurcation Chaos, 2002, 12, (4), pp. 783–813 (doi: 10.1142/S0218127402004681).
19. 19)
  - 6. Natsheh, A.N., Kettleborough, J.G., Janson, N.B.: ‘Experimental study of controlling chaos in a DC–DC boost converter’, Chaos Solitons Fractals, 2009, 40, pp. 2500–2508 (doi: 10.1016/j.chaos.2007.10.048).
20. 20)
  - 10. Orabi, M., Ninomiya, T.: ‘Nonlinear dynamics of power-factor correction converter’, IEEE Trans. Ind. Electron., 2003, 50, (6), pp. 1116–1125 (doi: 10.1109/TIE.2003.819576).
21. 21)
  - 21. Nayfeh, A., Balachandran, B.: ‘Applied nonlinear dynamics’ (John Wiley & Sons, Inc., 1995).
22. 22)
  - 12. Wang, F., Zhang, H., Ma, X.: ‘Analysis of slow scale instability in boost PFC converter using the method of Harmonic Balance and Floquet theory’, IEEE Trans. Circuits Syst. I, 2010, 57, (2), pp. 405–414 (doi: 10.1109/TCSI.2009.2023933).
23. 23)
  - 15. Deivasundari, P., Uma, G., Umamaheswari, M.G., Kavitha, A.: ‘Coexistence of fast-scale and slow-scale instability in Cuk power factor correction AC-DC pre-regulators under nonlinear current-mode control’, IET Power Electr.2013, 6, (1), pp. 78–87 (doi: 10.1049/iet-pel.2012.0156).
24. 24)
  - 16. Robert, B., Robert, C.: ‘Border collision bifurcations in a one dimensional piecewise smooth map for a PWM current programmed H-bridge inverter’, Int. J. Contr., 2002, 75, (16), pp. 1356–1367 (doi: 10.1080/0020717021000023771).
25. 25)
  - 8. Cafagna, D., Grassi, G.: ‘Bifurcation analysis and chaotic behaviour in boost converters: Experimental results’, Nonlinear Dyn., 2006, 44, pp. 251–262 (doi: 10.1007/s11071-006-1997-2).

Period-bubbling and mode-locking instabilities in a full-bridge DC–AC buck inverter

References

Related content