Summary
Power electronic converters are nonlinear dynamical systems. The complex behavior for stand-alone converters, such as Hopf bifurcation, period doubling, border colliding, etc., has been studied in the past decades. In parallel-connected converter systems, several converters are connected together and mandatory control is needed to ensure proper current sharing. In such kind of systems, the effect of nonlinearity becomes more significant due to the complex interaction of the coupled systems.
In this chapter, we attempt to study the complex behavior for parallel-connected buck converters under proportional-integral (PI) control. Basically, we find that for parallel-connected DC/DC converters, the desired operating orbit is not always reached from all initial conditions, even though the orbit has been found locally stable (e.g., from a linearized model). Depending on the initial state, the system may converge to different attractors, which can be a stable period-one orbit, a limit cycle of a long period, quasi-periodic orbit or chaotic orbit. Basins of attraction of desired and undesired attractors will be identified for different parametric perspectives. Furthermore, two distinct types of bifurcations have been identified for parallel-connected converters under PI control, namely, slow-scale bifurcation [1, 2, 3] and fast-scale bifurcation [4, 5]. The determining parameters are the integral-control time constants τ F1 and τ F2. We will study the effects of τ F1 and τ F2 and identify the boundaries between these two types of bifurcations. Finally, we will analyze the bifurcation scenarios using the discrete-time mapping approach.
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References
Huang, Y., Tse, C.K.: On the basins of attraction of parallel connected buck switching converters. In: Proceedings of IEEE International symposium on Circuits and Systems, pp. 5647–5650 (2006)
Orabi, M., Ninomiya, T.: Nonlinear dynamics of power-factor-correction converter. IEEE Transactions on Industrial Electronics 50(6), 1116–1125 (2003)
Wong, S.C., Tse, C.K., Orabi, M., Ninomiya, T.: The method of double averaging: an approach for modeling power-factor-correction power converters. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 53(2), 454–462 (2006)
Iu, H.H.C., Tse, C.K.: Instability and bifurcation in parallel-connected buck converters under a master-slave current sharing scheme. In: Proceedings of IEEE Power Electronics Specialists Conference, pp. 708–713 (2000)
Mazumder, S.K., Nayfeh, A.H., Boroyevich, D.: Stability analysis of parallel dc-dc converters using a nonlinear approach. In: Proceedings of IEEE Power Electronics Specialists Conference, pp. 1283–1288 (2001)
Tse, C.K.: Complex Behavior of Switching Power Converters. CRC Press, Boca Raton (2003)
Banerjee, S., Verghese, G.C. (eds.): Nonlinear Phenomena in Power Electronics: Attractors, Bifurcations, Chaos, and Nonlinear Control. IEEE Press, New York (2001)
Pegna, G., Marrocu, R., Tonelli, R., Meloni, F.: Experimental definition of the basin of attraction for Chua’s circuit. International Journal of Bifurcation and Chaos 10(5), 959–970 (2003)
Banerjee, S.: Coexisting attractors, chaotic saddles and fractal basins in a power electronic circuit. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 44(9), 847–849 (1997)
Ogata, K.: Modern Control Engineering. Prentice Hall, New York (1997)
Chryssis, G.C.: High-Frequency Switching Power Supplies: Theory and Design. McGraw-Hill, New York (1989)
Mohan, N., Undeland, T.M., Robbins, W.P.: Power Electronics: Converters, Applications and Design. Wiley, New York (2003)
Alligood, K.T., Sauer, T.D., Yorke, J.A.: Chaos: An Introduction to Dynamical Systems. Springer, New York (1996)
Wu, X., Tse, C.K., Wong, S.C., Lu, J.: Fast-scale bifurcation in single-stage PFC power supplies operating with DCM boost stage and CCM forward stage. International Journal of Circuit Theory and Applications 34(3), 341–355 (2006)
Wiggins, S.: Introduction to Applied Nonlinear Dynamics Systems and Chaos. Springer, New York (1990)
Kuznetsov, K.A.: Elements of Applied Bifurcation Theory. Springer, New York (1996)
Zou, J., Ma, X., Tse, C.K., Dai, D.: Fast-scale bifurcation in power-factor-correction buck-boost converters and effects of imcompatible periodicities. International Journal of Circuit Theory and Applications 34(3), 251–264 (2006)
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Huang, Y., Tse, C.K. (2009). Complex Behavior of Parallel-Connected DC/DC Converters from Nonlinear Viewpoint. In: Kocarev, L., Galias, Z., Lian, S. (eds) Intelligent Computing Based on Chaos. Studies in Computational Intelligence, vol 184. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95972-4_13
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DOI: https://doi.org/10.1007/978-3-540-95972-4_13
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