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Taking buck converter operating in pseudo-continuous conduction mode (PCCM) for example, through a detailed description of the switch state of the switching converter, its accurate discrete-time model is established in this paper. On the basis of the model, bifurcation diagrams of the PCCM buck converter with the variations of circuit parameters are obtained, including load resistance, equivalent series resistance (ESR) of inductor, inductance, capacitance, reference current, and input voltage. And the complex dynamical behaviors existing in PCCM buck converter, such as subharmonic oscillation, period-double bifurcation and chaos, are revealed. Under different load resistances, time-domain simulation waveforms and phase portraits of PCCM buck converter are obtained by Runge-Kutta algorithm based on the piecewise smooth switch model. The working states of PCCM buck converter, reflected by the time-domain waveforms and phase portraits, are consistent well with those described by the bifurcation diagrams. It is shown that the time-domain simulation results verify the validation of the discrete-time model.#br#From theoretical analysis and simulation results, some conclusions can be obtained below. 1) When the load resistance gradually decreases, PCCM buck converter has a unique bifurcation route, i. e. , from PCCM period-1 state, PCCM multi-period oscillation via period-double bifurcation, chaos, CCM-PCCM multi-period oscillation, to CCM period-1 state via inverse period-double bifurcation. What is more, the bifurcation analysis with the load resistance serving as parameter indicates that the PCCM buck converter is more suitable for light load conditions, and its stable state will be lost and operation mode can be shifted (from PCCM to CCM) with increasing the load. 2) The ESR of inductor is closely related to the power loss and will affect the stability of the PCCM converter. The larger the ESR, the more the power loss will be. However, the PCCM converter is more stable if the ESR is larger. 3) Period-double bifurcation or inverse period-double bifurcation exists in the PCCM buck converter with the other circuit parameters varied in a wide range except for the load resistance, and there are three working states of buck operating in PCCM, i.e., stable period-1 state, multi-period sub-harmonic oscillation, and chaos. The research results in this paper are useful for designing and controlling PCCM switching converter.
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Keywords:
- buck converter /
- pseudo-continuous conduction mode /
- discrete-time model /
- subharmonic oscillation
[1] Cafagnad D, Grassi G 2006 Nonlinear Dyn. 44 251
[2] Xie F, Yang R, Zhang B 2011 IEEE Trans. Circ. Syst. I 58 2269
[3] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[4] Bao B C, Xu J P, Liu Z 2009 Chin. Phys. B 18 4742
[5] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[6] Zhou Y F, Chen J N, Iu H H C, Tse C K 2008 Int. J. Bifurc. Chaos 18 121
[7] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[8] Wang F Q, Ma X K 2013 Chin. Phys. B 22 120504
[9] Moreno-Font V, El Aroudi A, Calvente J, Giral R, Benadero L 2010 IEEE Trans. Circ. Syst. I 57 415
[10] Bao B C, Zhou G H, Xu J P, Liu Z 2011 IEEE Trans. Power Electron. 26 1968
[11] Zhou G H, Xu J P, Bao B C, Wang J P, Jin Y Y 2011 Acta Phys. Sin. 60 010503(in Chinese) [周国华, 许建平, 包伯成, 王金平, 金艳艳 2011 60 010503]
[12] Zhou G H, Bao B C, Xu J P 2013 Int. J. Bifurc. Chaos 23 1350062
[13] Liu F 2010 Chin. Phys. B 19 080511
[14] Ma D S, Ki W H 2007 IEEE Trans. Circuits Syst. I 54 825
[15] Kanakasabai V, Ramesh O, Dipti S 2005 IEEE Trans. Power Electron. 20 790
[16] Tan C, Liang Z S 2014 Acta Phys. Sin. 63 070502(in Chinese) [谭程, 梁志珊 2014 63 070502]
[17] Tan C, Liang Z S, Zhang Q J 2014 Acta Phys. Sin. 63 200502(in Chinese) [谭程, 梁志珊, 张丘举 2014 63 200502]
[18] Parui S, Banerjee S 2003 IEEE Trans. Circuits Syst. I 50 1464
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[1] Cafagnad D, Grassi G 2006 Nonlinear Dyn. 44 251
[2] Xie F, Yang R, Zhang B 2011 IEEE Trans. Circ. Syst. I 58 2269
[3] Wang F Q, Zhang H, Ma X K 2012 Chin. Phys. B 21 020505
[4] Bao B C, Xu J P, Liu Z 2009 Chin. Phys. B 18 4742
[5] Zhou G H, Xu J P, Bao B C, Jin Y Y 2010 Chin. Phys. B 19 060508
[6] Zhou Y F, Chen J N, Iu H H C, Tse C K 2008 Int. J. Bifurc. Chaos 18 121
[7] Zhou G H, Bao B C, Xu J P, Jin Y Y 2010 Chin. Phys. B 19 050509
[8] Wang F Q, Ma X K 2013 Chin. Phys. B 22 120504
[9] Moreno-Font V, El Aroudi A, Calvente J, Giral R, Benadero L 2010 IEEE Trans. Circ. Syst. I 57 415
[10] Bao B C, Zhou G H, Xu J P, Liu Z 2011 IEEE Trans. Power Electron. 26 1968
[11] Zhou G H, Xu J P, Bao B C, Wang J P, Jin Y Y 2011 Acta Phys. Sin. 60 010503(in Chinese) [周国华, 许建平, 包伯成, 王金平, 金艳艳 2011 60 010503]
[12] Zhou G H, Bao B C, Xu J P 2013 Int. J. Bifurc. Chaos 23 1350062
[13] Liu F 2010 Chin. Phys. B 19 080511
[14] Ma D S, Ki W H 2007 IEEE Trans. Circuits Syst. I 54 825
[15] Kanakasabai V, Ramesh O, Dipti S 2005 IEEE Trans. Power Electron. 20 790
[16] Tan C, Liang Z S 2014 Acta Phys. Sin. 63 070502(in Chinese) [谭程, 梁志珊 2014 63 070502]
[17] Tan C, Liang Z S, Zhang Q J 2014 Acta Phys. Sin. 63 200502(in Chinese) [谭程, 梁志珊, 张丘举 2014 63 200502]
[18] Parui S, Banerjee S 2003 IEEE Trans. Circuits Syst. I 50 1464
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