Abstract
High-order switched DC-DC converters, such as SEPIC, Ćuk and Zeta, are classic energy processing elements, which can be used in a wide variety of applications due to their capacity to step-up and/or step-down voltage characteristic. In this paper, a novel methodology for analyzing the previous converters operating in discontinuous conduction mode (DCM) is applied to obtain full-order dynamic models. The analysis is based on the fact that inductor currents have three differentiated operating sub-intervals characterized by a third one in which both currents become equal, which implies that the current flowing through the diode is zero (DCM). Under a small voltage ripple hypothesis, the currents of all three converters have similar current piecewise linear shapes that allow us to use a graphical method based on the triangular shape of the diode current to obtain the respective non-linear average models. The models’ linearization around their steady-state operating points yields full-order small-signal models that reproduce accurately the dynamic behavior of the corresponding switched model. The proposed methodology is applicable to the proposed converters and has also been extended to more complex topologies with magnetic coupling between inductors and/or an damping network in parallel with the intermediate capacitor. Several tests were carried out using simulation, hardware-in-the-loop, and using an experimental prototype. All the results validate the theoretical models.
Highlights
Discontinuous conduction mode (DCM) appears in current unidirectional DC-DC elementary switching converters such as buck, boost or buck-boost, whose switch consists of a transistor and diode, when the inductor current becomes zero in the diode conduction subinterval
The model proposed in this work can be adapted to versions of the Single-Ended Primary-Inductor converter (SEPIC), Ćuk and Zeta converters depicted in Figure 1 in which the inductors are magnetically coupled and/or an RC damping network is added in parallel to the intermediate capacitor
Theoretical results: these are results in the time or frequency domains obtained from the transfer functions of the small-signal models; Switched results: they are obtained from simulations in the PSIM software; Hardware-in-the-loop results: measurements carried out on the hardware-in-the-loop tools (PLECS RT-box 1, Interface and Texas Instruments LAUNCHXL-F28069M); Experimental results: direct measurements in a real proof-of-concept reconfigurable prototype of high-order converters
Summary
Discontinuous conduction mode (DCM) appears in current unidirectional DC-DC elementary switching converters such as buck, boost or buck-boost, whose switch consists of a transistor (usually a MOSFET or an IGBT) and diode, when the inductor current becomes zero in the diode conduction subinterval. The model proposed in this work can be adapted to versions of the SEPIC, Ćuk and Zeta converters depicted in Figure 1 in which the inductors are magnetically coupled and/or an RC damping network is added in parallel to the intermediate capacitor. The main benefits of the proposed methodology are listed below: Because it is based in simple graphical representations of inductor’s and diode current waveforms it is easy to understand and apply; Provides a full-order model that can be particularized to any of the three high-order step up/down switching converters with or without positive/negative magnetic coupling between inductors and damping networks in the intermediate capacitor; The three converters and its variants can be analyzed in the classical forms depicted, where the MOSFET and diode do not share any common node. The non-linear model provided initially by the proposed method, that will be linearized around the steady-state equilibrium point, has considered the following assumptions: Ideal no-losses components, without parasitics; Constant switching frequency f s and period T; Capacitors large enough so that their average voltages can be considered approximately constant through a switching cycle and small voltage ripple amplitudes
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