A Time-Domain Asymptotic Approach to Predict Saddle-Node and Period Doubling Bifurcations in Pulse Width Modulated Piecewise Linear Systems

There are many applications in power electronics that demand high step-up conversion ratio between the source and the load. A simple way of achieving such a high voltage ratio is by cascading DC-DC boost converters in a few stages. The individual converters in such a cascaded system are usually designed separately applying classical design criteria. This paper investigates the stability of the overall system of a cascade connection of two boost converters under current mode control. We first demonstrate the bifurcation behavior of the system, and it is shown that the desired periodic orbit can undergo fast-scale period doubling bifurcation leading to subharmonic oscillations and chaotic regimes under parameter variation. The value of the intermediate capacitor is taken as a design parameter, and we determine the minimum ramp slope in the first stage required to maintain stability. It is shown that smaller capacitance values give rise to wider stability range. We explain the bifurcation phenomena using a full-order model. Then, in order to simplify the analysis and to obtain a closed-form expression to explain the previous observation, we develop a reduced-order model by treating the second stage as a current sink. This allows us to obtain design-oriented stability boundaries in the parameter space by taking into account slope interactions between the state variables in the two stages.where m ref1,ON is the slope of the current reference i ref1 during the ON phase to be determined in the 1138 A. EL AROUDI ET AL.

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“…In [17,18], it has been shown that at the onset of subharmonic oscillation boundary, the following condition is fulfilled:…”

Section: Simplified Stability Boundaries In the Parameter Spacementioning

confidence: 99%

Fast‐scale stability limits of a two‐stage boost power converter

Aroudi

Mandal

Giaouris

et al. 2015

Circuit Theory & Apps

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“…The literature reports the exhaustive scope of the Fourier series expansion of the steady-state feedback signal, time domain analysis of steady-state feedback signal and the introduction of auxiliary state vector for the process of modelling the converters [22][23][24]. A summary of contributions of modelling techniques of the nonlinearities in various DC-DC converter with remarkable elucidation of consequences in the study of stability of such systems are reported in Tab.1.…”

Section: Modelling Techniques For Nonlinear Analysis Of Dc-dc Convertermentioning

confidence: 99%

Bifurcation and Chaos in Converter Interfaces in Solar PV Systems-A Review

Subashini¹,

Ramaswamy²

2017

JESTR

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The paper attempts to present a detailed study of the nonlinear phenomena that includes bifurcations, sub-harmonics and chaos in an effort to arrive at the appropriate choice of converter interface suitable for specific PV systems and evolve criterions for their design and control. The resurgence of switching dc-dc converters as power processing units in renewable energy applications appear to open up new perceptions for harnessing energy efficiency. The focus orients to review the modelling techniques used for nonlinear analysis in the different operating modes of the converter and identify the gap in the related domain with special relevance to the converter interfaces in solar PV systems. The exercise incites to explain the forms of bifurcations, the routes to chaos and the associated control techniques for arbitrating its significance in this perspective. The benefits of analysis of nonlinear phenomena in regulatory applications claim a new space in energy processing applications and forge to explore their role as maximum power point (MPP) trackers. The emphasis endeavours to enhance the scope of use of solar energy and offer a fresh dimension to support the clean energy act and perpetuate the desire to enliven a greener world.

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“…A significant amount of knowledge has been reached about the occurrence of this phenomenon in these systems under both Current Mode Control (CMC) and Voltage Mode Control (VMC) [6] for buck converters and in [7] for general bilinear converters. This bifurcation behavior can cause sever jeopardizing of the system functioning of the system by introducing high ripples in the controlled variables and high stress in the switches and therefore its analytical determination is of high importance.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation behavior in a two-loop DC-DC quadratic boost converter

Aroudi

García

Fournier

et al. 2015

2015 IEEE International Symposium on Circuits and Systems (ISCAS)

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The dynamic behavior and stability analysis of a quadratic boost converter for high conversion ratio applications is addressed. After studying the stability of the system by using the monodromy matrix, a closed form stability condition is used for predicting the boundary of subharmonic oscillation in the system in terms of the duty cycle and the slope of the ramp modulator. The derived theoretical conditions are validated by numerical simulations using a system-level switched model obtaining a good matching between the results. This work provides a convenient means of stability boundary determination in the parameter space hence facilitating the design of quadratic boost converters.

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A Time-Domain Asymptotic Approach to Predict Saddle-Node and Period Doubling Bifurcations in Pulse Width Modulated Piecewise Linear Systems

Cited by 8 publications

References 21 publications

Fast‐scale stability limits of a two‐stage boost power converter

Fast‐scale stability limits of a two‐stage boost power converter

Bifurcation and Chaos in Converter Interfaces in Solar PV Systems-A Review

Bifurcation behavior in a two-loop DC-DC quadratic boost converter

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