Kuntal Mandal

Complex Interaction Between Tori and Onset of Three-Frequency Quasi-Periodicity in a Current Mode Controlled Boost Converter

It is known that power electronic circuits like dc-dc converters are highly nonlinear systems, and that period doubling and Neimark-Sacker bifurcations are common sources of instability in such systems. It has also been shown that these two types of bifurcation may interact, giving rise to interesting dynamical phenomena. In this paper we show that in a current mode controlled dc-dc converter, periodic, quasi-periodic, and saturation behavior can coexist for the same parameter value, and there can be complex interactions between them. Furthermore, abrupt exit to saturation mode can be triggered by a torus-torus collision. Finally, we report the first observation of three-frequency quasi-periodicity in a power electronic system.

Symmetry-Breaking Bifurcation in Series-Parallel Load Resonant DC-DC Converters

This paper reports the occurrence of symmetry-breaking bifurcation in the series-parallel load-resonant dc-dc converter with L-C output filter. The constant frequency phase shift modulation technique is employed with proportional-integral controller in the output voltage regulation. The complexity of the system is contributed by the fact that a six dimensional state space is divided into twelve subsystems by six switching surfaces. It is shown that the dynamics are not only related to the resonant components but are also heavily dependent on the output filter design. The understanding of the dynamics resulting from the interaction between the resonant tank and the filter circuit helps in designing more reliable converters. We show that the first instability can be caused by Neimark-Sacker as well as symmetry-breaking bifurcations. Stable as well as unstable periodic orbits are identified, and their characteristic multipliers are computed by a newly developed algorithm based on a combination of Filippovs theory and shooting method with Newton-Raphson algorithm.

Nonlinear dynamics and bifurcation analysis of a boost converter for battery charging in photovoltaic applications

Photovoltaic (PV) systems with a battery back-up form an integral part of distributed generation systems and therefore have recently attracted a lot of interest. In this paper, we consider a system of charging a battery from a PV panel through a current mode controlled boost dc-dc converter. We analyze its complete nonlinear/nonsmooth dynamics, using a piecewise model of the converter and realistic nonlinear v–i characteristics of the PV panel. Through this study, it is revealed that system design without taking into account the nonsmooth dynamics of the converter combined with the nonlinear v–i characteristics of the PV panel can lead to unpredictable responses of the overall system with high current ripple and other undesirable phenomena. This analysis can lead to better designed converters that can operate under a wide variation of the solar irradiation and the batterys state of charge. We show that the v–i characteristics of the PV panel combined with the batterys output voltage variation can increase or decrease the converters robustness, both under peak current mode control and average current mode control. We justify the observation in terms of the change in the discrete-time map caused by the nonlinear v–i characteristics of the PV panel. The theoretical results are validated experimentally.

A New Algorithm for Small-Signal Analysis of DC–DC Converters

This paper presents a new approach for small-signal analysis of all types of dc-dc converters with any number of topological modes within a switching cycle. So far, sampled-data modeling and sensitivity analysis are mostly used for such a purpose. In both cases, the switching conditions implicitly appear in the small-signal matrices which increases the complexity of the computation for the system with a larger number of topological modes. Here, we propose an alternative approach based on Filippovs method, which studies the effects of each switching separately. It uses a shooting method with an event detector to locate a periodic steady-state, and, when the Newton-Raphson search process of the shooting method converges, it also gives the Jacobian matrix. The algorithm can be easily implemented in a software program as an analytical tool which is expected to be useful for fast and accurate frequency-domain analysis (by small-signal transfer functions) to facilitate controller design. Moreover, since it uses the Filippovs method, this algorithm can also predict the slow- and fast-timescale instabilities.

Bifurcations in load resonant DC-DC converters

The paper demonstrates, both numerically and experimentally, the quasiperiodic and subharmonic operation in a load resonant DC-DC converter. The output voltage of the converter is controlled by a closed loop, applying constant-frequency pulse width modulation. The complexity of the system is contributed by fact that the state space is five-dimensional, with four switching surfaces dividing it into 9 subsystems. A method is developed to perform the stability analysis and to investigate the bifurcation sequences following the first instability in such a complex switching system.

Synchronization Phenomena in Interconnected Power Electronic Systems

It is considered desirable to operate converters connected to a dc microgrid at the same clock frequency, but this may not be feasible in practice as the converters are often procured from different sources. There exists a natural coupling between the converters in a dc microgrid because their controllers and timers obtain power supply from the same intermediate bus. This brief shows that this nonlinear coupling can cause frequency synchronization leading to a desirable operating condition if the coupling parameters are chosen appropriately. This brief also presents the experimental results to validate the above observations.

Synchronization Phenomena in Microgrids With Capacitive Coupling

Multiple converters connected to a microgrid must have the same clock frequency, else interaction among the frequencies may cause beating noise. But the frequency equalization is difficult to achieve in practice. We show that the nonlinearity present in all power electronic systems offers an interesting possibility: the clocks may synchronize spontaneously if appropriate coupling exists among the converters. We further show that if the control circuits of the converters receive their power supply from the intermediate bus of the microgrid, the small ripple voltage across the intermediate bus capacitor can cause minute changes in the frequencies of the clocks-which may result in synchronization of the converters. The desirable periodic synchronization is achieved over specific ranges of the intermediate bus capacitance that depend on the frequency ratios of the converters in the uncoupled state.

Symmetry-breaking bifurcation in load resonant dc-dc converters

This paper reports the occurrence of symmetry-breaking bifurcation in the series-parallel load-resonant dc-dc converter with L-C output filter. The constant frequency phase shift modulation technique is employed with proportional-integral controller in the output voltage regulation. It is shown that the dynamics are not only related to the resonant components but are also heavily dependent on the output filter design. The first instability can be caused by smooth and non-smooth symmetry breaking bifurcations. Stable as well as unstable periodic orbits are identified by a newly developed algorithm based on fundamental solution matrix. As a significant result of this paper, it is shown that the symmetry-breaking can be caused by a grazing event.

Quasi-periodic route to chaos in load resonant DC-DC converters

This paper reports first time, both numerically and experimentally, the quasi-periodic, subharmonic and chaotic behavior in a phase shift modulated load resonant converter. The study presented in this paper is restricted to third order seriesparallel load resonant converter. From hybrid system point of view, the system consists of four switching surfaces and nine possible modes. After undergoing a Hopf bifurcation of a period-one orbit, quasi-periodic behavior is obtained. Two kinds of route lead to the chaotic operation: a quasi-periodic one and a period doubling scenario.

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

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. Copyright