Narrow Results

We present a classification of border-collision bifurcations in one-dimensional discontinuous maps depending on the parameters of the piecewise linear approximation in the neighborhood of the point of discontinuity. For each range of parameter values we derive the condition of existence and stability of various periodic orbits and of chaos. This knowledge will help in understanding the bifurcation phenomena in a large number of practical systems which can be modeled by discontinuous maps in discrete domain.

This paper presents, in a tutorial manner, nonlinear phenomena such as bifurcations and chaotic behavior in DC–DC switching converters. Our purpose is to present the different modeling approaches, the main results found in the last years and some possible practical applications. A comparison of the different models is given and their accuracy in predicting nonlinear behavior is discussed. A general Poincaré map is considered to model any multiple configuration of DC–DC switching converters and its Jacobian matrix is derived for stability analysis. More emphasis is done in the discrete-time approach as it gives more accurate prediction of bifurcations. The results are reproduced for different examples of DC–DC switching converters studied in the literature. Some methods of controlling bifurcations are applied to stabilize Unstable Periodic Orbits (UPOs) embedded in the dynamics of the system. Statistical analysis of these systems working in the chaotic regime is discussed. An extensive list of references is included.

In this letter, a symbolic method is proposed for analyzing the bifurcation in switching power converters. This method focuses on the cyclic operation of the system which characterizes its bifurcation behavior. The concept of block switching sequence is introduced, which, in conjunction with the waveform periodicity of the system, can be used to distinguish the various types of bifurcation behavior, e.g. "smooth" period doubling and "nonsmooth" border collision. This concept explicitly exposes the mechanism of border collision from a circuit operational viewpoint and leads to a direct detection criterion for this global bifurcation. The proposed method is applied, as an illustrative example, to develop two-dimensional bifurcation diagrams for a voltage-mode controlled buck converter.

Bifurcation analysis has been applied to many power electronics circuits. Literature abounds with results regarding the various ways in which such circuits lose stability under variation of some selected parameters, e.g. via period-doubling bifurcation, Hopf bifurcation, border collision, etc. The current status of research in the identification of bifurcation behavior in power electronics has reached a stage where the salient types of bifurcation behavior, their underlying causes and the theoretical parameters affecting them have been well understood. Currently, the emphasis of research in this field has gradually shifted toward applications that are of direct relevance to practical design of power electronics. One direction is to apply some of the available research results in bifurcation behavior to the design of practical power electronics circuits. The main difficulty is that the abstract mathematical presentations of the available results are not directly applicable to practical design problems. In this paper we will discuss how research efforts may be directed to bridge this gap.

A piecewise linear (PWL) continuous map is used to analyze the nonsmooth bifurcation phenomena in a single-inductor two-output (SITO) DC–DC converter under a PWM interleaved control scheme. This map models the dynamical behavior of the converter when the waveforms of the inductor current can be approximated by straight lines during each switching subinterval. The parameter space is constrained by the interleaving control and the physical restriction on the values of some parameters. The main focus of this paper is on the existence and stability conditions of the rich variety of k-periodic orbits and the different bifurcation patterns that can be exhibited in this system. The analytical results in the form of 1-D and 2-D bifurcation diagrams are compared with numerical simulations obtained from the circuit-based switched model getting a good agreement between the two approaches.

One topology widely known for use in high-voltage high-power converter in medical equipment is the Series Loaded Resonant (SLR) converter. As the power level required by medical equipment increases, there is a need to parallel the SLR converter for improved efficiency and performance. This paper presents the development of a circuit model for paralleled SLR converter to aid circuit designers evaluate circuit performance before the actual hardware is implemented. Each section of the circuit is modeled individually using sinusoidal approximation and circuit network methods. The derived model is then extended to include the parallel connection of the converter. The validity of the model is then tested by using computer simulation and hardware setup to demonstrate the converter's switching waveforms, output voltage and efficiency. Results from both simulation and hardware show good agreement, which demonstrate the validity of the derived model and its usefulness in the initial design of the converter.

Renewable energy sources connected in distribution systems utilizing power electronics devices to interface lead to various power quality problems. This chapter presents a review on power quality issues associated with the grid-connected renewable energy systems and mitigation techniques. To mitigate the power quality issues, an effective role is played by power electronic devices and custom power devices such as active power filters (APFs) and flexible AC transmission systems (FACTs). This chapter also discusses IEC and IEEE standards for grid-connected renewable energy system.