Power electronics is a discipline spawned by real-life applications in industrial, commercial, residential, and aerospace environments. Much of its development revolves around some immediate need for solving specific power conversion problems. This comprehensive book focuses on the typical bifurcation scenarios and nonlinear behavior observed in switching power converters, expounding on their most relevant aspects from a practical viewpoint. A balanced emphasis on theory, computer methods, and laboratory experiments bridges the gap between the theoretical research and practical engineering applications.

Complex Behavior of Switching Power Converters

Power electronics circuits are rich in nonlinear dynamics. Their operation is characterized by cyclic switching of circuit topologies, which gives rise to a variety of nonlinear behavior. This paper provides an overview of the chaotic dynamics and bifurcation scenarios observed in power converter circuits, emphasizing the salient features of the circuit operation and the modeling strategies. In particular this paper surveys the key publications in this field, reviews the main modeling approaches, and discusses the salient bifurcation behaviors of power converters with particular emphasis on the disruption of standard bifurcation patterns by border collisions.

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Complex behavior in switching power converters

Permanent magnet synchronous motor (PMSM) will demonstrate chaotic phenomena when its parameters fall into a certain area. The performance of PMSM will degrade because of chaos. Therefore, chaos should be suppressed or eliminated. According to the features of this practical plant, the drawbacks of existing control methods are analyzed, and the nonlinear feedback control method is suggested to control the chaos in PMSM. The nonlinear feedback principle is developed using the direct axis and the quadrature axis stator voltage as manipulated variables. The control target will become a unique asymptotically stable equilibrium under the nonlinear feedback principle, by this way, the controlled states can reach the target and the control objective can be implemented. This method can be physically realized using nonlinear state feedback. The control forces can be put into effect at any time. The target of the method may be any point in the strange attractor. The influence of the model error and the measurement noise upon the control performance is studied via simulations. Simulation results show the effectiveness of this method under the presence of the model error and the measurement noise

Nonlinear feedback control of chaos in permanent magnet synchronous motor

Voltage-source converters are commonly employed as rectifiers for providing a regulated dc voltage from an ac power source. In a typical microdistribution system, the power grid is nonideal and often presents itself as a voltage source with significant impedance. Thus, power converters connected to the grid interact with each other via the nonideal grid. In this paper, we study how stability can be compromised in a system of interacting grid-connected converters, which are used typically as rectifiers. Specifically, the stable operating regions in the selected parameter space may shrink when grid-connected converters interact under certain conditions. We consider the effect of both source (grid) impedance and transmission line impedance between converters, and derive bifurcation boundaries in the parameter space. A small-signal model in the dq-frame is adopted to analyze the interacting system using an impedance-based approach. It is shown that the system of interacting converters can become unstable. Moreover, results are presented in design-oriented forms so as to facilitate the identification of variation trends of stable operation boundaries. Experimental results verify the instability phenomenon.

Effects of Interaction of Power Converters Coupled via Power Grid: A Design-Oriented Study

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Chaos in Power Electronics: An Overview

The main objective of the paper is to highlight the strange and complex behaviour of a motor drive consisting of a three-phase induction machine fed by a voltage source inverter (VSI) and controlled by a hysteresis current controller (HCC). This system exhibits either periodic, subharmonic or chaotic trajectory movements, and shows bifurcation phenomena. The paper presents simulation results to introduce some astonishing properties, and applies two techniques in reaching them: continuous trajectory; and trajectory with discrete time steps. The first approach is theoretically significant while the second one represents the model of practical hardware implementation. Maps showing the chaotic and periodic regions are presented. After convincing maps regarding the chaotic nature of the system the influence of such important variables as the load torque or the speed command and parameters as the stator resistance and transient inductance is investigated. It could help either in stabilizing the periodic motions or inducing chaos. It can be concluded that periodic process cannot be maintained in wide range of change in system variables without additional measures.

http://ieeexplore.ieee.org/iel4/5671/15202/00701908.pdf

Avoiding chaotic processes in current control of AC drive

Motion control has been a fruitful ground for applying variable structure systems (VSS) theory. This paper provides an assessment of the state of the art of the relevant theoretical results for motion control, and through a number of control design problems (namely classical, discrete-time, observer based discrete-time and frequency shaped discrete-time sliding mode control) demonstrates the practical use of sliding mode in solving a number of critical design problems which are universal to both motion control and robotic manipulator control. Experimental results of a transputer-controlled single-degree-of-freedom motion-control system are presented.

Optimal sliding mode design for motion control

The analysis, design aspects, and numerical results of a current-controlled three-phase space-vector-modulated (SVM) voltage-source converter (VSC) are presented. The aim of the current controller of the VSC is to track the sinusoidal reference currents in each phase. The current controller includes a complex saturation function in order to avoid overmodulation in the SVM. Due to this strong nonlinearity, the study leads to system states not treated so far. An approximate Poincare map is derived. The paper reports saddles in the state space as a consequence of fold bifurcation and other phenomena in conjunction with saddles. Design conditions are derived to avoid undesired operation.

Analysis of nonlinear phenomena and design aspects of three-phase space-vector-modulated converters

The paper presents briefly the concepts, the targets and some of the methods, approaches applied, results reached in two European e-learning projects. Both projects were supported by the European Union and participants from more than 10 European countries had been working in them mostly from Universities. The projects exploits the rich possibilities offered by Internet based remote laboratories, interactive multimedia materials developed for class room, self-learning at home, distance learning etc. The projects are intended to assist the education of electrical engineering students on BSc and MSc level.

Integrated e-learning projects in the European Union

The paper first briefly summaries and highlights the colorful world of nonlinear dynamic systems for those who are not familiar in it. In the second part it presents the overview of the results obtained by the analysis of two frequently employed nonlinear controlled electric drives.

Z. Suto

Papers

Avoiding chaotic processes in current control of AC drive

Optimal sliding mode design for motion control

Analysis of nonlinear phenomena and design aspects of three-phase space-vector-modulated converters

Integrated e-learning projects in the European Union

Nonlinearity in Controlled Electric Drives: Review