Nonlinear Analysis and Control of Interleaved Boost Converter Using Real-Time Cycle to Cycle Variable Slope Compensation

Switched-mode power converters are inherently nonlinear and piecewise smooth systems that may exhibit a series of undesirable operations that can greatly reduce the converter's efficiency and lifetime. This paper presents a nonlinear analysis technique to investigate the influence of system parameters on the stability of interleaved boost converters. In this approach, Monodromy matrix that contains all the comprehensive information of converter parameters and control loop can be employed to fully reveal and understand the inherent nonlinear dynamics of interleaved boost converters, including the interaction effect of switching operation. Thereby not only the boundary conditions but also the relationship between stability margin and the parameters given can be intuitively studied by the eigenvalues of this matrix. Furthermore, by employing the knowledge gained from this analysis, a real-Time cycle to cycle variable slope compensation method is proposed to guarantee a satisfactory performance of the converter with an extended range of stable operation. Outcomes show that systems can regain stability by applying the proposed method within a few time periods of switching cycles. The numerical and analytical results validate the theoretical analysis, and experimental results verify the effectiveness of the proposed approach

Linear Time Periodic Analysis of Dc-Dc converter

Aim of this thesis is to analyze Dc-Dc converters by using the techniques of Linear Periodic Time varying (LTP) systems to estimate the amount of subharmonics injected in the load. Dc-Dc converters are used to transform a Dc input to a Dc output of different voltage. In this thesis we study in particular the so called "switch mode" converters. In this kind of devices the conversion is obtained by using fast commutations of (at least) two switches. Due to the discrete switch-positions these converters are considered a typical example of hybrid systems. Linear models with fixed coefficients (LTI system) give a description of the system inadequate to predict and to analyze harmonic effects, while linear models with coefficients that vary periodically, namely LTP system, can be used effectively to this aim. We use therefore a Linear Time Periodic (LTP) system to describe the converter. This kind of description in much more accurate but the model and the tools used to study it are more complex. In the thesis we first introduce the LTP system theory and its main results. In particular we introduce the concept of Harmonic Transfer Function (HTF). A LTP model for a Dc-Dc converter is then derived and it is shown that this model accurately describes the response of the converter. Furthermore this LTP model is used to analyze the open and closed loop behavior of the system. It is shown that the linear model estimates correctly the amplitude of the subharmonics in the output. The thesis has been developed at the Automatic Control Department, Lund University, Sweden under the supervision of Andreas Wernrud and Anders Rantzer. The Italian supervisor of this thesis is Giorgio Picci, Dipartimento di Ingegneria dell' Informazione, Università degli studi di Padova, Ital

EMI Analysis and Modeling of Switching Circuits

Nowadays, switching power converters are massively used in almost any electrical and electronic equipment and appliances. This class of circuits are inherently time-varying systems that are characterized by the periodic activity of their internal switches which leads to discontinuous absorbed currents. The above currents, that play the role of high frequency noisy disturbances feeding the power distribution system, become a serious concern for designers that need to comply with the electromagnetic compatibility (EMC) regulation for the conducted emission (CE). In this frame- work, modeling and simulation tools for switching circuits are key resources in the early design phase for the prediction of the conducted emission and for the assessment of alternative design scenarios. The classical approach to CE prediction is via physical-based models and time-domain simulations. This solution, however, requires intimate knowledge of the internal device structure. Also, large simulation times are in general needed to avoid integration errors and to achieve accurate results (the CE are in fact computed by applying the Fourier transform on the steady-state portion of the current response of the circuit). As an alternative, frequency-domain behavioral approaches are available in literature. In the latter case, the proposed models are small-signal time-invariant approximations computed from the external observation of the circuit behavior. These approaches, that are based on simplified equivalents, do not take into account the internal time-varying nature of the circuit and in many cases unavoidably lead to a model accuracy that strongly depends on the operating condition of devices. To overcome the above limitations, this thesis proposes an alternative approach to CE assessment based on the mathematical framework developed for time-varying circuits and systems. The proposed method allows for the steady-state prediction of circuit responses directly in the frequency-domain. A topological approach is used, where the original time-varying circuit is suitably replaced by an augmented time-invariant equivalent solved via standard tools for circuit analysis. The new augmented variables in the above equivalent turn out to be the harmonic coefficients of the Fourier series expansion of the corresponding voltage and current variables in the original circuit. A second important contribution in this work is the application of the pro- posed mathematical tool to the modeling of a switching converter and of its CE disturbances from measured data. The converter is seen as a black-box element that is characterized via a limited set of port voltage and current observations, leading to an equivalent augmented admittance fully describing the time-varying nature of the system. Summarizing, this thesis provides a comprehensive theoretical discussion together with several tutorial examples. What is more important, it proposes a novel approach to CE prediction with improvements with respect to state-of-the-art approaches and linear time-invariant surrogates. A real application test case involving a dc-dc boost converter and real measured data is also used to validate the method and stress its features for both numerical simulation and black-box modeling

Stability Boundary Analysis of Islanded Droop-Based Microgrids Using an Autonomous Shooting Method

This paper presents a stability analysis for droop-based islanded AC microgrids via an autonomous shooting method based on bifurcation theory. Shooting methods have been used for the periodic steady-state analysis of electrical systems with harmonic or unbalanced components with a fixed fundamental frequency; however, these methods cannot be directly used for the analysis of microgrids because, due to the their nature, the microgrids frequency has small variations depending on their operative point. In this way, a new system transformation is introduced in this work to change the droop-controlled microgrid mathematical model from an non-autonomous system into an autonomous system. By removing the explicit time dependency, the steady-state solution can be obtained with a shooting methods and the stability of the system calculated. Three case studies are presented, where unbalances and nonlinearities are included, for stability analysis based on bifurcation analysis; the bifurcations indicate qualitative changes in the dynamics of the system, thus delimiting the operating zones of nonlinear systems, which is important for practical designs. The model transformation is validated through time-domain simulation comparisons, and it is demonstrated through the bifurcation analysis that the instability of the microgrid is caused by supercritical Neimark–Sacker bifurcations, and the dynamical system phase portraits are presented

Complex behavior in switching power converters

Author name used in this publication: Chi K. Tse2001-2002 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Measurements, Models, Systems and Design

531 s.

Modelling of power electronics controllers for harmonic analysis in power systems

The research work presented in this thesis is concerned with the modelling of this new generation of power electronics controllers with a view to conduct comprehensive power systems harmonic analyses. An issue of paramount importance in this research is the representation of the self-commutated valves used by the controllers addressed in this work. Such a representation is based on switching functions that enable the realization of flexible and comprehensive harmonic models. Modularity is another key issue of great importance in this research, and the model of the voltage source converter is used as the basic building block with which to assemble harmonic models of actual power systems controllers. In this research the complex Fourier series in the form of operational matrices was used to derive the harmonic models. Also, a novel methodology is presented in this thesis for conducting transient analysis of electric networks containing non-linearities and power electronic components. The methodology is termed the extended harmonic domain. This method is based on the use of time-dependent Fourier series, operational matrices, state-space representation and averaging methods. With this method, state-space equations for linear circuit, non-linear circuits, and power electronics controllers models are obtained. The state variables are the harmonic coefficients of x(t) instead of x(t) itself. The solution of the state-space equations gives the dynamic response of the harmonic coefficients of x(t). Moreover, a new harmonic power flow methodology, based on the instantaneous power flow balance concept, the harmonic domain, and Newton-Raphson method, is developed and explained in the thesis. This method is based on the instantaneous power balance as opposed to the active and reactive power balance, followed by traditional harmonic power flow methods. The power system and the power electronics controllers are modelled entirely in the harmonic domain