Abdelali El Aroudi

A Review on Stability Analysis Methods for Switching Mode Power Converters

In distributed power generation systems a pivotal role is played by DC-DC power converters that are employed to connect local loads to local power sources. These converters are used either in combinations of series/parallel connections or as stand-alone devices. A lot of work has taken place in the stability analysis of these converters and several methods have been used/proposed with different properties, strengths and weaknesses. Describing all existing methods is probably a never ending task and therefore in this tutorial paper four different methods will be presented by pointing out their main properties and explaining briefly how they can be used in applications that involve power converters. More specifically, the chosen methods are based on 1) the Poincaré map, 2) Saltation matrix, 3) trajectory sensitivity, and 4) steady-state-response analysis of the discrete-time model. Simple case studies from previous publications are collected and presented in order to further explain these methodologies. Finally, this paper intents to describe some of the future challenges that exist in the area of stability analysis of power converters especially when these are employed in distributed generation applications.

LMI Robust Control of PWM Converters: An Output-Feedback Approach

This chapter proposes a systematic approach for the synthesis of robust controllers for dc-dc converters. The approach is based on the Linear Matrix Inequalities (LMIs) framework and the associated optimization algorithms. The aim of this approach is to allow the designer to describe the uncertainty of the converter and to deal with the requirements of the application beforehand. The aforementioned dc-dc converters (see Figure 1) are devices that deliver a dc output voltage, with different properties from those in the input voltage (Erickson & Maksimovic, 1999). They are usually employed to adapt energy sources to the load requirements (or vice versa). These devices present several challenges regarding their robust control. First, the converter must maintain a tight regulation or tracking of the output. Moreover, the controller design is focused on maximizing the bandwidth of the closed-loop response in order to reject the usual disturbances that appear in these systems. Finally, the response of the converter must satisfy desirable transient characteristics, as for example, the shortest possible output settling time or the minimum overshoot. Besides of these common requirements, the converter can be affected by uncertainty in its components or by input or output disturbances that may appear.

QFT design for current-mode PWM buck converters operating in continuous and discontinuous conduction modes

A design method using quantitative feedback theory (QFT) for robust control of current-mode PWM dc-dc converters is described. The proposed method considers both continuous and discontinuous conduction mode models (CCM and DCM respectively), taking into account large load perturbations. This technique results in a robust design insensitive to parameter variations and also to model changes

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

Analysis of Discontinuity Induced Bifurcations in a Dual Input DC-DC Converter

DC-DC power converters with multiple inputs and a single output are used in numerous applications where multiple sources, e.g. two or more renewable energy sources and/or a battery, feed a single load. In this work, a classical boost converter topology with two input branches connected to two different sources is chosen, with each branch independently being controlled by a separate peak current mode controller. We demonstrate for the first time that even though this converter is similar to other well known topologies that have been studied before, it exhibits many complex nonlinear behaviors that are not found in any other standard PWM controlled power converter. The system undergoes period incrementing cascade as a parameter is varied, with discontinuous hard transitions between consecutive periodicities. We show that the system can be described by a discontinuous map, which explains the observed bifurcation phenomena. The results have been experimentally validated.

A Combined Analytical-Numerical Methodology for Predicting Subharmonic Oscillation in H-Bridge Inverters Under Double Edge Modulation

In this paper, a combined analytical-numerical methodology is developed for detecting subharmonic oscillation in H-bridge inverters with an LC filter and under double edge modulation. The prediction of this phenomenon is accomplished accurately by combining analytical expressions and computational procedures to determine the switching instants and the corresponding periodic orbits. Different approximate closed-form expressions for the stability boundary are derived revealing the effect of the parameters of the system on its dynamical behavior and showing that the stability boundary is different from the ones corresponding to single edge modulation strategies such as trailing edge and leading edge modulations. The theoretical results are validated by numerical simulations using a system-level switched model. Also, a prototype is implemented to validate he theoretical derivations and the numerical simulations getting a good matching.

Power quality issues in single-stage AC-DC HBLED drivers at low power levels: Problems and solutions

In this paper the design of efficient single-stage High Brightness Light Emitting Diodes (HBLEDs) ac-dc drivers for low power applications is addressed using variable frequency hysteretic control. An adaptive hysteresis window modulated by the input voltage and the output LED current reference is used. The double modulation strategy helps to avoid the distortion near the zero crossings of the input current and to improve the dimming performance of the HBLEDs. This results in a low value of Total Harmonic Distortion (THD) under low current/power conditions and therefore in a very good dimming performance in single-stage ac-dc HBLEDs drivers with PFC. The operation principle of the proposed technique is presented and numerical simulations are shown to demonstrate its functionality. A laboratory prototype is designed and tested to verify its feasibility obtaining a significant improvement in terms of power quality. Under universal input line voltage operation, good efficiency and low THD can be achieved at low power levels.

Guest Editorial Design of Energy-Efficient Distributed Power Generation Systems

The articles in this special section focus on energy efficient distributed power generation systems. The papers address circuit topologies, dynamics, control aspects, stability analysis, efficiency study and design of power converters for distributed power generation systems and aspects related to control of power systems from a network perspective.

EFFECTS OF THE DIGITAL MODULATOR DELAY ON THE BIFURCATION BEHAVIOR OF A TWO-CELL DC-DC BUCK CONVERTER

Abstract Recent findings on nonlinear analysis of a two-cell DC-DC buck converter under an ideal Digital Pulse Width Modulation (DPWM) control reveal that the system undergoes a non smooth period doubling bifurcation and border collision route to chaos. Here we give a more complete dynamic model that take into account some imperfections in the feedback loop like delays in the DPWM controller. The analysis of this new model shows that the system undergoes discontinuous Neimark-Sacker bifurcation and quasiperiodic route to chaos rather than a period doubling phenomenon. Morever the critical values of the parameters where bifurcations take place are modified by the delay effect. Numerical simulations confirm the theoretical predictions.

QUASI-PERIODIC PHENOMENA AND PHASE-LOCKED ORBITS IN DC-DC BOOST SWITCHING REGULATORS

Abstract Quasi-periodic route to chaos is a common feature in DC-DC switching converters like the Boost and the Buck-Boost. A periodic orbit bifurcates into a T 2 torus through a Neimark-Sacker bifurcation, and then, quasi-periodic behavior is obtained. Further changes in the parameters may breakdown such torus resulting in chaotic behavior. Analytical expressions are deduced for the stability character of the orbits, although numerical simulations and experimental measurements are also provided to reinforce the theory.