Advanced Modeling and Control of DC-DC Converters E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 819

Veröffentlichungsjahr: 2025

Beschreibung

Advanced Modeling and Control of DC-DC Converters is essential for anyone looking to master the intricacies of power electronics, as it offers comprehensive insights into advanced modeling techniques, control strategies, and practical applications across various high-impact industries.

Advanced Modeling and Control of DC-DC Converters delves into the intricate field of power electronics and its applications for DC-DC converters. This subject plays a crucial role in a wide range of industries, including renewable energy systems, electric vehicle technology, aerospace, telecommunications, and more. This volume focuses on the advanced modeling and control strategies of DC-DC converters, covering various converter topologies, such as buck, boost, buck-boost, and isolated converters, exploring their unique characteristics and challenges. Furthermore, it delves into the integration of advanced semiconductor devices, which offer higher efficiency and power density. One of the key features of this book is the exploration of advanced control algorithms that enhance the performance, stability, and efficiency of DC-DC converters. These algorithms encompass traditional control techniques such as proportional-integral-derivative (PID) control and contemporary approaches like sliding-mode control, adaptive control, and advanced model predictive control. Advanced Modeling and Control of DC-DC Converters provides detailed explanations, design guidelines, and simulation examples to aid readers in implementing these control strategies effectively, making it an invaluable resource for students and industry veterans alike.

Leseprobe

Scrivener Publishing100 Cummings Center, Suite 541JBeverly, MA 01915-6106

Publishers at ScrivenerMartin Scrivener ([email protected])Phillip Carmical ([email protected])

Advanced Modeling and Control of DC-DC Converters

Majid Pakdel

This edition first published 2025 by John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA and Scrivener Publishing LLC, 100 Cummings Center, Suite 541J, Beverly, MA 01915, USA© 2025 Scrivener Publishing LLCFor more information about Scrivener publications please visit www.scrivenerpublishing.com.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

Wiley Global Headquarters111 River Street, Hoboken, NJ 07030, USA

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

The manufacturer’s authorized representative according to the EU General Product Safety Regulation is Wiley-VCH GmbH, Boschstr. 12, 69469 Weinheim, Germany, e-mail: [email protected].

Limit of Liability/Disclaimer of WarrantyWhile the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchant-ability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read.

Library of Congress Cataloging-in-Publication Data

ISBN 9781394289417

Top Cover Image: Generated with AI using Adobe FireflyBottom Cover Image: Courtesy of Wikimedia CommonsCover design by Russell Richardson

Preface

This book is designed as an advanced text in modeling and control of DC-DC converters, aimed specifically at graduate electrical engineering students. It assumes that the student has a basic understanding of general circuit analysis techniques typically taught at the sophomore level. The student should also be familiar with electronic devices like diodes and transistors, although the focus of this text is on circuit topology and function rather than the devices themselves. A primary background requirement is understanding the voltage-current relationships for linear devices, and knowledge of Fourier series is also important. Most of the topics covered in this text are appropriate for postgraduate electrical engineering students as well. To solve the equations describing power electronics circuits, the student should utilize all available software tools. These tools range from calculators with integrated functions like integration and root finding to moradvanced computer software packages like MATLAB or Python. It is the responsibility of the student to choose and adapt the various computer tools that are readily available to the specific power electronics scenario. In addition to analytical circuit solution techniques, this text incorporates computer simulation using LTspice and PSIM. While some prior experience with LTspice and PSIM is beneficial, it is not necessary. Most of the content of this book relates to my personal notes from the online course “Modeling and Control of Power Electronics Specialization” on Coursera.

I dedicate this book to the loving memory of my mother, Rahimeh Ghorbani, a great and kind soul who dedicated her entire blessed life to education and love for her children. It is a regret that I did not fully appreciate her while she was alive, and only after her passing did I realize what a precious gem she was. Unfortunately, I lost her, and nothing in the world can replace her. I hope she will forgive me, and I pray that her soul rests in eternal peace.

1Averaged-Switch Modeling and Simulation

1.1 Introductory Example (Synchronous Buck Converter)

We are going to start off with just taking an example and working through it. So here is what we would refer to commonly as a synchronous buck converter. You can organize the buck converter structure with a single pole double throw switch, followed by an LC filter as shown in Figure 1.1[2].

Figure 1.1 Synchronous buck converter.

How difficult can that be? You take the input voltage, vg, there. You switch the two devices repeatedly at a switching frequency, fs. You create a pulsating waveform at the switching node. The duty cycle of that pulsating waveform is the control variable that we refer to as d, and then you will pass filter that pulsating waveform to generate an output DC voltage that is directly proportional to the control variable, d, and directly proportional to the DC value of the input voltage. So that’s your buck converter. The inputs, in this case here, would be the input voltage, the load current, and the control voltage that really sets the value of the duty cycle, d. The outputs would be the output voltage. But also, we treat the input current curve as an “output” and we’ll see that as particularly important when we get to the point of designing an input filter. Then the responses from, for example, the duty cycle to input current are going to be particularly important in studying how the input filter is going to respond to that type of perturbation. The state variables in the converter can be commonly associated with the energy storage elements. So here we have two energy storage elements in the low pass filter, the inductor L and the capacitor C, and the voltage across the capacitor and the inductor current are the state variables in the converter. To make this a little bit more realistic, we are including there some of the non-idealities in the converter. We will say that these two switches have, when on, behaved as on resistances. They’re not necessarily the same. We say Ron1 and Ron2 right there. We also take into account some series resistance for the inductor, and on the output filter capacitor, we take into account the fact that it’s also not an ideal capacitor but has some equivalent series resistance. Why is that called the synchronous buck converter? Normally in a buck converter, we have the main control switch and the rectifying diode right there as depicted in Figure 1.2.

Figure 1.2 Rectifying diode in a buck converter.

You could just as well have a single controllable switch with the rectifying diode performing function of the single pole double throw switch in the buck converter. That’s perfectly fine. Then instead of diode, we can employ an active switch, in particular a MOSFET, to have the switch conducting at a time when the diode would be conducting current. So, when you turn off the main control MOSFET, then normally the rectifying diode would be conducting automatically. You will have automatic commutation between the main control MOSFET and the diode. But if in the process you actually turn on the MOSFET, right there, you will have the current actually flying through the channel of the MOSFET from source to drain. That’s actually opposite to what normally the current would flow through a controllable MOSFET and that MOSFET really serves the purpose that the rectifying diode would serve in just a regular transistor plus diode buck converter. Now, that MOSFET, let’s call it Q2, and Q1 are turned on and off in complementary manner and will never have them both on at the same time, of course, as illustrated in Figure 1.3.

Figure 1.3 Opposite current flow in MOSFET Q2 turn on.

So that MOSFET Q2 has to be synchronized to the operation of the control MOSFET Q1 and in fact, it has to be performing the rectification function in a synchronous manner, in a timed manner that corresponds to what the diode would be doing if the diode were present, which is why we have this term “synchronous” in the buck converter. Synchronous buck converter is a very common component. You probably have 10 of those in your pocket right now performing conversion from the battery down to various pieces of your smartphone. It is a very commonly applied converter circuit. One little question, since we are discussing the review of the Intro to Politics materials, why would we want to use here a synchronous rectifier and MOSFET instead of just a plane diode? The point of using the MOSFET Q2 here is that the resistance of the synchronous rectifier, Ron2, times the current that would be flowing through that synchronous rectifier from source to drain, i, would be less than the diode voltage drop, VD, i.e., we have Ron2 i << VD. So that implies reduced conduction losses and that’s particularly important in cases where you’re trying to make this converter serve as a power supply with a very low output voltage. The example that we are going to do in just a moment is going to regulate the output voltage to 1.8 volts. If you were to use a diode that has a forward voltage, drop of 0.8 volts, the efficiency of that converter would be horrendous, because that forward voltage drop would be comparable to the voltage you’re trying to regulate. Instead, you employ a MOSFET that has a very, very small resistance and has the forward voltage drop in conducting current much lower than the forward voltage drop of a diode. One last comment about the synchronous rectification right there is that whether you sketch this diode here explicitly or not, we would like to remind you that the diode, in fact, does physically exist as a body diode of the rectifying MOSFET. So the MOSFET comes in with the PN junction diode between the source and drain terminals. We don’t like that diode to conduct, because it has a large forward voltage drop. Instead, we bypass that PN junction diode that’s built into the MOSFET structure itself by turning on the MOSFET channel and conducting current through the channel of the MOSFET with a voltage drop much smaller than the forward voltage drop of what would be the drop across the body diode. All right, so this is the type of little bit of a review of the very beginning of the Intro to Politics. You learn how converters work, how they switch, and some of the details related to conduction losses, and so on. If you need to go back and review some of that some more, go ahead. What we will do, for the most part in this book, is look into the dynamic modeling and control aspects in the next steps.

1.2 Synchronous Buck Converter State Equations

Let’s see what we do with the synchronous buck converter. Typically, when we do the analysis, we can certainly write converters state equations very easily. If you notice that depending on the position of these switches, whether they are on or off, you will see we’re going to have really two main states of the converter. One when the Q1 switch is on, the other one when the Q2 switch is on, and that’s decided entirely by the control signal. The control signal here is denoted as c. That’s a logic level signal that’s produced by a controller that decides which one of the two switches should be on. Notice here that conceptually we’ve split this into a gate driver and an inverting gate driver for the two switches to make sure we understand that the switching between these two devices is complementary. A further detail on that note is that there is a certain amount of dead time between these two MOSFETs, so they should never be turned on at the same time. Logic-wise, this is what we do.

Figure 1.4 State and output equations.

Details circuit-wise, we also insert small dead times between the conduction state of the MOSFET 1 versus the MOSFET 2. So how do we write the state equations? Well, we’ll look at the two positions of the switches. Thus, when the control signal, c, is in logic 1 state, switch 1 is on, and we have the following equation as shown in Figure 1.4:

(1.1)

That is the voltage loop equation for the state of the switch 1, so that’s for c is equal to 1. When c is equal to 0, and MOSFET 2 is on, and MOSFET 1 is off, then you have similarly the dynamic equation for the inductor now being a different voltage path right there, and that voltage path, the voltage loop equation looks like the following equation as shown in Figure 1.4.

(1.2)

Now, the output equations here, well, there is a state equation for the capacitor current, which is pretty easy; it doesn’t depend on the state of the switches, so we have the following equation as depicted in Figure 1.4.

(1.3)

Then output equations are the input current is either equal to the inductor current when c is 1, or is equal to 0 when c is 0, and the output voltage is as follows as illustrated in Figure 1.4.

(1.4)

We just write down the equations for the two states of the switches and how we actually generate the control pulsating signal of how a pulse-width modulator operates in a conceptually simple manner, having just a voltage comparator that compares an analog control input that we call it vc(t) to a sort of periodic waveform. The period of that waveform is equal to the switching period, and the amplitude of that waveform is called VM. The amplitude of that waveform sets the gain of the pulse-width modulator because you see that the duty cycle that is obtained by comparing the analog control input to the saw-tooth waveform has a duty cycle directly proportional to that control voltage, vc(t), with a constant proportionality being vc(t) over VM, where VM is the amplitude of the saw-tooth waveform as shown in Figure 1.5.

Figure 1.5 Generating the control pulsating signal [1].

1.3 Synchronous Buck Converter Averaging and Dynamic Modeling

From state equations that describe the operation of a converter in time domain, you can certainly do very quickly steady state analysis by applying the principles of what you do. This is like a volt second balance, charge balance for steady state analysis, and that’s what we do. We basically average out the state equations so that we weigh the voltage applied across an inductor during the first-time interval of dTs and the second time interval of d’Ts, d’ being 1-d, and we obtain a dynamic average equation for the inductor current in the following form as shown in Figure 1.6.

Figure 1.6 State-space averaging.

Maybe one of the most important steps we ever do in modeling power electronics is this averaging step. Notice that since the capacitor equation does not depend at all on the position of the switches, we don’t see any d’s in the dynamic equation on average for the capacitor current and also, the output voltage average value is equal to the average value of the capacitor voltage plus the Resr times the difference between average values of the inductor current and the load current. Now, in a dynamic equation, this is not necessarily equal to 0 and dynamically, we can have an imbalance between the average value of the inductor current and the load current that the imbalance is going to charge up or discharge the capacitor dynamically. So now we have these average equations in the state space form for the converter. Why do we like the large-signal averaged model equations so much better than the switching model equations right here? What is the reason that this averaging step was applied in the first place? What is the main reason for doing that? And what is the fundamental reason of going through this step of averaging state space equations into that form? The raw answer to this is that the first set of equations gives us only the DC operating point, and the second set of equations gives us the dynamics of the converter. We would not agree with that statement. Why would the switching model equations not be able to give us the dynamics of the converter? They contain complete behavior in time domain of the converter. In fact, as we go through the end of this review material of the book at the beginning, we’ll do a spice simulation of the time domain equations and all kinds of dynamics there. It’s not just steady state. That is so wrong. These switching model equations are the equations that describe the converter as is. Switching behavior, including dynamics, and including the possibility to round those dynamics into steady state if you wish to do so. But it is incorrect to say that these equations cannot possibly describe dynamics of the converter. They can, and they do, so the answer is that it is much more computationally efficient to handle average equations as opposed to the switching model equations, and we would say that’s actually correct and that is entirely true. You’ll see this later on when we do simulations of a converter circuit model using switching circuit model. It takes a certain amount of time to do that. If you do that with an average model, it takes towards the remaining to less time so there is less computational effort. Although true is not fundamentally why we do this. If the computing power were the only problem, we would not have done this step here, because we have really plenty of computing power available. Another answer is that we’re going to remove the switching ripple by doing this step of averaging. We think they’re getting closer so that’s, again, true, but still not the fundamental answer we’re looking for. What is the fundamental