Switch-Mode Power Converters - K. Wu (Elsevier, 2006)

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Switch-Mode Power Converters - K. Wu (Elsevier, 2006)


This is not a cookbook, for switch-mode power converter design is a
serious topic that must be treated with the utmost care. Therefore, the
book makes a major departure from most existing texts covering the
same subjects. It uses mathematics extensively, employing, for example,
symbolic closed-form solutions for conduction times of a loaded fullwave-
rectifier with a capacitor filter. At the first sight, readers may feel
discouraged, but there is no shortcut. I sincerely urge readers to be
patient, for the reward is profound.
The book covers in depth the three basic topologies: step-down
(buck, forward), step-up (boost), step-down/up (flyback); push–pull;
current-fed; resonant converters and their derivatives; AC–DC power
factor correction. Depending on the operating conditions, switch-mode
power converters may operate either in continuous conduction mode
(CCM) or discontinuous conduction mode (DCM). Under transient
conditions, the operation of power converters may slide in and out of
both modes. For closed-loop control of converters, two fundamental
mechanisms, voltage-mode control or current-mode control, are generally
employed. Current-mode control has been understood to offer superior
performance. Current mode control is further subdivided into
average-current control and peak-current control. While most switchmode
converters utilize pulse-width modulation, resonant converters
use frequency modulation. In addition to the main operation mechanism,
many supporting circuits are also needed to make power converters
viable. These include switch drivers, error amplifiers, and feedback
isolators.
The presentation follows a fairly consistent pattern. The relationship
between steady-state output and control variables (duty cycle, in the case
of PWM, or frequency, in the case of resonance) is established first for
both the CCM and the DCM operation. By examining the cyclical
current waveforms of CCM, geometrical properties of the waveforms
xiii
are extracted. These lead to the identification of critical inductance,
which marks the boundary distinguishing CCM and DCM operation.
Under each operation mode and given a selected control mechanism,
steady-state closed-loop output formulation that includes feedback
ration, error amplifier, PWM gain (or frequency-modulation gain), and
power stage is then established. In some simplified cases that
exclude losses, the output formulation may be placed in the explicit
form. When losses are included, the desire to obtain an explicit form is
prohibitively impractical and abandoned. Instead, implicit functions and
Jacobian determinants are employed to study output sensitivity and
regulation.
With the steady state firmly established, the small-signal AC stability
issues are examined for both control modes. Loop stability with voltagemode
control based on the average model (Dr. R. Middlebrook) is
formulated and validated. Current-mode control necessitates the addition
of current-loop gains surrounding the original average mode. In
effect, the Middlebrook average model is extended to current-mode
control and remains as valid.
This book also introduces accelerated steady-state analysis in the
time domain. The technique connects the concept of the continuity of
state and the periodic, steady-state output of converters. The analysis
uses two approaches: Laplace transformation and state transitions. The
latter calls on eigenvalues, eigenvectors, and matrix exponentials, the
core of matrix theory associated with system theory.
Nowadays, simulations always play some role in almost all fields of
studies. For power converters, there is no exception. This book, however,
approaches it from a more fundamental way, which is quite distinctive
from the graphic-based simulations available commercially. The latter
suffers convergence issues frequently. Our approach avoids such nagging
difficulties.
The book is written for those already exposed to the basics of switchmode
power converters and seek higher dimensions. It is suitable for
graduate students and professionals majoring in electrical engineering. In
particular, readers with training in linear algebra will find the techniques
of state transition being applied very inspiring.
.


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Digital Control in Power
Electronics


2006 by Morgan & Claypool

Simone Buso
Department of Information Engineering
University of Padova, Italy
Paolo Mattavelli
Department of Electrical, Mechanical and
Management Engineering
University of Udine, Italy

This book presents the reader, whether an electrical engineering student in power electronics
or a design engineer, some typical power converter control problems and their basic digital
solutions, based on the most widespread digital control techniques. The presentation is focused
on different applications of the same power converter topology, the half-bridge voltage source
inverter, considered both in its single- and three-phase implementation. This is chosen as
the case study because, besides being simple and well known, it allows the discussion of a
significant spectrum of the more frequently encountered digital control applications in power
electronics, fromdigital pulse width modulation(DPWM)and space vector modulation (SVM),
to inverter output current and voltage control. The book aims to serve two purposes: to give
a basic, introductory knowledge of the digital control techniques applied to power converters,
and to raise the interest for discrete time control theory, stimulating new developments in its
application to switching power converters.

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semico_ljj

Preface
This is not a cookbook, for switch-mode power converter design is a
serious topic that must be treated with the utmost care. Therefore, the
book makes a major departure from most existing texts covering the
same subjects. It uses mathematics extensively, employing, for example,
symbolic closed-form solutions for conduction times of a loaded fullwave-
rectifier with a capacitor filter. At the first sight, readers may feel
discouraged, but there is no shortcut. I sincerely urge readers to be
patient, for the reward is profound.

semico_ljj

The book covers in depth the three basic topologies: step-down
(buck, forward), step-up (boost), step-down/up (flyback); push–pull;
current-fed; resonant converters and their derivatives; AC–DC power
factor correction. Depending on the operating conditions, switch-mode
power converters may operate either in continuous conduction mode
(CCM) or discontinuous conduction mode (DCM). Under transient
conditions, the operation of power converters may slide in and out of
both modes. For closed-loop control of converters, two fundamental
mechanisms, voltage-mode control or current-mode control, are generally
employed. Current-mode control has been understood to offer superior
performance. Current mode control is further subdivided into
average-current control and peak-current control. While most switchmode
converters utilize pulse-width modulation, resonant converters
use frequency modulation. In addition to the main operation mechanism,
many supporting circuits are also needed to make power converters
viable. These include switch drivers, error amplifiers, and feedback
isolators.

semico_ljj

Under each operation mode and given a selected control mechanism,
steady-state closed-loop output formulation that includes feedback
ration, error amplifier, PWM gain (or frequency-modulation gain), and
power stage is then established. In some simplified cases that
exclude losses, the output formulation may be placed in the explicit
form. When losses are included, the desire to obtain an explicit form is
prohibitively impractical and abandoned. Instead, implicit functions and
Jacobian determinants are employed to study output sensitivity and
regulation.
With the steady state firmly established, the small-signal AC stability
issues are examined for both control modes. Loop stability with voltagemode
control based on the average model (Dr. R. Middlebrook) is
formulated and validated. Current-mode control necessitates the addition
of current-loop gains surrounding the original average mode. In
effect, the Middlebrook average model is extended to current-mode
control and remains as valid.

semico_ljj

This book also introduces accelerated steady-state analysis in the
time domain. The technique connects the concept of the continuity of
state and the periodic, steady-state output of converters. The analysis
uses two approaches: Laplace transformation and state transitions. The
latter calls on eigenvalues, eigenvectors, and matrix exponentials, the
core of matrix theory associated with system theory.
Nowadays, simulations always play some role in almost all fields of
studies. For power converters, there is no exception. This book, however,
approaches it from a more fundamental way, which is quite distinctive
from the graphic-based simulations available commercially. The latter
suffers convergence issues frequently. Our approach avoids such nagging
difficulties.
The book is written for those already exposed to the basics of switchmode
power converters and seek higher dimensions. It is suitable for
graduate students and professionals majoring in electrical engineering. In
particular, readers with training in linear algebra will find the techniques
of state transition being applied very inspiring.

semico_ljj

Digital Control in Power
Electronics


ABSTRACT
This book presents the reader, whether an electrical engineering student in power electronics
or a design engineer, some typical power converter control problems and their basic digital
solutions, based on the most widespread digital control techniques. The presentation is focused
on different applications of the same power converter topology, the half-bridge voltage source
inverter, considered both in its single- and three-phase implementation. This is chosen as
the case study because, besides being simple and well known, it allows the discussion of a
significant spectrum of the more frequently encountered digital control applications in power
electronics, fromdigital pulse width modulation(DPWM)and space vector modulation (SVM),
to inverter output current and voltage control. The book aims to serve two purposes: to give
a basic, introductory knowledge of the digital control techniques applied to power converters,
and to raise the interest for discrete time control theory, stimulating new developments in its
application to switching power converters.
KEYWORDS
Digital control in power electronics, Discrete time control theory, Half-bridge voltage source
converters, Power converters, Power electronics