Page 29 - Rashid, Power Electronics Handbook

P. Krein
1212 P . Krein
control approaches derive from averages of switching func- related to the linear active ®lter op-amp circuits used in analog
tions [2, 8]. Their utility comes from their application in signal processing. In ac cases, there is a continuing opportu-
writing circuit equations. For example, in the boost converter nity for innovation in ®lter design.
of Fig. 1.9, the loop and node equations change depending
on which switch is acting at a given moment. The two
possible circuit con®gurations each have distinct equations. 1.6 Summary
Switching functions allow them to be combined. By assigning
switching functions q ðtÞ and q ðtÞ to the left and right Power electronics is the study of electronic circuits for the
1
2
switching devices, respectively, we obtain control and conversion of electrical energy. The technology is a
critical part of our energy infrastructure, and supports almost

di L dv C v C all important electrical applications. For power electronics
q 1 V ÿ L ¼ 0 ; q 1 C þ ¼ 0 ; left switch on design, we consider only those circuits and devices that, in
in
dt dt R
principle, introduce no loss and can achieve near-perfect

di L dv C v C reliability. The two key characteristics of high ef®ciency and
q 2 V ÿ L ¼ v C ; q 2 C þ ¼ i L ; right switch on
in
dt dt R high reliability are implemented with switching circuits,
supplemented with energy storage. Switching circuits in turn
ð1:9Þ can be organized as switch matrices. This facilitates their
analysis and design.
Because the switches alternate, and the switching functions In a power electronic system, the three primary challenges
must be 0 or 1, these sets of equations can be combined to give are the hardware problem of implementing a switching matrix,
the software problem of deciding how to operate that matrix,
di L dv C v C and the interface problem of removing unwanted distortion
V ÿ L ¼ q v ; C þ ¼ q i ð1:10Þ
in 2 C 2 L
dt dt R and providing the user with the desired clean power source.
The hardware is implemented with a few special types of
The combined expressions are simpler and easier to analyze power semiconductors. These include several types of transis-
than the original equations. tors, especially MOSFETs and IGBTs, and several types of
For control purposes, the average of equations such as thyristors, especially SCRs and GTOs. The software problem
(1.10) often proceeds with the replacement of switching can be represented in terms of switching functions. The
functions q with duty ratios d. The discrete time action of a frequency, duty ratio, and phase of the switching functions
switching function thus will be represented by an average duty are available for operational purposes. The interface problem
cycle parameter. Switching functions, the advantages gained by is addressed by means of lossless ®lter circuits. Most often,
averaging, and control approaches such as PWM are discussed these are lossless LC passive ®lters to smooth out ripple or
at length in several chapters in this handbook. reduce harmonics. More recently, active ®lter circuits have
been applied to make dynamic corrections in power conver-
sion waveforms.
1.5.5 Resolving the Interface Problem: Improvements in devices and advances in control concepts
Lossless Filter Design
have led to steady improvements in power electronic circuits
Lossless ®lters for power electronics applications are some- and systems. This is driving tremendous expansion of their
times called smoothing ®lters [9]. In applications in which dc application. Personal computers, for example, would be
outputs are of interest, such ®lters are commonly implemen- unwieldy and inef®cient without power electronic dc supplies.
ted as simple lowpass LC structures. The analysis is facilitated Portable communication devices and computers would be
because in most cases the residual output waveform, termed impractical. High-performance lighting systems, motor
ripple, has a known shape. Filter design for recti®ers or dc-dc controls, and a wide range of industrial controls depend on
converters is a question of choosing storage elements large power electronics. In the near future, we can expect strong
enough to keep ripple low, but not so large that the whole growth in automotive applications, in dc power supplies for
circuit becomes unwieldy or expensive. communication systems, in portable applications, and in high-
Filter design is more challenging when ac outputs are end converters for advanced microprocessors. During the next
desired. In some cases, this is again an issue of lowpass ®lter generation, we will reach a time when almost all electrical
design. In many applications, lowpass ®lters are not adequate energy is processed through power electronics somewhere in
to meet low noise requirements. In this situation, active ®lters the path from generation to end use.
can be used. In power electronics, the term active ®lter refers to
lossless switching converters that actively inject or remove References
energy moment-by-moment to compensate for distortion. 1. J. Motto, Ed., Introduction to Solid State Power Electronics, Westing-
The circuits (discussed elsewhere in this handbook) are not house, Youngwood, PA, 1977.