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18
Pulse-Width Modulated Rectifiers
To obtain low ac line current THD, the passive techniques described in the previous chapter rely on low-
frequency transformers and/or reactive elements. The large size and weight of these elements are objec-
tionable in many applications. This chapter covers active techniques that employ converters having
switching frequencies much greater than the ac line frequency. The reactive elements and transformers of
these converters are small, because their sizes depend on the converter switching frequency rather than
the ac line frequency.
Instead of making do with conventional diode rectifier circuits, and dealing after-the-fact with
the resulting low-frequency harmonics, let us consider now how to build a rectifier that behaves as ide-
ally as possible, without generation of line current harmonics. In this chapter, the properties of the
ideal
rectifier
are explored, and a model is described. The ideal rectifier presents an effective resistive load to
the ac power line; hence, if the supplied ac voltage is sinusoidal, then the current drawn by the rectifier is
also sinusoidal and is in phase with the voltage. Converters that approximate the properties of the ideal
rectifier are sometimes called
power factor corrected,
because their input power factor is essentially
unity [1].
The boost converter, as well as a variety of other converters, can be controlled such that a near-
ideal rectifier system is obtained. This is accomplished by control of a high-frequency switching con-
verter, such that the ac line current waveform follows the applied ac line voltage. Both single-phase and
three-phase rectifiers can be constructed using PWM techniques. A typical dc power supply system that
is powered by the single-phase ac utility contains three major power-processing elements. First, a high-
frequency converter with a wide-bandwidth input-current controller functions as a near-ideal rectifier.
Second, an energy-storage capacitor smooths the pulsating power at the rectifier output, and a low-band-
width controller causes the average input power to follow the power drawn by the load. Finally, a dc–dc
converter provides a well-regulated dc voltage to the load. In this chapter, single-phase rectifier systems
are discussed, expressions for rms currents are derived, and various converter approaches are compared.
638
Pulse-Width Modulated Rectifiers
The techniques developed in earlier chapters for modeling and analysis of dc-dc converters are
extended in this chapter to treat the analysis, modeling, and control of low-harmonic rectifiers. The CCM
models of Chapter 3 are used to compute the average losses and efficiency of CCM PWM converters
operating as rectifiers. The results yield insight that is useful in power stage design. Several converter
control schemes are known, including peak current programming, average current control, critical con-
duction mode control, and nonlinear carrier control. Ac modeling of the rectifier control system is also
covered.
18.1
PROPERTIES OF THE IDEAL RECTIFIER
It is desired that the ideal single-phase rectifier present a resistive load to the ac system. The ac line cur-
rent and voltage will then have the same waveshape and will be in phase. Unity power factor rectification
is the result. Thus, the rectifier input current
should be proportional to the applied input voltage
where is the constant of proportionality. An equivalent circuit for the ac port of an ideal rectifier is
therefore an effective resistance as shown in Fig. 18.1 (a). is also known as the
emulated resistance.
It should be noted that the presence of does not imply the generation of heat: the power apparently
18.1 Properties of the Ideal Rectifier
639
“consumed” by is actually transferred to the rectifier dc output port. simply models how the ideal
rectifier loads the ac power system.
Output regulation is accomplished by variation of the effective resistance and hence the
value of must depend on a control signal as in Fig. 18. l(b). This allows variation of the recti-
fier power throughput, since the average power consumed by is
Note that changing results in a time-varying system, with generation of harmonics. To avoid genera-
tion of significant amounts of harmonics and degradation of the power factor, variations in and in the
control input must be slow with respect to the ac line frequency.
To the extent that the rectifier is lossless and contains negligible internal energy storage, the
instantaneous power flowing into must appear at the rectifier output port. Note that the instantaneous
power throughput
is dependent only on and the control input and is independent of the characteristics of the
load connected to the output port. Hence, the output port must behave as a source of constant power,
obeying the relationship
The
dependent power source
symbol of Fig. 18.2(a) is used to denote such an output characteristic. As
illustrated in Fig. 18.1(c), the output port is modeled by a power source that is dependent on the instanta-
neous power flowing into
Thus, a two-port model for the ideal unity-power-factor single-phase rectifier is as shown in Fig.
18.1(c) [2–4]. The two port model is also called a
loss-free resistor
(LFR) because (1) its input port obeys
Ohm’s law, and (2) power entering the input port is transferred directly to the output port without loss of
640
Pulse-Width Modulated Rectifiers
energy. The defining equations of the LFR are:
When the LFR output port is connected to a resistive load of value
R,
the dc output rms voltages and cur-
rents
and
are related to the ac input rms voltages and currents
and
as follows:
The properties of the power source and loss-free resistor network are discussed in Chapter 11. Regard-
less of the specific converter implementation, any single-phase rectifier having near-ideal properties can
be modeled using the LFR two-port model.
18.2
REALIZATION OF A NEAR-IDEAL RECTIFIER
Feedback can be employed to cause a converter that exhibits controlled dc transformer characteristics to
obey the LFR equations. In the single-phase case, the simplest and least expensive approach employs a
full-wave diode rectifier network, cascaded by a dc–dc converter, as in Fig. 18.3. The dc–dc converter is
represented by an ideal dc transformer, as discussed in Chapter 3. A control network varies the duty
cycle, as necessary to cause the converter input current
to be proportional to the applied input volt-
18.2 Realization of a Near-Ideal Rectifier
641
age as in Eq. (18.1). The effective turns ratio of the ideal transformer then varies with time. Ideal
waveforms are illustrated in Fig. 18.4. If the applied input voltage
is sinusoidal,
then the rectified voltage
is
It is desired that the converter output voltage be a con-
stant dc value
v
(
t
)
= V.
The converter conversion ratio
must therefore be
This expression neglects the converter dynamics. As can
be seen from Fig. 18.4, the controller must cause the
conversion ratio to vary between infinity (at the ac line
voltage zero crossings) and some minimum value
(at the peaks of the ac line voltage waveform).
is
given by
Any converter topology whose ideal conversion ratio
can be varied between these limits can be employed in
this application.
To the extent that the dc–dc converter is ideal
(i.e., if the losses can be neglected and there is negligible
low-frequency energy storage), the instantaneous input
and output powers are equal. Hence, the output current
i
(
t
) in Fig. 18.3 is given by
Substitution of Eq. (18.11) into Eq. (18.14) then leads to
Hence, the converter output current contains a dc component and a component at the second harmonic of
the ac line frequency. One of the functions of capacitor
C
in Fig. 18.3 is to filter out the second harmonic
component of
i
(
t
), so that the load current (flowing through resistor
R
)is essentially equal to the dc com-
ponent
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