chap18.pdf

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.

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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

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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

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).

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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