Pulse-Width Modulated Rectifiers

To obtain low ж line current TllD, the passive teebniques described in the previous chapter rely oii low-frequency transformers and/or reactive elements. The large size and weight of these elements are objectionable ill many applications. This chapter covers active techniques that employ converters having switching frequencies much greater than tlie 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 du with cunventionai diode rectifter circuits, and dealing after-the-fact with the resulting low-frequency harmonics, let us consider nuw how to buiid a rectifier that behaves as ideally 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, liecause 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 converter, such that the ac line current waveform follows the applied nc hne voltage. Buth single-phase and three-phase rectifiers cnn be constructed using PWIVI 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-bandwidth 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 sy.stems are discussed, expressions for rms currents are derived, and various converter approache.s are compared.

The lechniqiies developed in earlier chapiers lor modeling and analysis of dc-dc converters are extended tn this chapter to treat the analysts, modeling, and control of low-hEirmontc rectirteis. 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 lhat is useful in power stage design. Several converter ct>ntrt)l schemes are known, including peak current programming, average current control, critical conduction mode control, and ntmlinear 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 current 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 iit) should be proportional lo the applied input voltage

(18.1)

where is the constant of proportionality. An equivalent circuit for the ac port of an ideal rectifier is therefore an effective resistance R, as shown in Fig. 18.1 (a). is also known as the emiilaied resistance. h should be noted that the presence of/(, does not imply the generation of heat: the power apparently

Ideal rectifier {LFR)

input

coiuiot

i{t)

dc output

Fig, IS.l Development of the ideal rectifier equivalent ciicuit model: (a) inptit port resistor emulation; (b) the value of the emulated resi.stance, and hence the power tliroughput, is controlhible; (c) cmtput porl power source characteristic, and complete model.

v<0

Pit)

Fig. XS.2 The deiiendeni puwer source: (a) power source schemalic symboh fb) power sink schematic symbol, (c} i-v characteristic,

consumed by is actually transferred to the rectifier dc output port. simply models how the ideal rectifier loads the ac power system.

Output regulatitni is accotnplished by variation of the effective resistance R, and hence the value of must depend on a control signal , ((0 as in Fig. 18.1(b). This allows variation of the rectifier power throughput, since the average power consumed by is

(18.2)

Note that changing results in a time-varying system, with generation of harmoiiics. To avoid generation of significant amounts of harmonics and degradation of the power factor, variations inR 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 in.stantaneous power flowing into if, must appear at the rectifier output port. Note that the instantaneous power throughput

18.3)

is dependent only on v,(0 and the control input ( (О. and is independent ofthe characteristics ofthe load connected to the output ptm. Hence, the output pun must behave as a source of constant power, obeying the relationship

(IM)

The dependent power source symbol of Fig. i8.2(a) is used to denote such nn output characteristic. As illustrated in Fig. 18.1 (c), the output port is inodeled by a power soiu-ce that is dependent on the instantaneous power flowing into Rg.

Thus, a two-port model for the ideal unity-power-factor single-phase rectifier is as shown in Fig. 18. i(c) [2-4]. The two pun model is al.so called a loss-free resistor (LFR) because (1) its input port obey.s Ohms law, and (2) power entering the inpul port is tran.sferted directly to the tmipul port without lo.ss of