chap17.pdf

Line-Commutated Rectifiers

Conventional diode peak-detection rectifiers are inexpensive, reliable, and in widespread use. Their

shortcomings are the high harmonic content of their ac line currents, and their low power factors. In this

chapter, the basic operation and ac line current waveforms of several of the most common single-phase

and three-phase diode rectifiers are summarized. Also introduced are phase-controlled three-phase recti-

fiers and inverters, and passive harmonic mitigation techniques. Several of the many references in this

area are listed at the end of this chapter [1–15].

Rigorous analytical design of line-commutated rectifier and filter circuits is unfeasible for all

but the simplest of circuits. Typical peak-detection rectifiers are numerically ill-conditioned, because

small changes in the dc-side ripple voltage lead to large changes in the ac line current waveforms. There-

fore, the discussions of this chapter are confined to mostly qualitative arguments, with the objective of

giving the reader some insight into the physical operation of rectifier/filter circuits. Waveforms, harmonic

magnitudes, and power factors are best determined by measurement or computer simulation.

17.1

THE SINGLE-PHASE FULL-WAVE RECTIFIER

A single-phase full-wave rectifier, with uncontrolled diode rectifiers, is shown in Fig. 17.1. The circuit

includes a dc-side L–C filter. There are two conventional uses for this circuit. In the traditional full-wave

rectifier, the output capacitor is large in value, and the dc output voltage v ( t ) has negligible ripple at the

second harmonic of the ac line frequency. Inductor L is most often small or absent. Additional small

inductance may be in series with the ac source A second conventional use of this circuit is in the

low-harmonic rectifiers discussed in the next chapter. In this case, the resistive load is replaced by a dc-

dc converter that is controlled such that its power input port obeys Ohm’s law. For the purposes of under-

standing the rectifier waveforms, the converter can be modeled by an effective resistance R, as in the cir-

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Line-Commutated Rectifiers

cuit of Fig. 17.1. In this application, the L–C filter is required to filter the conducted electromagnetic

interference (EMI) generated by the converter. The inductor and capacitor element values are typically

small in value, and v ( t ) is approximately a rectified sinusoid. More generally, there may be several sec-

tions of L–C filter networks, connected to both the dc and ac sides of the diode rectifier, which filter EMI,

smooth the dc output voltage, and reduce the ac line current harmonics.

The presence of any filter degrades the ac current waveform of the rectifier. With no reactive

elements ( L = 0 and C = 0), the rectifier presents a purely resistive load to the ac input. The output volt-

age v ( t ) is then a rectified sinusoid, there are no ac line current harmonics, and the power factor is unity.

Addition of reactive elements between the rectifier diodes and the load leads in general to ac line current

harmonics. Given that such a filter is necessary, one might ask what can be done to keep these harmonics

as small as possible. In this section, the dependence of the ac line current total harmonic distortion on the

filter parameters is described.

The circuit of Fig. 17.1 generates odd harmonics of the ac line voltage in the ac line current. The

dc output voltage contains dc and even harmonics of the ac line voltage. The circuit exhibits several

modes of operation, depending on the relative values of L, C, and R. It is easiest to understand these

modes by considering the limiting cases, as follows.

17.1.1 Continuous Conduction Mode

When the inductor L is very large, then the inductor current is essentially constant. This follows

from the inductor definition For a given applied inductor voltage waveform the

slope can be made arbitrarily small by making L sufficiently large. In the limiting case where L

is infinite, the slope becomes zero, and the inductor current is constant dc. To provide a path for

the constant inductor to flow, at least two of the rectifier diodes must conduct at any given instant in time.

For the circuit of Fig. 17.1, diodes and conduct when the ac line voltage is positive, and

and conduct when is negative. The ac line current waveform is therefore a square wave, with

when is positive, and when is negative. The diode conduction angle

defined as the angle through which one of the diodes conducts, is equal to 180° in CCM.

The rms value of a square wave is equal to its peak value

in this case the dc load current.

The fundamental component of a square wave is equal to

, The square-wave contains odd harmon-

ics which vary as 1/ n . The distortion factor is therefore

The total harmonic distortion is

17.1 The Single-Phase Full-Wave Rectifier

611

So the limiting case of the large inductor leads to some significant harmonic distortion, although it is not

as bad as the peak detection rectifier case. Since the square wave is in phase with the ac input voltage, the

displacement factor is unity, and hence the power factor is equal to the distortion factor.

Whenever the inductor is sufficiently large, the rectifier diodes conduct continuously (i.e., there

is no time interval in which all four diodes are reverse-biased). This is called the continuous conduction

mode (CCM). A typical ac line current waveform is plotted in Fig. 17.2 for a finite but large value of L. It

can be seen that the ac line current is discontinuous at the ac line voltage zero crossing, as in the square-

wave limiting case. Some ringing is also present. This waveform contains a total harmonic distortion of

approximately 29%.

17.1.2 Discontinuous Conduction Mode

The opposite case occurs when the inductor is very small and the capacitor C is very large. This is the

peak detector circuit. In the limit as L goes to zero and C goes to infinity, the ac line current approaches a

string of delta (impulse) functions that coincide with the peaks of the sinusoidal input voltage waveform.

It can be shown that, in this limiting case, the THD becomes infinite while the distortion factor and

power factor become zero. Of course, in the practical case the current is not infinite; nonetheless, large

THD with low power factor is quite possible. The diodes conduct for less than one-half of the ac line

period, and hence in DCM.

Whenever the capacitor is large and the inductor is small, the rectifier tends to “peak detect,”

and the rectifier operates in the discontinuous conduction mode (DCM). There exist time intervals of

nonzero length where all four rectifier diodes are reverse-biased. A typical set of waveforms is plotted in

Fig. 17.3, where the capacitor is large but finite, and the inductor is small but nonzero. The ac line volt-

age and the value of the load resistance are the same as in Fig. 17.2, yet the peak current is substantially

larger. The THD for this waveform is 145%, and the distortion factor is 57%.

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Line-Commutated Rectifiers

17.1.3 Behavior When C is Large

A variety of authors have discussed the solution of passive rectifier circuits; several works are listed in

the references [8–15]. Analysis of even the simple circuit of Fig. 17.1 is surprisingly complex. For the

case when C is infinite, it was shown in [8] that the rectifier waveshapes can be expressed as a function of

a single dimensionless parameter

defined as

where is the ac line period. Equation (17.3) is of the same form as Eq. (5.6), used to define the

dimensionless parameter K which governs the DCM behavior of PWM converters. Figure 17.4 illustrates

the behavior of the single-phase rectifier circuit of Fig. 17.1, as a function of and for infinite C [8].

When is greater than approximately 0.1, the rectifier operates in CCM, with waveforms similar to

those in Fig. 17.2.

The voltage conversion ratio M is defined as

where is the peak value of the sinusoidal ac input voltage. In CCM, the output voltage is ideally inde-

pendent of load, with Addition of ac-side inductance can cause the output voltage to exhibit a

dependence on load current. The total harmonic distortion in CCM is nearly constant and equal to the

value given by Eq. (17.2).

Near the boundary between CCM and DCM, the fundamental component of the line current

significantly lags the line voltage. The displacement factor reaches a minimum value slightly less than

80%, and power factors between 70% and 80% are observed.

For the rectifier operates heavily in DCM, as a peak-detection rectifier. As is

decreased, the displacement factor approaches unity, while the THD increases rapidly. The power factor

is dominated by the distortion factor. The output voltage becomes dependent on the load, and hence the

rectifier exhibits a small but nonzero output impedance.

For less than approximately 0.05, the waveforms are unchanged when some or all of the

inductance is shifted to the ac side of the diode bridge. Figure 17.4 therefore applies to rectifiers contain-

17.1 The Single-Phase Full-Wave Rectifier

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ing both ac-side and dc-side inductance, provided that the circuit operates sufficiently deeply in DCM.

The parameter is computed according to Eq. (17.3), with L taken to be the total ac-side plus dc-side

inductance. A common example is the case where the circuit contains no physical discrete inductor; the

performance is then determined by parasitic elements such as the capacitor equivalent series inductance,

the inductance of the utility distribution wiring, and transformer leakage inductances.

17.1.4 Minimizing THD When C is Small

Let us now consider the performance of the second case, in which the inductor and capacitor are small

and are intended solely to prevent load-generated EMI from reaching the ac line. In this case, dc-side fil-

tering of the low-frequency even voltage harmonics of the ac line frequency is not necessary. The filter

can be characterized by a corner frequency characteristic impedance and Q- factor, where

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