Power electronic handbook

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196 J. Rodríguez et al.

(c)

(b)

(d)

(a)

(e)

, i

Load

FIGURE 11.33 Single-phase PWM rectiﬁer in bridge connection: (a) power circuit; (b) equivalent circuit with T

and T

on; (c) equivalent circuit

with T

and T

on; (d) equivalent circuit with T

and T

or T

and T

on; and (e) waveform of the input current during regeneration.

Finally, Fig. 11.33d shows the equivalent circuit with tran-

sistors T

and T

or T

and T

are in the on-state. In this case,

the input voltage source is short-circuited through inductor L,

which yields

= L

= v

(t) + V

> 0 (11.32)

Equation (11.32) implies that the current value will depend on

the sign of v

The waveform of the input current i

can be controlled by

appropriately switching transistors T

–T

or T

–T

, originat-

ing a similar shape to the one shown in Fig. 11.18a for the

single-phase boost rectiﬁer.

The control strategy for the rectiﬁer is similar to the one

illustrated in Fig. 11.31, for the voltage doubler topology.

The quality of the input current obtained with this rectiﬁer

is the same as presented in Fig. 11.32 for the voltage doubler

conﬁguration.

The input current waveform can be slightly improved if the

state of Fig. 11.33d is used. This can be done by replacing the

hysteresis current control with a more complex linear con-

trol plus a three-level PWM modulator. This method reduces

the semiconductor switching frequency and provides a more

deﬁned current spectrum.

Finally, it must be said that one of the most attractive char-

acteristics of the fully controlled PWM converter in bridge

connection and the voltage doubler is their regeneration capa-

bility. In effect, these rectiﬁers can deliver power from the load

to the single-phase supply, operating with sinusoidal current

and a high power factor of PF > 0.99. Figure 11.33e shows that

during regeneration, the input current i

is 180

◦

out of phase

with respect to the supply voltage v

, which means operation

with power factor PF ≈−1 (PF is approximately 1 because of

the small harmonic content in the input current).

11.3.6 Applications of Unity Power Factor

Rectiﬁers

11.3.6.1 Boost Rectiﬁer Applications

The single-phase boost rectiﬁer has become the most popular

topology for power factor correction (PFC) in general purpose

power supplies. To reduce the costs, the complete control sys-

tem shown in Fig. 11.19 and the gate drive circuit of the power

transistor have been included in a single integrated circuit (IC),

like the UC3854 [10] or MC33262, shown in Fig. 11.34.

11 Single-phase Controlled Rectiﬁers 197

UC 3854

MC33262

LOAD

VOLTAGE

SENSE

CURRENT

SENSE

WAVEFORM

INPUT

LINE

FIGURE 11.34 Simpliﬁed circuit of a power factor corrector with control integrated circuit.

EMI

FILTER

Line

PFC

Dimming

Control

Output Stage

Lamp

Rectifier

FIGURE 11.35 Functional block diagram of electronic ballast with power factor correction.

Today there is increased interest in developing high-

frequency electronic ballasts to replace the classical electro-

magnetic ballast present in ﬂuorescent lamps. These electronic

ballasts require an ac–dc converter. To satisfy the harmonic

current injection from electronic equipment and to maintain

a high power quality, a high power factor rectiﬁer can be used,

as shown in Fig. 11.35 [11].

MAINS

FIGURE 11.36 Low-cost induction motor drive.

11.3.6.2 Voltage Doubler PWM Rectiﬁer

The development of low-cost compact motor drive sys-

tems is a very relevant topic, particularly in the low-power

range. Figure 11.36 shows a low-cost converter for low-power

induction motor drives. In this conﬁguration, a three-phase

induction motor is fed through the converter from a single-

phase power supply. Transistors T

and capacitors C

, C

198 J. Rodríguez et al.

constitute the voltage doubler single-phase rectiﬁer, which

controls the dc link voltage and generates sinusoidal input

current, working with close-to-unity power factor [12]. On

the other hand, transistors T

, and T

and capacitors

and C

constitute the power circuit of an asymmetric

inverter that supplies the motor. An important characteris-

tic of the power circuit shown in Fig. 11.36 is the capability of

regenerating power to the single-phase mains.

11.3.6.3 PWM Rectiﬁer in Bridge Connection

Distortion of the input current in the line-commutated recti-

ﬁers with capacitive ﬁltering is particularly critical in the UPS

fed from motor-generator sets. In effect, due to the higher

value of the generator impedance, the current distortion can

originate an unacceptable distortion on the ac voltage, which

affects the behavior of the whole system. For this reason, it is

very attractive to use rectiﬁers with low distortion in the input

current.

Figure 11.37 shows the power circuit of a single-phase UPS,

which has a PWM rectiﬁer in bridge connection at the input

Output

1f100 V

Input

1f100 V

Inverter

Converter

THY2

THY SW

THY1

TR1

FIGURE 11.37 Single-phase UPS with PWM rectiﬁer.

Line +

transformer

4-quadrant

converter

DC - Link Inverter Motor

FIGURE 11.38 Typical power circuit of an ac drive for locomotive.

side. This rectiﬁer generates a sinusoidal input current and

controls the charge of the battery [13].

Perhaps the most typical and widely accepted area of

application of high power factor single-phase rectiﬁers is in

locomotive drives [14]. An essential prerequisite for proper

operation of voltage source three-phase inverter drives in

modern locomotives is the use of four-quadrant line-side con-

verters, which ensure motoring and braking of the drive, with

reduced harmonics in the input current. Figure 11.38 shows

a simpliﬁed power circuit of a typical drive for a locomotive

connected to a single-phase power supply [14], which includes

a high power factor rectiﬁer at the input.

Finally, Fig. 11.39 shows the main circuit diagram of the

300 series Shinkansen train [15]. In this application, ac power

from the overhead catenary is transmitted through a trans-

former to single-phase PWM rectiﬁers, which provide the dc

voltage for the inverters. The rectiﬁers are capable of control-

ling the input ac current in an approximate sine waveform

and in phase with the voltage, achieving power factor close to

unity on powering and on regenerative braking. Regenerative

braking produces energy savings and an important operational

ﬂexibility.

11 Single-phase Controlled Rectiﬁers 199

PWM

CONVERTER SMOOTHING CAPACITOR

PWM INVERTER

OVERHEAD

CATENARY

TRANSFORMER

INDUCTION

MOTORS

GTO THYRISTOR

FIGURE 11.39 Main circuit diagram of 300 series Shinkansen locomotives.

Acknowledgment

The authors gratefully acknowledge the valuable contribution

of Dr. Rubén Peña, and support provided by the Millennium

Science Initiative (ICM) from Mideplan, Chile.

References

1. R. Dwyer and D. Mueller, “Selection of transformers for comercial

buildings,” in Proc. of IEEE/IAS 1992 Annual Meeting, U.S.A., Oct

1992, pp. 1335–1342.

2. D. C. Martins, F. J. M. de Seixas, J. A. Brilhante, and I. Barbi, “A

family of dc-to-dc PWM converters using a new ZVS commutation

cell,” in Proc. IEEE PESC’93, 1993, pp. 524–530.

3. J. Bassett, “New, zero voltage switching, high frequency boost con-

verter topology for power factor correction,” in Proc. INTELEC’95,

1995, pp. 813–820.

4. R. Streit and D. Tollik, “High efﬁciency telecom rectiﬁer using

a novel soft-switched boost-based input current shaper,” in Proc.

INTELEC’91, 1991, pp. 720–726.

5. Y. Jang and M. M. Jovanovic´, “A new, soft-switched, high-power-

factor boost converter with IGBTs,” presented at the INTELEC’99,

1999, Paper 8-3.

6. M. M. Jovanovic´, “A technique for reducing rectiﬁer reverse-

recovery-related losses in high-voltage, high-power boost convert-

ers,” in Proc. IEEE APEC’97, 1997, pp. 1000–1007.

7. D. M. Mitchell, “AC-DC converter having an improved power

factor,” U.S. Patent 4 412 277, Oct 25, 1983.

200 J. Rodríguez et al.

8. A. F. de Souza and I. Barbi, “A new ZVS-PWM unity power fac-

tor rectiﬁer with reduced conduction losses,” IEEE Trans. Power

Electron, Vol. 10, No. 6, Nov 1995, pp. 746–752.

9. A. F. de Souza and I. Barbi, “A new ZVS semiresonant power factor

rectiﬁer with reduced conduction losses,” IEEE Trans. Ind. Electron,

Vol. 46, No. 1, Feb 1999, pp. 82–90.

10. P. Todd, “UC3854 controlled power factor correction circuit design,”

Application Note U-134, Unitrode Corp.

11. J. Adams, T. Ribarich, and J. Ribarich, “A new control IC for

dimmable high-frequency electronic ballast,” IEEE Applied Power

Electronics Conference APEC’99, USA,1999, pp. 713–719.

12. C. Jacobina, M. Beltrao, E. Cabral, and A. Nogueira, “Induc-

tion motor drive system for low-power applications,” IEEE

Transactions on Industry Applications, Vol. 35, No. 1. Jan/Feb 1999,

pp. 52–60.

13. K. Hirachi, H. Yamamoto, T. Matsui, S. Watanabe, and M. Nakaoka,

“Cost-effective practical developments of high-performance 1kVA

UPS with new system conﬁgurations and their speciﬁc control imple-

mentations,” European Conference on Power Electronics EPE 95,

Spain 1995, pp. 2035–2040.

14. K. Hückelheim and Ch. Mangold, “Novel 4-quadrant converter con-

trol method,” European Conference on Power Electronics EPE 89,

Germany 1989, pp. 573–576.

15. T. Ohmae and K. Nakamura, “Hitachi’s role in the area of power

electronics for transportation,” Proc. of the IECON’93. Hawai, Nov

1993, pp. 714–718.

Three-phase Controlled Rectiﬁers

Juan W. Dixon, Ph.D.

Department of Electrical

Engineering, Pontiﬁcia

Universidad Católica de Chile

Vicuña Mackenna 4860,

Santiago, Chile

12.1 Introduction .......................................................................................... 201

12.2 Line-commutated Controlled Rectiﬁers....................................................... 201

12.2.1 Three-phase Half-wave Rectiﬁer • 12.2.2 Six-pulse or Double Star Rectiﬁer • 12.2.3 Double

Star Rectiﬁer with Interphase Connection • 12.2.4 Three-phase Full-wave Rectiﬁer or Graetz Bridge

• 12.2.5 Half Controlled Bridge Converter • 12.2.6 Commutation • 12.2.7 Power Factor

• 12.2.8 Harmonic Distortion • 12.2.9 Special Conﬁgurations for Harmonic Reduction

• 12.2.10 Applications of Line-commutated Rectiﬁers in Machine Drives • 12.2.11 Applications in

HVDC Power Transmission • 12.2.12 Dual Converters • 12.2.13 Cycloconverters

• 12.2.14 Harmonic Standards and Recommended Practices

12.3 Force-commutated Three-phase Controlled Rectiﬁers ................................... 221

12.3.1 Basic Topologies and Characteristics • 12.3.2 Operation of the Voltage Source Rectiﬁer

• 12.3.3 PWM Phase-to-phase and Phase-to-neutral Voltages • 12.3.4 Control of the DC Link

Voltage • 12.3.5 New Technologies and Applications of Force-commutated Rectiﬁers

Further Reading ..................................................................................... 242

12.1 Introduction

Three-phase controlled rectiﬁers have a wide range of appli-

cations, from small rectiﬁers to large high voltage direct

current (HVDC) transmission systems. They are used for

electrochemical processes, many kinds of motor drives, trac-

tion equipment, controlled power supplies and many other

applications. From the point of view of the commutation

process, they can be classiﬁed into two important categories:

line-commutated controlled rectiﬁers (thyristor rectiﬁers) and

force-commutated pulse width modulated (PWM) rectiﬁers.

12.2 Line-commutated Controlled

Rectiﬁers

12.2.1 Three-phase Half-wave Rectiﬁer

Figure 12.1 shows the three-phase half-wave rectiﬁer topol-

ogy. To control the load voltage, the half-wave rectiﬁer uses

three common-cathode thyristor arrangement. In this ﬁgure,

the power supply and the transformer are assumed ideal. The

thyristor will conduct (ON state), when the anode-to-cathode

voltage v

is positive and a ﬁring current pulse i

is applied to

the gate terminal. Delaying the ﬁring pulse by an angle α con-

trols the load voltage. As shown in Fig. 12.2, the ﬁring angle α

is measured from the crossing point between the phase supply

voltages. At that point, the anode-to-cathode thyristor voltage

begins to be positive. Figure 12.3 shows that the possible

range for gating delay is between α = 0

◦

and α = 180

◦

, but

because of commutation problems in actual situations, the

maximum ﬁring angle is limited to around 160

◦

. As shown

in Fig. 12.4, when the load is resistive, current i

has the

same waveform of the load voltage. As the load becomes more

and more inductive, the current ﬂattens and ﬁnally becomes

constant. The thyristor goes to the non-conducting condition

(OFF state) when the following thyristor is switched ON,or

the current, tries to reach a negative value.

With the help of Fig. 12.2, the load average voltage can be

evaluated, and is given by:

MAX

π/3+α



−π/3+α

cos ωt ·d

(

ωt

)

= V

MAX

sin

·cos α ≈ 1.17 ·V

rms

f −N

·cos α (12.1)

where V

MAX

is the secondary phase-to-neutral peak voltage,

rms

f −N

its root mean square (rms) value and ω is the angu-

lar frequency of the main power supply. It can be seen from

Eq. (12.1) that the load average voltage V

is modiﬁed by

201

202 J. W. Dixon

Y Y

LOAD

FIGURE 12.1 Three-phase half-wave rectiﬁer.

MAX

ωt

−π/3 π/3

FIGURE 12.2 Instantaneous dc voltage v

, average dc voltage V

, and ﬁring angle α.

ωt

range of α

0°

180°

FIGURE 12.3 Possible range for gating delay in angle α.

changing ﬁring angle α. When α<90

◦

, V

is positive and

when α>90

◦

, the average dc voltage becomes negative. In

such a case, the rectiﬁer begins to work as an inverter and the

load needs to be able to generate power reversal by reversing

its dc voltage.

The ac currents of the half-wave rectiﬁer are shown in

Fig. 12.5. This drawing assumes that the dc current is constant

(very large L

). Disregarding commutation overlap, each valve

conducts during 120

◦

per period. The secondary currents (and

thyristor currents) present a dc component that is undesirable,

and makes this rectiﬁer not useful for high power applications.

The primary currents show the same waveform, but with the

dc component removed. This very distorted waveform requires

an input ﬁlter to reduce harmonics contamination.

The current waveforms shown in Fig. 12.5 are useful for

designing the power transformer. Starting from:

prim

= 3 ·V

rms

(prim)f −N

·I

rms

prim

sec

= 3 ·V

rms

(sec)f −N

·I

rms

sec

(12.2)

= V

·I

12 Three-phase Controlled Rectiﬁers 203

(a) R > 0, L

(b) R > 0, L

(d) R small, L

very large

large

FIGURE 12.4 DC current waveforms.

where VA

prim

and VA

sec

are the ratings of the transformer

for the primary and secondary side respectively. Here P

the power transferred to the dc side. The maximum power

transfer is with α = 0

◦

(or α = 180

◦

). Then, to establish a

relation between ac and dc voltages, Eq. (12.1) for α = 0

◦

required:

= 1.17 ·V

rms

(sec)f −N

(12.3)

and:

= 1.17 ·a ·V

rms

(prim)f −N

(12.4)

where a is the secondary to primary turn relation of the trans-

former. On the other hand, a relation between the currents is

also possible to obtain. With the help of Fig. 12.5:

rms

sec

√

(12.5)

rms

prim

= a ·

√

(12.6)

Combining Eqs. (12.2) to (12.6), it yields:

prim

= 1.21 ·P

sec

= 1.48 ·P

(12.7)

Equation (12.7) shows that the power transformer has to be

oversized 21% at the primary side, and 48% at the secondary

side. Then, a special transformer has to be built for this recti-

ﬁer. In terms of average VA, the transformer needs to be 35%

larger that the rating of the dc load. The larger rating of the

secondary with respect to primary is because the secondary

carries a dc component inside the windings. Furthermore, the

transformer is oversized because the circulation of current har-

monics does not generate active power. Core saturation, due to

204 J. W. Dixon

MAX

–I

/ 3

FIGURE 12.5 AC current waveforms for the half-wave rectiﬁer.

∆

FIGURE 12.6 Six-pulse rectiﬁer.

the dc components inside the secondary windings, also needs

to be taken in account for iron oversizing.

12.2.2 Six-pulse or Double Star Rectiﬁer

The thyristor side windings of the transformer shown in

Fig. 12.6 form a six-phase system, resulting in a six-pulse

starpoint (midpoint connection). Disregarding commutation

overlap, each valve conducts only during 60

◦

per period. The

direct voltage is higher than that from the half-wave rectiﬁer

and its average value is given by:

MAX

π/6+α



−π/6+α

cos ωt ·d

(

ωt

)

= V

MAX

sin

·cos α ≈ 1.35 · V

rms

f −N

·cos α (12.8)

The dc voltage ripple is also smaller than the one gener-

ated by the half-wave rectiﬁer, due to the absence of the third

harmonic with its inherently high amplitude. The smoothing

12 Three-phase Controlled Rectiﬁers 205

∆

FIGURE 12.7 AC current waveforms for the six-pulse rectiﬁer.

reactor L

is also considerably smaller than the one needed

for a three-pulse (half-wave) rectiﬁer.

The ac currents of the six-pulse rectiﬁer are shown in

Fig. 12.7. The currents in the secondary windings present a

dc component, but the magnetic ﬂux is compensated by the

double star. As can be observed, only one valve is ﬁred at a time

and then this connection in no way corresponds to a parallel

connection. The currents inside the delta show a symmetrical

waveform with 60

◦

conduction. Finally, due to the particular

transformer connection shown in Fig. 12.6, the source currents

also show a symmetrical waveform, but with 120

◦

conduction.

Evaluation of the the rating of the transformer is done in

similar fashion to the way the half-wave rectiﬁer is evaluated:

prim

= 1.28 ·P

sec

= 1.81 ·P

(12.9)

Thus the transformer must be oversized 28% at the primary

side and 81% at the secondary side. In terms of size it has an

average apparent power of 1.55 times the power P

(55% over-

sized). Because of the short conducting period of the valves,

the transformer is not particularly well utilized.

12.2.3 Double Star Rectiﬁer with Interphase

Connection

This topology works as two half-wave rectiﬁers in parallel, and

is very useful when high dc current is required. An optimal

way to reach both good balance and elimination of harmon-

ics is through the connection shown in Fig. 12.8. The two

rectiﬁers are shifted by 180

◦

, and their secondary neutrals

are connected through a middle-point autotransformer called

“interphase transformer.” The interphase transformer is con-

nected between the two secondary neutrals and the middle

point at the load return. In this way, both groups operate in

parallel. Half the direct current ﬂows in each half of the inter-

phase transformer, and then its iron core does not become

saturated. The potential of each neutral can oscillate inde-

pendently, generating an almost triangular voltage waveform

) in the interphase transformer, as shown in Fig. 12.9.

As this converter work like two half-wave rectiﬁers connected

in parallel, the load average voltage is the same as in Eq. (12.1):

≈ 1.17 ·V

rms

f −N

·cos α (12.10)

where V

rms

f −N

is the phase-to-neutral rms voltage at the valve

side of the transformer (secondary).

The Fig. 12.9 also shows the two half-wave rectiﬁer voltages,

related to their respective neutrals. Voltage v

represents the

potential between the common cathode connection and the

neutral N1. The voltage v

is between the common cathode

connection and N2. It can be seen that the two instantaneous

voltages are shifted, which gives as a result, a voltage v

that

is smoother than v

and v

Figure 12.10 shows how v

, v

, and v

change when

the ﬁring angle changes from α = 0

◦

to 180

◦