Three-phase Diode Rectifiers

10.3 Three-phase Diode Rectifiers

Full-wave V s = 1.11V dc (10.36)

It has been shown in Section 10.2 that single-phase diode recti- fiers require a rather high transformer VA rating for a given dc

Another important design parameter is the V RRM rating of output power. Therefore, these rectifiers are suitable only for the diodes employed.

low to medium power applications. For power output higher In the case of a half-wave rectifier, from Eq. (10.3),

than 15 kW, three-phase or poly-phase diode rectifiers should

be employed. There are two types of three-phase diode rectifier

V dc that convert a three-phase ac supply into a dc voltage, namely, Half-wave V RRM =V m =

= 3.14V dc (10.37)

star rectifiers and bridge rectifiers. In the following subsections,

TABLE 10.2 Important design parameters of basic single-phase rectifier circuits with resistive load

Half-wave

Full-wave rectifier

Full-wave bridge

rectifier

with center-tapped

rectifier

transformer

Peak repetitive reverse voltage V RRM

3.14V dc 3.14V dc 1.57V dc

RMS input voltage per transformer leg V s

2.22V dc 1.11V dc 1.11V dc

Diode average current I

F (AV)

1.00I dc 0.50I dc 0.50I dc

Peak repetitive forward current I FRM

3.14I

F (AV)

1.57I

F (AV)

1.57I

F (AV)

Diode rms current I

F (RMS)

1.57I dc 0.785I dc 0.785I dc

Form factor of diode current I

F (RMS) /I

F (AV)

Rectification ratio

Form factor

Ripple factor

0.482 Transformer rating primary VA 2.69P dc 1.23P dc 1.23P dc Transformer rating secondary VA 3.49P dc 1.75P dc 1.23P dc

Output ripple frequency f r

1f i

2f i

2f i

10 Diode Rectifiers 155 the operations of these rectifiers are examined and their perfor-

mances are analyzed and compared in tabulated form. For the

RN

sake of simplicity, the diodes and the transformers are consid- ered to be ideal, i.e. the diodes have zero forward voltage drop

BN

R D i D and reverse current, and the transformers possess no resistance

R v L and no leakage inductance. Furthermore, it is assumed that the Y

v YN

load is purely resistive, such that the load voltage and the load current have similar waveforms. In Section 10.5 Filtering Sys-

FIGURE 10.7 Three-phase star rectifier. tems in Rectifier Circuits, the effects of inductive load and capacitive load on a diode rectifier are considered in detail.

Taking phase R as an example, diode D conducts from π/6 to 5π/6. Therefore, using Eq. (10.1) the average value of the output can be found as

10.3.1 Three-phase Star Rectifiers

10.3.1.1 Basic Three-phase Star Rectifier Circuit

V dc =

V m sin θdθ (10.42)

A basic three-phase star rectifier circuit is shown in Fig. 10.7.

This circuit can be considered as three single-phase half-wave or rectifiers combined together. Therefore it is sometimes referred to as a three-phase half-wave rectifier. The diode in a particu-

lar phase conducts during the period when the voltage on that

V dc =V m

= 0.827V m (10.43)

phase is higher than that on the other two phases. The voltage waveforms of each phase and the load are shown in Fig. 10.8.

Similarly, using Eq. (10.6), the rms value of the output It is clear that, unlike the single-phase rectifier circuit, the con- voltage can be found as duction angle of each diode is 2π/3, instead of π. This circuit finds uses where the required dc output voltage is relatively

low and the required output current is too large for a practical 2 V L = ( V m sin θ) dθ (10.44)

single-phase system.

–1.73V m

FIGURE 10.8 Waveforms of voltage and current of the three-phase star rectifier shown in Fig. 10.7.

156 Y. S. Lee and M. H. L. Chow TABLE 10.3 Important design parameters of the three-phase rectifier circuits with the resistive load

star rectifier

double-star rectifier

bridge rectifier

with inter-phase transformer

Peak repetitive reverse voltage V RRM

2.092V dc 1.06V dc 1.05V dc

RMS input voltage per transformer leg V s

0.855V dc 0.855V dc 0.428V dc

Diode average current I

F (AV)

0.333I dc 0.167I dc 0.333I dc

Peak repetitive forward current I FRM

3.63I

F (AV)

3.15I

F (AV)

3.14I

F (AV)

Diode rms current I

F (RMS)

0.587I dc 0.293I dc 0.579I dc

Form factor of diode current I

F (RMS) /I

F (AV)

Rectification ratio

Form factor

Ripple factor

0.042 Transformer rating primary VA 1.23P dc 1.06P dc 1.05P dc Transformer rating secondary VA 1.51P dc 1.49P dc 1.05P dc

Output ripple frequency f r

or to zero. Therefore it is preferable not to have star-connected primary windings.

L =V

= 0.84V m

10.3.1.2 Three-phase Inter-star Rectifier Circuit

The transformer core saturation problem in the three-phase In addition, the rms current in each transformer secondary star rectifier can be avoided by a special arrangement in its sec-

winding can also be found as ondary windings, known as zig-zag connection. The modified circuit is called the three-phase inter-star or zig-zag rectifier

3 circuit, as shown in Fig. 10.9. Each secondary phase voltage

I s =I m

= 0.485I m

(10.46) is obtained from two equal-voltage secondary windings (with 2π 3 4 a phase displacement of π/3) connected in series so that the

dc magnetizing forces due to the two secondary windings on where I m =V m /R.

any limb are equal and opposite. At the expense of extra sec- Based on the relationships stated in Eqs. (10.43), (10.45), ondary windings (increasing the transformer secondary rating and (10.46), all the important design parameters of the three- factor from 1.51 to 1.74 VA/W), this circuit connection elimi- phase star rectifier can be evaluated, as listed in Table 10.3, nates the effects of core saturation and reduces the transformer which is given at the end of Subsection 10.3.2. Note that, as primary rating factor to the minimum of 1.05 VA/W. Apart with a single-phase half-wave rectifier, the three-phase star rec- from transformer ratings, all the design parameters of this tifier shown in Fig. 10.7 has direct currents in the secondary circuit are the same as those of a three-phase star rectifier windings that can cause a transformer core saturation prob- (therefore not separately listed in Table 10.3). Furthermore, a lem. In addition, the currents in the primary do not sum star-connected primary winding with no neutral connection

FIGURE 10.9 Three-phase inter-star rectifier.

10 Diode Rectifiers 157 is equally permissible because the sum of all primary phase The diodes are numbered in the order of conduction sequences

currents is zero at all times. and the conduction angle of each diode is 2π/3. The conduction sequence for diodes is 12, 23, 34, 45,

56, and 61. The voltage and the current waveforms of the

10.3.1.3 Three-phase Double-star Rectifier with

three-phase bridge rectifier are shown in Fig. 10.13. The line

Inter-phase Transformer

voltage is 1.73 times the phase voltage of a three-phase star- This circuit consists essentially of two three-phase star rectifiers connected source. It is permissible to use any combination

with their neutral points interconnected through an inter- of star- or delta-connected primary and secondary windings phase transformer or reactor (Fig. 10.10). The polarities of the because the currents associated with the secondary windings corresponding secondary windings in the two interconnected are symmetrical. systems are reversed with respect to each other, so that the rec-

Using Eq. (10.1) the average value of the output can be tifier output voltage of one three-phase unit is at a minimum found as

when the rectifier output voltage of the other unit is at a max- imum as shown in Fig. 10.11. The function of the inter-phase

transformer is to cause the output voltage v L to be the aver-

V dc =

3V m sin θdθ (10.47)

age of the rectified voltages v1 and v2 as shown in Fig. 10.11. In addition, the ripple frequency of the output voltage is now or six times that of the mains and therefore the component size

of the filter (if there is any) becomes smaller. In a balanced

= 1.654V m (10.48) circuit, the output currents of two three-phase units flowing

V dc =V m

in opposite directions in the inter-phase transformer wind- ing will produce no dc magnetization current. Similarly, the

Similarly, using Eq. (10.6), the rms value of the output

dc magnetization currents in the secondary windings of two voltage can be found as three-phase units cancel each other out. By virtue of the symmetry of the secondary circuits, the

( V m sin θ) 2 three primary currents add up to zero at all times. Therefore,

dθ (10.49)

a star primary winding with no neutral connection would be equally permissible.

or