Three-phase to Three-phase Cyclo-converters - Module 4 AC to AC Voltage Converters Lesson 31 Notes | EduRev

Created by: Sahil Setia

: Three-phase to Three-phase Cyclo-converters - Module 4 AC to AC Voltage Converters Lesson 31 Notes | EduRev

 Page 1


 
 
 
 
 
 
 
 
 
Module 
4 
 
AC to AC Voltage 
Converters 
Version 2 EE IIT, Kharagpur 1
Page 2


 
 
 
 
 
 
 
 
 
Module 
4 
 
AC to AC Voltage 
Converters 
Version 2 EE IIT, Kharagpur 1
 
 
 
 
 
 
 
 
 
 
Lesson 
31 
 
Three-phase to Three-
phase Cyclo-converters 
Version 2 EE IIT, Kharagpur 2
Page 3


 
 
 
 
 
 
 
 
 
Module 
4 
 
AC to AC Voltage 
Converters 
Version 2 EE IIT, Kharagpur 1
 
 
 
 
 
 
 
 
 
 
Lesson 
31 
 
Three-phase to Three-
phase Cyclo-converters 
Version 2 EE IIT, Kharagpur 2
Instructional Objectives 
 
Study of the following: 
• The three-phase to three-phase cyclo-converter circuit, using six three-phase half-wave 
thyristorised converters   
• The operation of the above cyclo-converter circuit 
• The analysis of the cyclo-converter output waveform   
 
Introduction 
 In the last lesson - second one in the second half of this module, firstly, the circuit and the 
operation of the three-phase to single-phase cyclo-converter, with both resistive and inductive 
loads, are described in detail. Two three-phase full-wave bridge converters (rectifiers) connected 
back to back, with six thyristors as power switching devices in each bridge, are used. The mode 
of operation is non-circulating current one, in which only one converter is conducting at a time. 
The following are briefly presented - the circulating current mode of operation with both 
converters conducting at a time, and the same type of  cyclo-converter, using two three-phase 
half-wave converters, stating mainly the merits.   
 In this lesson - the third one in the second half, firstly, the three-phase to three-phase cyclo-
converter circuit, using six three-phase half-wave thyristorised converters (two per each phase), is 
described. The operation of the above cyclo-converter circuit is briefly discussed. The mode of 
operation is the non-circulating current one. Lastly, the analysis of the cyclo-converter output 
waveform is presented. The procedure for obtaining the expression for the output voltage (rms) 
per phase for cyclo-converter is described. 
Keywords: Three-phase to three-phase cyclo-converter, Three-phase half-wave converters. 
Output waveform analysis 
 
Three-phase to Three-phase Cyclo-converter 
 The circuit of a three-phase to three-phase cyclo-converter is shown in Fig. 31.1. Two three-
phase half-wave (three-pulse) converters connected back to back for each phase, with three 
thyristors for each bridge, are needed here. The total number of thyristors used is 18, thus 
reducing the cost of power components, and also of control circuits needed to generate the firing 
pulses for the thyristors, as described later. This may be compared to the case with 6 (six) three-
phase full-wave (6-pulse) bridge converters, having six thyristors for each converter, with total 
devices used being 36. Though this will reduce the harmonic content in both output voltage and 
current waveforms, but is more costly. This may be used, where the total cost may be justified, 
along with the merit stated. This has also been discussed in the last section of the previous lesson 
(#30). The ripple frequency is 150 Hz, three times the input frequency of 50 Hz. In Fig. 31.1, the 
circulating current mode of operation is used, in which both (positive and negative) converters in 
each phase, conduct at the same time. Inter-group reactor in each phase as shown, is needed here. 
But, if non-circulating current mode of operation is used, where only one converter (positive or 
negative) in each phase, conducts at a time, the reactors are not needed.   
 
 
 
Version 2 EE IIT, Kharagpur 3
Page 4


 
 
 
 
 
 
 
 
 
Module 
4 
 
AC to AC Voltage 
Converters 
Version 2 EE IIT, Kharagpur 1
 
 
 
 
 
 
 
 
 
 
Lesson 
31 
 
Three-phase to Three-
phase Cyclo-converters 
Version 2 EE IIT, Kharagpur 2
Instructional Objectives 
 
Study of the following: 
• The three-phase to three-phase cyclo-converter circuit, using six three-phase half-wave 
thyristorised converters   
• The operation of the above cyclo-converter circuit 
• The analysis of the cyclo-converter output waveform   
 
Introduction 
 In the last lesson - second one in the second half of this module, firstly, the circuit and the 
operation of the three-phase to single-phase cyclo-converter, with both resistive and inductive 
loads, are described in detail. Two three-phase full-wave bridge converters (rectifiers) connected 
back to back, with six thyristors as power switching devices in each bridge, are used. The mode 
of operation is non-circulating current one, in which only one converter is conducting at a time. 
The following are briefly presented - the circulating current mode of operation with both 
converters conducting at a time, and the same type of  cyclo-converter, using two three-phase 
half-wave converters, stating mainly the merits.   
 In this lesson - the third one in the second half, firstly, the three-phase to three-phase cyclo-
converter circuit, using six three-phase half-wave thyristorised converters (two per each phase), is 
described. The operation of the above cyclo-converter circuit is briefly discussed. The mode of 
operation is the non-circulating current one. Lastly, the analysis of the cyclo-converter output 
waveform is presented. The procedure for obtaining the expression for the output voltage (rms) 
per phase for cyclo-converter is described. 
Keywords: Three-phase to three-phase cyclo-converter, Three-phase half-wave converters. 
Output waveform analysis 
 
Three-phase to Three-phase Cyclo-converter 
 The circuit of a three-phase to three-phase cyclo-converter is shown in Fig. 31.1. Two three-
phase half-wave (three-pulse) converters connected back to back for each phase, with three 
thyristors for each bridge, are needed here. The total number of thyristors used is 18, thus 
reducing the cost of power components, and also of control circuits needed to generate the firing 
pulses for the thyristors, as described later. This may be compared to the case with 6 (six) three-
phase full-wave (6-pulse) bridge converters, having six thyristors for each converter, with total 
devices used being 36. Though this will reduce the harmonic content in both output voltage and 
current waveforms, but is more costly. This may be used, where the total cost may be justified, 
along with the merit stated. This has also been discussed in the last section of the previous lesson 
(#30). The ripple frequency is 150 Hz, three times the input frequency of 50 Hz. In Fig. 31.1, the 
circulating current mode of operation is used, in which both (positive and negative) converters in 
each phase, conduct at the same time. Inter-group reactor in each phase as shown, is needed here. 
But, if non-circulating current mode of operation is used, where only one converter (positive or 
negative) in each phase, conducts at a time, the reactors are not needed.   
 
 
 
Version 2 EE IIT, Kharagpur 3
 
3- f supply
 
P
 
P
 P
 
N
 
N
 
N
 
Phase A
 
3-phase 
load
Fig. 31.1: Three-phase to three-phase cycloconverter
 
Phase B
 
Phase C
 
A
 
B
 
C
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    
 It may be noted that the circuit in each of the three phases is similar to the cyclo-converter 
circuit shown in Fig. 30.5. The firing sequence of the thyristors for the phase groups, B & C are 
same as that for phase group A, but lag by the angle, and , respectively. Thus, a 
balanced three-phase voltage is obtained at the output terminals, to be fed to the three-phase 
load. The average value of the output voltage is changed by varying the firing angles (
° 120 ° 240
a ) of the 
thyristors, whereas its frequency is varied by changing the time interval ( ), after 
which the next (incoming) thyristor is triggered. With a balanced load, the neutral connection is 
not necessary, and may be omitted, thereby suppressing all triplen harmonics.  
) 3 /( 1 3 /
0
f T · =
 Normally, the output frequency of the cyclo-converter is lower than the supply (input) 
frequency (step-down region), limited to about one-third of it ( 3 /
0 i
f f = ). This is necessary for 
obtaining reasonable power output, efficiency and harmonic content. If the output frequency is to 
be increased, the harmonic distortion in the output voltage increases, because its waveform is 
composed of fewer segments of the supply voltage. Thus, the losses in cyclo-converter and also 
in ac motor become excessive. By using more complex converter circuits with higher pulse 
numbers, the output voltage waveform is improved, with the maximum useful ratio of output to 
input frequency is increased to about one-half.   
Analysis of the Cyclo-converter Output Waveform 
 An expression for the fundamental component of the phase voltage (rms) delivered by the 
cyclo-converter is obtained by the procedure given here. 
 An m-phase converter circuit is assumed in which each phase conducts for ( m / ) 2 ( p · ) 
electrical radians in one cycle of supply (input) voltage. For example, in a three-phase, half-wave 
(three-pulse) converter (m = 3), each phase conducts for ( ° = · 120 3 / ) 2 ( p ) radians in a cycle of 
Version 2 EE IIT, Kharagpur 4
Page 5


 
 
 
 
 
 
 
 
 
Module 
4 
 
AC to AC Voltage 
Converters 
Version 2 EE IIT, Kharagpur 1
 
 
 
 
 
 
 
 
 
 
Lesson 
31 
 
Three-phase to Three-
phase Cyclo-converters 
Version 2 EE IIT, Kharagpur 2
Instructional Objectives 
 
Study of the following: 
• The three-phase to three-phase cyclo-converter circuit, using six three-phase half-wave 
thyristorised converters   
• The operation of the above cyclo-converter circuit 
• The analysis of the cyclo-converter output waveform   
 
Introduction 
 In the last lesson - second one in the second half of this module, firstly, the circuit and the 
operation of the three-phase to single-phase cyclo-converter, with both resistive and inductive 
loads, are described in detail. Two three-phase full-wave bridge converters (rectifiers) connected 
back to back, with six thyristors as power switching devices in each bridge, are used. The mode 
of operation is non-circulating current one, in which only one converter is conducting at a time. 
The following are briefly presented - the circulating current mode of operation with both 
converters conducting at a time, and the same type of  cyclo-converter, using two three-phase 
half-wave converters, stating mainly the merits.   
 In this lesson - the third one in the second half, firstly, the three-phase to three-phase cyclo-
converter circuit, using six three-phase half-wave thyristorised converters (two per each phase), is 
described. The operation of the above cyclo-converter circuit is briefly discussed. The mode of 
operation is the non-circulating current one. Lastly, the analysis of the cyclo-converter output 
waveform is presented. The procedure for obtaining the expression for the output voltage (rms) 
per phase for cyclo-converter is described. 
Keywords: Three-phase to three-phase cyclo-converter, Three-phase half-wave converters. 
Output waveform analysis 
 
Three-phase to Three-phase Cyclo-converter 
 The circuit of a three-phase to three-phase cyclo-converter is shown in Fig. 31.1. Two three-
phase half-wave (three-pulse) converters connected back to back for each phase, with three 
thyristors for each bridge, are needed here. The total number of thyristors used is 18, thus 
reducing the cost of power components, and also of control circuits needed to generate the firing 
pulses for the thyristors, as described later. This may be compared to the case with 6 (six) three-
phase full-wave (6-pulse) bridge converters, having six thyristors for each converter, with total 
devices used being 36. Though this will reduce the harmonic content in both output voltage and 
current waveforms, but is more costly. This may be used, where the total cost may be justified, 
along with the merit stated. This has also been discussed in the last section of the previous lesson 
(#30). The ripple frequency is 150 Hz, three times the input frequency of 50 Hz. In Fig. 31.1, the 
circulating current mode of operation is used, in which both (positive and negative) converters in 
each phase, conduct at the same time. Inter-group reactor in each phase as shown, is needed here. 
But, if non-circulating current mode of operation is used, where only one converter (positive or 
negative) in each phase, conducts at a time, the reactors are not needed.   
 
 
 
Version 2 EE IIT, Kharagpur 3
 
3- f supply
 
P
 
P
 P
 
N
 
N
 
N
 
Phase A
 
3-phase 
load
Fig. 31.1: Three-phase to three-phase cycloconverter
 
Phase B
 
Phase C
 
A
 
B
 
C
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
    
 It may be noted that the circuit in each of the three phases is similar to the cyclo-converter 
circuit shown in Fig. 30.5. The firing sequence of the thyristors for the phase groups, B & C are 
same as that for phase group A, but lag by the angle, and , respectively. Thus, a 
balanced three-phase voltage is obtained at the output terminals, to be fed to the three-phase 
load. The average value of the output voltage is changed by varying the firing angles (
° 120 ° 240
a ) of the 
thyristors, whereas its frequency is varied by changing the time interval ( ), after 
which the next (incoming) thyristor is triggered. With a balanced load, the neutral connection is 
not necessary, and may be omitted, thereby suppressing all triplen harmonics.  
) 3 /( 1 3 /
0
f T · =
 Normally, the output frequency of the cyclo-converter is lower than the supply (input) 
frequency (step-down region), limited to about one-third of it ( 3 /
0 i
f f = ). This is necessary for 
obtaining reasonable power output, efficiency and harmonic content. If the output frequency is to 
be increased, the harmonic distortion in the output voltage increases, because its waveform is 
composed of fewer segments of the supply voltage. Thus, the losses in cyclo-converter and also 
in ac motor become excessive. By using more complex converter circuits with higher pulse 
numbers, the output voltage waveform is improved, with the maximum useful ratio of output to 
input frequency is increased to about one-half.   
Analysis of the Cyclo-converter Output Waveform 
 An expression for the fundamental component of the phase voltage (rms) delivered by the 
cyclo-converter is obtained by the procedure given here. 
 An m-phase converter circuit is assumed in which each phase conducts for ( m / ) 2 ( p · ) 
electrical radians in one cycle of supply (input) voltage. For example, in a three-phase, half-wave 
(three-pulse) converter (m = 3), each phase conducts for ( ° = · 120 3 / ) 2 ( p ) radians in a cycle of 
Version 2 EE IIT, Kharagpur 4
( p · 2 ) radians. Similarly, in a three-phase, full-wave (six-pulse) converter (m = 6), the 
conduction period of the periodic waveform is ( ° = = · 60 3 / 6 / ) 2 ( p p ) radians in one cycle.  
 The output voltage waveform for an m-phase converter with firing delay angle a , is shown 
in Fig. 31.2.  With the time origin, P P ' taken at the peak value of the supply voltage, the 
instantaneous phase voltage is given by t E t E e
ph m
? ? cos 2 cos = = 
where,  = Supply voltage per phase (rms).  
ph
E
 
- p/m p/m
P
2p/m
E
m
P '
a
?t 
( p/m + a)
(- p/m + a)
E
c
Fig. 31.2: Output voltage waveform for m-phase converter with firing angle a
 
 
 
 
 
 
 
 
 
 
 
From Fig. 31.2, it can be observed that the conduction period is from ( m / p - ) to ( m / p ), if the 
firing delay angle is ° = 0 a . For the firing delay angle a , the conduction period is from 
( a p + - ) / ( m ) to ( a p + ) / ( m ). From the above cases, the total conduction period is ( m / ) 2 ( p · ). 
The average value of the output voltage is, 
 a
p
p
? ?
p
a p
a p
cos sin 2 ) ( cos 2
2
) ) / ((
) ) / ( (
·
?
?
?
?
?
?
·
?
?
?
?
?
?
· = ·
?
?
?
?
?
?
·
=
?
+
+ -
m
m
E t d t E
m
E
ph
m
m
ph dc
 
This expression is obtained for dc to ac converter in module 2, and also available in text book. 
When the firing delay angle is ° = 0 a ,  has the maximum value of  
dc
E
?
?
?
?
?
?
· ?
?
?
?
?
?
· · =
m
m
E E
ph d
p
p
sin 2
0
 
If the delay angle in the cyclo-converter is slowly varied as given earlier, the output phase 
voltage at any point of the low frequency cycle may be calculated as the average voltage for the 
appropriate delay angle. This ignores the rapid fluctuations superimposed on the average low 
frequency waveform. Assuming continuous conduction, the average voltage is a cos
0
· =
d dc
E E . 
 If  is the fundamental component of the output voltage (rms) per phase for the cyclo-
converter, then the peak output voltage for firing angle of  is, 
r
E
0
° 0
 ?
?
?
?
?
?
· ?
?
?
?
?
?
· · = = ·
m
m
E E E
ph d r
p
p
sin 2 2
0 0
 
or, ?
?
?
?
?
?
· ?
?
?
?
?
?
· =
m
m
E E
ph r
p
p
sin
0
 
However, the firing angle of the positive group, 
p
a cannot be reduced to zero ( ), for this value 
corresponds to a firing angle of (
° 0
° = 180
n
a ) in the negative group. It may be noted that the firing 
delay angles of the two (positive and negative) converters are related by ( ° = + 180
n P
a a ), or 
n p
a a - ° = 180 . In practice, inverter firing cannot be delayed by , because sufficient margin ° 180
Version 2 EE IIT, Kharagpur 5
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