HOW-TO GUIDE
Introduction of Three Phase
Half/Full Wave Converter
THREE PHASE HALF/FULL CONVERTER
INTRODUCTION
Single phase half controlled bridge converters & fully
controlled bridge converters are used extensively in industrial
applications up to about 15kW of output power. The single
phase controlled rectifiers provide a maximum dc output of
Vdc max
2Vm
The output ripple frequency is equal to the twice the ac
supply frequency. The single phase full wave controlled
rectifiers provide two output pulses during every input supply
cycle and hence are referred to as two pulse converters.
Three phase converters are 3-phase controlled rectifiers
which are used to convert ac input power supply into dc output
power across the load.
Features of 3-phase controlled rectifiers are
Operate from 3 phase ac supply voltage.
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They provide higher dc output voltage and higher dc
output power.
Higher output voltage ripple frequency.
Filtering requirements are simplified for smoothing out
load voltage and load current
Three phase controlled rectifiers are extensively used in
high power variable speed industrial dc drives.
3-PHASE HALF WAVE CONVERTER
Three single phase half-wave converters are connected
together to form a three phase half-wave converter as shown in
the figure.
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THREE PHASE SUPPLY VOLTAGE EQUATIONS
We define three line neutral voltages (3 phase voltages) as
follows
vRN
van
Vm sin t ; Vm
vYN
vbn
Vm sin
t
vYN
vbn
Vm sin
t 1200
vBN
vcn
Vm sin
t
vBN
vcn
Vm sin
t 1200
vBN
vcn
Vm sin
t 2400
Max. Phase Voltage
2
3
Vector diagram of 3-phase supply
voltages
2
3
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The 3-phase half wave converter combines three single
phase half wave controlled rectifiers in one single circuit
feeding a common load. The thyristor
the supply phase windings
'a n'
T1
acts as one half wave
controlled rectifier. The second thyristor
supply phase winding
'b n '
'c n '
T2
in series with the
acts as the second half wave
controlled rectifier. The third thyristor
supply phase winding
in series with one of
in series with the
T3
acts as the third half wave controlled
rectifier.
The 3-phase input supply is applied through the star
connected supply transformer as shown in the figure. The
common neutral point of the supply is connected to one end of
the load while the other end of the load connected to the
common cathode point.
When the thyristor
phase voltage
van
T1
is triggered at
t
300
6
appears across the load when
T1
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, the
conducts. The
load current flows through the supply phase winding
'a n'
and
through thyristor T as long as T conducts.
1
When thyristor
1
is triggered at
T2
t
5
6
1500
,
T1
becomes reverse biased and turns-off. The load current flows
through the thyristor
'b n ' .
and through the supply phase winding
T2
When T conducts the phase voltage
2
vbn
appears across the
load until the thyristor T is triggered .
3
When the thyristor
T3
is triggered at
is reversed biased and hence
T2
3
2
,
T2
turns-off. The phase voltage
vcn
t
2700
appears across the load when T conducts.
3
When
T1
is triggered again at the beginning of the next
input cycle the thyristor
naturally as soon as
T1
T3
turns off as it is reverse biased
is triggered. The figure shows the 3-
phase input supply voltages, the output voltage which appears
across the load, and the load current assuming a constant and
ripple free load current for a highly inductive load and the
current through the thyristor T .
1
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For a purely resistive load where the load inductance ‘L =
0’ and the trigger angle
6
, the load current appears as
discontinuous load current and each thyristor is naturally
commutated when the polarity of the corresponding phase
supply voltage reverses. The frequency of output ripple
frequency for a 3-phase half wave converter is
3 fS ,
where
fS
is
the input supply frequency.
The 3-phase half wave converter is not normally used in
practical converter systems because of the disadvantage that
the supply current waveforms contain dc components (i.e., the
supply current waveforms have an average or dc value).
TO DERIVE AN EXPRESSION FOR THE AVERAGE OUTPUT
VOLTAGE OF A 3-PHASE HALF WAVE CONVERTER FOR
CONTINUOUS LOAD CURRENT
The reference phase voltage is v
RN
angle
van Vm sin t .
The trigger
is measured from the cross over points of the 3-phase
supply voltage waveforms. When the phase supply voltage
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van
begins its positive half cycle at
appears at
t
6
0,
the first cross over point
radians 300 .
The trigger angle
for the thyristor
the cross over point at
during the period
t
t
300 .
300 to 1500 ,
t
is measured from
T1
The thyristor
T1
is forward biased
when the phase supply voltage
van
has higher amplitude than the other phase supply voltages.
Hence
T1
T1
can be triggered between 30
0
to 1500 .
When the thyristor
is triggered at a trigger angle , the average or dc output
voltage for continuous load current is calculated using the
equation
Vdc
3
2
5
6
vO .d
t
6
Output voltage
Vdc
vO
3
2
van
Vm sin t for t
300
to 1500
5
6
Vm sin t.d
t
6
As the output load voltage waveform has three output
pulses during the input cycle of
2
radians
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3Vm
2
Vdc
5
6
sin t.d
t
6
5
6
3Vm
2
Vdc
cos t
6
3Vm
2
Vdc
cos
5
6
cos
6
Note from the trigonometric relationship
cos A B
cos A.cos B sin A.sin B
Vdc
3Vm
2
cos
Vdc
3Vm
2
cos 1500 cos
Vdc
3Vm
2
cos 1800 300 cos
Note:
5
cos
6
sin
sin 1500 sin
cos 1800 300
sin 1800 300
5
sin
6
cos
6
.cos
sin
cos 300 .cos
sin 1800 300 sin
6
sin
sin 300 sin
cos 300 .cos
cos 300
sin 300
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sin 300 sin
Therefore
Vdc
3Vm
2
cos 300 cos
Vdc
3Vm
2cos 300 cos
2
Vdc
3Vm
2
2
Vdc
3Vm
2
Vdc
3VLm
cos
2
sin 300 sin
cos 300 .cos
sin 300 sin
3
cos
2
3 cos
3 3Vm
cos
2
Where
VLm
3Vm
Max. line to line supply voltage
for a 3-phase star connected
transformer.
The maximum average or dc output voltage is obtained at
a delay angle
Vdc max
= 0 and is given by
Vdm
3 3 Vm
2
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Where
Vm
Is the peak phase voltage.
And the normalized average output voltage is
Vdcn
Vn
Vdc
Vdm
cos
TO DERIVE AN EXPRESSION FOR THE RMS VALUE OF THE
OUTPUT VOLTAGE OF A 3-PHASE HALF WAVE CONVERTER FOR
CONTINUOUS LOAD CURRENT
The rms value of output voltage is found by using the equation
VO RMS
3
2
1
2
5
6
Vm2 sin 2 t.d
t
6
and we obtain
VO RMS
3Vm
1
6
3
8
1
2
cos 2
Three phase half wave controlled rectifier output voltage
waveforms for different trigger angles with RL load
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Van
Vbn
Vcn
V0
=30
0
30
0
60
0
90
0
120
0
0
150
180
0
210
0
240
Van
0
270
0
300
0
330
0
360
Vbn
0
0
390
420
t
0
Vcn
V0
=60
0
30
0
60
0
90
0
120
0
0
150
180
0
210
0
240
0
270
0
300
0
330
0
360
Vbn
Van
0
0
0
390
420
0
t
0
Vcn
V0
=90
0
30
0
60
0
90
0
120
0
0
150
180
0
210
0
240
0
270
0
300
0
330
0
360
0
0
390
420
0
0
t
Three phase half wave controlled rectifier output voltage
waveforms for different trigger angles with R load
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Vbn
Van
Vcn
=0
Vs
0
30
0
60
0
90
0
120
0
150
0
0
180
210
0
0
240 270
0
0
0
300 330 360
0
Vbn
Van
0
390
420
t
0
Vcn
=150
V0
0
30
0
60
0
90
0
120
0
150
0
0
180
210
0
0
240 270
0
0
0
300 330 360
0
Vbn
Van
0
390
420
t
0
Vcn
=300
V0
0
30
0
60
0
90
0
120
0
150
0
0
180
210
0
0
240 270
0
0
0
300 330 360
0
Vbn
Van
0
390
420
t
0
Vcn
=60
V0
0
30
0
60
0
90
0
120
0
150
0
0
180
210
0
0
240 270
0
0
0
300 330 360
0
0
390
420
0
0
t
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TO DERIVE AN EXPRESSION FOR THE AVERAGE OR DC OUTPUT
VOLTAGE OF A 3 PHASE HALF WAVE CONVERTER WITH
RESISTIVE LOAD OR RL LOAD WITH FWD.
In the case of a three-phase half wave controlled rectifier
with resistive load, the thyristor
conducts up to
T1
voltage
van
t 1800
300
to 1800
T1
is triggered at
t
300
and
radians. When the phase supply
decreases to zero at
zero and the thyristor
t
T1
t
, the load current falls to
turns off. Thus
T1
conducts from
.
Hence the average dc output voltage for a 3-pulse
converter (3-phase half wave controlled rectifier) is calculated
by using the equation
Vdc
vO
3
2
van
1800
vO .d
t
300
Vm sin t; for t
300 to 1800
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Vdc
Vdc
Vdc
Vdc
3
2
3Vm
2
1800
Vm sin t.d
30
t
0
1800
sin t.d
t
300
1800
3Vm
2
cos t
3Vm
2
cos1800 cos
300
Since
cos1800
We get
Vdc
300
1,
3Vm
1 cos
2
300
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THREE PHASE FULL CONVERTER
Three phase full converter is a fully controlled bridge
controlled rectifier using six thyristors connected in the form of
a full wave bridge configuration. All the six thyristors are
controlled switches which are turned on at a appropriate times
by applying suitable gate trigger signals.
The three phase full converter is extensively used in
industrial power applications upto about 120kW output power
level, where two quadrant operations is required. The figure
shows a three phase full converter with highly inductive load.
This circuit is also known as three phase full wave bridge or as a
six pulse converter.
The thyristors are triggered at an interval of
3
radians
(i.e. at an interval of 60 ). The frequency of output ripple voltage
0
is
6 fS
and the filtering requirement is less than that of three
phase semi and half wave converters.
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At
t
thyristor
6
, thyristor
is turned on by applying the gating signal to the gate
T1
of T . During the time period
1
T6
is already conducting when the
T6
t
to
6
2
, thyristors
T1
and
conduct together and the line to line supply voltage
vab
appears across the load.
At
t
2
, the thyristor
biased immediately and
commutation.
During
thyristor
T2
voltage
T1
vac
and
the
T6
T2
is triggered and
T6
is reverse
turns off due to natural
time
period
t
2
to
5
6
,
conduct together and the line to line supply
appears across the load.
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The thyristors are numbered in the circuit diagram
corresponding to the order in which they are triggered. The
trigger sequence (firing sequence) of the thyristors is 12, 23, 34,
45, 56, 61, 12, 23, and so on. The figure shows the waveforms
of three phase input supply voltages, output voltage, the
thyristor current through
T1
and
T4
, the supply current through
the line ‘a’.
We define three line neutral voltages (3 phase voltages) as
follows
vRN
van Vm sin t
vYN
vbn
Vm sin
t
2
3
Vm sin
t 1200
vBN
vcn
Vm sin
t
2
3
Vm sin
t 1200
Where
Vm the
;
Vm
Max. Phase Voltage
Vm sin
t 2400
peak phase voltage of a star (Y) is connected
source.
The corresponding line-to-line voltages are
vRY
vab
van vbn
3Vm sin
t
6
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vYB
vbc
vbn vcn
3Vm sin
t
vBR
vca
vcn van
3Vm sin
t
2
2
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T6
T1
T2
T3
T4
T5
T6
T1
T2
iG1
t
0
iG2
0
(30 + )
0
60
0
(360 +30 + )
t
0
iG3
60
t
0
iG4
60
t
0
iG5
60
t
0
iG6
60
t
Gating (Control) Signals of 3-phase full converter
To derive an expression for the average output voltage of three
phase full converter with highly inductive load assuming
continuous and constant load current
The output load voltage consists of 6 voltage pulses over a
period of 2
radians, hence the average output voltage is
calculated as
VO dc
Vdc
6
2
2
vO .d t
;
6
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vO
vab
3
Vdc
3Vm sin
t
6
2
3Vm sin
t
6
.d t
6
Vdc
3 3Vm
Where
3VmL
cos
VmL
3Vm
cos
Max. line-to-line supply voltage
The maximum average dc output voltage is obtained for a delay
angle
= 0,
Vdc max
3 3Vm
Vdm
3VmL
The normalized average dc output voltage is
Vdcn
Vn
Vdc
Vdm
cos
The rms value of the output voltage is found from
1
2
VO rms
6
2
2
vO2 .d
t
6
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1
2
VO rms
6
2
2
2
vab
.d
t
6
1
2
VO rms
3
2
2
3Vm2 sin 2
t
6
.d
t
6
VO rms
3Vm
1
2
3 3
cos 2
4
1
2
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