unit 2
TRANSCRIPT
UNIT II
PHASE CONTROLLED CONVERTERS
EE2301- POWERELECTRONICS
Phase-Control ConvertersPhase-Control Converters
Single-PhaseSingle-Phase
SemiconverterSemiconverter
Three-PhaseThree-Phase
Full converterFull converter
Dual converterDual converter
SemiconverterSemiconverter
Full converterFull converter
Dual converterDual converter
EE2301- POWERELECTRONICS
Semiconverter..is a one-quadrant converter and it has one polarity
Semiconverter..is a one-quadrant converter and it has one polarity
Full converter..is a two-quadrant converter and the polarity of its
output can be either positive or negative.However
the output current of full converter has one polarity only
Full converter..is a two-quadrant converter and the polarity of its
output can be either positive or negative.However
the output current of full converter has one polarity only
Dual converter..can operate in four quadrants ; both the output
voltage and current can be either positive or negative
Dual converter..can operate in four quadrants ; both the output
voltage and current can be either positive or negative
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
cos12
sin2
1 mmdc
VttdVV
cos12
sin2
1 mmdc
VttdVV
Average Output VoltageAverage Output Voltage
m
dm
VV
m
dm
VV Maximum
Output Voltage
MaximumOutput Voltage
cos15.0 dm
dcn V
VV cos15.0
dm
dcn V
VVNormalizing
Output Voltage
NormalizingOutput Voltage
2
2sin1
2sin
2
1 22
mmrms
VttdVV
2
2sin1
2sin
2
1 22
mmrms
VttdVV
RMS Output VoltageRMS Output Voltage
EE2301- POWERELECTRONICS
If the converter has a purely resistive load of R and the delay angle is , determine
(a) the rectification efficiency(b) the form factor FF(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
If the converter has a purely resistive load of R and the delay angle is , determine
(a) the rectification efficiency(b) the form factor FF(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
2/
EE2301- POWERELECTRONICS
%27.203536.0
1592.0
3536.02
22
sin2
1
2
1592.0
2cos1
2sin
2
1
2
2
2
2
2
m
m
rms
dc
mm
rms
mdc
mmdc
V
V
V
V
VV
V
VV
VttdVV
%27.203536.0
1592.0
3536.02
22
sin2
1
2
1592.0
2cos1
2sin
2
1
2
2
2
2
2
m
m
rms
dc
mm
rms
mdc
mmdc
V
V
V
V
VV
V
VV
VttdVV
EE2301- POWERELECTRONICS
If the converter has a purely resistive load of R and the delay angle is , determine
(a) the rectification efficiency(b) the form factor FF(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
If the converter has a purely resistive load of R and the delay angle is , determine
(a) the rectification efficiency(b) the form factor FF(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
2/
221.21592.0
3536.0
m
m
dc
rms
V
V
V
VFF 221.2
1592.0
3536.0
m
m
dc
rms
V
V
V
VFF
EE2301- POWERELECTRONICS
If the converter has a purely resistive load of R and the delay angle is , determine
(a) the rectification efficiency(b) the form factor FF(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
If the converter has a purely resistive load of R and the delay angle is , determine
(a) the rectification efficiency(b) the form factor FF(c) the ripple factor RF
and (d) the peak inverse voltage PIV of thyristor T1
2/
983.11221.21 22 FFRF 983.11221.21 22 FFRF
mVPIV mVPIV
EE2301- POWERELECTRONICSSemiconverter
EE2301- POWERELECTRONICS
Single-Phase SemiconverterSingle-Phase Semiconverter
ttdVV
VttdVV
mrms
mmdc
22 sin2
2
cos1sin2
2
ttdVV
VttdVV
mrms
mmdc
22 sin2
2
cos1sin2
2
EE2301- POWERELECTRONICS
Single-Phase Semiconverter (RL-load)Single-Phase Semiconverter (RL-load)
L
R
L
R
LLL
LL
eR
EeItiI
ERidt
diL
1
0
011
11
L
R
L
R
LLL
LL
eR
EeItiI
ERidt
diL
1
0
011
11
tL
RS
LS
L
SLL
eZ
V
R
EI
R
Et
Z
VI
tVERidt
diL
sin2
sin2
sin2
12
22
tL
RS
LS
L
SLL
eZ
V
R
EI
R
Et
Z
VI
tVERidt
diL
sin2
sin2
sin2
12
22
Mode 1Mode 1 t0
Mode 2Mode 2 t
R
L 1tan R
L 1tan 22 LRZ 22 LRZ
EE2301- POWERELECTRONICS
Single-Phase Semiconverter (RL-load)Single-Phase Semiconverter (RL-load)
RMS Currentfor Thyristor
RMS Currentfor Thyristor
tdiI LR
222
1
RMS Currentfor Thyristor
RMS Currentfor Thyristor
tdiI LA 22
1
RMS OutputCurrent
RMS OutputCurrent
tditdiI LLrms
220
21 2
1
2
1
AVG OutputCurrent
AVG OutputCurrent
tditdiIdc 20 1 2
1
2
1
EE2301- POWERELECTRONICS
The single-phase semiconverter has an RL load of L = 6.5mH, R = 2.5 Ohm, and E = 10 V. The input v
oltage is VS = 120 V(rms) at 60 Hz. Determine(a) the load current IL0 at , and the load curren
t IL1 at ,(b) the average thyristor current IA
(c) the rms thyristor current IR
(d) the rms output current Irms
and (e) the average output current Idc
The single-phase semiconverter has an RL load of L = 6.5mH, R = 2.5 Ohm, and E = 10 V. The input v
oltage is VS = 120 V(rms) at 60 Hz. Determine(a) the load current IL0 at , and the load curren
t IL1 at ,(b) the average thyristor current IA
(c) the rms thyristor current IR
(d) the rms output current Irms
and (e) the average output current Idc
0t 60t
EE2301- POWERELECTRONICS
Single-PhaseFull Converter
RectificationMode
RectificationMode
InversionMode
InversionMode
EE2301- POWERELECTRONICS
Single-Phase Full ConverterSingle-Phase Full Converter
2
sin2
2
cos2
sin2
2
22 mmrms
mmdc
VtdtVV
VtdtVV
2
sin2
2
cos2
sin2
2
22 mmrms
mmdc
VtdtVV
VtdtVV
EE2301- POWERELECTRONICS
Single-Phase Full Converter (RL-load)Single-Phase Full Converter (RL-load)
tL
RS
LS
L eZ
V
R
EI
R
Et
Z
VI
sin2
sin2
0 tL
RS
LS
L eZ
V
R
EI
R
Et
Z
VI
sin2
sin2
0
Mode 1 = Mode 2Mode 1 = Mode 2R
L 1tan R
L 1tan 22 LRZ 22 LRZ
EE2301- POWERELECTRONICS
Single-Phase Full Converter (RL-load)Single-Phase Full Converter (RL-load)
RMS Currentfor Thyristor
RMS Currentfor Thyristor
tdiI LR
2
2
1
RMS Currentfor Thyristor
RMS Currentfor Thyristor
tdiI LA 2
1
RMS OutputCurrent
RMS OutputCurrent RRRrms IIII 222
AVG OutputCurrent
AVG OutputCurrent AAAdc IIII 2
EE2301- POWERELECTRONICS
DualConverter
EE2301- POWERELECTRONICS
Single-Phase Dual ConverterSingle-Phase Dual Converter
High-Power Variable-Speed DrivesHigh-Power Variable-Speed Drives
21
22
11
cos2
cos2
dcdc
mdc
mdc
VV
VV
VV
21
22
11
cos2
cos2
dcdc
mdc
mdc
VV
VV
VV
EE2301- POWERELECTRONICS
Three-PhaseSemiconverter
EE2301- POWERELECTRONICS
3 Phase Controlled Rectifiers
• Operate from 3 phase ac supply voltage.
• They provide higher dc output voltage.
• Higher dc output power.
• Higher output voltage ripple frequency.
• Filtering requirements are simplified for smoothing out load voltage and load current.
EE2301- POWERELECTRONICS
• Extensively used in high power variable speed industrial dc drives.
• Three single phase half-wave converters can be connected together to form a three phase half-wave converter.
EE2301- POWERELECTRONICS
3-Phase Half Wave Converter(3-Pulse Converter)
with RL Load
Continuous & ConstantLoad Current Operation
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
Vector Diagram of 3 Phase Supply Voltages
V A N
V C N
V B N
1 2 00
1 2 00
1 2 00 RN AN
YN BN
BN CN
v v
v v
v v
EE2301- POWERELECTRONICS
3 Phase Supply Voltage Equations
We deifine three line to neutral voltages
(3 phase voltages) as follows
EE2301- POWERELECTRONICS
0
0
0
sin ;
Max. Phase Voltage
2sin
3
sin 120
2sin
3
sin 120
sin 240
RN an m
m
YN bn m
m
BN cn m
m
m
v v V t
V
v v V t
V t
v v V t
V t
V t
EE2301- POWERELECTRONICS
van vbn vcn van
EE2301- POWERELECTRONICS
io=Ia
Constant Load Current
Ia
Ia
Each thyristor conducts for 2/3 (1200)
EE2301- POWERELECTRONICS
To Derive an Expression for the
Average Output Voltage of a 3-Phase Half Wave Converter
with RL Loadfor Continuous Load Current
EE2301- POWERELECTRONICS
01
02
03
0
306
5 150
6
7 270
6
2Each thytistor conducts for 120 or radians
3
T is triggered at t
T is triggered at t
T is triggered at t
EE2301- POWERELECTRONICS
5
6
6
5
6
6
3sin .
2
3cos
2
3 5cos cos
2 6 6
mdc
mdc
mdc
VV t d t
VV t
VV
EE2301- POWERELECTRONICS
0 0
0
Note from the trigonometric relationship
cos cos .cos sin .sin
5 5cos cos sin sin
6 63
2co
cos 150 cos sin 150 sin3
2 cos 30
s .cos sin sin6 6
.cosm
dc
mdc
A
VV
B A B A B
VV
0sin 30 sin
EE2301- POWERELECTRONICS
0 0
0 0 0 0
0 0
0 0
0
0
0
0
0 0
Note: cos 1
cos 180 30 cos sin 180 30 sin3
2 cos 30 .cos sin 30 sin
cos 30 cos sin 30 sin3
2 cos 30 .cos sin 30 s
80 30 cos 30
sin 180 30 sin 30
in
mdc
mdc
VV
VV
EE2301- POWERELECTRONICS
032cos 30 cos
2
3 32 cos
2 2
3 3 33 cos cos
2 23
cos2
Where 3 Max. line to line supply voltage
mdc
mdc
m mdc
Lmdc
Lm m
VV
VV
V VV
VV
V V
EE2301- POWERELECTRONICS
max
The maximum average or dc output voltage is
obtained at a delay angle 0 and is given by
3 3
2Where is the peak phase voltage.
And the normalized average output voltage is
mdmdc
m
ddcn n
VV V
V
VV V
cosc
dmV
EE2301- POWERELECTRONICS
15 26
2 2
6
1
2
The rms value of output voltage is found by
using the equation
3sin .
2
and we obtain
1 33 cos 2
6 8
mO RMS
mO RMS
V V t d t
V V
EE2301- POWERELECTRONICS
3 Phase Half Wave Controlled Rectifier Output Voltage Waveforms For RL
Load at
Different Trigger Angles
EE2301- POWERELECTRONICS
0
0
300
300
600
600
900
900
1200
1200
1500
1500
1800
1800
2100
2100
2400
2400
2700
2700
3000
3000
3300
3300
3600
3600
3900
3900
4200
4200
V an
V 0
V 0
V an
= 300
= 600
V bn
V bn
V cn
V cn
t
t
=300
=600
EE2301- POWERELECTRONICS
030
060
090
0120
0150
0180
0210
0240
0270
0300
0330
0360
0390
0420
0
V 0
V an
= 900
V bn V cn
t
=900
EE2301- POWERELECTRONICS
3 Phase Half Wave Controlled Rectifier With
R Load and
RL Load with FWD
EE2301- POWERELECTRONICS
a a
b b
c c
RV 0
L
R V 0
+
T 1
T 2
T 3
n n
T 1
T 2
T 3
EE2301- POWERELECTRONICS
3 Phase Half Wave Controlled Rectifier Output
Voltage Waveforms For R Load or RL Load with FWD
atDifferent Trigger Angles
EE2301- POWERELECTRONICS
0
0
3 00
3 00
6 00
6 00
9 00
9 00
1 2 00
1 2 00
1 5 00
1 5 00
1 8 00
1 8 00
2 1 00
2 1 00
2 4 00
2 4 00
2 7 00
2 7 00
3 0 00
3 0 00
3 3 00
3 3 00
3 6 00
3 6 00
3 9 00
3 9 00
4 2 00
4 2 00
V s
V 0
V a n
= 0
= 1 5 0
V b n V c n
t
V a n V b n V c n
t
=00
=150
EE2301- POWERELECTRONICS
0
0
3 00
3 00
6 00
6 00
9 00
9 00
1 200
1 200
1 500
1 500
1 800
1 800
2 100
2 100
2 400
2 400
2 700
2 700
3 000
3 000
3 300
3 300
3 600
3 600
3 900
3 900
4 200
4 200
V 0
= 3 0 0
V a nV b n V c n
t
V 0
= 6 0 0
V a nV b n V c n
t
=300
=600
EE2301- POWERELECTRONICS
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
EE2301- POWERELECTRONICS
01
0 01
02
0 02
0
306
30 180 ;
sin
5 150
6
150 300 ;
sin 120
O an m
O bn m
T is triggered at t
T conducts from to
v v V t
T is triggered at t
T conducts from to
v v V t
EE2301- POWERELECTRONICS
03
0 03
0
0
7 270
6
270 420 ;
sin 240
sin 120
O cn m
m
T is triggered at t
T conducts from to
v v V t
V t
EE2301- POWERELECTRONICS
0
0
0
0
0
0
180
30
0 0
180
30
180
30
3.
2
sin ; for 30 to 180
3sin .
2
3sin .
2
dc O
O an m
dc m
mdc
V v d t
v v V t t
V V t d t
VV t d t
EE2301- POWERELECTRONICS
0
0
180
30
0 0
0
0
3cos
2
3cos180 cos 30
2
cos180 1, we get
31 cos 30
2
mdc
mdc
mdc
VV t
VV
VV
EE2301- POWERELECTRONICS
Three Phase Semiconverters
• 3 Phase semiconverters are used in Industrial dc drive applications upto 120kW power output.
• Single quadrant operation is possible.• Power factor decreases as the delay angle
increases.• Power factor is better than that of 3 phase half
wave converter.
EE2301- POWERELECTRONICS
3 Phase Half Controlled Bridge Converter
(Semi Converter)with Highly Inductive Load & Continuous Ripple free Load
Current
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
Wave forms of 3 Phase Semiconverter for
> 600
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
0 0
1
3 phase semiconverter output ripple frequency of
output voltage is 3
The delay angle can be varied from 0 to
During the period
30 210
7, thyristor T is forward biased
6 6
Sf
t
t
EE2301- POWERELECTRONICS
1
1 1
If thyristor is triggered at ,6
& conduct together and the line to line voltage
appears across the load.
7At , becomes negative & FWD conducts.
6The load current contin
ac
ac m
T t
T D
v
t v D
1 1
ues to flow through FWD ;
and are turned off.mD
T D
EE2301- POWERELECTRONICS
1
2
1 2
If FWD is not used the would continue to
conduct until the thyristor is triggered at
5, and Free wheeling action would
6
be accomplished through & .
If the delay angle , e3
mD T
T
t
T D
ach thyristor conducts
2for and the FWD does not conduct.
3 mD
EE2301- POWERELECTRONICS
0
0
0
We deifine three line neutral voltages
(3 phase voltages) as follows
sin ; Max. Phase Voltage
2sin sin 120
3
2sin sin 120
3
sin 240
RN an m m
YN bn m m
BN cn m m
m
v v V t V
v v V t V t
v v V t V t
V t
V
is the peak phase voltage of a wye-connected source.m
EE2301- POWERELECTRONICS
3 sin6
53 sin
6
3 sin2
3 sin6
RB ac an cn m
YR ba bn an m
BY cb cn bn m
RY ab an bn m
v v v v V t
v v v v V t
v v v v V t
v v v v V t
EE2301- POWERELECTRONICS
Wave forms of 3 Phase Semiconverter for
600
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
To derive an Expression for the
Average Output Voltage of 3 Phase Semiconverter
for > / 3 and Discontinuous Output Voltage
EE2301- POWERELECTRONICS
76
6
76
6
For and discontinuous output voltage:3
the Average output voltage is found from
3.
2
33 sin
2 6
dc ac
dc m
V v d t
V V t d t
EE2301- POWERELECTRONICS
max
3 31 cos
23
1 cos2
3 Max. value of line-to-line supply voltage
The maximum average output voltage that occurs at
a delay angle of 0 is
3 3
mdc
mLdc
mL m
mdmdc
VV
VV
V V
VV V
EE2301- POWERELECTRONICS
17 26
2
6
The normalized average output voltage is
0.5 1 cos
The rms output voltage is found from
3.
2
dcn
dm
acO rms
VV
V
V v d t
EE2301- POWERELECTRONICS
• Resistive Load
)3/4sin(2
)3/2sin(2
)sin(2
tVv
tVv
tVv
PHc
PHb
PHa
)6/sin(2 tVvvv LLbaab
Supply Voltages:
ai
bi
ci
1D 3D 5D
4D 6D 2D
dv
av
bv
cv
di
dR
a
b
c
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Waveforms
dvabv acv
1A
bcv cav cbvdv
bav
doV
I II
bv cv avv
0
0
0
ai
61, DD 21, DDON
2t
t
t2
abv
6
2
av
ON
)(6/sin23/
13/
area 2/6/ tdtVV LLdo
1A
LLLL VV 35.123
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Capacitive Load
dCdV
(a)
dV
(b)
R
ai
bi
ci
1D 3D 5D
4D 6D 2D
di
a
b
c
sLav
bv
cv
sL
sL
Assumption:
constant dd VC
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Waveforms
t
t
t
t
t
abv acv bcv bav cav cbv abv acv
2ai
bi
di
61, DD 2
ci
ON21, DD
ON
v
0
0
0
0
0
dV
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Discontinuous Current Operation
3/
1 2 3
di
v abv acv
t
t
dV
3/
4
0
0
pI
5
LL
d
V
V
2sin 1
1
12
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Discontinuous Current Operation
3/
1 2 3
di
v abv acv
t
t
dV
3/
4
0
0
pI
5
Differential Equation: dabd
s Vvdt
idL 2 31 t
11 coscos22
1
sin22
11
dLLs
dLLs
d
VVL
tdVtVL
iSolution:
dV
ai
bi
ci
1D 3D 5D
4D 6D 2D
di
a
b
c
sLav
bv
cv
sL
sL
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Discontinuous Current Operation
3/
1 2 3
di
v abv acv
t
t
dV
3/
4
0
0
pI
5
Peak dc current:
Average dc current:
2121 coscos22
1
dLLs
p VVL
I
Voltage – theta relation:31
31 coscos
2
LL
d
V
V
diI dd 3
13/
1
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Continuous Current Operation
di
ici
D2 , D3D1 , D2
D1D2D3
I IIIII
On-stateDiode
2
pIbi
t
t
ai
pI
aibi ci
cdV
ai
bi
ci
1D 3D 5D
4D 6D 2D
di
a
b
c
sLav
bv
cv
sL
sL
Note: - With the increase of the load current, the rectifier will enter into continuous current operation. - During commutation interval, three diodes are on.
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Definition of Total Harmonic Distortion (THD)
Phase voltage (pure sine):
Line current (distorted):
RMS line current:
Line current THD:
nnann
a tIi
)(sin2,...3,2,1
2/1
,...3,2,1
22/1
2
0
2 )(2
1
nanaa ItdiI
1
21
2
a
aa
I
IITHD
tVv aa 1sin2
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
• Definition of Power Factor (PF)
Per-phase average (real) power:
Per-phase apparent power:
Total power factor (PF):
Distortion factor (DF) :
Displacement power factor (DPF) :
tdivP aa
2
02
111 cosaa IV
aa IVS
DPFDFI
I
IV
IV
S
PPF
a
a
aa
aa 1111 cos
cos
aa IIDF /1
1cosDPF
PF = f (THD) :21 THD
DPFPF
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
ai
1ai 1.41
0 2 3 4
0.282
ai
1ai
1.00
0.50
0.00
-0.50
-1.00
2.00
1.00
0.00
-1.00
-2.00
(a) Ia1 = 0.2 pu
(b) Ia1 = 1 pu
Harmonics n
5 7 11 13 17 19 23 25 THD (%)
1/ aan II (%)
pu2.01aI 63.4 38.7 8.99 8.64 4.22 3.61 2.48 2.02 75.7
1/ aan II (%)
pu11aI 30.4 8.79 6.31 3.40 2.30 1.89 1.04 1.03 32.7
• Typical Waveforms / Harmonic Content
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
A
B
C
1.0PF
0.6
0.8
0.7
0.9
A
B
C
(b) PF
100THD(%)
20
60
40
80
(a) THD
A: Ls = 0.05B: Ls = 0.10C: Ls = 0.15
A: Ls = 0.05B: Ls = 0.10C: Ls = 0.15
0.2 0.4 0.6 0.8 1aI0 (pu) 0.2 0.4 0.6 0.8 1aI0 (pu)
• THD and PF
Six-pulse Diode Rectifier
EE2301- POWERELECTRONICS
Inductive load, quantitative analysis Differential equation
The RMS value of output voltage, output current, and thyristor current can then be
calculated.
0
sin2d
d
o
1oo
ti
tURit
iL
0 20 10060 140 180
20
100
4-3图
60
/(°
)
180
140
/(° )
( 4 - 5 )
S o l u t i o n
tetZ
Ui
t
tg1o )sin()sin(
2
( 4 - 6 ) C o n s i d e r i n g i o = 0 w h e n ω t = α + θ
W e h a v e
tg)sin()sin(
e ( 4 - 7 )
EE2301- POWERELECTRONICS
Three Phase Dual Converters
• For four quadrant operation in many industrial variable speed dc drives , 3 phase dual converters are used.
• Used for applications up to 2 mega watt output power level.
• Dual converter consists of two 3 phase full converters which are connected in parallel & in opposite directions across a common load.
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
EE2301- POWERELECTRONICS
Outputs of Converters 1 & 2
• During the interval (/6 + 1) to (/2 + 1), the line to line voltage vab appears across the output of converter 1 and vbc appears across the output of converter 2
EE2301- POWERELECTRONICS
0
0
0
We deifine three line neutral voltages
(3 phase voltages) as follows
sin ;
Max. Phase Voltage
2sin sin 120
3
2sin sin 120
3
sin 240
RN an m
m
YN bn m m
BN cn m m
m
v v V t
V
v v V t V t
v v V t V t
V t
EE2301- POWERELECTRONICS
0
0
0
We deifine three line neutral voltages
(3 phase voltages) as follows
sin ;
Max. Phase Voltage
2sin sin 120
3
2sin sin 120
3
sin 240
RN an m
m
YN bn m m
BN cn m m
m
v v V t
V
v v V t V t
v v V t V t
V t
EE2301- POWERELECTRONICS
To obtain an Expression for the Circulating Current
If vO1 and vO2 are the output voltages of converters 1 and 2 respectively, the instantaneous voltage across the current limiting inductor during the interval (/6 + 1) t (/2 + 1) is given by
EE2301- POWERELECTRONICS
1 2
3 sin sin6 2
3 cos6
The circulating current can be calculated by
using the equation
r O O ab bc
r m
r m
v v v v v
v V t t
v V t
EE2301- POWERELECTRONICS
1
1
6
6
1
max
1.
13 cos .
6
3sin sin
6
3
t
r rr
t
r mr
mr
r
mr
r
i t v d tL
i t V t d tL
Vi t t
L
Vi
L
EE2301- POWERELECTRONICS
Four Quadrant Operation
EE2301- POWERELECTRONICS
• There are two different modes of operation. Circulating current free
(non circulating) mode of operation Circulating current mode of operation
EE2301- POWERELECTRONICS
Non Circulating Current Mode Of Operation
• In this mode of operation only one converter is switched on at a time
• When the converter 1 is switched on,
For 1 < 900 the converter 1 operates in the Rectification mode
Vdc is positive, Idc is positive and hence the average load power Pdc is positive.
• Power flows from ac source to the load
EE2301- POWERELECTRONICS
• When the converter 1 is on,
For 1 > 900 the converter 1 operates in the Inversion mode
Vdc is negative, Idc is positive and the average load power Pdc is negative.
• Power flows from load circuit to ac source.
EE2301- POWERELECTRONICS
• When the converter 2 is switched on,
For 2 < 900 the converter 2 operates in the Rectification mode
Vdc is negative, Idc is negative and the average load power Pdc is positive.
• The output load voltage & load current reverse when converter 2 is on.
• Power flows from ac source to the load
EE2301- POWERELECTRONICS
• When the converter 2 is switched on,
For 2 > 900 the converter 2 operates in the Inversion mode
Vdc is positive, Idc is negative and the average load power Pdc is negative.
• Power flows from load to the ac source.• Energy is supplied from the load circuit to the ac
supply.
EE2301- POWERELECTRONICS
• Both the converters are switched on at the same time.
• One converter operates in the rectification mode while the other operates in the inversion mode.
• Trigger angles 1 & 2 are adjusted such that (1 + 2) = 1800
Circulating Current Mode Of Operation
EE2301- POWERELECTRONICS
When 1 < 900, converter 1 operates as a controlled rectifier. 2 is made greater than 900 and converter 2 operates as an Inverter.
• Vdc is positive & Idc is positive and Pdc is positive.
EE2301- POWERELECTRONICS
• When 2 < 900, converter 2 operates as a controlled rectifier. 1 is made greater than 900 and converter 1 operates as an Inverter.
• Vdc is negative & Idc is negative and Pdc is positive.