voltage controllers
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POWER ELECTRONICSPOWER ELECTRONICS
AC VOLTAGE AC VOLTAGE CONTROLLERSCONTROLLERS
Dr. Adel GastliEmail: [email protected]
http://adel.gastli.net
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 2
INTRODUCTIONINTRODUCTION
•• Purpose:Purpose: control the output rms voltage using SCR- or Triac-type switch.
•• Name:Name: AC Voltage Controller, AC to controlled AC converters or AC regulators
•• Types:Types: there are single-phase and three-phase types of ac voltage controllers
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 3
CHAPTER’S CONTENTCHAPTERCHAPTER’’S CONTENTS CONTENT
1. 1-PHASE AC VOLTAGE CONTROLLERS
2. 3-PHASE AC VOLTAGE CONTROLLERS
3. CYCLOCONVERTERS
4. APPLICATIONS & SUMMARY
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 4
Section 1Section 1
11--PHASE AC VOLTAGE PHASE AC VOLTAGE CONTROLLERSCONTROLLERS
LZ
)sin( tVv sms ω=
Lv
Li
1T
2T
LZ
)sin( tVv sms ω=
Lv
Li
Triac
≡
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 5
SECTION’S CONTENTSSECTIONSECTION’’S CONTENTSS CONTENTS
1. ON-OFF CONTROL
2. PHASE CONTROL
3. SECTION SUMMARY
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 6
ONON--OFF CONTROLOFF CONTROLIntegral half cycle control. Usually used for resistive load.
TN period during cycle half ofnumber :
kVN
nV
N
nVV s
smsrmsrms ===
20
R
)sin( tVv sms ω=
Lv
Li
TN
: period
sv
t0
smV
n
on switch during cycles half ofnumber :nSimilar to chopper principle.Duty
cycle
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 7
PHASE CONTROL: BIPHASE CONTROL: BI--DIRECTIONALDIRECTIONAL
1.1. Resistive LoadResistive Load
sin 1 2
2
0
20 ∫∫ ⋅==
π
α
πθθ
πθ
πd
VdvV sm
Lrms
R
)sin( tVv sms ω=
Lv
Li sv
tω0
smV
απ +α απ +2
( )
2
2sin-
10 ⎟
⎠⎞
⎜⎝⎛ +=
ααππsrms VV
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 8
SIMULINK SIMULATIONSIMULINK SIMULATION
vA
+i
-
iA
g
+
-v
+
-v
a
gk
Triac
g
v0vs
ia
Press toPlot Results
(sp_ac_regm.m)
R=10Ω120V50Hz
(sp_ac_reg.mdl)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 9
0 200 400 600 800 10000
0.5
1
1.5
Ga
te s
ign
al
0 200 400 600 800 1000-200
0
200
Vol
tage
, (V
) vsv0
0 200 400 600 800 1000-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
o45=α
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 10
2.2. Inductive LoadInductive Load
sv
tω0
smV
R
)sin( tVv sms ω=
0v
0i
L
απ +α απ +2
0v
Three cases to be distinguished:i. α > θii. α < θiii. α = θ
0iβ
i) i) αα > > θθ : Discontinuous current
⎟⎠⎞
⎜⎝⎛= −
R
Lωθ 1tan
φ
Current equation is obtained similarly to Chapter 10 (single-phase controlled rectifier).
β is obtained by taking i1(β)=0.
⎟⎠⎞
⎜⎝⎛ −+−=
2
2sin
2
2sin10
βααβπsrms VV
( ) ( )⎥⎥⎦
⎤
⎢⎢⎣
⎡−−−=
⎟⎠⎞
⎜⎝⎛ −⎟⎠⎞
⎜⎝⎛ t
L
R
s etZ
Vi ω
α
θαθω sinsin2
1
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 11
Conduction in one alternance.
ii) ii) αα < < θθ : Not Practical because conduction angle cannot exceed π
srmssm
rms VV
V ==2
0
παβ +>
To be avoidedTo be avoided
iii) iii) αα = = θθ : Continuous conduction
παβ +=
If triac gate pulse is large enough then we will obtain continuous conduction.
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 12
SIMULINK SIMULATIONSIMULINK SIMULATION
R=10Ω120V50Hz
(sp_ac_regm.m)
(sp_ac_reg.mdl)
+ i-
iA
g
+- v
+- v
a
g k
Triac
g
v0vs
ia
Press toPlot Results
R=10ΩL=10mH
120V50Hz
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 13
0 200 400 600 800 10000
0.5
1
1.5
Gat
e si
gnal
0 200 400 600 800 1000-200
0
200
Vol
tage
, (V
) vsv0
0 200 400 600 800 1000-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
o45=α
oo 44.1745 =>= θα
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 14
0 200 400 600 800 10000
0.5
1
1.5
Ga
te s
ign
al
0 200 400 600 800 1000-200
0
200
Vol
tage
, (V
)
vsv0
0 200 400 600 800 1000-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
oo 44.1710 =<= θα Short gate pulse
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 15
oo 44.1710 =<= θα
0 200 400 600 800 10000
0.5
1
1.5
Gat
e si
gna
l
0 200 400 600 800 1000-200
0
200
Vol
tage
, (V
) vsv0
0 200 400 600 800 1000-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
Long gate pulse
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 16
o44.17==θα
0 200 400 600 800 10000
0.5
1
1.5
Ga
te s
ign
al
0 200 400 600 800 1000-200
0
200
Vol
tage
, (V
) vsv0
0 200 400 600 800 1000-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
Continuous conduction
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 17
SECTION SUMMARYSECTION SUMMARY
Single-phase AC voltage rms can be controlled by on-off control or phase delay control.
By controlling the phase delay it is possible to control the AC output voltage rms value between 0 and the source rms voltage value.
It is important to know beforehand the load angle in order to be able to control the output voltage properly.
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 18
Section 2Section 2
33--PHASE AC VOLTAGE PHASE AC VOLTAGE CONTROLLERSCONTROLLERS
LZ
AvAi0
Bv
CvLZLZ
Bi0
Ci0
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 19
SECTION’S CONTENTSSECTIONSECTION’’S CONTENTSS CONTENTS
1. TOPOLOGIES
2. OPERATION
3. SIMULINK SIMULATION
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 20
TOPOLOGIES TOPOLOGIES
LZ
AvAi0
Bv
CvLZLZ
Bi0
Ci0
1
2
3
1T
2T
3T
LZ
AvAi0
Bv
CvLZLZ
Bi0
Ci0
1
2
3
N
1T
2T
3TN
AvAi0
Bv
Cv
Bi0
Ci0
1
2
3
1T
2T
3T
LZ
LZ
LZ
Av
Bv
Cv2T
1
32
1T
3TLZ
LZ
LZ
Equivalent to 3 single-phases Is studied in this chapter
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 21
OPERATION OPERATION
line on line off v12 v1N
A,B, C None VAB VA
A,B C VAB VAB/2A,C B VAC/2 VAC/2B,C A -VBC/2 0None A,B,C 0 0A ImpossibleB ImpossibleC Impossible
LZ
AvAi0
Bv
CvLZLZ
Bi0
Ci0
1
2
3
N
1T
2T
3T
⎪⎪
⎩
⎪⎪
⎨
⎧
=⇒>
⇒<≤
⇒<≤
⇒<≤
V0 conduction no is there150
timeaat conduct switches 2 and 015090
timeaat conduct switches 2only 9060
switches 3 and 2between alternate600
outo
oo
oo
o
vα
α
α
α
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 22
(sp_ac_regm.m)
(sp_ac_reg.mdl)
vCvBvA
+ i-
iC
+ i-
iB
+ i-
iA
+- v
+- v
+- v
+- v
+- v
+- vAin
Bin
Cin
Aout
Bout
Cout
Triac Converter
vAN
van
vCA
vBC
vAB
vab
ic
ib
ia
Press toPlot Results
A
B
C
A
B
C
3- Phase Y-connected Load
120V50Hz
10Ω
SIMULINK SIMULATIONSIMULINK SIMULATION
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 23
0 50 100 150 200 250 300 350
-200
0
200V
olta
ge, (
V)
0 50 100 150 200 250 300 3500
0.5
1
1.5
Ga
te s
ign
al
0 50 100 150 200 250 300 350-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
α
avacv5.0
av
π
abv5.0
3
π απ+
3 3
2π απ+
3
2
av
o30=α Purely resistive load
Pulse width 50%
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 24
0 50 100 150 200 250 300 350
-200
0
200
Vol
tage
, (V
)
0 50 100 150 200 250 300 3500
0.5
1
1.5
Ga
te s
ign
al
0 50 100 150 200 250 300 350-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
o60=α Purely resistive load
abv5.0 acv5.0
α3
2π απ+
3
2
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 25
o120=α Purely resistive load
0 100 200 300 400 500
-200
0
200V
olta
ge, (
V)
0 100 200 300 400 5000
0.5
1
1.5
Ga
te s
ign
al
0 100 200 300 400 500-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
α απ+
3 6
7π6
5π
abv5.0 acv5.0
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 26
o150=α Purely resistive load
0 100 200 300 400 500
-200
0
200
Vol
tage
, (V
)
0 100 200 300 400 5000
0.5
1
1.5
Ga
te s
ign
al
0 100 200 300 400 500-20
0
20
Cur
rent
, (A
)
Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 27
MATHEMATICAL ANALYSIS: (Resistive Load)MATHEMATICAL ANALYSIS: (Resistive Load)
( )
⎟⎠⎞
⎜⎝⎛ +=
⎟⎠⎞
⎜⎝⎛ −=
=
3
2sin2
3
2sin2
sin2
πθ
πθ
θ
sBN
sBN
sAN
Vv
Vv
Vv
iaiL
vAN van
R=1o
T1
T4
vBN
vCN
T3
T6
T5
T2
R=1o
R=1o
ib
ic
NB
C
a
b
A
⎟⎠⎞
⎜⎝⎛ −=
⎟⎠⎞
⎜⎝⎛ −=
⎟⎠⎞
⎜⎝⎛ +=
6sin6
2sin6
6sin6
πθ
πθ
πθ
sCA
sBC
sAB
Vv
Vv
Vv
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 28
( )
( ) ( ) ( ) ( ) ( )⎥⎦
⎤⎢⎣
⎡++++=
=
∫∫∫∫∫
∫
+
+
+
+tdvtd
vtdvtd
vtdv
tdvV
aac
aab
a
an
ωωωωωπ
ωπ
π
απ
απ
π
π
απ
απ
π
π
α
π
3/2
23/2
3/2
23/2
3/
23/
3/
23/ 2
2
0
20
44
1
2
1
o600 <≤α
0 50 100 150 200 250 300 350
-200
0
200
Vol
tage
, (V
)
α
avacv5.0
av
π
abv5.0
3
π απ+
3 3
2π απ+
3
2
av
( ) ( ) ( ) ( ) ( ) ( ) ( )⎥⎦
⎤⎢⎣
⎡+
−++
++= ∫ ∫ ∫∫∫
+
+ +
+απ
π
π
απ
π
απ
απ
π
π
αωωωπωωωωπωωω
π3/
3/
3/2
3/ 3/2
23/2
3/2
2223/
2
0 3
sin
4
6/sin
3
sin
4
6/sin
3
sin16 td
ttd
ttd
ttd
ttd
tVV s
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 29
⎟⎠⎞
⎜⎝⎛ +−=
8
2sin
46
160
ααππsVV
R
VI 0
0 = 000 3 VIP =
Output powerrms output Phase Current
rms Output phase voltage
( ) ( ) ( ) ( ) ( ) ( ) ( )⎥⎦
⎤⎢⎣
⎡+
−++
++= ∫ ∫ ∫∫∫
+
+ +
+απ
π
π
απ
π
απ
απ
π
π
αωωωπωωωωπωωω
π3/
3/
3/2
3/ 3/2
23/2
3/2
2223/
2
0 3
sin
4
6/sin
3
sin
4
6/sin
3
sin16 td
ttd
ttd
ttd
ttd
tVV s
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 30
( )
( ) ( )⎥⎦
⎤⎢⎣
⎡+=
=
∫∫
∫+
+
+td
vtd
v
tdvV
acab
an
ωωπ
ωπ
απ
απ
απ
α
π
3/2
3/
23/
2
2
0
20
44
1
2
1
oo 9060 <≤α
( ) ( ) ( ) ( )⎥⎦
⎤⎢⎣
⎡ −+
+= ∫ ∫
+ +
+
απ
α
απ
απωπωωπω
π3/ 3/2
3/
22
0 4
6/sin
4
6/sin16 td
ttd
tVV s
0 50 100 150 200 250 300 350
-200
0
200
Vol
tage
, (V
)
ααπ
+3
απ+
3
2
abv5.0 acv5.0
( ) ( )⎥⎦
⎤⎢⎣
⎡+= ∫ ∫
++
+
−+
−+
6/3/
6/
6/3/2
6/3/
22
0 4
sin
4
sin16
παπ
πα
παπ
παπωωωω
πtd
ttd
tVV s
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 31
⎟⎟⎠
⎞⎜⎜⎝
⎛++=
16
2cos3
16
2sin3
12
160
ααππsVV
R
VI 0
0 = 000 3 VIP =
Output powerrms output Phase Current
rms Output phase voltage
( ) ( )⎥⎦
⎤⎢⎣
⎡+= ∫ ∫
+
+
+
+
απ
πα
απ
απωωωω
π2/
6/
2/
6/
22
0 4
sin
4
sin16 td
ttd
tVV s
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 32
( )
( ) ( )⎥⎦
⎤⎢⎣
⎡+=
=
∫∫
∫
+td
vtd
v
tdvV
acab
an
ωωπ
ωπ
π
απ
π
α
π
6/7
3/
26/5
2
2
0
20
44
1
2
1
oo 15090 <≤α
( ) ( ) ( )⎥⎦
⎤⎢⎣
⎡ −+
+= ∫ ∫ +
6/5 6/7
3/
22
0 )(4
6/sin
4
6/sin16
π
α
π
απωπωωπω
πtd
ttd
tVV s
⎥⎦
⎤⎢⎣
⎡+= ∫ ∫
+
+
−
−+
6/6/5
6/
6/6/7
6/3/
22
0 )(4
sin)(
4
sin16
ππ
πα
ππ
παπωωωω
πtd
ttd
tVV s
0 100 200 300 400 500
-200
0
200
Vol
tage
, (V
)
α απ+
3 6
7π6
5π
abv5.0 acv5.0
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 33
⎟⎟⎠
⎞⎜⎜⎝
⎛++−=
16
2cos3
16
2sin
424
5160
αααππsVV
R
VI 0
0 = 000 3 VIP =
Output powerrms output Phase Current
rms Output phase voltage
⎥⎦
⎤⎢⎣
⎡+= ∫ ∫+ +
π
απ
π
απωωωω
π 6/ 6/
22
0 )(4
sin)(
4
sin16 td
ttd
tVV s
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 34
Section 3Section 3
CYCLOCONVERTERSCYCLOCONVERTERS
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 35
SECTION’S CONTENTSSECTIONSECTION’’S CONTENTSS CONTENTS
1. SINGLE-PHASE
2. THREE-PHASE
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 36
SINGLESINGLE--PHASE CYCLOCONVERTERPHASE CYCLOCONVERTER
+
−
sv 01v
Load
3T1T
4T 2T
'4T
'2T
'3T '
1T
02v
+
−
P-converter N-converter
sv
t0
smV
P-converter on
N-converter on
cycles) half positive ofnumber (n ==n
ff s
out
⎟⎠⎞
⎜⎝⎛ +−=
= ∫
πααπ
π
θπ
π
α
2sin1
1 20
s
s
V
dvV
α
Variable voltage variable frequency converter output voltage.
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 37
THREETHREE--PHASE CYCLOCONVERTER PHASE CYCLOCONVERTER
+
−
A01v
Load
1T
4T
'2T
'5T
'6T
'3T
02v
+
−P-converter N-converter
3T
6T
5T
2T
BC
'4T
'1T
ABC
Three-phase/single-phase cycloconverter
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 38
Three-phase/three-phase cycloconverter
P N P NP N
Phase a load
Phase b load
Phase c load
Neutral
Three-phase supply
18 thyristors are used to obtain a 3 full-wave three-phase converter.
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 39
Section 4Section 4
APPLICATIONS & SUMMARYAPPLICATIONS & SUMMARY
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 40
APPLICATIONSAPPLICATIONS
Light dimmer.
Soft starting of ac motors (compressors, pumps, etc.)
Variable speed drives for appliances an tools.
Transformer static tap changers.0v
pv
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 41
SUMMARYSUMMARYAc voltage controllers can use on-off control or phase-angle control.The on-off control is more suitable for systems having a high time constant.Due to the switching characteristics of thyristors, an inductive load makes the solutions of equations describing the performance of controllers very complex and simulation is more convenient.The input power factor of controllers, which vary with the delay angle, is generally poor, especially at low voltage output range.