Chapter 2 AC to DC Converters (Rectifiers)libvolume3.xyz/electrical/btech/semester7/computer...Power...
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P o w e r E l e c t r o n i c s P o w e r E l e c t r o n i c s Chapter 2 AC to DC Converters (Rectifiers)
Transcript of Chapter 2 AC to DC Converters (Rectifiers)libvolume3.xyz/electrical/btech/semester7/computer...Power...
Power ElectronicsPower Electronics
Chapter 2
AC to DC Converters
(Rectifiers)
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OutlineOutline2.1 Single2.1 Single--phase controlled rectifierphase controlled rectifier
2.2 Three2.2 Three--phase controlled rectifier phase controlled rectifier
2.3 Effect of transformer leakage inductance on 2.3 Effect of transformer leakage inductance on rectifier circuitsrectifier circuits
2.4 Capacitor2.4 Capacitor--filtered uncontrolled rectifierfiltered uncontrolled rectifier
2.5 Harmonics and power factor of rectifier circuits2.5 Harmonics and power factor of rectifier circuits
2.6 High power controlled rectifier2.6 High power controlled rectifier
2.7 Inverter mode operation of rectifier circuit2.7 Inverter mode operation of rectifier circuit
2.8 2.8 ThyristorThyristor--DC motor systemDC motor system
2.9 Realization of phase2.9 Realization of phase--control in rectifier circuitscontrol in rectifier circuits
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2.1 Single2.1 Single--phase controlled phase controlled (controllable) rectifier(controllable) rectifier
2.1.1 Single2.1.1 Single--phase halfphase half--wave controlled rectifierwave controlled rectifier
2.1.2 Single2.1.2 Single--phase bridge fullyphase bridge fully--controlled rectifier controlled rectifier
2.1.3 Single2.1.3 Single--phase fullphase full--wave controlled rectifierwave controlled rectifier
2.1.4 Single2.1.4 Single--phase bridge halfphase bridge half--controlled rectifiercontrolled rectifier
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2.1.1 Single2.1.1 Single--phase halfphase half--wavewavecontrolled rectifiercontrolled rectifier
HalfHalf--wave, singlewave, single--pulsepulseTriggering delay angle, delay angle, firing angleTriggering delay angle, delay angle, firing angle
Resistive loadResistive load
T VT
Ru1 u2
uVTud
id
a)
0 ωt1 π 2π ωt
ωt
ωt
ωt
u2
ug
ud
uVT
α θ
0
b)
c)
d)
e)
0
0
∫+
=+==π
α
ααπ
ωωπ 2
cos145.0)cos1(22)(sin2
21
22
2d UUttdUU (2-1)
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2.1.1 Single2.1.1 Single--phase halfphase half--wave wave controlled rectifiercontrolled rectifier
Inductive (resistorInductive (resistor--inductor) loadinductor) loadu2
0 ωt1 π 2π ωt
ωt
ωt
ωt
ωt
ug
0
ud
0
id
0uVT
0
θ
α
b)
c)
d)
e)
f)
+ +
a) u1
TVT
u2
uVTud
id
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Basic thought process of timeBasic thought process of time--domain domain analysis for power electronic circuitsanalysis for power electronic circuits
The timeThe time--domain behavior of a power electronic domain behavior of a power electronic circuit is actually the combination of consecutive circuit is actually the combination of consecutive transients of the different linear circuits when the transients of the different linear circuits when the power semiconductor devices are in different states.power semiconductor devices are in different states.
a) b)
VT
R
L
VT
R
L
u2u2
tURitiL ωsin2
dd
2dd =+
)sin(2)sin(2 2)(
2d ϕωϕα
αωω −+−−=
−−t
ZUe
ZUi
tL
R
ωt = α ，id= 0
(2-3)
(2-2)
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SingleSingle--phase halfphase half--wave controlled wave controlled rectifier with freewheeling dioderectifier with freewheeling diode
Maximum forward voltage, maximum reverse voltageMaximum forward voltage, maximum reverse voltageDisadvantages:Disadvantages:–– Only single pulse in one line cycleOnly single pulse in one line cycle–– DC component in the transformer currentDC component in the transformer current
Inductive load (L is large enough) Inductive load (L is large enough) VT i
a)
T
u 1 u 2
uVT
L
R
d
ud
VD
i
R
VDR
u2
ud
id
uVT
iVT Id
Id
ωt1 ωt
ωt
ωt
ωt
ωt
ωtO
O
O
O
O
O
π-α π+α
b)
c)
d)
e)
f)
g)
iVDR
ddVT 2II
παπ −
=
d2dVT 2
)(21 ItdII
παπω
ππ
α
−== ∫
(2-5)
(2-6)
(2-7)
(2-8)
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2.1.2 Single2.1.2 Single--phase bridge phase bridge fullyfully--controlled rectifiercontrolled rectifier
For For thyristorthyristor: maximum forward voltage, maximum reverse : maximum forward voltage, maximum reverse voltagevoltageAdvantages: Advantages: –– 2 pulses in one line cycle2 pulses in one line cycle–– No DC component in the transformer currentNo DC component in the transformer current
Resistive loadResistive load
d
R
T
u 1 u2
i2a
bV
T1
VT
3
VT 2
VT
4
ud
i π ωt
ωt
ωt0
0
0
i2
udid
b)
c)
d)
ud(id)
α α
uVT1,4
a)
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2.1.2 Single2.1.2 Single--phase bridge fullyphase bridge fully--controlled rectifiercontrolled rectifier
Resistive loadResistive load
Average output (rectified) voltage Average output (rectified) voltage
((22--9)9)
Average output currentAverage output current
(2(2--10)10)
For For thyristorthyristor
(2(2--11)11)
(2(2--12)12)
For transformerFor transformer
(2(2--13)13)
∫+
=+
==π
α
ααπ
ωωπ 2
cos19.02cos122)(dsin21
22
2d UUttUU
2cos19.0
2cos122 22d
dαα
π+
=+
==R
URU
RUI
2cos145.0
21 2
ddVTα+
==R
UII
παπα
πωω
ππ
α
−+== ∫ 2sin
21
2)(d)sin2(
21 222
VT RUtt
RUI
παπα
πωω
ππ
α
−+=== ∫ 2sin
21)()sin2(1 222
2 RUtdt
RUII
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2.1.2 Single2.1.2 Single--phase bridge phase bridge fullyfully--controlled rectifiercontrolled rectifier
CommutationCommutationThyristorThyristor voltages and currentsvoltages and currentsTransformer currentTransformer current
Inductive loadInductive load(L is large enough)(L is large enough)
T a
b R
L
a)
u1 u2
i2
VT 1
VT 3
VT 2
VT 4
ud
id
u2
O ωt
O ωt
O ωt
ud
id
i2
b)
O ωt
O ωt
uVT1,4
O ωt
O ωt
Id
Id
Id
Id
Id
iVT2,3
iVT1,4
∫+
===απ
ααα
πωω
πcos9.0cos22)(dsin21
222d UUttUU (2-15)
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ElectroElectro--motivemotive--force (EMF) loadforce (EMF) load
Discontinuous current iDiscontinuous current idd
With resistorWith resistor
a) b)
R
E
id
ud id
O
Eud
ωt
Id
O ωt
α θ δ
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ElectroElectro--motivemotive--force (EMF) loadforce (EMF) loadWith resistor and inductorWith resistor and inductor
When L is large enough, the output voltage and When L is large enough, the output voltage and current waveforms are the same as ordinary current waveforms are the same as ordinary inductive load.inductive load.When L is at a critical valueWhen L is at a critical value
O
ud
0
E
id
ωt
ωt
π
δα θ =π
dmin
23
dmin
2 1087.222IU
IUL −×==
πω(2-17)
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2.1.3 Single2.1.3 Single--phase fullphase full--wave wave controlled rectifiercontrolled rectifier
Transformer with center tapTransformer with center tapComparison with singleComparison with single--phase bridge fullyphase bridge fully--controlled rectifiercontrolled rectifier
a) b)
u1
T
R
u2u2
i1VT1
VT2 ud
ud
i1
O
O
α ωt
ωt
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2.1.4 Single2.1.4 Single--phase bridge phase bridge halfhalf--controlled rectifiercontrolled rectifier
HalfHalf--controlcontrolComparison with fullyComparison with fully--controlled rectifiercontrolled rectifierAdditional freewheeling diodeAdditional freewheeling diode
Ob)
u2
O
ud
id Id
O
O
O
O
Oi2
Id
Id
Id
Id
Idα
ωt
ωt
ωt
ωt
ωt
ωt
ωt
α
π−α
π−α
iVT1iVD4iVT2iVD3
iVDR
a
b R
Lu2
i2
ud
idVT
1
VT
2
VD
3
VD
4
VD
R
T
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Another singleAnother single--phase bridge phase bridge halfhalf--controlled rectifiercontrolled rectifier
Comparison with previous circuit:Comparison with previous circuit:–– No need for additional freewheeling diodeNo need for additional freewheeling diode–– Isolation is necessary between the drive circuits of the two Isolation is necessary between the drive circuits of the two
thyristorsthyristors
T
u2
VD
3V
D4
VT 1
VT 2
load
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Summary of some important Summary of some important points in analysispoints in analysis
When analyzing a When analyzing a thyristorthyristor circuit, start from a diode circuit with circuit, start from a diode circuit with the same topology. The behavior of the diode circuit is exactlythe same topology. The behavior of the diode circuit is exactlythe same as the the same as the thyristorthyristor circuit when firing angle is 0. circuit when firing angle is 0.
A power electronic circuit can be considered as different lineaA power electronic circuit can be considered as different linear r circuits when the power semiconductor devices are in different circuits when the power semiconductor devices are in different states. The timestates. The time--domain behavior of the power electronic domain behavior of the power electronic circuit is actually the combination of consecutive transients ofcircuit is actually the combination of consecutive transients ofthe different linear circuits. the different linear circuits.
Take different principle when dealing with different loadTake different principle when dealing with different load–– For resistive load: current waveform of a resistor is the same For resistive load: current waveform of a resistor is the same as as
the voltage waveformthe voltage waveform
–– For inductive load with a large inductor: the inductor current For inductive load with a large inductor: the inductor current can can be considered constantbe considered constant
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2.2 Three2.2 Three--phase controlled phase controlled (controllable) rectifier(controllable) rectifier
2.2.1 Three2.2.1 Three--phase halfphase half--wave controlled rectifierwave controlled rectifier
(the basic circuit among three(the basic circuit among three--phase rectifiers)phase rectifiers)
2.2.2 Three2.2.2 Three--phase bridge fullyphase bridge fully--controlled rectifier controlled rectifier
(the most widely used circuit among three(the most widely used circuit among three--phase phase rectifiers)rectifiers)
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2.2.1 Three2.2.1 Three--phase halfphase half--wave wave controlled rectifiercontrolled rectifier
CommonCommon--cathode connectioncathode connectionNatural commutation pointNatural commutation point
Resistive load, Resistive load, α α = 0= 0ºº
T
R
ud
id
VT2
VT1
VT3
u2ua ub uc
O ωt1 ωt2 ωt3
uG
Oud
O
O
uab uac
O
iVT1
uVT1
ωt
ωt
ωt
ωt
ωt
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Resistive load, Resistive load, α α = 30= 30ºº
T
R
ud
id
VT2
VT1
VT3
u2 ua ub uc
O ωt
O ωt
O ωt
O ωt
O ωt
uG
ud
uab uac
ωt1iVT1
uVT1 uac
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Resistive load, Resistive load, α α = 60= 60ºº
T
R
ud
id
VT2
VT1
VT3
ωt
ωt
ωt
ωt
u2 ua ub uc
O
O
O
O
uG
ud
iVT1
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Resistive load, quantitative analysisResistive load, quantitative analysisWhen When αα ≤≤ 3030ºº, load current , load current iidd is continuous.is continuous.
When When α α > > 3030ºº, load current , load current iidd is discontinuous.is discontinuous.
ααπ
ωωπαπ
απ cos17.1cos2
63)(sin2
321
226
5
62d UUttdUU === ∫
+
+
⎥⎦⎤
⎢⎣⎡ ++=⎥⎦
⎤⎢⎣⎡ ++== ∫ +
)6
cos(1675.0)6
cos(12
23)(sin2
321
26
2d απαππ
ωωππ
απ UttdUU
(2(2--18)18)
(2(2--19)19)
Average load current
Thyristor voltagesR
UI dd = (2(2--20)20)
0 30 60 90 120 150
0.4
0.8
1.21.17
32
1
α/(°)
Ud/
U2
1- resistor load 2- inductor load 3- resistor-inductor load
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Inductive load, L is large enoughInductive load, L is large enough
Load current Load current iidd is always continuous. is always continuous.
ThyristorThyristor voltage and currents, transformer currentvoltage and currents, transformer current
ab
c
T
R
Lu2
ud
eLid
VT1
VT2
VT3
ud
ia
ua ub uc
ib
ic
id
uacuab
uacO ωt
O ωt
O ωt
O ωt
O ωt
O ωtα
uVT1
ααπ
ωωπαπ
απ cos17.1cos2
63)(sin2
321
226
5
62d UUttdUU === ∫
+
+(2(2--18)18)
ddVT2 577.03
1 IIII === (2(2--23)23) dVT
VT(AV) 368.057.1
III ==
2RMFM 45.2 UUU ==
(2(2--24)24)
(2(2--25)25)
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2.2.2 Three2.2.2 Three--phase bridgephase bridgefullyfully--controlled rectifiercontrolled rectifier
CommonCommon--cathode group and commoncathode group and common--anode group of anode group of thyristorsthyristorsNumbering of the 6 Numbering of the 6 thyristorsthyristors indicates the trigger sequence. indicates the trigger sequence.
Circuit diagramCircuit diagram
ba
c
id
ud
VT1
VT3 VT 5
VT4
VT 6 VT 2
d2
d1
T
n
iaload
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Resistive load, Resistive load, α α = 0= 0ººu2ud1
ud2
u2Lud
uab uac
uab uac ubc uba uca ucb uab uac
uab uac ubc uba uca ucb uab uacⅠ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ
ua ucub
ωt1O ωt
O ωt
O ωt
O ωt
α = 0°
iVT1
uVT1
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Resistive load, Resistive load, α α = 30= 30ººud1
ud2
α = 30°
ia
O ωt
O ωt
O ωt
O ωt
ud
uab uac
ua ub uc
ωt1
uab uac ubc uba uca ucb uab uacⅠ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ
uab uac ubc uba uca ucb uab uacuVT1
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Resistive load, Resistive load, α α = 60= 60ººα = 60°
ud1
ud2
ud
uac uac
uab
uab uac ubc uba uca ucb uab uac
ua
Ⅰ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ
ub uc
O ωtωt1
O ωt
O ωt
uVT1
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Resistive load, Resistive load, α α = 90= 90ººud1
ud2
ud
ua ub uc ua ub
ωtO
ωtO
ωtO
ωtO
ωtO
ia
id
uab uac ubc uba uca ucb uab uac ubc uba
iVT1
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Inductive load, Inductive load, α α = 0= 0ºº
ud1
u2
ud2
u2Lud
id
ωtO
ωtO
ωtO
ωtO
uaα = 0° ub uc
ωt1
uab uac ubc uba uca ucb uab uacⅠ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ
iVT1
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Inductive load, Inductive load, α α = 30= 30ººud1
α = 30°
ud2
uduab uac ubc uba uca ucb uab uacⅠ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ
ωtO
ωtO
ωtO
ωtO
id
ia
ωt1
ua ub uc
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Inductive load, Inductive load, α α = 90= 90ººα = 90°
ud1
ud2uac ubc uba uca ucb uab uacuabⅠ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ
ud
uac
uab
uac
ωtO
ωtO
ωtO
ub uc ua
ωt1
uVT1
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Quantitative analysisQuantitative analysisAverage output voltageAverage output voltage
For resistive load, When For resistive load, When a a > > 6060ºº, load current , load current iidd is discontinuous.is discontinuous.
Average output current (load current)Average output current (load current)
Transformer currentTransformer current
ThyristorThyristor voltage and currentvoltage and current–– Same as threeSame as three--phase halfphase half--wave rectifierwave rectifier
EMF load, L is large enoughEMF load, L is large enough–– All the same as inductive load except the calculation of averageAll the same as inductive load except the calculation of average output output
currentcurrent
αωωπαπ
απ cos34.2)(sin6
3
12
32
32d UttdUU == ∫
+
+(2(2--26)26)
⎥⎦⎤
⎢⎣⎡ ++== ∫ +
)3
cos(134.2)(sin632
32d απωω
ππ
απ UttdUU
(2(2--20)20)
(2(2--27)27)
dd2
d2d2 816.0
32
32)(
32
21 IIIII ==⎟
⎠⎞
⎜⎝⎛ ×−+×=
ππππ (2(2--28)28)
REUI −
= dd (2(2--29)29)
RUI d
d =
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2.3 Effect of transformer leakage 2.3 Effect of transformer leakage inductance on rectifier circuits inductance on rectifier circuits
In practical, the transformer leakage inductance has to be In practical, the transformer leakage inductance has to be taken into account. taken into account. Commutation between Commutation between thyristorsthyristors thus can not happen instantly, thus can not happen instantly, but with a commutation process. but with a commutation process.
R
a
b
c
T
Lud
ic
ib
iaLB
LB
LB
ikVT1
VT2
VT3
ud
id
ωtO
ωtO γ
ic ia ib ic ia Id
ua ub ucα
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Commutation process analysisCommutation process analysisCirculating current Circulating current iikk during commutationduring commutation
Commutation angle Commutation angle Output voltage during commutationOutput voltage during commutation
ub-ua = 2·LB·dia/dt
ik: 0 Id
ia = Id-ik : Id 0
ib = ik : 0 Id
2dd
dd bak
Bbk
Baduu
tiLu
tiLuu +
=−=+= (2(2--30)30)
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Reduction of average output voltage due to the Reduction of average output voltage due to the commutation processcommutation process
Calculation of commutation angleCalculation of commutation angle
– Id ,,ΧΧ–– XXB B ,,ΧΧ
– For Α 9090o o , , Α , ΧΧ
Quantitative calculationQuantitative calculation
dB0 B6
5
65 B
65
65 Bbb
65
65 dbd
23d
23)(d
dd
23
)(d)]dd([
23)(d)(
3/21
IXiLttiL
ttiLuutuuU
I
πω
πω
π
ωπ
ωπ
πγα
πα
πγα
πα
πγα
πα
===
−−=−=∆
∫∫
∫∫++
+
++
+
++
+
d
kk
k
(2(2--31)31)
2
dB
62)cos(cos
UIX
=+− γαα (2(2--36)36)
≤
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Summary of the effect on rectifier circuitsSummary of the effect on rectifier circuits
ConclusionsConclusions–– Commutation process actually provides additional working states Commutation process actually provides additional working states
of the circuit. of the circuit. –– di/dtdi/dt of the of the thyristorthyristor current is reduced.current is reduced.–– The average output voltage is reduced. The average output voltage is reduced. –– Positive Positive du/dtdu/dt–– Notching in the AC side voltageNotching in the AC side voltage
dU∆d
B IXπ d
B2I
Xπ d
B
23
IXπ d
B3I
Xπ
dB
2I
mXπ
)cos(cos γαα +−2
Bd
2UXI
2
Bd
22
UXI
2
dB
62
UIX
2
dB
62
UIX
mU
XIπsin2 2
Bd
Single-phase full
wave
Single-phase bridge
Three-phase half-
wave
Three-phase bridge
m-pulse recfifier
①
②
Circuits
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2.4 Capacitor2.4 Capacitor--filtered uncontrolledfiltered uncontrolled(uncontrollable) rectifier(uncontrollable) rectifier
Emphasis of previous sectionsEmphasis of previous sections–– Controlled rectifier, inductive loadControlled rectifier, inductive load
Uncontrolled rectifier: diodes instead of Uncontrolled rectifier: diodes instead of thyristorsthyristorsWide applications of capacitorWide applications of capacitor--filtered uncontrolled filtered uncontrolled rectifierrectifier–– ACAC--DCDC--AC frequency converterAC frequency converter–– Uninterruptible power supplyUninterruptible power supply–– Switching power supplySwitching power supply
2.4.1 Capacitor2.4.1 Capacitor--filtered singlefiltered single--phase uncontrolledphase uncontrolledrectifierrectifier
2.4.2 Capacitor2.4.2 Capacitor--filtered threefiltered three--phase uncontrolled phase uncontrolled rectifierrectifier
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2.4.1 Capacitor2.4.1 Capacitor--filtered singlefiltered single--phase phase uncontrolled rectifieruncontrolled rectifier
SingleSingle--phase bridge, phase bridge, RCRC loadload
a)
+RCu1 u2
i2VD1 VD3
VD2 VD4
id
iC iR
ud
b)
0
i
ud
θ
δ
π 2π ωt
i,ud
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2.4.1 Capacitor2.4.1 Capacitor--filtered singlefiltered single--phase phase uncontrolled rectifieruncontrolled rectifier
SingleSingle--phase bridge, phase bridge, RLCRLC loadload
a) b)
-
+R
C
L+
u1 u2
i2
ud
uL
id
iC iR
VD2 VD4
VD1 VD3
u2 ud
i2
0δ θ π ωt
i2,u2,ud
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2.4.2 Capacitor2.4.2 Capacitor--filtered threefiltered three--phase phase uncontrolled rectifieruncontrolled rectifier
ThreeThree--phase bridge, phase bridge, RCRC loadload
a)
+a
b
c
T ia
RCud
id
iC iR
VD4 VD6
VD1 VD3 VD5
VD2
b)
O
ia
ud
id
uduab uac
0δ θ ωtππ3
ωt
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2.4.2 Capacitor2.4.2 Capacitor--filtered threefiltered three--phase phase uncontrolled rectifieruncontrolled rectifier
ThreeThree--phase bridge, phase bridge, RCRC loadloadWaveform when Waveform when ωωRCRC≤≤1.7321.732
ωt ωt
ωtωt
ia
id
ia
id
O
O
O
O
a）ωRC= b）ωRC<3 3
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2.4.2 Capacitor2.4.2 Capacitor--filtered threefiltered three--phase phase uncontrolled rectifieruncontrolled rectifier
ThreeThree--phase bridge, phase bridge, RLCRLC loadload
a)
b)
c)
+ab
c
T ia
RCud
idiC iR
VD4VD6
VD1VD3VD5
VD2
ia
ia
O
O ω t
ω t
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2.5 Harmonics and power factor of 2.5 Harmonics and power factor of rectifier circuitsrectifier circuits
Originating of harmonics and power factor issues in Originating of harmonics and power factor issues in rectifier circuitsrectifier circuits–– Harmonics: working in switching statesHarmonics: working in switching states——nonlinearnonlinear–– Power factor: firing delay angle causes phase delayPower factor: firing delay angle causes phase delay
Harmful effects of harmonics and low power factorHarmful effects of harmonics and low power factorStandards to limit harmonics and power factorStandards to limit harmonics and power factor
2.5.1 Basic concepts of harmonics and reactive power2.5.1 Basic concepts of harmonics and reactive power2.5.2 AC side harmonics and power factor of 2.5.2 AC side harmonics and power factor of
controlled rectifiers with inductive loadcontrolled rectifiers with inductive load2.5.3 AC side harmonics and power factor of 2.5.3 AC side harmonics and power factor of
capacitorcapacitor--filtered uncontrolled rectifiersfiltered uncontrolled rectifiers2.5.4 Harmonic analysis of output voltage and current2.5.4 Harmonic analysis of output voltage and current
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For pure sinusoidal waveformFor pure sinusoidal waveform
For periodic nonFor periodic non--sinusoidal waveform sinusoidal waveform
oror
wherewhere
Fundamental componentFundamental component
Harmonic components (harmonics)Harmonic components (harmonics)
2.5.1 Basic concepts of harmonics 2.5.1 Basic concepts of harmonics and reactive powerand reactive power
∑∞
=
++=1
)sincos()(n
nno tnbtnaatu ωωω
(2(2--54)54)( ) 2 sin( )uu t U tω ϕ= +
(2(2--55)55)
∑∞
=
++=1
)sin()(n
nno tncatu ϕωω (2(2--56)56)
22nnn bac +=
)/arctan( nnn ba=ϕ
ϕsinnn ca =
ϕcosnn cb =
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HarmonicsHarmonics--related specificationsrelated specificationsTake current harmonics as examplesTake current harmonics as examples
Content of Content of nnth harmonicsth harmonics
IInn is the effective (RMS) value of is the effective (RMS) value of nnth harmonics.th harmonics.II11 is the effective (RMS) value of fundamental componentis the effective (RMS) value of fundamental component..
Total harmonic distortionTotal harmonic distortion
IIhh is the total effective (RMS) value of all the harmonic componenis the total effective (RMS) value of all the harmonic components.ts.
%1001
×=IIHRI n
n
%1001
×=IITHD h
i
(2(2--57)57)
(2(2--58)58)
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Definition of power and power factorDefinition of power and power factorFor sinusoidal circuitsFor sinusoidal circuits
Active powerActive power
Reactive power Reactive power
Q=U IQ=U I sinsinϕϕ
Apparent powerApparent power
S=UIS=UI
Power factorPower factor
λ λ ==coscos ϕϕ
∫ ==π
ϕωπ
2
0cos)(
21 UItuidP
222 QPS +=
SP
=λ
(2(2--59)59)
(2(2--60)60)
(2(2--61)61)
(2(2--63)63)
(2(2--62)62)
(2(2--64)64)
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Definition of power and power factorDefinition of power and power factor
For nonFor non--sinusoidal circuitssinusoidal circuitsActive powerActive power
P=U IP=U I11 coscosϕϕ1 1
Power factorPower factor
Distortion factor (fundamentalDistortion factor (fundamental--component factor)component factor)
ν ν ==II1 1 / I/ I
Displacement factor (power factor of fundamental component)Displacement factor (power factor of fundamental component)
λλ11 = cos= cosϕϕ11
Definition of reactive power is still in dispute. Definition of reactive power is still in dispute.
11111 coscoscos ϕνϕϕλ ====II
UIUI
SP
(2(2--65)65)
(2(2--66)66)
Review of the reactive power conceptReview of the reactive power conceptThe reactive power The reactive power Q Q does not lead to net transmission of does not lead to net transmission of energy between the source and load. When energy between the source and load. When Q Q ≠≠ 0, the 0, the rmsrmscurrent and apparent power are greater than the minimum current and apparent power are greater than the minimum amount necessary to transmit the average power P.amount necessary to transmit the average power P.Inductor: current lags voltage by 90Inductor: current lags voltage by 90°°, hence displacement , hence displacement factor is zero. The alternate storing and releasing of energy ifactor is zero. The alternate storing and releasing of energy in n an inductor leads to current flow and nonzero apparent power, an inductor leads to current flow and nonzero apparent power, but but P P = = 0. Just as resistors consume real (average) power P, 0. Just as resistors consume real (average) power P, inductors can be viewed as consumers of reactive power Q.inductors can be viewed as consumers of reactive power Q.Capacitor: current leads voltage by 90Capacitor: current leads voltage by 90°°, hence displacement , hence displacement factor is zero. Capacitors supply reactive power Q. They are factor is zero. Capacitors supply reactive power Q. They are often placed in the utility power distribution system near often placed in the utility power distribution system near inductive loads. If inductive loads. If Q Q supplied by capacitor is equal to supplied by capacitor is equal to Q Q consumed by inductor, then the net current (flowing from the consumed by inductor, then the net current (flowing from the source into the capacitorsource into the capacitor--inductiveinductive--load combination) is in load combination) is in phase with the voltage, leading to unity power factor and phase with the voltage, leading to unity power factor and minimum minimum rmsrms current magnitude.current magnitude.
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2.5.2 AC side harmonics and power factor of 2.5.2 AC side harmonics and power factor of controlled rectifiers with inductive loadcontrolled rectifiers with inductive load
SingleSingle--phase bridge fullyphase bridge fully--controlled rectifiercontrolled rectifieru2
O ω t
O ω t
O ω t
ud
id
i2
b)
O ω t
O ω t
uVT1,4
O ω t
O ω t
Id
Id
Id
Id
Id
iVT2,3
iVT1,4
T a
b R
L
a)
u1 u2
i2
VT 1
VT 3
VT 2
VT 4
ud
id
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AC side current harmonics of singleAC side current harmonics of single--phase bridge phase bridge fullyfully--controlled rectifier with inductive loadcontrolled rectifier with inductive load
ConclusionsConclusions–– Only odd order harmonics existOnly odd order harmonics exist
–– IInn ∝∝ 1/1/nn
–– IInn / I/ I11 = 1/= 1/nn
where
∑∑==
==
+++=
,5,3,1,5,3,1d
d2
sin2sin14
)5sin513sin
31(sin4
nn
ntnItn
nI
tttIi
ωωπ
ωωωπ
n=1,3,5,…πn
II nd22
=
(2(2--72)72)
(2(2--73)73)
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Power factor of singlePower factor of single--phase bridge fullyphase bridge fully--controlled rectifier with inductive loadcontrolled rectifier with inductive load
Distortion factorDistortion factor
Displacement factorDisplacement factor
Power factorPower factor
νπ
= = ≈II1 2 2 0 9.
αϕλ coscos 11 ==
ααπ
ϕνλλ cos9.0cos22cos 11
1 ≈===II
(2(2--75)75)
(2(2--76)76)
(2(2--77)77)
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ThreeThree--phase bridge fullyphase bridge fully--controlled rectifiercontrolled rectifierud1
α = 30°
ud2
uduab uac ubc uba uca ucb uab uacⅠ Ⅱ Ⅲ Ⅳ Ⅴ Ⅵ
ωtO
ωtO
ωtO
ωtO
id
ia
ωt1
ua ub uc
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AC side current harmonics of threeAC side current harmonics of three--phase bridge phase bridge fullyfully--controlled rectifier with inductive loadcontrolled rectifier with inductive load
ConclusionsConclusions–– Only 6Only 6kk±±1 order harmonics exist (1 order harmonics exist (kk is positive integer)is positive integer)
–– IInn ∝∝ 1/1/nn
–– IInn / I/ I11 = 1/= 1/nn
∑∑=
±==
±=
−+=−+=
−++−−=
3,2,116
1
3,2,116
dd
da
sin2)1(sin2sin1)1(32sin32
]13sin13111sin
1117sin
715sin
51[sin32
kkn
nk
kkn
k tnItItnn
ItI
tttttIi
ωωωπ
ωπ
ωωωωωπ
(2(2--79)79)
16
6 , 6 1, 1,2,3,n
I I
I I n k kn
π
π
⎧=⎪⎪
⎨⎪ = = ± =⎪⎩
d
d
where
(2(2--80)80)
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Power factor of threePower factor of three--phase bridge fullyphase bridge fully--controlled controlled rectifier with inductive loadrectifier with inductive load
Distortion factorDistortion factor
Displacement factorDisplacement factor
Power factorPower factor
955.031 ≈==π
νII
αϕλ coscos 11 ==
ααπ
ϕνλλ cos955.0cos3cos 11
1 ≈===II
(2(2--81)81)
(2(2--82)82)
(2(2--83)83)
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2.5.3 AC side harmonics and power factor of 2.5.3 AC side harmonics and power factor of capacitorcapacitor--filtered uncontrolled rectifiersfiltered uncontrolled rectifiers
Situation is a little complicated than rectifiers with inductiveSituation is a little complicated than rectifiers with inductiveload. load.
Some conclusions that are easy to remember:Some conclusions that are easy to remember:–– Only odd order harmonics exist in singleOnly odd order harmonics exist in single--phase circuit, and only phase circuit, and only
66kk±±1 (1 (kk is positive integer) order harmonics exist in threeis positive integer) order harmonics exist in three--phase phase circuit. circuit.
–– Magnitude of harmonics decreases as harmonic order increases. Magnitude of harmonics decreases as harmonic order increases.
–– Harmonics increases and power factor decreases as capacitor Harmonics increases and power factor decreases as capacitor increases. increases.
–– Harmonics decreases and power factor increases as inductor Harmonics decreases and power factor increases as inductor increases. increases.
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2.5.4 Harmonic analysis of output voltage 2.5.4 Harmonic analysis of output voltage and currentand current
wherewhere
Output voltage of Output voltage of mm--pulsepulserectifier when α = 0º
ud
ωtOπm
πm
2πm
U22
⎥⎦
⎤⎢⎣
⎡−
−=
+=
∑
∑∞
=
∞
=
tnn
kU
tnbUu
mkn
mknn
ωπ
ω
cos1
cos21
cos
2d0
d0d0
mmUU ππ
sin2 2d0 =
d02 1cos2 Un
kbn −−=
π
(2(2--85)85)
(2(2--86)86)
(2(2--87)87)
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Ripple factor in the output voltageRipple factor in the output voltageOutput voltage ripple factorOutput voltage ripple factor
where Uwhere URR is the total RMS value of all the harmonicis the total RMS value of all the harmoniccomponents in the output voltagecomponents in the output voltage
and U is the total RMS value of the output voltageand U is the total RMS value of the output voltage
Ripple factors for rectifiers with different number of pulses Ripple factors for rectifiers with different number of pulses
d0
R
UU
u =γ
2d0
22R UUUU
mknn −== ∑
∞
=
(2(2--88)88)
(2(2--89)89)
m 2 3 6 12 ∞
γu（%） 48.2 18.27 4.18 0.994 0
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Harmonics in the output currentHarmonics in the output current
where where
)cos(dd nmkn
n tndIi ϕω −+= ∑∞
=
REUI −
= d0d
22 )( LnRb
zbd n
n
nn
ω+==
RLn
nωϕ arctan=
(2(2--92)92)
(2(2--93)93)
(2(2--94)94)
(2(2--95)95)
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Conclusions for Conclusions for α α = 0= 0ºº
Only Only mkmk ((kk is positive integer) order harmonics exist is positive integer) order harmonics exist in the output voltage and current of min the output voltage and current of m--pulse rectifierspulse rectifiers
Magnitude of harmonics decreases as harmonic Magnitude of harmonics decreases as harmonic order increases when order increases when mm is constant. is constant.
The order number of the lowest harmonics increases The order number of the lowest harmonics increases as as m m increases. The corresponding magnitude of the increases. The corresponding magnitude of the lowest harmonics decreases accordingly.lowest harmonics decreases accordingly.
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For For α α ≠≠ 00ºº
Quantitative harmonic Quantitative harmonic analysis of output voltage analysis of output voltage and current is very and current is very complicated for complicated for α α ≠≠ 00ºº. .
As an example, As an example, for 3for 3--phase bridge phase bridge fullyfully--controlled rectifiercontrolled rectifier
0 30 120 150 18060
0.1
0.2
0.3
90
n=6
n=12
n=18
α/(°)U
2L
c n
2∑
∞
=
++=kn
nnd tncUu6
)cos( θωd
(2(2--96)96)
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2.6 High power controlled rectifier2.6 High power controlled rectifier
2.6.1 Double2.6.1 Double--star controlled rectifierstar controlled rectifier
2.6.2 Connection of multiple rectifiers2.6.2 Connection of multiple rectifiers
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2.6.1 Double2.6.1 Double--star controlled rectifierstar controlled rectifier
Difference from 6Difference from 6--phase halfphase half--wave rectifierwave rectifier
CircuitCircuit Waveforms When Waveforms When αα = = 00ºº
T
a b c
L
R
niP LP
ud
id
VT 2
VT 6
VT 4
VT 1
VT 3
VT 5
c'a' b'
n1n2
ud1ua ub uc
ia
ud2
ia'
uc' ua
' ub' uc
'
O ωt
O ωt
O ωt
O ωt
Id12
Id16
Id12
Id16
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Effect of Effect of interphaseinterphase reactor reactor (inductor, transformer)(inductor, transformer)
n
L
R
+- +-
ud1
LP
ub'
ud2 ud
n2 n1
iP
ua
VT1 VT6
uP12
d1d2p uuu −=
)(21
21
21
d2d1pd1pd2d uuUuuuu +=+=−=
(2(2--97)97)
(2(2--98)98)
up
ud1,ud2
O
O
60
360
ωt1 ωt
ωtb)
a)
ua ub ucuc' ua
'ub' ub
'
。
。
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Quantitative analysis when Quantitative analysis when α α = 0= 0ºº
]9cos4016cos
3523cos
411[
263 2
d1 ⋅⋅⋅−+−+= tttUu ωωωπ
2
2
3 6 1 2 1[1 cos3( 60 ) cos6( 60 ) cos9( 60 ) ]2 4 35 40
3 6 1 2 1[1 cos3 cos6 cos9 ]2 4 35 40
Uu t t t
U t t t
ω ω ωπ
ω ω ωπ
= + − ° − − ° + − ° − ⋅⋅⋅
= − − − − ⋅⋅⋅
d2
]9cos2013cos
21[
263 2
p ⋅⋅⋅−−−= ttUu ωωπ
]6cos3521[
263 2
d ⋅⋅⋅−−= tUu ωπ
(2(2--99)99)
(2(2--100)100)
(2(2--101)101)
(2(2--102)102)
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Waveforms Waveforms when when α α > 0> 0ºº
。90=α
。60=α
。30=αud
ud
ud
ωtO
ωtO
ωtO
ua ub ucuc' ua
' ub'
ub ucuc' ua
' ub'
ub ucuc' ua
' ub'
αcos17.1 2UUd =
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Comparison with 3Comparison with 3--phase halfphase half--wavewaverectifier and 3rectifier and 3--phase bridge rectifierphase bridge rectifier
Voltage output capabilityVoltage output capability–– Same as 3Same as 3--phase halfphase half--wave rectifierwave rectifier
–– Half of 3Half of 3--phase bridge rectifierphase bridge rectifier
Current output capabilityCurrent output capability–– Twice of 3Twice of 3--phase halfphase half--wave rectifierwave rectifier
–– Twice of 3Twice of 3--phase bridge rectifierphase bridge rectifier
ApplicationsApplications
Low voltage and high current situationsLow voltage and high current situations
2.6.2 Connection of multiple rectifiers2.6.2 Connection of multiple rectifiersE
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Connection Connection of multiple of multiple rectifiersrectifiers
To increase the To increase the output capacityoutput capacity
To improve the AC side current waveform To improve the AC side current waveform and DC side voltage waveformand DC side voltage waveform
Larger output voltage: Larger output voltage: series connectionseries connection
Larger output current: Larger output current: parallel connectionparallel connection
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PhasePhase--shift connection of multiple rectifiersshift connection of multiple rectifiersParallel connectionParallel connection
1212--pulse rectifier realized by pulse rectifier realized by paralleled 3paralleled 3--phase bridge rectifiersphase bridge rectifiers
M
LTVT
1 2
c1
b1
a1
c2
b2
a2
LP
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PhasePhase--shift connection of multiple rectifiersshift connection of multiple rectifiers
1212--pulse rectifier realized by pulse rectifier realized by series 3series 3--phase bridge rectifiersphase bridge rectifiers
Series connectionSeries connection
0a)
b)
c)
d)
ia1
Id
180° 360°ia2
iab2'
iA
Idiab2
ωt
ωt
ωt
ωt
0
0
0
Id23
33 Id
33 Id
Id32 3
(1+ )Id32 3
(1+ )Id33
Id13
C▲
L
RB
A
1
*▲
▲
*
*
0
30°lagging
3
iAc1
b1
a1
1
c2
b2
a2
iab2 ua2b2
ua1b1
ia1 id
ud
I
II
I
II
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VoltageVoltage–– Average output voltageAverage output voltage
Parallel connection: Parallel connection:
Series connection:Series connection:–– Output voltage harmonicsOutput voltage harmonics
Only 12Only 12mm harmonics existharmonics exist
Input (AC side) current harmonicsInput (AC side) current harmonics–– Only 12kOnly 12k±±1 harmonics exist1 harmonics exist
Connection of more 3Connection of more 3--phase bridge rectifiersphase bridge rectifiers–– Three: 18Three: 18--pulse rectifier (20pulse rectifier (20ºº phase differencephase difference))–– Four: 24Four: 24--pulse rectifier (15pulse rectifier (15ºº phase differencephase difference))
Quantitative analysis of 12Quantitative analysis of 12--pulse rectifierpulse rectifier
22.34 cosU U α=d
24.68 cosU U α=d
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Sequential control of multiple Sequential control of multiple seriesseries--connected rectifiersconnected rectifiers
Circuit and waveforms of seriesCircuit and waveforms of series--connectedconnectedthree singlethree single--phase bridge rectifiersphase bridge rectifiers
L
i
a)
Ⅰ
Ⅱ
Ⅲ
u2
u2
u2
Id
VT 11
VT 13
VT 14
VT 12
VT 21
VT 23
VT 24
VT 22
VT 31
VT 33
VT 34
VT 32
ud b)
c)
i Id
2Id
ud
O α π+α
load
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2.7 Inverter mode operation 2.7 Inverter mode operation of rectifiersof rectifiers
Review of DC generatorReview of DC generator--motor systemmotor system
∑
−=
REEI MG
d∑
−=
REEI GM
d should be avoided
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Inverter mode operation of rectifiersInverter mode operation of rectifiersRectifier and inverter mode operation of singleRectifier and inverter mode operation of single--phasephasefullfull--wave converterwave converter
∑
−=
REUI Gd
d∑
−=
RUE
IdM
d
a) b)
R
+
-
EnergyM
1
0
2
u10
u20
udid
LVT1
VT2
u10ud u20 u10α
O
O ωt
ωt
Id
id
Ud>EM
EMM
R
+
-
1
0
2
udid
LVT1
VT2
u10udu20 u10
O
O ωt
ωt
Id
id
Ud<EM
α
EM
iVT1
iVT2
iVT1
iVT2
iVT1iVT2
iVT2
id=iVT +iVT1 2id=iVT +iVT1 2
iVT1iVT2
iVT1
Energy
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Necessary conditions for the inverter Necessary conditions for the inverter mode operation of controlled rectifiersmode operation of controlled rectifiers
There must be DC EMF in the load and the direction There must be DC EMF in the load and the direction of the DC EMF must be enabling current flow in of the DC EMF must be enabling current flow in thyristors. (In other word thyristors. (In other word EEMM must be negative if must be negative if taking the ordinary output voltage direction as taking the ordinary output voltage direction as positive.)positive.)
α α > > 9090ºº so that the output voltage so that the output voltage UUdd is also negative. is also negative.
dM UE >
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Inverter mode operation Inverter mode operation of 3of 3--phase bridge rectifierphase bridge rectifier
Inversion angle (extinction angle) Inversion angle (extinction angle) ββαα + + ββ =180=180ºº
uab uac ubc uba uca ucb uab uac ubc uba uca ucb uab uac ubc uba uca ucb uab uac ubc
ua ub uc ua ub uc ua ub uc ua ubu2
ud
ωtO
ωtO
β = π4β = π
3 β = π6
β = π4β = π
3 β = π6
ωt1 ωt3ωt2
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Inversion failure and minimum Inversion failure and minimum inversion angleinversion angle
Possible reasons of Possible reasons of inversion failuresinversion failures–– Malfunction of Malfunction of
triggering circuittriggering circuit–– Failure in Failure in thyristorsthyristors–– Sudden dropout of AC Sudden dropout of AC
source voltagesource voltage–– Insufficient margin for Insufficient margin for
commutation of commutation of thyristorsthyristors
Minimum inversion Minimum inversion angle (extinction angle)angle (extinction angle)ββminmin==δ δ ++γγ++θθ′′ （（22--109109））
La
b
c
+
-Mud
id
EM
LB
LB
LB
VT1
VT2
VT3
o
ud
O
O
id
ωt
ωt
ua ub uc ua ub
p
βγ β <γα
γβ
β >γ
iVT1iVT2
iVT3
iVT1iVT2
iVT3iVT1
iVT3
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2.8 2.8 ThyristorThyristor--DC motor systemDC motor system
2.8.1 Rectifier mode of operation2.8.1 Rectifier mode of operation
2.8.2 Inverter mode of operation2.8.2 Inverter mode of operation
2.8.3 Reversible DC motor drive system2.8.3 Reversible DC motor drive system
(four(four--quadrant operation)quadrant operation)
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2.8.1 Rectifier mode of operation2.8.1 Rectifier mode of operation
Waveforms of 3Waveforms of 3--phase halfphase half--wave wave rectifier with DC motor loadrectifier with DC motor load
ud
O
id
ωt
ua ub uc
α
ud
O
ia ib icic
ωt
EUd
idR
(2(2--112)112)
π23 B
MBXRRR ++=∑
UIREU dMd ∆++= ∑
Waveforms and equationsWaveforms and equations
(for 3(for 3--phase halfphase half--wave)wave)
wherewhere
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SpeedSpeed--torque (mechanic) characteristic torque (mechanic) characteristic when load current is continuouswhen load current is continuous
For 3For 3--phase halfphase half--wavewavenCE eM = (2(2--113)113)
αcos17.1 2UUd =
UIRUE dM ∆−−= ∑αcos17.1 2
e
d
e CUIR
CUn ∆+
−=∑αcos17.1 2
For 3For 3--phase bridgephase bridge
22.34 cosd
e e
U Rn IC C
α ∑= −
(2(2--114)114)
(2(2--115)115)
(2(2--116)116)
O
n
a1<a2<a3
a3
a2
a1
Id
(RB+RM+ )IdCe
3XB2π
For 3For 3--phase halfphase half--wavewave
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SpeedSpeed--torque (mechanic) characteristic torque (mechanic) characteristic when load current is discontinuouswhen load current is discontinuous
EMF at no load (taking 3EMF at no load (taking 3--phase phase halfhalf--wave as example)wave as example)
For For αα ≤≤ 6060ºº
For For αα > > 6060ºº
discontinuoutsmode continuous mode
EE0
E0'
O
Idmin
Id
(0.585U2)
( U2)2
)60cos(2 20 −= αUE
20 2UE =
For 3For 3--phase halfphase half--wavewave
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SpeedSpeed--torque (mechanic) characteristic torque (mechanic) characteristic when load current is discontinuouswhen load current is discontinuous
For different For different αα
The point of EMF at no The point of EMF at no load is raised up.load is raised up.
The droop rate becomes The droop rate becomes steer. (softer than the steer. (softer than the continuous mode)continuous mode)
O
a3
a2
a1
Id
boundary
discontinuousmode
continuous mode
a5
a4
E0
E
For 3-phase half-wave(α1< α2 < α3 ≤ 60º, α5 > α4 > 60º)
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2.8.2 Inverter mode of operation2.8.2 Inverter mode of operationEquationsEquations
–– are just the same as in the are just the same as in the rectifier mode of operation rectifier mode of operation except that except that UUdd, , EEMM and and nnbecome negative. E.g., in become negative. E.g., in 33--phase halfphase half--wavewave
–– Or in another formOr in another form
(2(2--114)114)
e
d
e CUIR
CUn ∆+
−=∑αcos17.1 2
(2(2--115)115)
(2(2--122)122)
(2(2--123)123)eC
n −= 1∑+ RIU dd βcos0
0 cos( ∑+−= RIUE ddM β
rectifiermode
n
α3
α2
α1
Id
α4
β2
β3
β4
β1
α =β = π2
α in
crea
sing
β in
crea
sing
invertermode
Speed-torque characteristic of a DC motor fed by a thyristorrectifier circuit
21.17 cosM dE U R I Uα ∑= − − ∆
)
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2.8.3 Reversible DC motor drive system2.8.3 Reversible DC motor drive system(4(4--quadrant operation)quadrant operation)
L
converter 1 converter 2
EMM
abc
Back-to-back connection of two 3-phase bridge circuits
+
-
+
-
+
-
+
-
+
-
+
-
+
-
+
-
ACsource
converter2
converter2converter2
converter 1 converter2
+T-T
reverse motoring
converter 2 inverting
forward braking(regenerating)
+n
IdId
Udα
M EM
Id
M EMMEM
Id
MEM
-n
Udβ
Udα Udβ
O
ACsource
ACsource
ACsource
Energy
Energy
Energy
Energy
converter 1
converter1
converter1
converter 1 rectifying
forward motoring
converter 2 rectifying converter 1 inverting
reverse braking(regenerating)
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44--quadrant speedquadrant speed--torque characteristic torque characteristic of Reversible DC motor drive systemof Reversible DC motor drive system
converter 1converter 2 n
α 3
α 2
α 1
Id
α 4
β 2
β 3
β 4
β 1
α =β = π2
α '=β '= π2
β '3
β '2
β '1
β '4
α '2
α '3
α '4
α '1α 1=β '1; α '1=β 1α 2=β '2; α '2=β 2
α in
crea
sing
'β
incr
easi
ng'
α in
crea
sing
β in
crea
sing
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Power ElectronicsPower Electronics
Supplement:Gate Triggering Control Circuit
for Thyristor Rectifiers
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2.9 Gate triggering control circuit for 2.9 Gate triggering control circuit for thyristorthyristor rectifiersrectifiersObjectObject
How to timely generate triggering pulses with How to timely generate triggering pulses with adjustable phase delay angleadjustable phase delay angle
ConstitutionConstitutionSynchronous circuitSynchronous circuitSawSaw--tooth ramp generating and phase shiftingtooth ramp generating and phase shiftingPulse generatingPulse generating
Integrated gate triggering control circuits are very Integrated gate triggering control circuits are very widely used in practice.widely used in practice.
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A typical gate triggering control circuitA typical gate triggering control circuit
220V 36V
+
BTP
+15V
AVS
+15V
-15V -15VX YDisable
RQ
uts
VD1 VD2
C1 R2
R4TS V2 R5
R8
R6
R7
R3
R9
R10
R11 R12
R13
R14
R16
R15
R18
R17
RP1
uco
up
C2
C3
C3
C5
C6C7
R1
RP2
V1
I1cV3
V4
V6
V5
V7
V8
VD4
VD10 VD5
VD6
VD7
VD9
VD8
VD15
VD11~VD14
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Waveforms of the typical Waveforms of the typical gate triggering control circuitgate triggering control circuit
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How to get synchronous voltage for the gate How to get synchronous voltage for the gate triggering control circuit of each thyristortriggering control circuit of each thyristor
For the typical circuit on page 20, the synchronous voltage of tFor the typical circuit on page 20, the synchronous voltage of the gate he gate triggering control circuit for each triggering control circuit for each thyristorthyristor should be lagging 180should be lagging 180ºº to the to the corresponding phase voltage corresponding phase voltage ofyyofyythat that thyristorthyristor..
D,y 11D,y 5-11
TR TS
uA uB uC
ua ub uc - usa- usb
- usc- usa
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Uc
Usc -Usa
Ub
Usb
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Ua
Usa
UAB
