POWERPOWER ELECTRONICSELECTRONICS
ACAC VOLTAGEVOLTAGE CONTROLLERSCONTROLLERS
Dr. Adel Gastli Email: [email protected] http://adel.gastli.net
INTRODUCTIONINTRODUCTION
• Purpose: control the output rms voltage using SCR- or Triac-type switch. • Name: AC Voltage Controller, AC to controlled AC converters or AC regulators • Types: there are single-phase and three- phase types of ac voltage controllers
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 2 CHAPTERCHAPTERCHAPTER’S’’SS CONTENTCONTENTCONTENT
1. 1-PHASE AC VOLTAGE CONTROLLERS 2. 3-PHASE AC VOLTAGE CONTROLLERS 3. CYCLOCONVERTERS 4. APPLICATIONS & SUMMARY
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 3
SectionSection 11
11--PHASEPHASE ACAC VOLTAGEVOLTAGE CONTROLLERSCONTROLLERS
T2
iL iL
T1 Triac
v Z vL Z L L ≡ L
vs = Vsm sin(ωt) vs = Vsm sin(ωt)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 4 SECTIONSECTIONSECTION’S’’SS CONTENTSCONTENTSCONTENTS
1. ON-OFF CONTROL 2. PHASE CONTROL 3. SECTION SUMMARY
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 5
ONON--OFFOFF CONTROLCONTROL Integral half cycle control. Usually used for resistive load.
iL vs Vsm v L R 0 t n v = V sin(ωt) s sm N T : period N : number of half cycle during period T n : number of half cycles during switch on Similar to n V n V = V = sm = V k chopper 0rms srms s Duty principle. N 2 N cycle
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 6 PHASEPHASE CONTROL:CONTROL: BIBI--DIRECTIONALDIRECTIONAL
1. Resistive Load i L vs Vsm
vL R 0 α π + α 2π + α ωt
vs = Vsm sin(ωt)
2 π π 1 2 Vsm 2 V0rms = vLdθ = sin θ ⋅ dθ π ∫0 π ∫α 1 ⎛ sin()2α ⎞ V0rms = Vs ⎜π -α + ⎟ π ⎝ 2 ⎠
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 7
SIMULINK SIMULATION
ia (sp_ac_reg.mdl)
a i k + g -
Triac iA
g
g + + v v0 R=10Ω v vs - 120V - 50Hz vA
Press to Plot Results
(sp_ac_regm.m)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 8 1.5
1
0.5 Gate signal Gate 0 0 200 400 600 800 1000 200 vs v0 0 α = 45o Voltage, (V) -200 0 200 400 600 800 1000 20
0 Current, (A) -20 0 200 400 600 800 1000 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 9
2. Inductive Load Three cases to be distinguished:
i0 i. α > θ L ii. α < θ iii. α = θ v0 R i) α > θ : Discontinuous current v = V sin(ωt) s sm Current equation is obtained similarly to Chapter 10 (single-phase controlled ⎛ ωL ⎞ θ = tan −1⎜ ⎟ rectifier). ⎝ R ⎠ ⎛ R ⎞⎛ α ⎞ ⎡ ⎜ ⎟⎜ −t ⎟ ⎤ 2Vs ⎝ L ⎠⎝ ω ⎠ i1 = ⎢sin()()ωt −θ − sin α −θ e ⎥ vs Z v ⎣⎢ ⎦⎥ Vsm 0
i0 β is obtained by taking i1(β)=0. 0 β φ α π + α 2π + α ωt 1 ⎛ sin 2α sin 2β ⎞ V0rms = Vs ⎜ β −α + − ⎟ π ⎝ 2 2 ⎠
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 10 ii) α < θ : / Not Practical because conduction angle cannot exceed π β > α + π Conduction in one alternance.
To be avoided
If triac gate pulse is large enough then we will obtain continuous conduction.
iii) α = θ : Continuous conduction
Vsm β = α + π V0rms = = Vsrms 2
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 11
SIMULINK SIMULATION
(sp_ac_reg.mdl) ia
a i k + g - Triac iA
g
g + R=10Ω + v v0 v vs - L=10mH - 120V 50Hz
Press to Plot Results
(sp_ac_regm.m)
120V Dr. Adel Gastli 50Hz R=10Ω AC VOLTAGE CONTROLLERS 12 α = 45o > θ =17.44o 1.5
1
0.5 Gate signal 0 0 200 400 600 800 1000 200 vs v 0 0 α = 45o Voltage, (V) -200 0 200 400 600 800 1000 20
0 Current, (A) -20 0 200 400 600 800 1000 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 13
α =10o < θ =17.44o Short gate pulse
1.5
1
0.5 Gate signal Gate 0 0 200 400 600 800 1000 200 vs v 0 0 Voltage, (V) -200 0 200 400 600 800 1000 20
0 Current, (A) -20 0 200 400 600 800 1000 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 14 α =10o < θ =17.44o Long gate pulse
1.5
1
0.5 Gate signal 0 0 200 400 600 800 1000 200 vs v 0 0 Voltage, (V) -200 0 200 400 600 800 1000 20
0 Current, (A) -20 0 200 400 600 800 1000 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 15
α = θ =17.44o Continuous conduction
1.5
1
0.5 Gate signal Gate 0 0 200 400 600 800 1000 200 vs v 0 0 Voltage, (V) -200 0 200 400 600 800 1000 20
0 Current, (A) -20 0 200 400 600 800 1000 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 16 SECTIONSECTION SUMMARYSUMMARY
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 17
SectionSection 22
33--PHASEPHASE ACAC VOLTAGEVOLTAGE CONTROLLERSCONTROLLERS
i0 A vA Z i0B L vB Z L ZL i0C vC
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 18 SECTIONSECTIONSECTION’S’’SS CONTENTSCONTENTSCONTENTS
1. TOPOLOGIES 2. OPERATION 3. SIMULINK SIMULATION
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 19
TOPOLOGIESTOPOLOGIES i v 0 A 1 A i0 A 1 T1 vA Z T i0B 2 L 1 v N i ZL B T 0B 2 2 ZL Z v L B T i 2 ZL Z v 0C 3 L C T i0C 3 3 vC N T3 Equivalent to 3 single-phases Is studied in this chapter 1 vA T Z i0 A 1 1 L vA T1 i0B T3 2 Z ZL Z vB L L T2 ZL Z i 2 L 3 0C 3 v vC B T3 T2 vC Dr. Adel Gastli AC VOLTAGE CONTROLLERS 20 OPERATIONOPERATION i0 A 1 vA ⎧0 ≤ α < 60o ⇒ alternate between 2 and 3 switches T1 ⎪ Z o o i0B 2 L ⎪60 ≤ α < 90 ⇒ only 2 switches conduct at a time vB N ⎨ o o T2 Z ⎪90 ≤ α <150 ⇒ 0 and 2 switches conduct at a time L ZL i ⎪ o 0C 3 ⎩α >150 ⇒ there is no conduction vout = 0V vC T3
line on line off v12 v1N A,B, C None VAB VA A,B C VAB VAB/2 A,C B VAC/2 VAC/2 B,C A -VBC/2 0 None A,B,C 0 0 A Impossible B Impossible C Impossible
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 21
SIMULINKSIMULINK SIMULATIONSIMULATION
ia (sp_ac_reg.mdl) Triac i + Converter - + Ain Aout v vab iA 10Ω - A A i ib Bin Bout + - B B
iB C C Cin Cout ic 3- Phase i + - Y-connected Load + v vAB + - iC v - van + v vBC -
+ v vCA - Press to + v Plot Results - vAN
120V vA vB vC 50Hz (sp_ac_regm.m)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 22 α = 30o Purely resistive load
0.5vab va 0.5vac 200 va va 0
Voltage, (V) -200
0 50 100 150 200 250 300 350 π π 2π 2π 1.5 α + α +α π 3 3 3 3 1 Pulse width
0.5 50% Gate signal Gate 0 0 50 100 150 200 250 300 350 20
0 Current, (A) -20 0 50 100 150 200 250 300 350 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 23
α = 60o Purely resistive load
0.5vab 0.5vac
200
0
Voltage, (V) -200 0 50α 1002π 1502π 200 250 300 350 1.5 + α 3 3 1
0.5 Gate signal Gate 0 0 50 100 150 200 250 300 350 20
0 Current, (A) -20 0 50 100 150 200 250 300 350 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 24 α = 120o Purely resistive load
0.5vab 0.5vac 200
0
Voltage, (V) -200
0 100 200 300 400 500 α 5π π 7π 1.5 +α 6 3 6 1
0.5 Gate signal Gate 0 0 100 200 300 400 500 20
0 Current, (A) -20 0 100 200 300 400 500 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 25
α = 150o Purely resistive load
200
0
Voltage, (V) -200
0 100 200 300 400 500 1.5
1
0.5 Gate signal Gate 0 0 100 200 300 400 500 20
0 Current, (A) -20 0 100 200 300 400 500 Angle, (Deg)
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 26 MATHEMATICAL ANALYSIS: (Resistive Load)
T1 iL ia
A a T4 vAN van R= T3 1o B ib R= N 1o b vBN T 6 R= v CN 1o T C 5 ic
T 2 ⎛ π ⎞ v = 2V sin()θ vAB = 6Vs sin⎜θ + ⎟ AN s ⎝ 6 ⎠ ⎛ 2π ⎞ π vBN = 2Vs sin⎜θ − ⎟ ⎛ ⎞ 3 vBC = 6Vs sin⎜θ − ⎟ ⎝ ⎠ ⎝ 2 ⎠ ⎛ 2π ⎞ π vBN = 2Vs sin⎜θ + ⎟ ⎛ ⎞ 3 vCA = 6Vs sin⎜θ − ⎟ ⎝ ⎠ ⎝ 6 ⎠
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 27
o 0.5vab va 0.5vac 0 ≤ α < 60 200 va va 0
Voltage, (V) -200
0 50 100 150 200 250 300 350 π π 2π 2π α +α +α π 3 3 3 3
2π 1 2 V0 = vand()ωt 2π ∫0
2 2 π /3 π /3+α 2π /3 2π /3+α π 1 ⎡ 2 vab 2 vac 2 ⎤ = va d()ωt + d()ω t + va d (ωt )+ d()ωt + va d ()ωt ⎢∫α ∫π /3 ∫π /3+α ∫2π /3 ∫2π /3+α ⎥ π ⎣ 4 4 ⎦
2 2 2 2 2 1 ⎡ π /3 sin ωt π /3+α sin ()ωt +π / 6 2π /3 sin ωt 2π /3+α sin ()ωt −π / 6 π sin ωt ⎤ V0 = 6Vs d()ωt + d()ωt + d()ωt + d()ωt + d()ωt ⎢∫α ∫∫π /3 π /3+α ∫2π /3 ∫2π /3+α ⎥ π ⎣ 3 4 3 4 3 ⎦
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 28 2 2 2 2 2 1 ⎡ π /3 sin ωt π /3+α sin ()ωt +π / 6 2π /3 sin ωt 2π /3+α sin ()ωt −π / 6 π sin ωt ⎤ V0 = 6Vs d()ωt + d()ωt + d()ωt + d()ωt + d()ωt ⎢∫α ∫∫π /3 π /3+α ∫2π /3 ∫2π /3+α ⎥ π ⎣ 3 4 3 4 3 ⎦
1 ⎛π α sin 2α ⎞ rms Output V0 = 6Vs ⎜ − + ⎟ π ⎝ 6 4 8 ⎠ phase voltage
V I = 0 P = 3I V 0 R 0 0 0 rms output Output power Phase Current
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 29
0.5v 0.5v 60o ≤ α < 90o ab ac 200
0
Voltage, (V) -200
0 50α 100π 1502π 200 250 300 350 + α + α 3 3 2π 1 2 V0 = vand()ωt 2π ∫0
2 2 1 ⎡ π /3+α v 2π /3+α v ⎤ = ab + d()ωt ac d()ωt ⎢∫α ∫π /3+α ⎥ π ⎣ 4 4 ⎦
2 2 1 ⎡ π /33++α sin ()ωt +π / 6 2π / α sin ()ωt −π / 6 ⎤ V0 = 6Vs d()ωt + d()ωt ⎢∫∫α π /3+α ⎥ π ⎣ 4 4 ⎦
2 2 1 ⎡ π /3+α +π / 6 sin ωt 2π /3+α −π / 6 sin ωt ⎤ V0 = 6Vs d()ωt + d()ωt ⎢∫∫α +π / 6 π /3+α −π / 6 ⎥ π ⎣ 4 4 ⎦
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 30 2 2 1 ⎡ π / 2+α sin ωt π / 2+α sin ωt ⎤ V0 = 6Vs d()ωt + d()ωt ⎢∫∫α +π / 6 π / 6+α ⎥ π ⎣ 4 4 ⎦
1 ⎛ π 3sin 2α 3 cos2α ⎞ rms Output V = 6V ⎜ + + ⎟ 0 s ⎜ ⎟ phase voltage π ⎝12 16 16 ⎠
V I = 0 P = 3I V 0 R 0 0 0 rms output Output power Phase Current
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 31
0.5vab 0.5vac o o 90 ≤ α <150 200
0
Voltage, (V) -200
0 100 200 300 400 500 5π π 7π α +α 6 3 6
2π 1 2 V0 = vand()ωt 2π ∫0
2 2 1 ⎡ 5π / 6 v 7π / 6 v ⎤ = ab d()ωt + ac d()ωt ⎢∫α ∫π /3+α ⎥ π ⎣ 4 4 ⎦
2 2 1 ⎡ 56π / 6 sin ()ωt +π / 6 7π / sin ()ωt −π / 6 ⎤ V0 = 6Vs d()ωt + d(ωt) ⎢∫∫α π /3+α ⎥ π ⎣ 4 4 ⎦
2 2 1 ⎡ 5π / 6+π / 6 sin ωt 7π / 6−π / 6 sin ωt ⎤ V0 = 6Vs d(ωt) + d(ωt) ⎢∫∫α +π / 6 π /3+α −π / 6 ⎥ π ⎣ 4 4 ⎦
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 32 2 2 1 ⎡ π sin ωt π sin ωt ⎤ V0 = 6Vs d(ωt) + d(ωt) ⎢∫∫π /66++α π / α ⎥ π ⎣ 4 4 ⎦
1 ⎛ 5π α sin 2α 3 cos2α ⎞ rms Output V = 6V ⎜ − + + ⎟ 0 s ⎜ ⎟ phase voltage π ⎝ 24 4 16 16 ⎠
V I = 0 P = 3I V 0 R 0 0 0 rms output Output power Phase Current
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 33
SectionSection 33
CYCLOCONVERTERSCYCLOCONVERTERS
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 34 SECTIONSECTIONSECTION’S’’SS CONTENTSCONTENTSCONTENTS
1. SINGLE-PHASE 2. THREE-PHASE
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 35
SINGLESINGLE--PHASEPHASE CYCLOCONVERTERCYCLOCONVERTER
P-converter N-converter + − T ' ' 1 T3 T2 T4 Variable voltage variable frequency v01 vs v02 Load converter output T ' ' voltage. T4 2 T3 T1 − +
vs fs fout = (n = number of positive half cycles) Vsm n N-converter π 1 2 on V = v dθ 0 π ∫ s 0 α α t 1 ⎛ sin 2α ⎞ P-converter = Vs ⎜π −α + ⎟ on π ⎝ π ⎠
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 36 THREETHREE--PHASEPHASE CYCLOCONVERTERCYCLOCONVERTER
Three-phase/single-phase cycloconverter
P-converter N-converter + − ' ' ' T1 T3 T5 T2 T T A 6 4 v C B 01 v02
Load B C A T ' ' ' T4 6 T2 T5 T3 T1 − +
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 37
Three-phase/three-phase cycloconverter
Three-phase supply P N P N P N
Phase a Phase b Phase c load load load
Neutral
18 thyristors are used to obtain a 3 full-wave three-phase converter.
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 38 SectionSection 44
APPLICATIONSAPPLICATIONS && SUMMARYSUMMARY
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 39
APPLICATIONSAPPLICATIONS
Light dimmer.
Soft starting of ac motors (compressors, pumps, etc.)
Variable speed drives for appliances an tools.
v Transformer static tap changers. p v0
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 40 SUMMARYSUMMARY ¾ Ac voltage controllers can use on-off control or phase-angle control. ¾ The on-off control is more suitable for systems having a high time constant. ¾ 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. ¾ The input power factor of controllers, which vary with the delay angle, is generally poor, especially at low voltage output range.
Dr. Adel Gastli AC VOLTAGE CONTROLLERS 41