Power Electronics
Chapter 4 AC to AC Converters ( AC Controllers and Frequency Converters )
Power Electronics
Classification of AC to AC converters Same frequency variable magnitude AC power
AC power
AC controllers
Variable frequency AC power
Frequency converters (Cycloconverters)
AC to AC converters 2
Power Electronics
Classification of AC controllers Phase control: AC voltage controller (Delay angle control) Integral cycle control: AC power controller
AC controller PWM control: AC chopper (Chopping control) On/off switch: electronic AC switch PWM: Pulse Width Modulation 3
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Classification of frequency converters Frequency converter (Cycloconverter)
Phase control: thyristor cycloconverter (Delay angle control) PWM control: matrix converter (Chopping control)
Cycloconverter is sometimes referred to – in a broader sense—any ordinary AC to AC converter – in a narrower sense—thyristor cycloconverter
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Power Electronics
Outline 4.1 AC voltage controllers 4.2 Other AC controllers 4.3 Thyristor cycloconverters 4.4 Matrix converters
5
Power Electronics
4.1 AC voltage controllers 4.1.1 Single-phase AC voltage controller 4.1.2 Three-phase AC voltage controller Applications Lighting control Soft-start of asynchronous motors Adjustable speed drive of asynchronous motors Reactive power control
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Power Electronics
4.1.1 Single-phase AC voltage controller Resistive load
u1
VT1 io
O
ωt
uo
u1
VT2
uo
R
O io
ωt
O
ωt
u VT
The phase shift range (operation range of phase delay angle):
O
ωt
0≤α≤π 7
Power Electronics
Resistive load, quantitative analysis RMS value of output voltage Uo =
( π∫ 1
π
α
)
2U1 sinω t d(ω t ) = U1 2
π −α 1 sin 2α + π 2π
(4-1)
RMS value of output current Io =
Uo R
(4-2)
RMS value of thyristor current 2
U1 1 ⎛⎜ 2U1 sinω t ⎞⎟ ( ) IT = d ω t = ⎟ R R 2π ∫α ⎜⎝ ⎠ π
α sin 2α 1 (1 − + ) (4-3) π 2 2π
Power factor of the circuit P UoIo Uo λ= = = = S U1 I o U1
π −α 1 sin 2α + π 2π
(4-4)
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Power Electronics
Inductive (Inductor-resistor) load, operation principle u1
VT1
u1
VT2
uo
ωt
O
io
uG1
R
The phase shift range: ϕ≤α≤π
0.6
O uG2
ωt
O uo
ωt
O io
ωt
O
ωt
uVT O
ωt
9
Differential equation 180
di L o + Rio = 2U 1 sin ω t dt (4-5) io ω t =α = 0
90° ϕ= ° 75 ° 60 ° 45 ° 30 ° 15 ° 0
140
Solution
θ /(°)
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Inductive load, quantitative analysis
100 60
(4-6)
Considering io=0 when ωt=α+θ We have sin( α + θ − ϕ ) = sin( α − ϕ ) e
20 0
−θ tg ϕ
20
60
100 α /(°)
140
180
(4-7)
The RMS value of output voltage, output current, and thyristor current can then be calculated. 10
Power Electronics
Inductive load, when α < ϕ The circuit can still work. u1
The load current will be continuous just like the thyristors are short-circuit, and the thyristors can no longer control the magnitude of output voltage. The start-up transient will be the same as the transient when a RL load is connected to an AC source at ωt =α (α < ϕ).
ωt
O iG1 π
Oα
ωt
iG2
O io
iT1α+π
Oα θ
ϕ
iT2
ωt ωt
Start-up transient
11
There is no DC component and even order harmonics in the current. – The current waveform is halfwave symmetric.
The higher the number of harmonic ordinate, the lower the harmonic content.
100 80 In/I*/%
Power Electronics
Harmonic analysis
Fundamental
60 40
3
20
5 7
α = 90° is when harmonics is the most severe. The situation for the inductive load is similar to that for the resistive load except that the corresponding harmonic content is lower and is even lower as ϕ is increasing.
0
60
120 α/( °)
180
Current harmonics for the resistive load
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Power Electronics
4.1.2 Three-phase AC voltage controller Classification of three-phase circuits
Y connection
Branch-controlled ∆ connection
Line-controlled ∆ connection
Neutral-point-controlled ∆ connection 13
Power Electronics
3-phase 3-wire Y connection AC voltage controller ia
U a0'
VT 1 a
ua
VT 3
VT 4 b
n u
b
VT 5
n'
VT 6 c
u
c
VT 2
For a time instant, there are 2 possible conduction states: – Each phase has a thyristor conducting. Load voltages are the same as the source voltages. – There are only 2 thyristors conducting, each from a phase. The load voltages of the two conducting phases are half of the corresponding line to line voltage, while the load voltage of the other phase is 0.
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Power Electronics
3-phase 3-wire Y connection AC voltage controller Resistive load, 0° ≤ α < 60° VT VT VT
VT 4
1
VT 1
VT 3
6
VT
5
u ab 2
ua
VT 6 VT
2
5
u ac 2
u ao' 0
π 3
α t
1
t
2
2π
4π
5 π
3 t
3
3
2 π
3
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Power Electronics
3-phase 3-wire Y connection AC voltage controller Resistive load, 60° ≤ α < 90° VT
VT
5
VT u
u
2 u
VT
6
ab
VT
1
u a
α
π 3 t
1
2π 3 t 2
VT
2
4
5
VT
6
ac
2
4π 3
ao'
0
VT
3
π t
5π 3 2π
3
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Power Electronics
3-phase 3-wire Y connection AC voltage controller Resistive load, 90° ≤ α < 150° VT
5
VT
VT VT u 4 ab
u
5
6
VT
1
VT VT 1
VT VT u 6u a
2
VT
VT
3
2
VT
3
4
VT
VT
VT
5
4
VT
5
6
ac
2
5π
2
ao'
3 0
π
2π
3
3
α
π
4π
2π
3
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Power Electronics
3-phase 3-wire branch-controlled ∆ connection AC voltage controller The operation principle is the same as 3 independent singlephase AC voltage controllers. Application—Thyristor-controlled reactor (TCR) – To control the effective current flowing through the reactor by controlling delay angle, therefore control the reactive power absorbed by the reactor. ua
n
ia
a
b ub
c uc
a)
b)
c)
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Power Electronics
4.2 Other AC controllers 4.2.1 Integral cycle control—AC power controller 4.2.2 Electronic AC switch 4.2.3 Chopping control—AC chopper
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Power Electronics
4.2.1 Integral cycle control —AC power controller uo VT1
2 U1
io
O
u1
VT2
uo
Conduction 2πN = M angle
R
π M
2π M
uo,io 3π M
u1 4π M
ωt
Line period Control period =M *Line period =2π
Circuit topologies are the same as AC voltage controllers. Only the control method is different. Load voltage and current are both sinusoidal when thyristors are conducting. 20
There is NO harmonics in the ordinary sense. There is harmonics as to the control frequency. As to the line frequency, these components become fractional harmonics.
0.6
In/I0m
Power Electronics
Spectrum of the current in AC power controller
0.5 0.4 0.3 0.2 0.1 0
0
2 4 6 8 10 12 14
Harmonic order as to control frequency
1
2
3
4
5
Harmonic order as to line frequency
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Power Electronics
4.2.2 Electronic AC switch Circuit topologies are the same as AC voltage controllers. But the back-to-back thyristors are just used like a switch to turn the equipment on or off. Application—Thyristor-switched capacitor (TSC)
I
U
22
Power Electronics
TSC waveforms when the capacitor is switched in/out us uVT
1
iC us
uC
uC
C
uVT1
t t
VT1 VT2
iC
t
VT1 VT2
t t1
t2
The voltage across the thyristor must be nearly zero when switching in the capacitor, and the current of the thyristor must be zero when switching out the capacitor. 23
Power Electronics
TSC with the electronic switch realized by a thyristor and an anti-parallel diode
The capacitor voltage will be always charged up to the peak of source voltage. The response to switching-out command could be a little slower (maximum delay is one line-cycle). 24
Power Electronics
4.2.3 Chopping control—AC chopper Principle of chopping control The mean output voltage over one switching cycle is proportional to the duty cycle in that period. This is also called Pulse Width Modulation (PWM).
Advantages Much better output waveforms, much lower harmonics For resistive load, the displacement factor is always 1.
Waveforms when the load is pure resistor 25
Power Electronics
AC chopper Modes of operation
u o >0, io>0: u o >0, io<0: u o <0, io>0: u o <0, io<0:
V1 charging, V3 freewheeling V4 charging, V2 freewheeling V3 charging, V1 freewheeling V2 charging, V4 freewheeling
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Power Electronics
4.3 Thyristor cycloconverters (Thyristor AC to AC frequency converter) Another name—direct frequency converter (as compared to AC-DC-AC frequency converter which is discussed in Chapter 8) Can be classified into single-phase and threephase according to the number of phases at output 4.3.1 Single-phase thyristor-cycloconverter 4.3.2 Three-phase thyristor-cycloconverter
27
Power Electronics
4.3.1 Single-phase thyristor-cycloconverter Circuit configuration and operation principle N
P uo
uo
O
αP= π 2
Output voltage
Z
α P=0
Average output voltage
αP= π 2
ωt
28
Power Electronics
Single-phase thyristor-cycloconverter uo,io
Modes of operation
uo
O t1 uP
io
iP uP
uo
iN
io t2
t3
t4
t
uo
t
O
uN
t5
uN
O
uo
t
iP O iN
t
O
t
P
Rectifi Inver cation sion
N Blocking
Blocking Rectifi Inver cation sion
29
Power Electronics
Single-phase thyristor-cycloconverter Typical waveforms uo
O
ωt
io
O
ωt 3
1 2
4
6 5
30
Power Electronics
Modulation methods for firing delay angle Calculation method – For the rectifier circuit u o = U d0 cos α (4-15)
u2
– For the cycloconverter output uo = U om sinω o t (4-16) – Equating (4-15) and (4-16) U cos α = om sin ω o t = γ sin ω o t U d0 (4-17) – Therefore
u3
u4
u5
u6
u1
ωt αP3 us2
us3
αP4 us4
us5
us6
us1
uo
ωt
α = cos −1 (γ sin ω o t ) (4-18)
Cosine wave-crossing method
Principle of cosine wave-crossing method 31
Output voltage ratio (Modulation factor) U om γ = (0 ≤ r ≤ 1) U d0
180
α/(°)
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Calculated results for firing delay angle
1.0 0.9 0.8 0.3 0.2 0.1
150 120 90
γ=0 γ = 0.1
0.2 0.3 0.8 0.9 1.0
60 30 0
π 2
π
3π 2
2π
ω0t
Output voltage phase angle
32
Maximum output frequency: 1/3 or 1/2 of the input frequency if using 6pulse rectifiers Input power factor Harmonics in the output voltage and input current are very complicated, and both related to input frequency and output frequency.
Input displacement factor
=1 .0
0.8
γ
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Input and output characteristics
0.6
0. 8 0 .6 0 .4 0. 2
0.4 0.2
0 0 0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2 0 Load power factor Load power factor (lagging) (leading)
33
Power Electronics
4.3.2 Three-phase thyristor-cycloconverter The configuration with common input line
34
Power Electronics
Three-phase thyristor-cycloconverter The configuration with star-connected output
35
Power Electronics
Three-phase thyristor-cycloconverter Typical waveforms Output voltage
Input current with Single-phase output
Input current with 3-phase output
0
200 t/ms
0
200 t/ms
0
200 t/ms
36
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Input and output characteristics The maximum output frequency and the harmonics in the output voltage are the same as in singlephase circuit. Input power factor is a little higher than singlephase circuit. Harmonics in the input current is a little lower than the single-phase circuit due to the cancellation of some harmonics among the 3 phases. To improve the input power factor: – Use DC bias or 3k order component bias on each of the 3 output phase voltages 37
Power Electronics
Features and applications Features – Direct frequency conversion—high efficiency – Bidirectional energy flow, easy to realize 4-quadrant operation – Very complicated—too many power semiconductor devices – Low output frequency – Low input power factor and bad input current waveform
Applications – High power low speed AC motor drive
38
Power Electronics
4.4 Matrix converter Circuit configuration Input
Output
39
Power Electronics
Matrix converter Usable input voltage
U1m Um
a)
a) Single-phase input voltage
3 2
1 2 Um
b)
b) Use 3 phase voltages to construct output voltage
U1m
c)
c) Use 3 line-line voltages to construct output voltage
40
Power Electronics
Features Direct frequency conversion—high efficiency Can realize good input and output waveforms, low harmonics, and nearly unity displacement factor Bidirectional energy flow, easy to realize 4-quadrant operation Output frequency is not limited by input frequency No need for bulk capacitor (as compared to indirect frequency converter) Very complicated—too many power semiconductor devices Output voltage magnitude is a little lower as compared to indirect frequency converter. 41
