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UNIT V
AC voltage controller and
cycloconverter

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4.1.1 Single-phase AC voltage controller

VT1 u1
io
VT2
O ωt
u1 uo R uo
O ωt
io
The phase shift range
(operation range of phase O ωt
delay angle): u VT
0 ≤α≤ π
O ωt

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• Resistive load, quantitative analysis

RMS value of output voltage

π −α
Uo =
1
π ∫ (
π

α
2U sinωt) d(ωt) =U
1
2
1
1
2π
sin2α +
π
(4-1)

RMS value of output current

Uo
Io = (4-2)
R
RMS value of thyristor current
2
1  2U1 sinωt 
π U1 1 α sin2α
2π ∫α 
IT =  d (ωt ) = (1− + ) (4-3)
R  R 2 π 2π
Power factor of the circuit
P UoIo Uo 1 π −α
λ= = = = sin 2α + (4-4)
S U1I o U1 2π π
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Inductive (Inductor- resistor) load , operation principle

u1
VT 1
O ωt
io uG1
VT2
O ωt
R uG2
u1 uo O ωt
L uo
O ωt
io
The phase shift range:
O
φ ≤α ≤ π uVT ωt

O
ωt

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4.2 Other AC controllers

4.2.1 Integral cycle control—AC power controller

VT1 Conduction 2πN

io uo angle = M
VT2 2U1 2π uo,io u1
M
u1 uo R O π 3π 4π
M ωt
M M
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.

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4.3 Thyristor cycloconverters

4.3.1 Single- phase thyristor-cycloconverter

• Circuit configuration and operation principle

P N

Output Average
uo π
a p= voltage a p=0 output voltage π
2 a p=
2

ο ωt

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• Single- phase thyristor-cycloconverter

Modes of operation
uo
uo,io io

O t1 t2 t3 t4 t5 t
uP uo

io t
iP iN O
uP uo uN uN

O uo t
iP
O t
iN
O t

P Rectifi Inver
blocking
cation sion
Rectifi Inver
N blocking
cation sion

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Typical waveforms

uo

O
ωt

io

O ωt
1 3 4 6
2 5
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• Modulation methods for firing delay angle

Calculation method
– For the rectifier circuit

u2 u3 u4 u5 u6 u1
u o = U d0 cos α (4-15)

–For the cycloconverter ωt

ap3 ap4
output
uo =Uom sinωot (4-16) us2 us3 us4 us5 us6 us1
uo
–Equating (4- 15) and (4-16)
ωt
Uom
cosα = sinωot = γ sinωot
Ud0 Principle of cosine
(4-17)
–therefore
wave-crossing method
α = cos−1 (γ sinωot) (4-18)

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Output voltage ratio

1.0
0.9
(Modulation factor)
150 0.8
0.3
Uom 120 0.2
γ= (0 ≤ γ ≤ 1) 0.1
Ud 0 γ=0
α/( º )
90
γ=0.1
60 0.2
0.3
0.8
30 0.9
1.0
0 π π 3π 2π ωο t
2 2
Output voltage phase angle

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• The configuration with common input line

4.3.2 Three- phase thyristor-cyclo converter

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• The configuration with star-connected output

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Typical waveforms

Output voltage
200t/ms

Input current with

Single-phase output
200 t/ms

Input current with

3-phase output
200 t/ms
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• Input and output characteristics

The maximum output frequency and the harmonics in the output voltage
are the same as in single-phase circuit. Input power factor is a little
higher than single-phase circuit. Harmonics in the input current is a
little lower thanthe 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
• 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

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4.4 Matrix converter

• Circuit configuration

input
a b c

u
S1 S1 S1
1 2 3 Sij
v
S2 S2 S2 output
1 2 3
w
S3 S3 S3
1 2 3
a) b)
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• Usable input voltage

U1m √3
Um 1 Um U1m
2
2

a) b) c)
a) Single-phase input b) Use 3 phase voltages c) Use 3 line-line voltages
voltage to construct output to construct output
voltage voltage

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• 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.

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