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Analisis Sistem Kendali Industri
Cycloconverters
Introduction
Cycloconverters directly convert ac
signals of one frequency (usually line
frequency) to ac signals of variable
frequency. These variable frequency ac
signals can then be used to directly
control the speed of ac motors.
Thyristor-based cycloconverters are
typically used in low speed, high power
(multi-MW) applications for driving
induction and wound field synchronous
motors.
Phase-Controlled Cycloconverters
The basic principle of cycloconversion is
illustrated by the single phase-to-single
phase converter shown below.
Phase-Controlled Cycloconverters
(cont’d)
A positive center-tap thyristor converter
is connected in anti-parallel with a
negative converter of the same type.
This allows current/voltage of either
polarity to be controlled in the load.
The waveforms are shown on the next
slide.
Phase-Controlled Cycloconverters
(cont’d)
Phase-Controlled Cycloconverters
(cont’d)
An integral half-cycle output wave is created
which has a fundamental frequency
f0=(1/n) fi where n is the number of input
half-cycles per half-cycle of the output. The
thyristor firing angle can be set to control
the fundamental component of the output
signal. Step-up frequency conversion can be
achieved by alternately switching high
frequency switching devices (e.g. IGBTs,
instead of thyristors) between positive and
negative limits at high frequency to generate
carrier-frequency modulated output.
Phase-Controlled Cycloconverters
(cont’d)
3 to single phase conversion can be
achieved using either of the dual
converter circuit topologies shown below:
Phase-Controlled Cycloconverters
(cont’d)
A Thevenin equivalent circuit for the dual
converter is shown below:
Phase-Controlled Cycloconverters
(cont’d)
The input and output voltages are adjusted to be
equal and the load current can flow in either
direction. Thus,
V0  Vd  Vd 0 cos  p  Vd 0 cos  n
where Vd0 is the dc output voltage of each
converter at zero firing angle and p and N are
the input and output firing angles. For a 3 halfwave converter Vd0 =0.675VL and Vd0 = 1.35VL
for the bridge converter (VL is the rms line
voltage).
Phase-Controlled Cycloconverters
(cont’d)
Voltage-tracking between the input and output voltages is
achieved by setting the sum of the firing angles to .
Positive or negative voltage polarity can be achieved as
shown below:
Phase-Controlled Cycloconverters
(cont’d)
A 3 to 3 cycloconverter can be
implemented using 18 thyristors as
shown below:
Phase-Controlled Cycloconverters
(cont’d)
Each phase group functions as a dual
converter but the firing angle of each
group is modulated sinusoidally with 2/3
phase angle shift -> 3 balanced voltage
at the motor terminal. An inter-group
reactor (IGR) is connected to each phase
to restrict circulating current.
Phase-Controlled Cycloconverters
(cont’d)
An output phase wave is achieved by
sinusoidal modulation of the thyristor
firing angles.
Phase-Controlled Cycloconverters
(cont’d)
A variable voltage, variable frequency
motor drive signal can be achieved by
adjusting the modulation depth and output
frequency of the converter.
The synthesized output voltage wave
contains complex harmonics which can be
adequately filtered out by the machine’s
leakage inductance.
Phase-Controlled Cycloconverters
(cont’d)
A 3 to 3 bridge cycloconverter
(widely used in multi-MW applications)
can be implemented using 36 thyristors
as shown below:
Phase-Controlled Cycloconverters
(cont’d)
The output phase voltage v0 can be written
as:
v0  2V0 sin 0t
where V0 is the rms output voltage and 0
is the output angular frequency. We can
also write:
v0  Vd 0 cos  p  Vd 0 cos  n  m f Vd 0 sin  0t
where the modulation factor, mf is given
by:
m f  2V0 / Vd 0
Phase-Controlled Cycloconverters
(cont’d)
From these equations, we can write:
 p  cos1[m f sin 0t ] and  N     P
Thus for zero output voltage, mf=0 and
P= N= /2. For max. phase voltage,
mf=1 => P=0, N= . See below figure
for P and N values for mf=0.5 and 1.
Phase-Controlled Cycloconverters
(cont’d)
The phase group of a cycloconverter can be
operated in two modes:
1) Circulating current mode
2) Non-circulating current (blocking) mode
In the circulating current mode, the current
continuously circulates between the +ve and
-ve converters. Although the fundamental
output voltage waves of the individual
converters are equal, the harmonics will
cause potential difference which will result in
short-circuits without an IGR.
Phase-Controlled Cycloconverters
(cont’d)
The equivalent circuit of a phase group with
an IGR is shown below.
The inclusion of an IGR leads to self-induced
circulating current as illustrated in the next
slide.
Phase-Controlled Cycloconverters
(cont’d)
Phase-Controlled Cycloconverters
(cont’d)
At t=0, +ve load current is taken by the +ve
converter only (iP=i0).
From 0->/2, rising +ve load current will
create a +ve voltage drop (vL=Ldi0/dt) in the
primary winding of the IGR. This creates a -ve
voltage drop in the secondary winding of the
IGR
-> DN reverse biased.  no current
flow in the -ve converter.
At /2, i0 peaks at Im-> vL=0. After this vL
tends to reverse polarity inducing current in
the -ve converter. Voltage across IGR becomes
clamped to 0 -> self-induced circulation
current between +ve and -ve converters.
Phase-Controlled Cycloconverters
(cont’d)
The +ve and -ve converter currents can be
expressed as:
iP  0.5I m  0.5I m sin 0t
iN  0.5I m  0.5I m sin 0t
The self-induced circulating current is
simply iP-iN.
In practice, the waves will not be pure
sine waves but include a ripple current.
Practical waveforms are shown on the
next slide.
Phase-Controlled Cycloconverters
(cont’d)
Phase-Controlled Cycloconverters
(cont’d)






Advantages of circulating current mode of
operation, over blocking mode include:
Output phase voltage wave has lower
harmonic content than in blocking mode.
Output frequency range is higher.
Control is simple.
Disadvantages
Bulky IGR increases cost and losses.
Circulating current increases losses in
thyristors.
Over-design increases cost.
Phase-Controlled Cycloconverters
(cont’d)
In the blocking mode of operation, no
IGR is used and only one converter is
conducting at any time.
Zero current crossing detection can be
used to select +ve or -ve converter
conduction as shown below:
Phase-Controlled Cycloconverters
(cont’d)
Since the cycloconverter is usually
connected directly to a motor, the
harmonics from the converter will induce
torque pulsations and machine heating
resulting in increased machine losses.
Also, since the cycloconverter is essentially
a matrix of switches without energy
storage (neglecting IGR) Pin=Pout . Thus
distortions in the output voltage waveform
reflect back into the line input. See text for
a discussion of the load voltage and line
harmonics.
Phase-Controlled Cycloconverters
(cont’d)
A major disadvantage of cycloconverters
is poor DPF (displacement power factor).
To calculate DPF, consider a phase group
of an 18-thyristor cycloconverter shown
below.
Phase-Controlled Cycloconverters
(cont’d)
Assume the +ve converter is operating in
continuous conduction and is connected to a
high inductance load and assume that the
cycloconverter is operating at low frequency.
Segments of the output current and voltage
waves are as shown below:
Phase-Controlled Cycloconverters
(cont’d)
The Fourier series of the line current is
given by:
i
i0
3
1
1
1

i0 [sin( t   P )  cos 2( t   P )  cos 4( t   P )  sin 5( t   P )  ...]
3 
2
4
5
where i0 is the load current and  is the
supply frequency. The current wave has a
dc component and a fundamental
component with a lagging phase angle, P.
Phase-Controlled Cycloconverters
(cont’d)
Since the supply’s active and reactive
power components are contributed only by
the fundamental current, the instantaneous
active Pi’ and reactive power Qi’ for the
positive converter is given by:
 3i0 
Pi  3Vs 
 cos  P
 2 
'
 3i0 
Q  3Vs 
 sin  P
 2 
'
i
where Vs =rms line voltage.
Phase-Controlled Cycloconverters
(cont’d)
These equations can be rewritten as:
Pi '  (1.17Vs cos  P )i0  Vd 0 cos  P i0  v0i0
Qi'  (1.17Vs sin  P )i0  Vd 0 sin  Pi0
If the firing angle is constant, the converter
acts as a rectifier and Vd=Vd0cosP and i0=Id.
In a cycloconverter P and i0 vary sinusoidally
and so Pi’ and Qi’ are also modulated. We
need to average these parameters to
determine loading on the source.
Phase-Controlled Cycloconverters
(cont’d)
Phase-Controlled Cycloconverters
(cont’d)
The expression for the average reactive
power contributed by the line, Qi, is given by:
Qi 
1
 
 
1

 /2

1
cycle
2

(1.17Vs sin  P )i0 d 0t
0

(1.17Vs cos 0t )( I m sin( 0t   ))d 0t   (1.17Vs cos  0t )( I m sin( 0t   ))d 0t 

 /2
 
where = load power factor angle.
Performing the integration above yields:
2Q0 
1

Qi 
cos  


sin
2



 
2

2 P0
2
where P0, Q0 are the real and reactive output
power per phase, respectively.
Phase-Controlled Cycloconverters
(cont’d)
P0 and Q0 are given by:
P0  V0 I 0 cos  and
Q0  V0 I 0 sin 
Since the real output power = real input
power, we can write:
2
1


2
Pi  jQi  Pi  j  Pi cos   Q0    sin 2  

2


The input DPF can be expressed as:
DPF = cosi =
Pi
Pi  jQi
Phase-Controlled Cycloconverters
(cont’d)
 DPF =
=
=
1
Q0 
2 2
1

1  j cos      sin 2  

Pi 
2

1
1 j
2 2
1


cos


tan



sin
2



 
2


1
1 j
2

(1   tan  )
where tan = Q0/Pi (=Q0/P0)
Phase-Controlled Cycloconverters
(cont’d)
This equation for DPF applies when
additional phase groups are added or if a
36-thyristor implementation is considered.
mf=1 was assumed in this derivation.
For mf 1:
mf
DPF 
1 j
2

(1   tan  )
The maximum value of line DPF is 0.843.
Phase-Controlled Cycloconverters
(cont’d)
See Bose text pp. 180-184 for methods
to improve DPF.
Phase-Controlled Cycloconverters
(cont’d)
The control of a cycloconverter is very
complex. A typical variable speed constant
frequency (VCSF) system is shown below:
Phase-Controlled Cycloconverters
(cont’d)
Generator bus with regulated voltage but
variable frequency (1333-2666 Hz) is fed
to the cycloconverter phase groups. (A
generator speed variation of 2:1 is
assumed). The dual converter in each
phase group uses a low-pass filter to
generate a sinusoidal signal.
 modulator receives biased cosine waves
from generator bus voltage and sinusoidal
control signal voltages to generate
thyristor firing angles.
Phase-Controlled Cycloconverters
(cont’d)
3 sinusoidal control signals are generated
through the vector rotator. The feedback
voltage Vs is generated from the output
phase voltages.
Phase-Controlled Cycloconverters
(cont’d)
Details of  modulator are shown below:
Matrix Converters
These types of cycloconverters use highfrequency, self-controlled ac switches (e.g.
IGBTs). A 3 to 3 converter is shown
below:
Matrix Converters (cont’d)
A matrix of nine switches where any input
phase can be connected to any output
phase. The switches are controlled by
PWM to fabricate an output fundamental
voltage whose amplitude and frequency
can be varied to control an ac motor.
The output waveform synthesis is shown
on the next slide.
Matrix Converters (cont’d)
Matrix Converters (cont’d)
Matrix converters offer the advantage
over thyristor cycloconverters of being
able to produce unity PF line current.
However, compared to PWM voltagefed converters, the parts count is
significantly higher.
High-Frequency Cycloconverters
See Bose text pp. 186-189