advantages of matrix over cycloconverters
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Topic 10: Cycloconverters
Spring 2004
ECE 8830 - Electric Drives
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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.
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Phase-Controlled Cycloconverters
The basic principle of cycloconversion isillustrated by the single phase-to-singlephase converter shown below.
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Phase-Controlled Cycloconverters(contd)
A positive center-tap thyristor converteris connected in anti-parallel with anegative converter of the same type. This
allows current/voltage of either polarity tobe controlled in the load.
The waveforms are shown on the nextslide.
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Phase-Controlled Cycloconverters(contd)
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Phase-Controlled Cycloconverters(contd)
An integral half-cycle output wave is created which has afundamental 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-upfrequency conversion can be achieved by alternately
switching high frequency switching devices (e.g. IGBTs,
instead of thyristors) between positive and negative limitsat high frequency to generate carrier-frequency modulated
output.
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Phase-Controlled Cycloconverters(contd)
3 to single phase conversion can beachieved using either of the dual convertercircuit topologies shown below:
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Phase-Controlled Cycloconverters(contd)
A Thevenin equivalent circuit for the dualconverter is shown below:
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Phase-Controlled Cycloconverters(contd)
The input and output voltages are adjusted to be equaland the load current can flow in either direction. Thus,
where Vd0 is the dc output voltage of each converter atzero firing angle and p and N are the input and outputfiring angles. For a 3 half-wave converter Vd0 =0.675VLand Vd0 = 1.35VL for the bridge converter (VL is the rmsline voltage).
0 0 0cos cosd d p d nV V V V = = =
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Phase-Controlled Cycloconverters(contd)
Voltage-tracking between the input andoutput voltages is achieved by setting thesum of the firing angles to . Positive or
negative voltage polarity can be achieved asshown below:
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Phase-Controlled Cycloconverters(contd)
A 3 to 3 cycloconverter can be implemented using 18 thyristors as shownbelow:
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Phase-Controlled Cycloconverters(contd)
Each phase group functions as a dualconverter but the firing angle of each group
is modulated sinusoidally with 2 /3 phase
angle shift -> 3 balanced voltage at themotor terminal. An inter-group reactor(IGR) is connected to each phase to restrict
circulating current.
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Phase-Controlled Cycloconverters(contd)
An output phase wave is achieved bysinusoidal modulation of the thyristorfiring angles.
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Phase-Controlled Cycloconverters(contd)
A variable voltage, variable frequencymotor drive signal can be achieved byadjusting the modulation depth and output
frequency of the converter.
The synthesized output voltage wave
contains complex harmonics which can beadequately filtered out by the machinesleakage inductance.
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Phase-Controlled Cycloconverters(contd)
A 3 to 3 bridge cycloconverter (widely used in multi-MW applications)can be implemented using 36 thyristors
as shown below:
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Phase-Controlled Cycloconverters(contd)
The output phase voltage v0 can be written as:
where V0 is the rms output voltage and 0 isthe output angular frequency. We can also write:
where the modulation factor, mf is given by:
0 0 02 sinv V t=
0 0 0 0 0cos cos sind p d n f d v V V m V t = = =
0 02 /f dm V V=
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Phase-Controlled Cycloconverters(contd)
From these equations, we can write:
and
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.
1
0cos [ sin ]p fm t =
N P =
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Phase-Controlled Cycloconverters(contd)
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 whichwill result in short-circuits without an IGR.
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Phase-Controlled Cycloconverters(contd)
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.
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Phase-Controlled Cycloconverters(contd)
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Phase-Controlled Cycloconverters(contd)
At t=0, +ve load current is taken by the +ve converteronly (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 secondarywinding 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.
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Phase-Controlled Cycloconverters(contd)
The +ve and -ve converter currents can be expressed
as:
The self-induced circulating current is simply iP-iN.
In practice, the waves will not be pure sine waves butinclude a ripple current. Practical waveforms are shown on
the next slide.
00.5 0.5 sin P m mi I I t = +
00.5 0.5 sin N m mi I I t =
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Phase-Controlled Cycloconverters(contd)
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Phase-Controlled Cycloconverters(contd)
Advantages of circulating current mode of operation,
over blocking mode include:
Output phase voltage wave has lower harmonic contentthan 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.
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Phase-Controlled Cycloconverters(contd)
In the blocking mode of operation, no IGR is usedand 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:
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Phase-Controlled Cycloconverters(contd)
Since the cycloconverter is usually connecteddirectly to a motor, the harmonics from theconverter will induce torque pulsations andmachine heating resulting in increased machine
losses. Also, since the cycloconverter is essentiallya matrix of switches without energy storage(neglecting IGR) Pin=Pout . Thus distortions in theoutput voltage waveform reflect back into the line
input. See text for a discussion of the load voltageand line harmonics.
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Phase-Controlled Cycloconverters(contd)
A major disadvantage of cycloconvertersis poor DPF (displacement power factor). Tocalculate DPF, consider a phase group of an
18-thyristor cycloconverter shown below.
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Phase-Controlled Cycloconverters(contd)
Assume the +ve converter is operating incontinuous conduction and is connected to a highinductance load and assume that thecycloconverter is operating at low frequency.Segments of the output current and voltage wavesare as shown below:
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Phase-Controlled Cycloconverters(contd)
The Fourier series of the line current isgiven by:
where i0 is the load current and is thesupply frequency. The current wave has a dc
component and a fundamental componentwith a lagging phase angle, P.
0
0
3 1 1 1[sin( ) cos 2( ) cos 4( ) sin 5( ) ...]
3 2 4 5 P P P P
ii i t t t t
= + +
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Phase-Controlled Cycloconverters(contd)
Since the supplys 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:
where Vs =rms line voltage.
' 033 cos2
i s P
iP V
=
' 0
33 sin
2i s P
iQ V
=
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Phase-Controlled Cycloconverters(contd)
These equations can be rewritten as:
If the firing angle is constant, the converter acts as arectifier and Vd=Vd0cos P and i0=Id.
In a cycloconverter P and i0 vary sinusoidally and so Piand Qi are also modulated. We need to average these
parameters to determine loading on the source.
'
0 0 0 0 0(1.17 cos ) cosi s P d P P V i V i v i = = =
'0 0 0(1.17 sin ) sini s P d P Q V i V i = =
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Phase-Controlled Cycloconverters(contd)
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Phase-Controlled Cycloconverters(contd)
The expression for the average reactive power contributed by the line, Qi, isgiven by:
where = load power factor angle.
Performing the integration above yields:
where P0, Q0 are the real and reactive output power per phase, respectively.
1
2
0 0
0
1(1.17 sin )
cycle
i s PQ V i d t
=
/ 20 0 0 0 0
/ 2
1(1.17 cos )( sin( )) ( 1.17 cos )( sin( ))
s m s mV t I t d t V t I t d
+= + +
20 02 2 1cos sin 22
i
P QQ
= + +
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Phase-Controlled Cycloconverters(contd)
P0 and Q0 are given by:
and
Since the real output power = real input power, we can write:
The input DPF can be expressed as:
DPF = cos i =
0 0 0 cos P V I = 0 0 0 sinQ V I =
2
0
2 1cos sin 2
2i i i i P jQ P j P Q
+ = + + +
i
i i
P
P jQ+
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Phase-Controlled Cycloconverters(contd)
DPF =
=
=
where tan = Q0/Pi (=Q0/P0)
2 0
1
2 11 cos sin 2
2i
Qj
P
+ + +
2
1
2 11 cos tan sin 2
2j
+ + +
12
1 (1 tan )j
+ +
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Phase-Controlled Cycloconverters(contd)
This equation for DPF applies when additionalphase groups are added or if a 36-thyristorimplementation is considered.
mf=1 was assumed in this derivation. For mf1:
The maximum value of line DPF is 0.843.
21 (1 tan )
fmDPF
j
=+ +
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Phase-Controlled Cycloconverters(contd)
See Bose text pp. 180-184 for methodsto improve DPF.
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Phase-Controlled Cycloconverters(contd)
The control of a cycloconverter is verycomplex. A typical variable speed constantfrequency (VCSF) system is shown below:
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Phase-Controlled Cycloconverters(contd)
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.
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Phase-Controlled Cycloconverters(contd)
3 sinusoidal control signals are generatedthrough the vector rotator. The feedbackvoltage Vs is generated from the output
phase voltages.
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M t i C t
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Matrix Converters
These types of cycloconverters use high-frequency, self-controlled ac switches (e.g.IGBTs). A 3 to 3 converter is shown below:
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Matrix Converters (contd)
A matrix of nine switches where any inputphase can be connected to any output phase.The switches are controlled by PWM to
fabricate an output fundamental voltagewhose amplitude and frequency can be
varied to control an ac motor.
The output waveform synthesis is shownon the next slide.
C ( )
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Matrix Converters (contd)
M i C ( d)
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Matrix Converters (contd)
Matrix converters offer the advantage over
thyristor cycloconverters of being able to produceunity PF line current.
However, compared to PWM voltage-fed
converters, the parts count is significantly higher.
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High-Frequency Cycloconverters
See Bose text pp. 186-189