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Transcript
ECE 8830 - Electric Drives
Topic 9: Current-Fed Inverters
Spring 2004
Introduction
Current-fed inverters requires a “stiff”
constant current source input - thus are
sometimes referred to as CSI (current
source inverters or current stiff inverters).
A large inductance can be used to change a
variable voltage input to a variable current
input.
VSI-inverters and CSI-inverters are dual to
each other.
Introduction (cont’d)
Power semiconductor devices used in CSI
inverters must be able to withstand large
reverse voltages. Therefore, power
MOSFETs, BJTs, IGBTs, MCTs, IGCTs and
GTOs.
Symmetric blocking GTOs and thyristors
can be used in CSI inverters.
Generally CSI inverters are now used in
very high power applications.
General Operation of a 6-Step
Thyristor Inverter
General Schematic of Thyristor Inverter
General Operation of a 6-Step
Thyristor Inverter (cont’d)
Initially, ignore commutation considerations.
Induction motor load is modeled by back emf
generator and leakage inductance in each
phase of the winding.
The constant dc current Id is switched
through the thyristors to create a 3 6-step
symmetrical line current waves as shown on
the next slide.
General Operation of a 6-Step
Thyristor Inverter (cont’d)
General Operation of a 6-Step
Thyristor Inverter (cont’d)
The load or line current may be expressed
by a Fourier series as:
1
1


ia 
I d cos  t  cos 5 t  cos 7 t  ...

5
7


2 3
where the peak value of the fundamental
component is2
given
/ 3 2 3I d /  . Each thyristor
conducts for
radians. At any instant
one upper thyristor and one lower thyristor
conduct.
General Operation of a 6-Step
Thyristor Inverter (cont’d)
The dc link is considered harmonic-free
and the commutation effect between
thyristors is ignored.
At steady state the voltage output from
the rectifier block = input voltage of
inverter.
For a variable speed drive the inverter
can be operated at variable frequency
and variable dc current Id.
General Operation of a 6-Step
Thyristor Inverter (cont’d)
If thyristor firing angle  > 0, inverter
behavior.
If thyristor firing angle =0, rectifier
behavior.
Max. power transfer occurs when =.
Inverter Operation Modes
Two inverter operation modes are
established depending on the thyristor
firing angle:
1) Load-commutated inverter
Applies when /2<<.
2) Force-commutated inverter
Applies when <<3/2.
Load-Commutated Inverter Mode
Consider =3/4. In this case vca < 0 =>
thyristor Q5 is turned off by the load. This
requires load to operate at leading power
factor => motoring mode of a synchronous
machine operating in over-excitation.
Vd=-Vd0cos
Force-Commutated Inverter Mode
Consider =5/4. In this case vca> 0 and
so thyristor Q5 is not turned off by the load.
Thus some type of forced commutation is
required in this case. Lagging VAR is
consumed by the load => motoring mode
of an induction motor. Vd=-Vd0cos
Force-Commutated Inverters
For driving an induction machine, a
force-commutated inverter is required
because of the phase lag characteristic of
the induction motor.
The topology of a 3 bridge inverter with
an auto-sequential method of forced
commutation is shown on the next slide.
Force-Commutated Inverters (cont’d)
Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives”
Force-Commutated Inverters (cont’d)
The current is switched sequentially into
one of the motor phases by the top half of
the inverter and returns to the dc link from
another of the phases via the bottom half
of the inverter. By switching every 2/3
radians, a 6-step current waveform can be
applied to the motor.
The series diodes and delta-connected
capacitors force the commutation of the
thyristors. The capacitors store a charge
with the correct polarity for commutation
and the diodes isolate them from the load.
Force-Commutated Inverters (cont’d)
Since current is constant, voltage drop
across stator windings = 0 and voltage
drop across winding resistances = constant.
Thus the motor terminal voltage is set by
the motor not by the inverter.
Since the motor is wound with sinusoidally
distributed windings, the voltages at the
motor terminals are nearly sinusoidal.
Force-Commutated Inverters (cont’d)
The current ideally follows a six-step
waveform. However, current cannot change
instantaneously through the winding
inductances and so the current transitions
have a finite slope.
During these transitions the current
transfers from one thyristor to the next via
one of the six commutating capacitors.
Force-Commutated Inverters (cont’d)
Example: Commutation from Q2 to Q4
Force-Commutated Inverters (cont’d)
When Q4 is fired, Q2 is impressed with a
reverse voltage across the capacitor bank.
=> Q2 turns off almost instantaneously. Id
flows through Q3 and D3, phases b and c,
D2, the capacitor bank and Q4. The
capacitor bank charges linearly with Id.
During this time D4 is reverse-biased.
When the capacitor bank voltage equals
the line voltage, diode D4 turns on and the
current Id flows through D4 and terminates
the commutation process.
Force-Commutated Inverters (cont’d)
Ref: D.W. Novotny and
T.A. Lipo, “Vector
Control and Dynamics of
AC Drives”
Force-Commutated Inverters (cont’d)
Note the large voltage spikes (Ldi/dt).
These can be suppressed either by
designing the motor with small leakage
inductance or by using a diode bridge at
the motor terminal with a zener diode load.
Force-Commutated Inverters (cont’d)
Two positive features of CSI inverters
compared to VSI inverters:
1) CSI inverters are able to ride through a
commutation failure and return naturally to
normal operation; costly preventive
measures used for VSI inverters.
2) CSI inverters can be switched to
regenerative mode simply by reversing the
polarity of the dc rectifier output voltage.
This is automatically accomplished when an
induction motor operates in a negative slip
mode. In the VSI inverter, the current flow
must be reversed - much harder.
Force-Commutated Inverters (cont’d)
On the other hand, CSI drives cannot be
operated in open loop operation as can VSI
drives. The torque-speed characteristics of
an induction motor driven by a voltage
source and a current source are shown below:
Ref: D.W. Novotny and T.A. Lipo,
“Vector Control and Dynamics of
AC Drives”
Force-Commutated Inverters (cont’d)
A distinct “peaking” occurs in the current
source case.
Two possible operating points:
1) One on the stable, negatively sloped
region, and
2) one above breakdown torque on the
positively sloped region where operation
is generally unstable (depending on load
torque vs. speed characteristics).
Force-Commutated Inverters (cont’d)
On the stable side, the working flux in the
machine is is high => saturated operation
and excessive magnetizing current and iron
losses. Thus, continuous operation is not
feasible on this side.
On the unstable side, the flux in the
machine is near its rated value and losses
are reasonable. However, being on the
unstable side, feedback control must be
used to maintain the operating point.
Force-Commutated Inverters (cont’d)
One system uses a motor voltage control
loop (see next slide) which regulates the
motor voltage by controlling the input
phase controlled rectifier. Also, an internal
current control loop is used with the
voltage error serving as a reference signal
for the current regulator. Some IR drop
compensation is often added as are
additional compensating circuits to improve
system dynamics.
Force-Commutated Inverters (cont’d)
Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives”
Force-Commutated Inverters (cont’d)
ASCI inverter-fed induction motor drives
for medium to high power applications
were popular.
However, the size and cost of the
commutating capacitors and the dc link
inductor are the major disadvantages of
this type of inverter.
ASCI inverters are being replaced with
inverters using self-controlled devices
(e.g. GTOs).
Six-Step CSI with Self-Commutated
Devices
Self-controlled symmetric blocking devices,
e.g. GTO’s can be turned on and off by gate
current pulses. This allows the 6-step
waveform to be directly controlled.
Six-Step CSI with Self-Commutated
Devices (cont’d)
In this circuit, the capacitors are freed
from their commutating requirement and
are simply placed across the terminals of
the induction motor. These capacitors are
much smaller and serve two roles:
1) primarily, to allow commutation from
the outgoing GTO to the incoming GTO,
2) secondarily, to load filter higher
harmonics
Six-Step CSI with Self-Commutated
Devices (cont’d)
Example: Commutation from Q1 to Q3.
Six-Step CSI with Self-Commutated
Devices (cont’d)
Initially current flows through Q1, phase a,
phase c, and Q2. The equivalent capacitance
Ceq and polarity of vba are as shown.
Next, Q3 is turned on at time A. But because
of voltage across Ceq, Q1 does not
automatically turn off.
Next, Q1 is turned off.The current Id transfers
to Q3 and through Ceq.
Ceq charges up overcoming the motor back
emf b/w phases a and b. Gradually the
current transfers to phase b. Commutation is
completed when ib=Id.
Six-Step CSI with Self-Commutated
Devices (cont’d)
Total commutation time is tc.
Once commutation is complete, current
can be commutated back to Q1. This
back and forth current commutation can
be used to create a PWM current wave
and with suitable selection of notch
angles, can be used to suppress higher
harmonics (just as in the VSI inverter).
Six-Step CSI with SelfCommutated Devices (cont’d)
A major disadvantage of this scheme is the
potential for resonance between the
capacitors and the motor inductance. Care
must be taken to avoid impressing current
harmonics into the motor/capacitor
network which will excite one of the
system resonance frequencies. This can be
avoided by careful use of PWM. However,
since the motor parameters must be
known to implement such an approach,
this drive is not popular for generalpurpose applications.
PWM Inverters
The six-step CSI inverter has several
disadvantages primarily associated with
harmonics in the current waves. Pulse
width modulation can be used to reduce the
harmonic content of the current waves. The
PWM methods are somewhat different from
those for the voltage-fed inverters.
Trapezoidal PWM
Similar to the sinusoidal PWM method for
voltage-fed converter. This method is
shown below:
Trapezoidal PWM
Trapezoidal wave has max. amplitude of B
and is compared to a triangle wave of
amplitude A.
For the first /3 radians both waves are
compared. For the next /3 radians no
triangular wave is applied. For the final /3
radians both waves are compared again.
Two variables: 1) modulation index m=B/A
2) pulse number M in halfcycle of inverter operation.
Trapezoidal PWM (cont’d)
For M=21, harmonics vs. m is as shown below:
At m=0.82,
5th harmonic =0, 7th harmonic=4%,
11th harmonic=1% and 13th harmonic=2%.
Trapezoidal PWM (cont’d)
The output current waves for these
conditions is shown below:
Trapezoidal PWM (cont’d)
To limit switching losses it is necessary to
control the device switching frequency,
irrespective of the fundamental frequency
of the current waveform. This can be
achieved by making the parameter M
constant in many segments of the
fundamental frequency (see next slide for
switching frequency 1kHz).
Note: In multi-MW GTO inverters the
switching frequency generally does not
exceed a few hundred Hz.
Trapezoidal PWM (cont’d)
Trapezoidal PWM can reduce harmonic
components up to order n=1.5(M+1)
for M > 9 but does produce a pair of
harmonics of order 3(M-1)1.
Selected Harmonic Elimination PWM
SHE-PWM can both lower the harmonic
content of the output current and, more
importantly, remove the resonant
harmonic. Unlike SHE-PWM for voltage-fed
inverters, several restrictions apply for
application of SHE-PWM to current-fed
inverters.
Consider the 3 current waveforms for
M=5 shown in the next slide.
Selected Harmonic Elimination
PWM (cont’d)
Selected Harmonic Elimination
PWM (cont’d)
Angles 1 and 2 are the variables and all the
other switching angles are in terms of these
two variables. With two variables, two
switching harmonics (e.g. 5th and 7th) can be
eliminated. The fundamental is controlled by
the dc link current frequency. The general
relation between # of harmonics removed (K)
and # of pulses per half cycle (M) is given by:
K=(M-1)/2
Both K and M are odd numbers.
Selected Harmonic Elimination
PWM (cont’d)
For M=3, only one harmonic (e.g. 5th)
can be eliminated and for M=7, three
harmonics (e.g. 5th, 7th and 11th) can be
eliminated.
Selected Harmonic Elimination
PWM (cont’d)
Double-Sided CSI Converter
As mentioned earlier, the CSI converter
can easily be used to send power back into
the rectifier when the machine acts as a
generator. In this case the load-side
converter acts as a rectifier and the lineside converter acts as an inverter.
Duality of Current-Fed and
Voltage-Fed Inverters
Ref: D.W. Novotny
and T.A. Lipo,
“Vector Control and
Dynamics of AC
Drives”
Current-Fed vs. Voltage-Fed
Inverters
Current-Fed Inverters Voltage-Fed Inverters
1. More interactive with
the load and hence
require a close match
to the machine.
2. Inherent 4-quadrant
operation.
3. Robust through load
short circuits/inverter
misfirings.
Not so interactive with
machine and can thus
be designed to be more
general purpose.
Requires additional
circuitry to operate in
all 4 quadrants.
Shoot-through faults
need to be avoided (use
freewheel diodes).
Current-Fed vs. Voltage-Fed
Inverters
Current-Fed Inverters Voltage-Fed Inverters
4. Devices must be
symmetric blocking.
5. Multi-machine or
multi-inverter system
inverter system very
difficult to implement.
6. Relatively sluggish
response.
Devices must be
assymmetric blocking.
Normally used for
multi-machine or multiinverter system
applications.
PWM inverters can
demonstrate relatively
fast dynamic response.
Current-Fed vs. Voltage-Fed
Inverters
Current-Fed Inverters Voltage-Fed Inverters
7. Cannot be operated
open-loop.
Can be operated openloop.
8. Minimum load required. Can operate at no-load.
Based on these differences, PWM voltage-fed
inverters are most widely used for motor
drives. However, current-fed inverters are used
for high-power applications, particularly loadcommutated synchronous motor drives.
d,q Model for CSI Inverter
The duality of VSI and CSI systems implies
that the switching function models for CSI
systems should be the duals of those for
the VSI systems.
The exact dual of a VSI feeding a Y
connected load is a CSI feeding a 
connected load. However, since we
generally want to consider Y connected
loads, the model for the CSI inverter will
not be the exact dual of the VSI inverter
(but it will be close).
d,q Model for CSI Inverter (cont’d)
The d,q equations for each switching mode
for the CSI inverter are obtained in the
same way as for the VSI inverter. The six
switching modes for the CSI inverter are
shown on the next slide.
d,q Model for CSI Inverter (cont’d)
Ref: D.W. Novotny and T.A.
Lipo, “Vector Control and
Dynamics of AC Drives”
d,q Model for CSI Inverter (cont’d)
The d,q equations, in the stationary stator
reference frame, can be written in terms
of CSI inverter switching functions, h as:
i 
s
qs
2 3

h i ; i 
s
qs i
s
ds
2 3
s
ds i
h i
; vi 
3 3
(vqss hqss  vdss hdss )


where the switching functions (shown on
the next slide) can be expressed as
Fourier series by:
1
1
h  cos  et  cos 5 et  cos 7 et  ...
5
7
1
1
hdss  sin  et  sin 5 et  sin 7 et  ...
5
7
s
qs
d,q Model for CSI Inverter (cont’d)
Ref: D.W. Novotny and
T.A. Lipo, “Vector
Control and Dynamics
of AC Drives”
d,q Model for CSI Inverter (cont’d)
These equations can be written in complex
form as:
i
s
qds

2 3

vi 
where
h
s
qds
ii (h  jh ) 
s
qs
3 3
e

j et
s
ds
s
s
2 3

s
ii h qds
†
Re[v qds h qds ]
1 5 jet 1 7 jet
 e
 e
 ...
5
7
Note that these are very similar to the VSI
equations. In particular, only the signs in
hqdss are altered.
d,q Model for CSI Inverter (cont’d)
As before we observe that the complex
vector current is constant in each mode
and simply shifts by 60 at each mode
transition. We can write:
i
s
qds
2

ii e j[ / 6( k 1)( / 3)]
3
for k=1, 2, 3, 4, 5, and 6. The six vectors
corresponding to the switching of a CSI
inverter are shown in the next slide.
d,q Model for CSI Inverter (cont’d)
Ref: D.W. Novotny and T.A. Lipo, “Vector Control and Dynamics of AC Drives”
d,q Model for CSI Inverter (cont’d)
See handout for d,q model for CSI
inverter in stationary reference frame.