resonance and multilevel converters
TRANSCRIPT
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Industrial Electrical Engineering and Automation
Lund University, Sweden
Resonance and Multilevel
converters
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Conventional 2-level Inverter
• Topology reference
• Two level output: ±Vdc/2
• High dv/dt (=𝑉𝑑𝑐
𝑡𝑠𝑤)
• Few components
• Easy to control
• EMC reducing
implementation required
One phase leg of a 2-level inverter
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Multilevel Inverters
Introduction:
• Inverters with 3+ voltage levels are
called multilevel inverters
• m-1 capacitors split the DC voltage into
m levels (m-1 levels in the line voltage)
• The switches select the correct level
• The output only changes 1 level
up/down at a time (𝑑𝑣
𝑑𝑡=
𝑉𝑑𝑐/(𝑚−1)
𝑡𝑠𝑤)
Example in figure:
Assume m = 5 which means 4 capacitors are
used to split up the DC voltage.
Then the output shown in the figure is:
𝑉𝑜𝑢𝑡 =𝑉𝑑𝑐2−𝑉𝑑𝑐4
=𝑉𝑑𝑐4
Simplified m-level
inverter
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Multilevel Inverters pros/cons
Benefits:
• Less total harmonic distortion
• Can run on lower switching frequency
• Less component stress
• Lower component voltage rating
Drawbacks:
• Higher complexity
• Higher amount of components
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Neutral Point Clamped Multilevel
Inverter (NPCMLI )
Principle:
• The DC voltage is split into smaller
levels by the capacitors.
• Diodes are used to clamp each
switch to one capacitor voltage
level.
• Switch state determines output
voltage
Components:
• Number of capacitors: m-1
• Number of clamping diodes: (m-
1)(m-2) per phase
• Number of switches: 2(m-1) per
phase
• All components must have voltage
rating higher than Vdc/(m-1)
5-level Natural Point
Clamped Inverter
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NPCMLI pros/cons
Benefits:
• Easy to control.
Drawbacks:
• High amount of clamping
diodes when number of
voltage levels is high.
• Capacitor unbalance
occurs when transferring
real power.
3-level Natural Point
Clamped Converter
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Capacitor Clamped Multilevel
Inverter (CCMLI )
Principle:
• Same basic principle as the NPCMLI
• Capacitors are used to clamp the
device voltage to one voltage level
• Has redundant switching states, which
makes capacitor balancing possible.
Components:
• Number of DC-bus capacitors: m-1
• Number of clamping capacitors: (m-
1)(m-2)/2 per phase
• Number of switches: 2(m-1) per phase
• All components must have voltage
rating higher than Vdc/(m-1)
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CCMLI pros/cons
Benefits:
• Redundant switch combinations makes voltage
balancing possible
Drawbacks:
• High amount of clamping capacitors when
number of voltage levels is high
• Capacitors are more expensive and bulky than
diodes
• Balancing modulation is very complicated and
requires high switching frequency resulting in
high switching losses
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Modular Multilevel Inverter (MMI)
Principle:
• Modularized setup with submodules.
• Each submodule have a capacitor
charged to Vdc/(m-1).
• The submodules can be inserted to
make their capacitor contribute to the
output.
• Has redundant switching states, which
makes capacitor balancing possible.
Components:
• Number of capacitors: 2(m-1) per phase
+2
• Number of switches: 4(m-1) per phase
• 2 inductors per phase (to take up
voltage difference when switching
occurs)
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MMI pros/cons
Benefits:
• Modularized setup
• Redundant switch combinations makes voltage
balancing possible
• The number of required components dose not
grow quadratic with number of levels.
Drawbacks:
• Complicated balancing modulation
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Matrix Converter
© Mats Alaküla L5 – 3-phase modulation
• Three VARYING levels IN
• Modulation to any
number of potentials
OUT
• No intermediate Energy
Storage
• Simple modulation
• Sort the three input
levels in [min med
max] and ”think 3-
level”
• Difiicult Switching
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Star C
Principle:
• The switches generate block-shaped voltage pulse
• The pulse is shaped to a semi-sinusoidal pulse
• This pulse is fed to the output capacitor for one of the phases
The Star C topology got two different approaches: a) The
series resonant (soft switched) and b) the inductive (hard
switched).
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Star C pros/cons
Benefits:
• Low number of semiconductor switches (compared to MLI:s)
• Very low output voltage derivatives
Drawbacks of series resonant Star C:
• May run in to problems if the load is
unsymmetrical
Drawbacks of inductive Star C:
• Higher switching losses as a result of hard
switching
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2- and 3-level inverter simulations
One phase leg of the 2-lvl inverter
One phase leg of the 3-lvl inverter
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Modulation - Control of voltage
time area
Electric Drives
Control
0when
1when
sv
svv
b
a
c
0when 0
1when
s
suusvvsu
k
kba
i
u e
L R ,
a v
b v
0
+ b v
+ a v
k u c v 1 s
0 s
15
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Output voltage
Electric Drives
Control
v
t
u
v
v
a
b
u k
0
T 2T 3T
c
t
1 y 2 y 3 y
16
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Control with both flanks
Electric Drives
Control
++ + yyy ),(
+
-
u
T 0
+ y y
k u
+
+
+
0
0
2/
dtuYdtuy k
T
k
+
2/
2/
T
T
k dtuy
2/
0
0
T
k dtuY
T/2
17
+ - 0 T T
2
y
m y m y * 3 y y *
3 y y * 3 y *
3 y
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Industrial Electrical Engineering and Automation
Lund University, Sweden
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To Simulink !
© Mats Alaküla L5 – 3-phase modulation
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Balancing the capacitor clamped
inverter
One phase leg of a 5-lvl
capacitor clamped inverter
Available switch states and
corresponding voltage evolution (from “Flying Capacitor Multilevel Inverters and DTC
Motor Drive Applications” by M. Escalante, J. Vannier,
A. Arzandé)
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Simulation work to do
• Add the motor model
• Balancing modulation for the Modular
Multilevel Inverter
• Balancing circuit for the Diode Clamped
Multilevel Inverter
• Adjust all simulations to specifications
One phase leg of the 5-lvl diode
clamped inverter
One phase leg of the 5-lvl
modular inverter
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Capacitor Clamped MLI
- Kapacitanser i serie
- Mäta alla kapacitans
värden
- Look-up Table i
Spice
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CCMLI - Balansering
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Modular MLI
- Balansera en fas som i
CCMLI
- Balansera tre faser –
Se modular.pdf
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Natural Point Clamped MLI
- 3-level version (simulering)
- Fler nivåer => Balanserings
problem
- Balansera med extra krets
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NPCMLI - Balansering
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Two quadrant DC converters : II
u
0 T 2T 3T t
0 T 2T 3T t
u
u*
u m
U dc
U
U dc
dc,max
U dc,max
y1
y2
y3
+
Udc
-
+
u
-
i
27
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© Mats Alaküla L5 – 3-phase modulation
The generic 3-phase load
R
R
R
L
L
L
+ ae
+ be
+ ce
+ au
+ bu
+ cu
ai
bi
ci
edt
diLiRu
edt
diLiRue
edt
diLiRue
edt
diLiRu
ca
cc
j
ba
bb
j
aa
aa
++
+++
++
++
3
4
3
2
3
2
3
2
3
2
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© Mats Alaküla L5 – 3-phase modulation
Vectors in 3-phase systems
a i
b i
c i
a
b
3
4j
e
3
2j
e
1
bbaa iuiuiuiuiutp ccbbaa +++)(
Effekt-invarians
edt
diLiRu
edt
diLiRue
edt
diLiRue
edt
diLiRu
ca
cc
j
ba
bb
j
aa
aa
++
+++
++
++
3
4
3
2
3
2
3
2
3
2
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© Mats Alaküla L5 – 3-phase modulation
Symmetric emf
3
4cosˆ
3
2cosˆ
cosˆ
tee
tee
tee
c
b
a
R
R
R
L
L
L
+ ae
+ be
+ ce
+ au
+ bu
+ cu
ai
bi
ci
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© Mats Alaküla L5 – 3-phase modulation
Example, grid voltage vector
tj
j
c
j
ba
eEttjte
ttjte
jtt
jttt
e
jtjtte
eeeeee
+
++
++
+
+
+
+
+
+
+
+
++
)sin(cosˆ2
3
4
3
4
3)sin(
4
1
4
11cosˆ
3
2
2
3
2
1
3
4sinsin
3
4coscos
2
3
2
1
3
2sinsin
3
2coscoscos
ˆ3
2
2
3
2
1
3
4cos
2
3
2
1
3
2coscosˆ
3
2
3
2 3
4
3
2
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© Mats Alaküla L5 – 3-phase modulation
Rotating reference frame
2
00
tj
ttj
t
eE
j
edteEdte
Use the integral of
The grid back emf
vector: ie
t
2
t
a
b
d
q
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© Mats Alaküla L5 – 3-phase modulation
Voltage equation in the (d,q)-frame
eiLjdt
idLiRu
+++
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© Mats Alaküla L5 – 3-phase modulation
Active power ...
3
21
22
***** ReRe)(
qqqq
dd
qdiei
dt
diLi
dt
diLRiRi
ieiiLjidt
idLiiRiutp
eiLjdt
idLiRu
++++
+++
+++
Resistive
losses Energizing
inductances
Power absorbed
by the grid back emf
)cos()cos(ˆ)cos()( , phasermsphase IEiEiEtp 32
3
Stationarity:
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© Mats Alaküla L5 – 3-phase modulation
3-phase converters – 8 switch states
)0,0,1( )0,1,1( )0,1,0(
)1,1,0( )1,0,0( )1,0,1()1,1,1(
)0,0,0(
)0,0,1(u
)0,1,0(u
)1,0,0(u
)0,1,1(u
)1,1,0(u
)1,0,1(u
)1,1,1(u
)0,0,0(u
)1,1,1(0)0,0,0(
)0,1,1(3
2)1,0,0(
)1,0,1(3
2)0,1,0(
)1,1,0(3
2)0,0,1(
3
4
3
2
uu
ueUu
ueUu
uUu
j
dc
j
dc
dc
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© Mats Alaküla L5 – 3-phase modulation
3-phase converters - sinusoidal references
***
***
**
6
1
2
1
6
1
2
1
3
2
ab
ab
a
uuu
uuu
uu
c
b
a
***** )sin()cos( ba ujutjtueuu tj ++
)3
4cos(
3
2
)3
2cos(
3
2
)cos(3
2
**
**
**
tuu
tuu
tuu
c
b
a
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© Mats Alaküla L5 – 3-phase modulation
3-phase converters modulation
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 -400
-200
0
200
400
Simplest with sinusoidal references...
... but the DC link voltage is badly utilized.
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© Mats Alaküla L5 – 3-phase modulation
3-phase converters – symmetrization
3 phase potentials, only 2 vector components. One degree of
freedom to be used for other purposes.
***
***
***
zccz
zbbz
zaaz
vuv
vuv
vuv
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© Mats Alaküla L5 – 3-phase modulation
3-phase symmetrized modulation
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 -400
-200
0
200
400
Maximum phase voltage with sinusoidal modulation : Udc/2
Maximum phase-to phase voltage with symmetrized modulation : Udc -> Phase
voltage Udc/sqrt(3), i.e. 2/sqrt(3)=1.15 times larger than with sinusoidal
modulation.
2
),,min(),,max( ******* cbacbaz
uuuuuuv
+
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© Mats Alaküla L5 – 3-phase modulation
3-phase minimum switching modulation
****** ,,min
2,,,max
2min* cba
dccba
dcz uuu
Uuuu
Uv
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02-400
-200
0
200
400
One phase is not switching for 2 60 degree intervals ...
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© Mats Alaküla L5 – 3-phase modulation
Modulation sequence vs. ripple
av
bv
cv
*au
*bu
*cu
mu
)0,0,0(u )0,0,1(u
)0,1,1(u
)1,1,1(u
*u
b
1
0
1
0
1
0
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© Mats Alaküla L5 – 3-phase modulation
Modulation sequence vs. ripple
dcuu e
ei
iL
0
a
b
d
q
dte
L
eu
dt
id
-1 0 1
-1
0
1
-1 0 1
-1
0
1
-1 0 1
-1
0
1
Current ripple in the (d,q)-frame