Transcript The new electronic ballast generation - uni

Modulation and control for cascaded multilevel converters
Modulation and control for cascaded
multilevel converters
Marco Liserre
[email protected]
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
A glance at the lecture content
•
Cascaded multilevel converters:
•
hybrid solution
•
applications
•
PI-based control
•
Multilevel modulations in case of time-varying dc voltages:
•
generalized hybrid modulation
•
generalized phase-shifting carrier modulation
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
A glance at the lecture content
•
Cascaded multilevel converters:
•
hybrid solution
•
applications
•
PI-based control
•
Multilevel modulations in case of time-varying dc voltages:
•
generalized hybrid modulation
•
generalized phase-shifting carrier modulation
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
H-bridge multilevel converters
n

1
x1  (e  Rx1 )   Pi x2i 
L 

i 1
x2i 
active rectifier
Marco Liserre
1
 Pi x1  i x2i 
Ci
x1 
n

1
(
e

Rx
)

Pi x2i 


1
L 
i 1

inverter
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Modulation and control for cascaded multilevel converters
H-bridge multilevel converters
•
•
Advantages
•
high voltage and high power
•
modularity and simple layout
•
reduced number of components compared to other multilevel
topologies
•
phase voltage redundancy
•
reduced stress for each component
•
small filters
Disadvantages
•
Marco Liserre
voltage unbalance of the dc link capacitors
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Modulation and control for cascaded multilevel converters
H-bridge multilevel converters
How does it work ?
•
io1
T31
T11
R
L
iL1
iC1
a
C1
if VC1=VC2=Vo
+
vc1
R1
-
i
T41
T21
Vao = -Vo T21 and T31 ON
e
io2
T12
iL2
T32
iC2
C2
+
vc2
b
T22
T42
Vao = Vo T11 and T41 ON
R2
Vao = 0 T11 and T31 ON
or
T21 and T41 ON
The lower bridge produces the same voltage levels by turning on/off the
corresponding switches
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
H-bridge multilevel converters
How does it work ?
•
Voltage Levels and Switching Configurations
io1
T31
T11
R
L
iL1
iC1
a
C1
+
vc1
R1
-
i
T41
T21
e
io2
T12
iL2
T32
iC2
C2
+
vc2
b
T22
Marco Liserre
T42
R2
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Vab
+2 Vo
Vo
Vo
Vo
Vo
0
0
0
0
0
0
-Vo
-Vo
-Vo
-Vo
-2 Vo
T11
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
T31
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
T12
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
T32
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
S1
1
1
1
0
0
0
0
0
0
1
-1
0
0
-1
-1
-1
S2
1
0
0
1
1
0
0
0
0
-1
1
-1
-1
0
0
-1
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Modulation and control for cascaded multilevel converters
Hybrid multilevel converter
 Multilevel converters based on the use
of hybrid cell of converters subjected to
different dc voltage levels.
 The basic idea is to use a converter
switching at low frequency hence
employing Gate-Turn Off thyristors or
IGCTs (as a quasi-square wave
modulation technique is used) and one
switching at higher frequency.
 the fact that the dc-link voltage levels
are in an integer relation among them
allow to have (for subtraction) more
voltage levels.
Marco Liserre
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Modulation and control for cascaded multilevel converters
Hybrid multilevel converter
•
The converter working at low switching frequency is the greatest
contributor to the fundamental component of the overall output
voltage and generates a considerable and well known harmonic
content (typical of quasi-square waveform), and the PWM converter
is generating an opposite harmonic content and the required
additional fundamental component to obtain the desired voltage.
•
The principle is very similar to that one of active filters. The positive
consequence is that the low frequency converter (that is the
converter with the higher dc-link voltage level) can be designed as an
high voltage converter while the other ones can be designed as low
voltage converters.
REF M. D. Manjrekar, P. K. Steimer, and T. A. Lipo, ” Hybrid Multilevel Power
Conversion System: A Competitive Solution for High-Power Applications,” IEEE
Transactions On Industry Applications, Vol. 36, No. 3, May/June 2000.
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
Applications
Active rectifier in traction systems
 reduced line current harmonic distortion
 reduced weight and encumbrance
 voltage regulation
Marco Liserre
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Modulation and control for cascaded multilevel converters
Applications
reduced EMI
Many dc-links by
one source
no step-down
transformer
Marco Liserre
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Modulation and control for cascaded multilevel converters
Applications
•
Hybrid electric vehicles with different electric storages
REF L. M. Tolbert, F. Z. Peng, T. Cunnyngham and J. N. Chiasson, ”Charge balance
control schemes for cascade multilevel converter in hybrid electric vehicles,” IEEE
Trans. on Industrial Electronics, vol. 49, n. 5, October 2002. pp. 1058 - 1064.
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
Applications
•
Distributed generation multilevel converters: photovoltaic system
REF F.-S. Kang, S.-J. Park, S.-E. Cho, C.-U. Kim and T. Ise, ”Multilevel PWM inverters
suitable for the use of stand-alone photovoltaic power systems,” IEEE Transactions
on Energy Conversion, vol. 20, n. 4, December 2005. pp. 906-915.
Marco Liserre
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Modulation and control for cascaded multilevel converters
Applications
•
In Unified Power Flow Controller , employing multilevel converters, the
regulation of the dc voltage levels can be used to meet different design
requirements in terms of harmonic compensation and losses reduction
Lg
Iload
Ig
VDVR
E
Ic
shunt
DVR
REF T. Gopalarathnam, M. D. Manjrekar and P. K. Steimer, ”Investigations on a unified
controller for a practical hybrid multilevel power converter,” in APEC 2002, vol. 2,
March 2002, pp. 1024-1030.
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
A glance at the lecture content
•
Cascaded multilevel converters:
•
hybrid solution
•
applications
•
PI-based control
•
Multilevel modulations in case of time-varying dc voltages:
•
generalized hybrid modulation
•
generalized phase-shifting carrier modulation
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
PI control of cascaded multilevel converters
In order to fulfil the control requirements above mentioned different
schemes based on PI controllers can be considered.
In ideal conditions completely
i
i
T3
T1
independent H-bridges
i
L
R
+
a
would be expected in order to
v
R
C
manage
i
T2
T4
distinct power transfers
and
e
i
i
different voltage levels
T1
T3
i
on each structure.
+
o1
L1
1
1
C1
1
1
c1
1
1
o2
2
L2
2
C2
C2
REF A. Dell’Aquila, M. Liserre, V.G: Monopoli, P.
Rotondo, “Overview of PI-based solutions
for the control of the dc-buses of a singlephase H-bridge multilevel active rectifier”,
IEEE Transactions on Industry
Applications, May/June 2008.
Marco Liserre
vc2
R2
b
T22
T42
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Modulation and control for cascaded multilevel converters
First control scheme of the multilevel rectifier
A. One voltage PI and one current P for each H-bridge
to control them independently
i
vc1*
+_
K pv ,1 
Kiv,1
i*
_
+
s
K pi ,1
vc1
_
+
1/Vd
S1
P1
e
e
PWM
1/E
P2
i
vc2*
+_
K pv ,1 
vc2
Kiv,1
s
i*
_
+
K pi ,2
_
+
1/Vd
S2
e
e
1/E
error
This results in ineffective control of the grid current leading the system to the instability.
Instability is caused by the attempt at independently controlling
the same current through two controllers.
Marco Liserre
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Modulation and control for cascaded multilevel converters
Second control scheme of the multilevel rectifier
B. Two PI’s for the two dc-links and one P for the current
The idea is to control the dc current in order to charge or discharge the dc-link.
e
1/E
i
vc1*
+_
K pv ,1 
Kiv,1
i*
++
s
_
+
vc1
vc2*
+_
vc2
K pi
vl
_
+
e
K pv ,2 
K iv,2
1/Vd
S1+S2
+_
P1
S1
PWM
S2
P2
S2
S2·i
÷
s
i
error
However the non-linear relation i02=S2·i can not be used to
the leads
switching
function Sproblems
2 simply both
dividing
by i. and
Thus calculate
the division
to instability
at start-up
when the two reference voltages for the dc-links are different.
Marco Liserre
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Modulation and control for cascaded multilevel converters
Third control scheme of the multilevel rectifier
C. One PI for the overall voltage, one PI for a dc-bus and
a P for the current
vc1*+vc2*
+_
K pv ,1 
Kiv,1
I*max
i*
i
_
+
s
K pi
vc1+vc2
vl
+
e
e
S1+S2
_
1/Vd
S1
+_
S2
PW
M
P1
P2
1/E
vc2*
+_
K pv ,2 
K iv,2
S2,max
S2
s
vc2
e
1/E
The
control
thevcurrent
voltage
vcontrolled
iscontrolled
made calculating
through another
controller
The
sum
ofof
the
and
visC2
the voltage
choice
of
Then
the
grid
the
C2is
C1
This
control
scheme
works
with
differentthrough
reference
voltages
thatgenerated
directly selects
the
switching
functionon
S2,max
current
amplitude
i.amplitude
bythe
thegrid
multilevel
converter
the ac side.
and loads
Marco Liserre
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Modulation and control for cascaded multilevel converters
Simulation for reference and load steps: scheme 1
ERROR !
start-up
Marco Liserre
dc-bus 1
load step
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Modulation and control for cascaded multilevel converters
Simulation for reference and load steps: scheme 2
Marco Liserre
ERROR !
ERROR !
start-up
dc-bus 2
reference
step
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Modulation and control for cascaded multilevel converters
Simulation for reference and load steps: scheme 3
Marco Liserre
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Modulation and control for cascaded multilevel converters
Tuning procedure: voltage loop
Vc1*(s)+Vc2*(s)
+_
K pv ,1 
Kiv,1
I*max(s)
s
Vc1+Vc2
voltage controller
Vc2*(s)
+_
K pv ,2 
1
1  m  Ts  s
Current
loop
Kiv,2
s
Vc2 voltage controller
S2,max(s)
Imax(s)
S1,max  S 2,max
Vc1(s)+Vc2(s)
2C  s
System
plant
I max
2C  s
Vc2(s)
System plant
The two voltage control loop have different plants
and they are designed following the “optimum
symmetrical” criteria
Marco Liserre
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Modulation and control for cascaded multilevel converters
Indipendent load transients
vC1
[150 V/div]
vC2
dc-bus1
load step
dc-bus2
load step
[150 V/div]
i
[10 A/div]
Marco Liserre
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Modulation and control for cascaded multilevel converters
Indipendent load transients
vvC1
C1
[150
[150V/div]
V/div]
vvC2C2
[150
[150V/div]
V/div]
dc-bus1
dc-bus1
load step
load step
dc-bus2
dc-bus2
load step
load step
ii
[10
[10A/div]
A/div]
Marco Liserre
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Modulation and control for cascaded multilevel converters
Indipendent voltage steps
dc-bus1
ref. step
vC1
[150 V/div]
vC2
[150 V/div]
dc-bus2
ref. step
i
[10 A/div]
Marco Liserre
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Modulation and control for cascaded multilevel converters
Indipendent voltage steps
ddcc--bbuuss1
1
rreeff.. sstteepp
C1
vvC1
[150 V/div]
[150 V/div]
vC2
vC2
[150 V/div]
[150 V/div]
dc-bus2
d c -b u s
r e f . s t e p2
ref. step
i
i
[10 A/div]
[10 A/div]
Marco Liserre
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Modulation and control for cascaded multilevel converters
Loads unbalance condition
dc-link 1 voltage
load step on
the dc-link
Marco Liserre
load step on the
other dc-link
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Modulation and control for cascaded multilevel converters
Different dc voltages condition
dc-link 1 voltage
reference step
on the dc-link
Marco Liserre
reference step on
the other dc-link
[email protected]
Modulation and control for cascaded multilevel converters
A glance at the lecture content
•
Cascaded multilevel converters:
•
hybrid solution
•
applications
•
PI-based control
•
Multilevel modulations in case of time-varying dc voltages:
•
generalized hybrid modulation
•
generalized phase-shifting carrier modulation
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
Hybrid modulation techniques

These techniques have been developed in order to optimize the
harmonic content of the voltage generated by multilevel converters
with different dc-voltage levels

The basic principle can be easily explained in case two bridges are
adopted:

One converter switches at low frequency (semi-square waveform). It carries all
the fundamental power but it produces also low frequency harmonics

The other converter switches at high frequency (PWM), it works as an active filter
compensating the harmonics generated by the first bridge
REF M. D. Manjrekar, P. K. Steimer and T. A. Lipo, ”Hybrid multilevel power conversion system: a
competitive solution for high-power applications,” IEEE Trans. on Industry Applications, vol. 36,
n. 3, May-June 2000. pp. 834-841.
C. Rech, H. A. Grundling, H. L. Hey, H. Pinheiro and J. R. Pinheiro, ”A generalized design
methodology for hybrid multilevel inverters,” in IECON 02, vol. 1, November 2002. pp. 834-839.
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
Hybrid modulation techniques

More voltage levels are obtained as subtraction of the different dc-link
voltages

Hence four of the multilevel states that, in case of equal dc-link
voltages, generate zero voltage on the ac side, in case of hybrid
modulation, and non-equal dc-link voltages, generate one voltage level
more both positive and negative

Major drawbacks:
 It is difficult to control the dc-link voltages in case of active rectifier application
 The dc-link currents have an heavy harmonic content (that is compensated on the
ac-side and not on the dc-side)
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
Carrier shifting cascaded PWM techniques

These techniques have been developed in order to obtain optimum
harmonic cancellation

Asymmetric PWM allows harmonic cancellation up to the 2n-th carrier
multiple
v(t )  NVdc M cos0t  


N


1

J 2n1 mM cosm  n  1  cos2mc t  2n  10t  2m i 
 m1 n 2m
i 1
4Vdc
(i  1)
m  kN , k  1, 2,3...
N
These techniques allow different power transfers and different voltage
levels for each bridge
• carrier shifting


Marco Liserre
i 
However in case of different voltage levels for each bridge the
harmonic cancellation is not perfect
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Modulation and control for cascaded multilevel converters
v ,V
tri
Carrier shifting cascaded PWM techniques
1
ref
0
-1
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
t [s]
0
v
ab
[V]
100
-100
ref
v ,V
tri
0.02
0.03
0.035
0.04
t [s]
0.045
0.05
0.055
0.06
0.025
0.03
0.035
0.04
t [s]
0.045
0.05
0.055
0.06
0.025
0.03
0.035
0.04
t [s]
0.045
0.05
0.055
0.06
0.025
0.03
0.035
0.04
t [s]
0.045
0.05
0.055
0.06
1
0
-1
0.02
100
0
v
cd
[V]
0.025
-100
200
0
v
ad
[V]
0.02
-200
A [pu]
0.02
1
0.5
0
Marco Liserre
0
10
20
30
h
40
50
60
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Modulation and control for cascaded multilevel converters
Carrier shifting and hybrid modulation

Carrier Shifting and Hybrid modulation (CSM and HM) techniques
performances rely on time-invariant dc-voltages

However many applications such as traction, distributed generation and
active filter could take advantage by using time-variant dc-link voltages

In this case both the techniques are not adequate:

CSM fails in obtaining optimum harmonic cancellation while preserving
fundamental voltage control

HM cannot preserve fundamental voltage control, even if optimal harmonic
cancellation could be possible
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
Proposed generalized hybrid modulation

The proposed Generalized Hybrid Modulation (GHM) technique
considers non-integer relationships between dc-link voltages which can
be time-dependent

Then, switching signals will depend on the instantaneous values of the
dc-link voltages and can not be evaluated independently for each PWM
converter, it means that independent power management is lost

in case two bridges are adopted:

One converter switches at low frequency (semi-square waveform). It carries all
the fundamental power but it produces also low frequency harmonics

The other converter switches at high frequency (PWM), adjusting switching
signals to compensate the effect of time-variant dc-link levels and the absence of
an integer ratio among them. The final objective is to minimize the output voltage
THD
REF M. Liserre, A. Pigazo,V. G. Monopoli, A. Dell’Aquila, V. M. Moreno, “A Generalised Hybrid
Multilevel Modulation Technique Developed in Case of Non-Integer Ratio Among the dc-Link
Voltages” ISIE 2005, Dubrovnik (Croatia), June 2005.
Marco Liserre
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Modulation and control for cascaded multilevel converters
Proposed generalized hybrid modulation
Low voltage converter
High voltage converter
Marco Liserre
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Modulation and control for cascaded multilevel converters
Proposed generalized hybrid modulation

Example:
v*(k)>V1(k)


k
Variations in V1(k) and V2(k) must be
at a lower frequency than fsw=1/TC
LV converter must be centered on TC
for a minimum final THD and
v * k TC  V1 k TC  V2 (k )t2 (k )
hence:
t (k ) v * (k )  V1 (k )
D2 (k )  2

TC
V2 (k )
t2(k)
k+1
V1(k)+V2(k)
v*(k)
V1(k)
V2(k)
0
TC
D1D(k)
2 (k )  1
Marco Liserre
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Modulation and control for cascaded multilevel converters
Proposed generalized hybrid modulation
Marco Liserre

Switching plane

4 regions more
respect to the
traditional hybrid
modulation

The proposed
modulation has 9 regions
in order to obtain
optimum harmonic
content and exact
fundamental voltage also
in case of time-varying
dc-link voltages
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Modulation and control for cascaded multilevel converters
Proposed generalized hybrid modulation
The fundamental frequency
harmonics compensate, as in the
hybrid modulation
technique, the higher voltage
converter harmonics.
Marco Liserre
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Modulation and control for cascaded multilevel converters
Comparison in terms of modulation signals
Marco Liserre
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Modulation and control for cascaded multilevel converters
Simulation results: conditions and parameters

Analyzed modulation techniques: CSM, HM, GHM

Linear region

Modulation index (M) has been chosen in [0.6, 1.4] (step = 0.1)

LV converter dc-voltage (V2) is varied in [0.51,0.99] (step = 0.05)

Equal switching losses => mf = 40 for HM and GHM mf = 20 for CSM

Evaluation parameters:
- Amplitude of the output voltage fundamental frequency component
- Weighted Harmonic Content (WHC)
- Weighted Total Harmonic Distortion (WTHD)
max(v *(k ))
M
V1
Marco Liserre

V 
WHC    n 
n2  n 
2
WHC
WHC 
WTHD
V1
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Modulation and control for cascaded multilevel converters
Simulation results: generalized hybrid modulation technique
overall output
voltage waveform
High voltage
converter output
waveform
Low voltage
converter output
waveform
M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40
Marco Liserre
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Modulation and control for cascaded multilevel converters
Simulation results: time-domain comparison
GHM
HM
LV converter uses
only its DC voltage to
establish duty cycles
CSM
Expects equal DC
voltages
M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40, mfshifting=20
Marco Liserre
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Modulation and control for cascaded multilevel converters
Simulation results: spectra comparison
GHM
I1=1.2 V (p.u.)
WHC=7.17 10-4
HM
I1=0.96 V (p.u.)
WHC=1.19 10-2
CSM
I1=1.2 V (p.u.)
WHC=5.1 10-3
M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40, mfshifting=20
Marco Liserre
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Modulation and control for cascaded multilevel converters
Simulation results: overall comparison

% error in the output signal at the fundamental frequency
Technique
minimum
average
maximum
GHM
6.2 10-4
0.12
0.5
23.6
61.3
0.14
0.5
CSM – WHC improves
when arriving HM
to equal DC 10-2
voltages
-3
CSM

10
WHC
GHM - There Technique
is not a clearminimum
dependency on GHM
dc-link
3.9 10-4
voltage values
-4
average
maximum
8.7 10-4
1.6 10-3
HM
5.5 10
3.5 10-2
0.13
CSM
8.6 10-4
3.6 10-3
6.6 10-3
M in [0.6,1.4], V2/V1 in [0.51,0.99], mfhybrid =40, mfshifting=20
Marco Liserre
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Modulation and control for cascaded multilevel converters
Experimental results
Hybrid Modulation.
Generalised Hybrid Modulation.
Time and frequency domains overall Time and frequency domains
overall output voltage using
output voltage
using V1 = 100 V (V1 = 1.0 pu), V2 = V1 = 100 V (V1 = 1.0 pu), V2 =
61 V (V2 = 0.61 pu) and M = 120 V 61 V (V2 = 0.61 pu) and M =
120 V (M = 1.2 pu)
(M = 1.2 pu)
Marco Liserre
Carrier shifting technique.
Time and frequency domains
overall output voltage using
V1 = 100 V (V1 = 1.0 pu), V2 =
61 V (V2 = 0.61 pu) and M =
120 V (M = 1.2 pu)
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Modulation and control for cascaded multilevel converters
Discussion on the drawbacks of hybrid techniques

Both converters introduce low frequency current harmonics
M =1.2, V1 =1 V (p.u.), V2 =0.61 V (p.u.), mfhybrid =40
Marco Liserre
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Modulation and control for cascaded multilevel converters
Discussion on the drawbacks of hybrid techniques

The major drawback is the fact that is very difficult to control directly
the different converters to have full control on the voltage generated by
each of them.

In other words it is only possible to decide the overall multilevel
modulation signal and not the modulation signal of each converter
independently

The direct consequence is that it is difficult to control the dc-link
voltages separately in an active rectifier application unless the phase of
the converter ac voltages is controlled
Marco Liserre
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Modulation and control for cascaded multilevel converters
Carrier shifting cascaded PWM techniques

These techniques have been developed in order to obtain optimum
harmonic cancellation

A suitable phase-shifting among the carrier signals relevant to n
different bridges has to be introduced: (i-1)/n, (for i=1, 2, …, n)

Asymmetric PWM allows harmonic cancellation up to the 2n-th carrier
multiple

These techniques allow different power transfers and different voltage
levels for each bridge

However in case of different voltage levels for each bridge the
harmonic cancellation is not perfect
REF M. Liserre, V. G. Monopoli, A. Dell’Aquila, A. Pigazo, V. Moreno, “Multilevel Phase-Shifting
Carrier PWM Technique in Case of Non-Equal DC-Link Voltages”, IECON 2006, Paris (France),
November 2006.
Marco Liserre
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Modulation and control for cascaded multilevel converters
Principles of the PSC-PWM technique

2 converters: The weighted total harmonic distortion (WTHD) of the
output signal can be reduced if the carriers of leg A and B are shifted
 rad

N cascaded converters: Using symmetrical PWM, the carrier of leg A in
2
each converter must be shifted N i  1 rad.

The phasorial representation for
the carrier signals is:
Inv 1
Inv 3
Inv 1
Inv 2
Inv 1
Inv 2
N=2
N=3
Marco Liserre
Inv 2
Inv 3
N=4
Inv 4
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Modulation and control for cascaded multilevel converters
Principles of the PSC-PWM technique

The overall output voltage:


N
1
v(t )  NVdc M cos0t  
cos2mct  2n  10t  2mi 
  J 2n1 mM cosm  n 1 
 m1 n 2m
i 1
4Vdc
It can be reduced
by applying
where:






Marco Liserre
(i  1)
N is the number of cascaded converters,
i 
N
M is the amplitude modulation coefficient,
m  kN , k  1,2,3...
is
the
pulsation
of
the
modulating
signal,
0
c is the pulsation of the carrier signal,
J 2 n1 is the Bessel function of order 2n-1 and
 i is the relative phase of the carrier signal applied to the leg A of
each converter
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Modulation and control for cascaded multilevel converters
Proposed PSC-PWM technique

The overall output voltage with non-equal dc-link voltages:
N


N
1
v(t )  M Vi cos0t    
J 2 n1 mM  cosm  n  1 Vi dc cos2mct  2n  10t  2mi 
 m1 n 2m
i 1
i 1
dc
4
A reduced WTHD can be obtained if:
N
V
And, hence:
i 1
i
dc
cos2mct  2n  10t  2mi   0
 N dc
Vi cos2m i   0


i 1
N
 Vi dc sin 2m i   0

 i 1
which depend on the considered m and can not be verified for all m and  i
Marco Liserre
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Modulation and control for cascaded multilevel converters
Proposed PSC-PWM technique

The mathematical expression of the WTHD is

Vn2

2
n2 n
WTHD 
V1
the minimum WTHD will be reached for m=1:
 N dc
Vi cos2 i   0


i 1
N
 Vi dc sin 2 i   0

 i 1
 dc
Vi  0
N
i 1

Vi dc is a phasor with amplitude
matching the i th converter dc-link
voltage and phase  i
Reduced WTHD condition:
The dc-link voltage phasors generate a polygon in the complex plane
whose center should match the system origin.
Marco Liserre
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Modulation and control for cascaded multilevel converters
Original and proposed PSC-PWM. N=3
Vdc1=3.2 pu, Vdc2=1.4 pu and Vdc3=4.4 pu
original
Shifting angles =0º, 120º and 240º


modified
Shifting angles =0º, 36º and 191º
The original PSC-PWM angles can be obtained as a particular solution
Asymmetrical PWM angles can be obtained dividing the obtained results
by 2
Marco Liserre
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Modulation and control for cascaded multilevel converters
Comparison of PSC-PWM techniques (N=3)
0.7248%
original
V1dc+V2dc+V3dc= 360V
V1dc<V2dc<V3dc
M=0.6
V1dc=60V…120V
V2dc=60V…120V
f0=50 Hz
fc=1.6 kHz
0.5928%
modified
Marco Liserre
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Modulation and control for cascaded multilevel converters
Comparison of PSC-PWM techniques (N=3)



improvement
V1dc+V2dc+V3dc= 360V
V1dc<V2dc<V3dc
M=0.6
The reduced WTHD
condition can not be
verified. Improvement
around 20%
Limit of the reduced
WTHD condition
Improvement region ->
Up to 50.6%
Evaluation errors ->
worst behaviour (-13.6%)
Marco Liserre
[email protected]
Modulation and control for cascaded multilevel converters
Comparison of PSC-PWM techniques (N=3)
At medium M values the proposed
method improves the WTHD
V1dc=70V
V2dc=120V
V3dc=170V
f0=50 Hz
fc=1.6 kHz
At high M values the
proposed method
improves the WTHD
around a 20%
Low M. The original technique
operates better. In average, a 3%
Marco Liserre
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Modulation and control for cascaded multilevel converters
Conclusions
•
It is possible to control independently the dc buses of a cascaded
multilevel converter both with a linear controller (PI-based control)
both with a non-linear controller (Passivity-based control)
•
Multilevel modulators should be adapted in case of time-varying dc
voltages:
•
•
generalized hybrid modulation
•
generalized phase-shifting carrier modulation
A well design controller and a well designed modulation technique
are indispensable in order to do not loose the harmonic advantages
of the multilevel converter and do not lead the system to instability
Marco Liserre
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