Algebraic PWM Strategies of a ...

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Algebraic PWM Strategies of a Five-Level
NYC
Voltage Source Inverter.
Application to a Great Power Induction Machine Drive.
N.LOURCI*, R.AM EUR", E.M.BERKOUK*, G.MAN ESSE*
*
*
Laboratoire d'Electronique de Puissance et Commande
(ENP)
-DER de Genie Electrique
&
Informatique.
10,
Avenue Pasteur, El-Harrach, Alger, Algerie, BP 182.
Fax
:
(02)
52-29-72. E-mail Berkouk
@
ist.cerist.DZ
**Laboratoired'Electricite Industrielle (CNAM), 292, Rue Saint Martin 75
14 1,
Paris, Cedex
03,
France
2.
llie
induction machine niodelluin
:
Abstract :
In
this paper, we study the control of the three
phases five level
NPC
source voltage inverter
(VS9
and
its
application to the induction machine drive. Forthat,
we elaborate in the
first
time the working model ofthis
inverter, without presumption on its control
by
using the
methodology Design associated to Petri nets
131.
Then,
we propose a knowledge and control models of
this
converter using connection functions
I3,lOI.
As
application
of
this control model, we develop two
algorithms
of
algebric
PWM
strategies of
this
converter.
We also study the performances of the drive of the
induction machine fed by this inverter controlled by
these
PWM
strategies. The results obtained are full of
promise to use the five-level inverter
in
the
high
voltage
and grent power applications
ns
electricnl traction.
The
fignre
1
shows
Uie six windings of the three
phases
illduction
inachuic
I
I].
@"
Key word
:
inductioii machine, voltage source inverter,
NPC,
live-level inverter, Petri nets, connection function,
generating fiuictioii, control model,
Figure.
1
:
hiduction machine representation.
knowledge model,
algebric
PWM
strategies.
?lie
stator
and
rotor
voltages of the induction machine
are
defined
by
the following equations:
d
['
:Y
I
=
I
R,
1[1,1+
;7;l%
1
I.
Introduction
:
The modelling
of
each system is very itiiportaiit to study its
control.
In tlus work,
Uie
system to riiodcliieis constituted
by two subsystems
:
thc
iiiductioii machitic
and its
supply
RSSIU~
(1)
n
l~l=l~rII~r1+
zl@rl
by
a
fivc-level NIT invertcr.
The inductioii nt?cliine is
not a
simple system because
several phenomenons intervene in its working,
as
saturation,
Foucault curraits, skin erect
..
.elc
[I
I.
I
lowever, we
\vi11
neglect these phenomenons because their mathematical
formulation is dificult, and their ell-ecki
on
the
bclirivior of
the
machine is considcrcxl
as
neglectd
in
some conditioiis.
With
the developniciit of
powcr
clcctroiuic
ruid
semi-
conductors
components,
scvcral
structures
of Uie static
converters arc possible.
For
the
dternating nmchines supply,
we generally use
the
two-level invaltrs,
but
seen
tlicir
litnitation
in
voltage
atid
power, and
in order
to
improve
the
output
voltage spectrum, we
start
to
itse
tlie
Uirce-level
inverters
[3,8,Y].
In
this
way, we present
a
novel structure of
NIAC
converter
:
five-level
NPC
VSI.
2n
2n
COS(Q
+
-)
COS(
0
-
-)
cosQ
3
3
215
215
COS(^--)
COS(^+-)
[Afsr]=Afsr
COS/?
3
3
2n
COS(
Q
+
-)
215
COS(
Q
-
-)
COS
Q
3
3
We retnembcr in
Uie
first
p<art
the
I'ark
model of
thc
induction tnacliiiie,
Uiai
we
dcvclop
a
kiiowledge
arid
control
models
of
Uus
new inverter.
ln
he
last
part,
we
propose
two
algetsic
pw~
IA,fsrIr
~h~rsl=
l3y
using
Park
tiansfonnation
at
stator,
the equations
(I
)
and
(2) kmme
strategies using
control
rnodcl
of this inverter The
pcdhiances
of
Uic
induction
niacliine drive fed by this invL71m
coiitrollul
by
these
strategiesarc discussed
niitl
ciiitilyzed.
fi)IIOw
:
697
0-7803-5546-6/99/$10.00
0
1999 IEEE
The conliguration
El
Ilie configuraiion
E,,
3.
Three
D~SS
five-level
NIT
VSl modelling
:
Ill.
1-
The three phases five-level
NIT
VSI structure.
The three phases five-level
NPC
VSI
is constituted by three
anns
and four
Dc
voltage sources. Every arni has eight bi-
directional switches,
six
in series and two
in
parallel, and
two diodes (Figure
2)
Every switch is composed by
a
transistor and
a
diode in anti-parallel.
The configuration
E2
The configuration
E3
The configuration
E,,
Ihe configuration
E5
The configuration
E6
Figure
2
:
Three phases five-level
NIT
invcrtcr
:
The
diflerentconfigurations
of
an
arm
k.
3
2.
finerentcokigurations oran
mi
:
A
topologic analysis
of
an
ann
shows sevcn configurations
possible 'Ihese differimt configurations are presented
by
the
figure
3.
The
table
1
gives
lhe
electtical component
characlerized
wch
configuration.
The receptivities-between the diflercnt configurationsare
logic functions between
.
-
external control
Bh
of the
switches
-
.-
internal control
defined
by the sign of
Uic
currentsand
voltages of each switches
--
Table.1
:
the electricalquantitiescharacterized each
con
li
guration
.
698
0-7803-5546-6/99/$10.00
0
1999 IEEE
 3.3-
Petri ncts of an
arE:
-111~
shows
tlic
I'ctri
~icts
d:ni
ann
or the
iiivcrtc7.
'l'his l'ch
i
nets
icprcwnls
tlic
working
model
of
Ihc
iiivcilcr
witliout presuniptioii on control
[
31
The variable
R,,
represents the receptivity of
the
kinsition
between the configurations
E,,,
and
En.
Some receplivilies
are
given below
:
Table
2
:
Excitation table
of
the switchesof the five-level
NPC inverter.
The
systeni
(3)
shows that
a
five-level
NPC
VSIcanbe
considerod
as
four two-level
VSI
or
two three-level
VSI
in
series.
The simple output voltage are defined
as
follow
Thus,
the
input current
or
the inverter
are
given
as
follow
Figure
4
:
Tlie Petri nets of
an
ann
or the
inverter.
3.4.
Knowledge
model
:
switch coiuicction function
l?kv
indicates
the openod
and
closed state
or
Uie switch
TDk,
:
If
TDh
is
shut.
In
Ihe
opposite
case
.
r
We deruie
too a half
ann connection function
Pkn
as
:
Fl
=
pk{
.Fk2
.FkA
ll~c
Fh
=
0
{
F:o
=
P7k4
.Fk>
.Fk(j
With
:
k
:
tinii nunilxr,
ni=
I
Cor
tlic uppx IiaIlLu-ni,
mid
m=O
ror thc
lower
oiic.
wlicre
[~(r)]
:
tile
simple conversion matrix.
I;or
an
ann
k
or
three
phascs fivc-levcl NIT
VSI,
several
complementary laws control are possible. l'lie control law
witch lets an optimal control of this inverter is
:
-
'jk4 =nk2
=Ekl
lhc
shows the global knowledge model
of
Uie three
pliases
five-level
NPC
VSI associated
to
the
DC
input
voltage source
aid
its
Uuee
phases load.
I
Bk6
=
Bk3
We distinguish
:
-
Control block
represented
by the
Petri
nets.
This
part
generates the simple conversion matrix.
-
Opemtive bloc
is
constituted
by
:
-
Wiere
Rb
represents
the gate control
of
the switch
T,
6
a discontinuous block which gives the internal inputs
'lhe
represcnts the excitation table
of
Uie switches
of
an
ann of
the converter.
generated by
Uie
converter(conversion relation).
.
a
continuous block represents
a
state
model
ofthe
inverter's load
and
its input
Dc
voltage source.
699
0-7803-5546-6/99/$10.00
0
1999 IEEE
 4 Al&xnic I'WM skatwics
:
111
this
pii~I,
we
will
picsciil
lwo
I'WM dgorilliins which use
II
control
inodcl
of
Ute
live-lcvcl NI'C
VSI.
'1
hc
gencrnl
flow
char1
of
;in algebraic I'WM
stmlcgy
is
presented in
Uie
following figure
Figure
5
:
Kno\vledge tnoticl of
the
three phases five-level
NI'C
VSI.
I
3.5.
Contfol
model
:
Conlpute
or
tho switches
cotmeclwn
finclinns
The global
knowledge
tnodcl
prcsentod
above (figure
5)
is
we11
adapted
for
siniulation,
aid
so
lo
validate control
algoriUims.
lo
adapt this model in order
to use
it
to
drive the
inverier, we defile
tlie
generating liinctions. The generating
coiinection function
Fkrg
is a continuous function which
represents
its average value
on
a
modulation
period
Tc
:
Step 4
:
&
Figure
7
:
Vie general
flow
chart
of
mi
algebraic
PWM
stmlcgy
1i)r the
thIa
pha~scs
five-level NI'C VSI.
4.1.
Ngoritlini
1
:
wi/h
:
11
E
N
e/
7;
-+
0.
This
algoritlun is based
on
Uie
triangulo-sinusoidal strategy
with one carrier.
The
different
steps
of the
flow
chart of
the
7
for Uiis
algorithm are
as
follow
:
'rhe use
of the
generating functionslets
to
approximate
the
discontinuous
bloc
of the knowledge rnodcl by a continuous
one which
rtyresents
its average
rnodel
in a niodulation
period
7',
(Figure.5).
Tlie
use of
the
geueratingfunctions
lets
to
wile
Uic
relation
(4)
as
follow
:
Step
1
:
Compute
of
the
generating sirnple conversion
functions
iigk
:
flgk
-
--
;
k
=
1,2,3
(JC
Step2
:
Coiiipute of
Uie
generating connection functions
:
with
[Ng(t)J
:
generating simplecoilversion nlakix
The
shows
the
control
inodcl
of
Uie
three
phases
live-level NI'C
VSI,
wliac
till
qimililics.
NJIJ
'l'hesc
two
algorithins
arc
developed
Ibr
-2
<
it,,$
<
2
(c-A-d
:
re[0,11).
Step
3
:
Compute of instantaneous connection functiotis:
Wc
define
in
Uiis
algorithni,
the
fol1ov.ing
variables:
'l'hc
going
past
or
the
gcncrating
connection
ftinctions
to
their ins(aiitaricous
oiies
is done
by
using the following
elgoriUun
:
Figure
6
:
Control
motlel of
the
tlirec pliascs
live-level
NIT
VSI.
0-7803-5546-6/99/$10.00
0
1999
IEEE
700
 Figure
9
:
Adjusting characteristicof the output voltage
VA
of
thc
three phases
five-level
NET
VSI controlled
by
algebmic
PWM
strategy (Algorithm
1)
(in=
12).
SteD
4
:
This
step is
common
to
Uic all dgcbraic
modulations.It suiiuiiarizcs in the
two
following parks
)
a- 1)ctcnnination
of
tlic
switc~ics
coiincction functions
(vkY
from the
halfanii's
one
(F:
)
:
b-
Ilctennination of the switchcscontrol
Figure
1O.a
:
The current ia
in
(ransieiitand steady state
of
the
hiduction
machine
fed
by
three
phases
five-level
NIT
VSI
controlled by
algehnic
PWM strategy
(Algorithm
1)
(ni=G,r=0.8).
For this
nlgoritliii~
the variable
t is
reinitializedat
the
aid
of
each
period
T,.
...,
.'.
I,
..-:-.n,N
I
400
200
0
-200
-400
-600
Y
20
-20
r-1--
--I-----
I
0
0.002
0,004 0.006 0.008
0,Ol
0.012
0,014 0,016 0,018
0,02
-
-
_-
.
- -
__
- - -
n
om
OQ
-0
.*O
I
I
-
-
z~~~zsza~s~az,
?
Figure 8
:
Siniplc voltage
VA
and
its
spectnim
Tor
the
three
pliases five-level NPC
VSI
cbntrolled by algebraic PWM
Figure
10.1)
:Ilic
clcctromagiiotic
torque
in
transient
arid
steady slate
of the induction tnachine fed
by
throe phases
live-level NIT
VSI
controlled by algebraicPWM
strategy
(Algoritlun
1)
(m=G,x=O.8).
sirategy
(
Algorithm
1)
(
m=12,F0.8)
701
0-7803-5546-6/99/$10.00
0
1999
IEEE
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