Energy and Power Engineering, 2013, 5, 28-35
doi:10.4236/epe.2013.53B007 Published Online May 2013 (http://www.scirp.org/journal/epe)
A Space Vector Modulation Based Three-level PWM
Rectifier under Simple Sliding Mode Control Strategy
Azeddine Draou, Senior Mieee
Department of Electrical Engineering, University of Hail, Hail, Kingdom of Saudi Arabia
Email: adraou@yahoo.com
Received 2013
ABSTRACT
In this paper, a voltage oriented control strategy for three-level PWM rectifier based on Sliding Mode Control (SMC) is
introduced in order to obtain fast and accurate response of dc-bus voltage. To verify the validity of the analysis and the
feasibility of the proposed control method a set of simulation tests have been conducted using Matlab/Simulink. The
simulation results show that compared to the conventional PI controller, the SMC can reduce drastically the three-level
rectifier’s voltage fluctuation and improve the dynamic response of dc-bus significantly.
Keywords: Three-level; PWM Rectifier; Voltage Oriented Control; Sliding Mode Control; Unbalanced Input Voltage
1. Introduction
Recent development of high-power and high switching
frequency power electronic devices and their large-scale
application have led to the study of converter systems
performing near unity power factor and digital imple-
mentation. This new wave of research has paved the way
to eliminate the power grid pollution and provide green
power requirements. Thus, research interest in three-
phase pulse with modulation (PWM) rectifiers has grown
rapidly due to their numerous advantages such as bidi-
rectional power flow, low harmonic distortion of source
current, near unity power factor, and adjustable dc-bus
voltage [1-14]. Moreover, the three-level neutral point
clamped (NPC) converter presents more advantages over
the conventional two-level converter in high power ap-
plications, such as lower voltage stress of semiconduc-
tors, smoother waveform, less distortion and less switch-
ing frequency stresses [15,16]. The PWM rectifier based
on three-level NPC technique is an attractive method
suitable for high power applications since it provides the
merits of both PWM rectifier and three-level converter.
The most prevalent control scheme for PWM rectifier is
the voltage oriented control (VOC) [17], which is im-
plemented by PI controllers for inner current control and
outer voltage control loops. The outer voltage loop is
traditionally implemented by fixed-gain proportional-
integral (PI) or proportional-integral-derivative (PID)
controller. However, the design of such a controller de-
pends on the precise system mathematical model used
which is difficult to develop.
Recently, much attention has been given to a sliding
mode controller (SMC) in order to overcome the above
drawbacks. (SMC) is a discontinuous system, and the
control character can force the system to move in tiny
extent and in high frequency according to the specified
state track under certain conditions. Because of the mer-
its of high speed response, insensitivity to the variable
parameters, and ease of implementation, the SMC has
been widely used in the non-linear system.
In this paper, a simple control strategy for three-level
PWM rectifier with voltage oriented control to improve
the system’s robustness and dynamic response of the dc-
bus voltage is proposed. The sliding mode control is used
in the outer voltage loop. In order to improve the dy-
namic performances of the source current loop, the anti-
windup IP controller of inner current controller is used
instead of the conventional PI controller [18-21]. Simula-
tion results show that compared to the conventional PI
controller, the SMC can reduce the three-level rectifier’s
voltage fluctuation and improve the dynamic response of
the dc-bus significantly.
2. Topology and Mathematical Model of
Three Level PWM Rectifier
The input of the rectifier is connected to the power net-
work, and the output is in the dc side. The main objective
of the control strategy of the rectifier is to make the input
current follow a sine wave and the output voltage to be a
controllable dc voltage.
The topology of the three-level PWM rectifier is
shown in Figure 1, [22-24].
s
L and
s
R are the equiva-
lent inductance and resistance of the three phase reactor
inserted between the grid source and the rectifier,
1dc
C
Copyright © 2013 SciRes. EPE
A. DRAOU, S. MIEEE 29
and 2dc are the dc-bus capacitances, 1dc
V and 2dc
V
are voltages of the two capacitors, is the sum of
1dc and 2dc
V. i, i and vi are the three-
level grid voltage, grid current and ac-side voltage of the
rectifier, respectively. Assuming that ip
C
dc
V
,,abcVe ii
s
, id
s
, in
s
(i) are the switching variables of the three level
PWM rectifier when the three phases of power source
voltages (bc
ee ) are sinusoidal and symmetrical. Then,
they can be defined according to different switch states
of the four switches in each phase as:
,,abc
1
ip
0
ip
0
ip
e
s
4i
Ss
4i
Ss
2i
S
,,
a
io
s
0i
s
0i
s
e
0
1
0
, , , when , on and ,
off.
0
0
in
s
in
s
in
s
1iS
2i
3i
S
S
S
2i
3i
S
4i
S
3i
S
1i
S
1i
S
, , , when , on and ,
off.
, , , when , on and ,
off.
1
Assuming that the three phase source voltages are
balanced, sinusoidal and symmetrical, the phase angle of
voltage a is
, denotes the RMS value of the
source phase voltage, thus
E


3
3
2cos
2cos 2
2cos 2
eE
eE
eE




a
b
c
(1)
The transformation equation from ab coordinates
to static
c
dq
coordinates and then to synchronous
rotating coordinates are
11212
2
a
b
c
2
303
23
x
x
x
x
x












d
q
x
(2)
cos sin
sin cos
x
x
x








(3)
According to “equation (1)”,
0
abc
eee (4)
In the three- phase inverter- wire system
0
abc
iii (5)
s
L
s
R
a
e
~
a
i
1dc
C
L
R
b
i
c
i
a
S1
s
L
b
e
~
s
L
c
e
~
s
R
s
R
2dc
C
1dc
V
1dc
V
2C
i
1C
i
N
P
a
S2
a
S3
a
S4
o
i
p
i
n
i
Figure 1. Topology of three-level PWM rectifier.
Therefore, “equation 2” is simplified to “equation 6”
in order to reduce the number of current sensors and im-
prove the quality of voltage.
10
3
21323
a
b
x
x
x
x

 

 

 
(6)
After some tedious mathematical processes on the
above equations, the mathematical model of the system
in static abc coordinates is as follows:
xAxBe
(7)
where






12
12
22
''
''
''
11111
00
00
00
00
00
sssdc dc
T
abc dcdc
T
abc
sapp
sbppbn
scppcnn
ap bp cp
an bn cn
ZdiagLLLC C
xiiiv v
Bdiag
eeeeii
ann
n
R
ss ss
R
ss ss
A
R
ss ss
sss
sss



 

and
''
,
33
ap bp cpan bn cn
pn
sss
ss
ss
 

The physical meaning of the mathematical model in
coordinates is pellucid, but variable parameters of
ac reactors are unstable which is not suitable for the de-
sign of control system, so the mathematical model in the
rotating
abc
dq
coordinates is:
'''
Z
xAxBe
(8)
where

'
12
12
'
11 1 1
00
00
s sdcdc
T
d qdcdc
T
dqLL
s
sdpdn
s
sqpqn
dp qp
dn qn
ZdiagLLC C
xiivv
Bdiag
eeeii
RLss
L
Rss
Ass
ss








If we suppose that and are the voltages of
d
vq
v
Copyright © 2013 SciRes. EPE
A. DRAOU, S. MIEEE
30
d-axis in the coordinates, it can be shown that: dq
ve
ve
dc


ddsqs sd
qqsds sq
Li LsRi
LiLsRi
  
 (9)
where, s is the arithmetic operator of differential coeffi-
cient.
Considering , then
12dc d
CCC

2
dc dc
ddpdn dqpqn q
L
dv v
sissi
dt R
Cs
,,
abc
e
d
i
*
q
v
(10)
From the aforementioned model, the equivalent circuit
of the three-level PWM rectifier in the coordi-
nates can be obtained as shown in Figure 2.
dq
3. Control Strategy for the Three-level PWM
Rectifier Based on SVPWM
Similarly to the two-level PWM rectifier [26-34], the
control target of the three-level PWM rectifier is to make
the dc output voltage dc follow its reference value ,
while keeping the input currents () approximately
sinusoidal and in phase with the corresponding grid
voltages ().
v*
dc
v
,,
abc
iii
ee
Furthermore, to ensure the reliability of the system [35]
the two special requirements of three-level PWM recti-
fier: balance of neutral-point voltage and avoidance of
excessive voltage jump in phase and line-to-line voltages
must be satisfied.
Voltage oriented control (VOC) which is the classical
and most popular control strategy for the three-level
PWM rectifiers [32] provides excellent steady-state per-
formance, acceptable dynamic performance and constant
switching frequency for the rectifier compared with other
strategies. The block diagram scheme of VOC strategy
based on sliding mode control for the three level PWM
rectifier is illustrated in Figure 3.
There are three control loops in the VOC strategy. The
error between the reference dc-bus voltage and the
sampled dc-bus voltage dc is processed by SMC,
which produces the reference active current . As in the
inner loops, -axis currents loop and -axis current
loop use anti-windup IP controllers to make the actual
currents and q) track their reference values (
and ). Generally, and in order to achieve near unity
power factor condition, the controlled value of the q-axis
current is set to zero.
*
dc
v
*
d
i
v
q
(d
i*
d
i
*
q
i
Then, the errors are processed in two conventional
anti-windup IP controllers to produce the output signals
of and , after coordinates transformation,
*
d
v*
v
and *
v
which can be obtained and used to produce
switching signals and c by three-level space
vector pulse with modulation (SVPWM).
,
ab
SS
,
a
e
S
As shown in Figure 3, in the three-level PWM grid
phase voltages (), two grid phase currents (
b
e,ii
)
and two dc-link voltages () are sampled.
1
,
dc dc
vv
2
3.1. Sliding Mode Control Design of the Output
Voltage Loop
The main goal of the voltage control of the rectifier is
keep the output voltage constant, ripple of the voltage
small, and overshoot small and the regulation course
short during transient conditions.
1dc
C
L
R
ddpis
2dc
C
1dc
V
2dc
V
2C
i
1C
i
o
i
p
i
n
i
N
P
ddnis
sqqpi
qqni
s
qsiL
s
R
d
e
+
d
v
s
L
+
d
i
dsiL
s
R
q
e
+
q
v
s
Lq
i
+
(a) (b)
Figure 2. Equivalent circuit of the three-level PWM recti-
fier in d - q coordinates.
*
dc
v
q
i
dc
v
0
*
q
i
a
r
*
d
i
d
i
s
L
+

abc
SVPWM
-
Antiwindup
IP
a
e
b
e
SMC
s
L
*
v
1dc
V
Three-level
rectifier
2dc
V
dq
a
i
b
i
b
c
dq

*
v
Antiwindup
IP
p
i
n
i
d
e
q
e
+
-
- -
+ +
+
+
-
-
+
+
+
-
a
S
b
S
c
S
*
d
v
*
q
v
q
i
d
i

Figure 3. Three-level rectifier control system.
Copyright © 2013 SciRes. EPE
A. DRAOU, S. MIEEE 31
There are two external variables (dc and q
ifor the
three-level PWM rectifier, where dc is determined by
v
v
d
s
, and q is controlled by q
i
s
. Considering dc
v and
q as contestable output variables, standard state space
can be obtained as
i
1
2
2
q
s
dq dc
sss
q
dc dd qqL
d
s
R
iiv e
LLL
i
d
vsi sii
dt
C

 







q
(11)
Substituting the error between reference and fact vari-
able into “equation (10)”, then


111qdc
iq
vdc
yE xtzEsv
e
d
e
e
dt




(12)
where,
, ,
refdc ref
iqiqq vdcdc
eiie vv
and
ref
e


So, it can be concluded that selecting the two follow-
ing sliding surfaces, the stability and robustness of the
system can be achieved:

10
iqiq ref
eiqe qq
ske kii  (13)
21 20
dc dc
dc dc
v
vv
de de
ske ke
dt dt

v
(14)
By combining the above equations, then 2
s
can be
rewritten as

 
2
2
2
dd qq
dc L
dcref dcdd
dc d
dcrefdcLq qd
d
si si
dv i
sv vdtC C
dv C
vv isi
dt Cs

 
 
d
i
(15)
In coordinates,
dq3
dRMS
, , in the
ideal sliding mode state,
eu0
q
e
q
s
can be calculated and sim-
plified as
2
s
d
qdc
Li
sv
 (16)
Similarly, the output voltage dc will follow the ref-
erence accurately, and based on the principle of
power balance,
v
*
dc
v
d
s
is obtained as:
3
dsd RMSsd
ddc dc
eRiu Ri
svv

(17)
By substituting “equation (16)” and “equation (17)”
into “equation (15)”, “equation (18)” can be deduced as


2
2
0
3
sdq
dc
dcref dcL
ddc
ddcd
RMSs d
Lii
dv
svv i
dt Cv
Cv i
uRi





(18)
Therefore, d
s
and q
s
will not be relevant to the
choice of sliding mode surface, and the sliding mode
surface can be obtained as

10
iqiq ref
eiqeqq
ske kii

(19)
20
ref
dd
si i
 (20)
From “equation (18)” and “equation (20)”, the control
rule for the outer voltage loop can be described as


2
3
dc
drefdcrefdcL
d
ddc
RMSs d
dv
ivvdt C
Cv
uRi
i

(21)
The block scheme of the VOC strategy based on SMC
for the three-level PWM rectifier is shown in Figure 3.
The error between reference dc-bus voltage and the
sampled dc-bus voltage dc is processed by SMC,
which produces the reference active current . and
, (for unity power factor control, ) are compared
with the measured grid current, d and q, respectively.
Then, the errors are processed in two anti-windup IP
controllers to produce the output signals of and ,
after coordinates transformation,
*
dc
v
*
d
i
*
q
v
v
*
d
i
*
q
i*0
q
i
i
*
v
i
*
d
v
and *
v
that can
be obtained and used to produce switching signals a,
b and c by the three- level space vector pulse width
modulation (SVPWM).
S
S S
3.2. Three-level Space Voltage Vector
Modulation Algorithm
There are 27 output voltage vectors in the three-level VSI
as shown in Figure 4. In Figure 5, suppose the desired
reference voltage vector lies in the triangle B which is in
the first 60° sector (sector I).
Then, the function time of each output voltage vector
should be calculated first as well as the corresponding
time for the power devices to turn on or turn off.
The desired output voltage vector consists of 13
and 4 by the adjacent three vector compounding prin-
ciple. Based on the volt-second balancing principle [36]:
,VV
V


21 sin3
2sin 31
2sin
as
bs
cs
TTk
TTk
TkT

 

(23)
where, 3
ref
kV is the modulation depth,
s
T is the
Copyright © 2013 SciRes. EPE
A. DRAOU, S. MIEEE
32
system sampling control cycle, ref and
V
is the am-
plitude and angle of the reference voltage vector .
ref
In the same way, the function time of the adjacent
three-vectors could be fixed when it lies in the triangle A,
C and D. The vector function time of the other five vec-
tors could be deduced in a symmetrical manner.
V
According to the function time of each vector and the
centro-symmetric vector sending sequence, the three
phase output vectors sequential chart could be fixed
when the reference vector ref lies in the triangle A, B,
C and D in sector I, which also gets the space voltage
vector modulation mode.
V
There are some similar SVPWM modes when the ref-
erence vector lies in other vectors. According to the
SVPWM mode and the function time of each vector cor-
responding to each sector, the power devices driven sig-
nal of the three phase arms could be obtained to control
the three-level inverter in SVPWM mode.
PON
PNO
ONN
POO
N OPN NPN
OPO
NON
NPO
NPP OPP
NOO
NOP OOP
NNO
ONP
NNP
PNN
PPO
OON
PP
POP
ONO
PNP
Figure 4. Space voltage vectors in three-level rectifier.
PO
N
N
N
ON
POO
PPO
OON
PPN
0
V
1
V
PN
3
V
ref
V
b
T
a
T
a
T
b
T
c
T
2
V
4
V
5
V
c
T
A
B
C
D
PPP
OOO
NNN
Figure 5. Synthesized reference vector in the first 60° sec-
tor.
4. Simulation Results
To validate the proposed control scheme proposed in this
paper, a series of simulation tests have been conducted
under Matlab/Simulink environment. The main parame-
ters of the simulation system are given in Table 1.
Figure 6(a) shows the DC voltage and current wave-
forms where the DC output voltage reaches the given
stable value (250 V) of the voltage in a short time. Fig-
ure 6(b) shows the grid phase voltage (a
e) and current
(a
i) waveforms. It can be seen that the grid current is in
phase with the grid voltage, and the power factor is
higher than 0.997.
Table 1. Rectifier parameter.
The input phase voltage 125 V
The Power source frequency 50 Hz
The input inductance 37 mH
The input resistance 0,3
DC-bus capacitor 1100μF
DC-bus voltage 250 V
(a) Output voltage and current
(b) Grid source side voltage and current
Figure 6. Simulation results of system.
Copyright © 2013 SciRes. EPE
A. DRAOU, S. MIEEE 33
Figure 7 shows the simulation results when the load
changes from 500 to 750 at t = 0.4 s. Figure 7(a)
shows the output DC voltage and current waveforms
when the load and input voltage fluctuates, the system
can adjust to the desired value of the voltage in a short
period of time. Figure 7(b) shows the waveforms of the
grid source side current, the current always maintains
unity power factor in the dynamic process.
Moreover, in view of the actual operating conditions,
there are more or less fluctuations of the three-phase in-
put voltage especially three-phase input voltage unbal-
ance in the operation of the circumstances. Figure 8(a)
shows unbalanced three-phase input voltage in the sys-
tem, single-phase unbalance is up to 20%, DC output
voltage fluctuations is less than 0.2 V as shown in Figure
8(b).
To validate the superiority of SMC over conventional
PI controller, comparative simulations are conducted and
the results are shown in Figure 9. Figure 9(a) shows the
waveform of the dc-bus voltage under conventional PI
controller while Figure 9(b) is that of SMC. It can be
seen clearly that the overshoots of the dc-bus voltage for
the rectifier with PI controller is much higher than that
with SMC, and the dynamic performance of the system is
improved significantly.
(a) Output voltage and current
(b) Grid source side current
Figure 7. Simulation waveforms at load changes.
(a) Three-phase input voltage fluctuations
(b) DC output voltage waveform
Figure 8. Voltage unbalance at the DC output waveforms.
(a) dc-bus voltage with conventional PI
(b) dc-bus voltage with SMC
Figure 9. DC output voltage waveforms.
Copyright © 2013 SciRes. EPE
A. DRAOU, S. MIEEE
34
5. Conclusions
The problem of the voltage control system of the three-
level rectifier is thoroughly analyzed and presented in
this paper. Through the study on the voltage equation of
the rectifier, the nonlinear characteristic of the voltage
control is carefully discussed and detailed based on a
new strategy which uses sliding mode control (SMC).
The proposed control strategy is adopted for the dc bus
voltage control to obtain better dynamic performance
based on the presented mathematical model. Simulation
results which are included in this paper, indicate that the
unity power factor is achieved and the proposed scheme
exhibits better dynamic and steady state performance
than conventional controller.
6. Acknowledgements
The author would like to express his deep gratitude to the
President of the University of Hail, in Saudi Arabia for
his continuous moral support and encouragement to re-
searchers as well as for financial support for undertaking
this research work.
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