Energy and Power Engineering, 2011, 3, 276-284
doi:10.4236/epe.2011.33035 Published Online July 2011 (http://www.SciRP.org/journal/epe)
Comparative Study between Different Modulation
Strategies for Five Levels NPC Topology Inverter
Noureddine Ould Cherchali1, Abdelhalim Tlemçani1, Mohemed Seghire Boucherit2, Linda Barazane3
1Laboratoire de Recherche en Electrotechnique et Automatique, Université de Médéa, Médéa, Alger
2Laboratoire de Commande des Processus, Ecole Nationale Polytechnique, Algiers, Alger
3Faculté d’Electronique, Université des Sciences et de la Technologie Houari Boumediene, Algiers, Alger
Received April 29, 2011; revised May 15, 2011; accepted May 23, 2011
Abstract
The object of this paper is the study of various modulation strategies applied to the five-level inverter neu-
tral-point-clamped NPC topology. Firstly we presented the structure of the voltage inverter three-phase
five-level NPC topology. After that we model the inverter and the inverter are controlled by different strate-
gies and then we made a comparative study between the results given by different strategies.
Keywords: Multilevel, Five Levels, NPC, SHEPWM, SPWM, Hysteresis Control
1. Introduction
In recent years, electrical industries have expanded and
the variety of loads has increasingly grown. Recently, the
industry has begun to apply high-voltage high-power
equipment that has reached the megawatt range. Today,
the direct connection of a single semiconductor switch to
a system with medium sized voltage grids (2.3, 3.2, 4.16
and 6.9 KV) is too difficult. To overcome the limitations
on semiconductor voltage and current ratings, some type
of series connection will be necessary. Therefore, multi-
level inverters have been introduced. Due to their ability
to synthesize waveforms with a better harmonic spec-
trum and attain a higher voltage without transformers,
they have been receiving increasing attention in the past
few years.
There is several structure of multi levels inverter. in
this work, we chose NPC topology [1] with five levels.
Today, there are many switching strategies which are
applied to multilevel inverter topologies. The most
known are [1]: the sinusoidal pulsewidth modulation
SPWM strategy, the selective harmonic eliminated pulse
width modulation method SHEPWM and hysteresis
current control. These strategies modulations, which are
very effective methods for controlling the multilevels
inverters, will be presented here to control a three-phase
voltage inverter five-level NPC topology [1-7].
In the first part, we will present the structure of the
voltage inverter three-phase five-level NPC topology.
Secondly, we will apply four strategies [1]:
 The sinusoidal pulse width modulation strategy with
a one carrier;
 The four carriers sinusoidal pulse width modulation
strategy;
 The selective harmonic eliminated pulse width
modulation method SHEPWM strategy;
 The hysteresis current control.
In the third part we made a comparative study between
these four strategies in several ways
2. Modeling of Three-Phase Inverter a
Five-Level NPC Topology
The topology modeled in this study is the voltage in-
verter Three phase five-level topology NPC (Neutral
Point Clamp) [2,3].
Figure 1 shows the voltage three phase five-level
NPC topology inverter. The symmetry of three-phase
five-level inverters can model them by leg. So we begin
by defining a global model of q leg without a priori on
the control (Figure 2).
A topological analysis of q leg of the five-level
inverter NPC topology shows seven configurations
(Table 1 and Figure 3).
For a leg k, several complementary control laws are
possible for the five-level NPC. The optimal control law
of this inverter is:

N. O. CHERCHALI ET AL.277
D13
D12
D11
D14
D15
D16
T13
T12
T11
T14
T15
T16
D18
T18
T23
T22
T21
T24
T25
T26
T33
T32
T31
T34
T35
T36
D23
D22
D21
D24
D25
D26
D33
D32
D31
D34
D35
D36
D28
T28
D38
T38
D17
T17
D27
T27
D37
T37
DD11 DD21 DD31
DD10 DD20 DD30
UC2
UC1
UC3
UC4
VA VB VC
N
M
i1 i2 i3
id0
id1
id2
id3
id4
Figure 1. Three-phase inverter a five-level NPC topology.
Tk3
Tk2
Tk1
Tk4
Tk5
Tk6
UC2
UC1
UC3
UC4
Dk3
Dk2
Dk1
Dk4
Dk5
Dk6
Dk7
Tk7
Dk8
Tk8
DD11
DD10
M
Umk3
Umk2
Umk1
Umk4
Umk5
Umk6
ik
Umk8
Umk7
UDk0
UDk1
Figure 2. Leg of three-phase inverter a five-level NPC.
Table 1. Electrical quantities for each configuration of one
leg k.
configuration electrical quantities
E0 Ik = 0
E1 VkM = UC1 + UC2 = 2UC
E2 VkM = UC1 = UC
E3 VkM = 0
E4 VkM = −UC3 = −UC
E5 VkM = −UC3 − UC4 = −2UC
E6 VkM = 0
Figure 3. The different configurations for q leg k of the
inverter.
42
5
63
1
1
1
kk
k
kk
1k
F
F
F
F
F
F






(1)
for the leg k, We define a half leg connection function
where k = 1, 2, 3: where b = 1 refers to the lower half leg
and b = 0 to the upper half leg
1123
0 456
b
kkkk
b
kkkk
F
FF F
F
FFF





(2)
Connect functions for switches in parallel are defined
as follows:


712 3
845 6
1
1
kkk k
kkkk
F
FF F
F
FF F





(3)
The potentials of nodes A, B and C of Three phase
five-level inverter relatively to the middle point M in the
case UC1 = UC2 = UC3 = UC4 = UC are given by the
following system:
1711 1810
2721 2820
37313830
22
22
22
bb
AM
bb
B
MC
bb
CM
FFFF
V
VFFFF
VFFFF
U













 





(4)
The simple voltages at the boundaries of the load are
given by the following system:

N. O. CHERCHALI ET AL. 278
1711 1810
2721 2820
37313830
22
211
112 122
3112 22
bb
A
bb
B
C
bb
C
FFFF
V
VFFFF
VFFFF



 


 
 
 
 
 
 
 
  


U (5)
3. Control Strategies of the Five Levels
Inverter
3.1. Sinusoidal Pulse Width Modulation Strategy
with One Carrier
The principle of this method [3,8] is to impose on the
machine terminals voltage pulses so that the fundamental
tension is nearest the reference sinusoidal voltage. The
moments of impulse control switches are determined by
the intersection of the signal voltage reference called
“modulator” with one triangular high frequency signal
called a carrier. The characteristics of the method are:
Modulation index m:
p
f
m
f
 (6)
Modulation ratio r:
2
m
p
m
V
rU . (7)
Figure 4 shows the reference voltages and the carrier.
The algorithm of this strategy for arm k of this inverter
is that

12 3
1: 0&
1;0; 0;
refk pmrefk p
kk k
CVUVU
FF F
 



123
2: 0&&0
1; 1;0;
refk pmrefk prefk
kk k
CVUVUV
FFF
 
 


123
3: 0&&0
0;0; 1;
refk pmrefk prefk
kk k
CVUVUV
FFF
 
 




123
4:2& '&0
1; 1;0;
pm refkpmrefkprefk
kk k
CU VUVUV
FFF
 
 




123
5:2& '&0
1; 1;0;
pm refkpmrefkprefk
kk k
CU VUVUV
FFF
 
 




123
6:2& '&0
1;1; 1;
pm refkpmrefkprefk
kk k
CU VUVUV
FFF
 
 




123
7:2& '&0
0;0; 0;
pm refkpmrefkprefk
kk k
CU VUVUV
FFF
 
 
;if 0
with ';if 0
refk pmrefk
refk
refk pmrefk
VU V
VVU V






Figure 4. Different signals for the sinusoidal pulsewidth
modulation strategy with a one carrier (m = 6, r = 0.8).
Figures 5(a), 5(b) and 5(c) represent the voltage VA of
a single inverter arm controlled by the sinusoidal pulse
width modulation strategy with a one carrier
3.2. The Four Carriers Sinusoidal Pulse Width
Modulation Strategy
In this section we will present the strategy sinusoidal
pulse width modulation with four triangular bipolar
carriers [3,9] (Figure 6). Where we use four triangular
carriers bipolar (Up1, Up2, Up3, Up4) dephased one quarter
of the period (Tp/4) one relative to another. As SPWM
strategy with a one carrier, this strategy is characterized
by the modulation index m,
p
m
m
f
m
f
 (8)
and the modulation ratio r:
m
p
m
V
rU  (9)
Algorithm of this strategy is as follows:
Step 1: determination of intermediate voltages (VK1,
Vk2, VK3, Vk4):
44
44
33
33
22
22
11
11
2
0
0
2
refk pkC
refk pkC
refk pkC
refk pk
refk pk
refk pkC
refk pkC
refk pkC
VUV U
VU VU
VU VU
VU V
VU V
VU VU
VU VU
VU VU
























(10)

N. O. CHERCHALI ET AL. 279
123
123
12 3
123
123
21;1;
1; 1;0
01;0;
0;0; 1
20;0;
km Ckkk
km Ckkk
kmk kk
km Ckkk
kmC kkk
VUF FF
VUF FF
VFFF
VUF FF
VUFFF
1
0
0

 



 



 



  



  

(12)
Figures 7(a), 7(b) and 7(c) represent the output
voltage VA and its spectrum of three-phase five-level
inverter controlled by the strategy sinusoidal pulse width
modulation with four triangular carriers
(a)
3.3. The Selective Harmonic Eliminated Pulse
Width Modulation SHEPWM Strategy
The principle of control by elimination of harmonics
[5,8-15] is to predetermine the moments of switching of
Semiconductors in order to eliminate one harmonic or
many harmonics of the desired row. To eliminate the
harmonics of the following ranges: 5, 7, 11, 13 and 17, it
will take 6 angles (α1, α2, α3, α4, α5 and α6) (Figure 8).
After analyzing the Fourier series will be a system of
nonlinear Equations (13). We must solve this system by
a numerical method (Newton-Rafson [10,11] or Genetic
Algorithms [12-15].
(b)
Uc: supply voltage.

i: switching angles.
The required solution must satisfy the following
condition
0 < α1 < α2 < α3 < α4 < α5 < α6 < /2 (14)
As mentioned, the system equations are nonlinear. In
order to solve these equations the genetic algorithm (GA),
which is based on natural evolution and populations, is
implemented. This algorithm is usually used to reach a
near global solution. In each iteration of the GA a new
set of trings, which are called chromosomes, with im-
proved fitness produced using genetic operators.
(c)
Figure 5. The simple voltage VA and its spectrum of Three-
phase five-level inverter controlled by The sinusoidal pulse
width modulation strategy with a one carrier, (a) m = 6, r =
0.8; (b) m = 9, r = 0.8; (c) m = 36, r = 0.8.
A more complete discussion of GAs including ex- ten-
sions o the general algorithm and related topics can be
found in books by Davis [16], Goldberg [17], Holland
[18], and Deb [19].
Step 2: determination the signal Vkm and control orders
Bks switches
Vkm = Vk1 + Vk2 + Vk3 + Vk4 (11)
     
     
     
     
  
123456
123456
123456
123456
123
π
cos coscoscoscoscos4
cos5 cos5cos5cos5cos5cos50
cos 7cos7cos 7cos 7cos 7cos 70
cos 11cos 11cos 11cos 11cos 11cos 110
cos 13cos 13cos 13
C
r
U










  
     
456
123456
cos 13cos 13cos130
cos 17cos 17cos 17cos 17cos 17cos 170


















(13)

N. O. CHERCHALI ET AL. 280
Figure 6. Different signals for the four carriers sinusoidal
pulsewidth modulation strategy (m = 6, r = 0.8).
(a)
(b)
(c)
Figure 7. The simple voltage VA and its spectrum of Three-
phase five-level inverter controlled by the four carriers
sinusoidal pulse width modulation strategy; (a) m = 6, r =
0.8; (b) m = 9, r = 0.8; (c) m = 36, r = 0.8.
0

1

2

3

4

5

6 /2
2Uc
Uc
VAM

(
rad
)
Figure 8. The waveform of the first quarter of tension VAM.
The structure of a simple GA consists mainly of three
operators: a selection operator, a crossover operator
which acts on a population of strings to perform the re-
quired reproduction and recombination, and a mutation
operator which randomly alters character values, usually
with a very low probability. The effect of these random
alterations is to maintain diversity within the population,
thereby preventing an early convergence of the algorithm
to a possibly false peak.
Figure 9 represents the flowchart of Genetic Algo-
rithm [12].
Figure 10 represents the values of the six switching
angles obtained after the resolution of the system (13) as
function of r.
Figures 11(a)-(c) represent the single voltage VA and
its spectrum of an inverter arm controlled by the
SHEPWM strategy.
3.4. The Hysteresis Current Control
The principle this method [20-23] is based on deter-
mination the switching angles of switches so that the
variation of current in each phase follows a sinusoidal
current reference with a range of error i where the cur-
rent slide into a sliding surface.
If one considers k the difference between the real
current ik and reference current irefk. ( 
k = ik − irefk with k
= 1.2 and 3).
The switches control commands Bks for the arm k are
given by the following algorithm
123
123
123
123
1: 20;0;0;
2:20;0; 1;
3: 21;1;0;
4;21;1;1;
if not the command doe no change
kik kk
ikikkk
iki kkk
kikkk
CFFF
CFF
CFF
CFFF




 

 

F
F

 





(15)
Figure 12 and Figure 13 show respectively the refe-
rence and real currents with the difference between them
two, the output voltage of the inverter and the harmonic

N. O. CHERCHALI ET AL.281
Generate Initial Population
Calculation
Reproduction
Termi nate
End
Start
Crossover
Mutation
Evaluation
Ye s
No
Figure 9. Flowchart of genetic algorithm.
i = 0.5 A and i = 0.1 A.
4. Comparative Study
The comparative study between the different strategies
for controlling the inverter three-phase five-level NPC
structure is performed to:
*The same frequency of output voltage (f = 50 Hz)
*The same the modulation ratio (r = 0.8) for both
strategies sinusoidal pulse width modulation strategy
with a one carrier and four carriers.
According to Figures 5 and 7, we note that the
increasing of the modulation index m can be pushed the
harmonics to the higher frequencies and therefore can
0.55 0.60.65 0.7 0.75 0.80.85 0.9 0.9511.05
0
10
20
30
40
50
60
70
80
90
r
angles (°)
Alpha1Alphja2Alpha3 Alpha4Alpha5Alpha6
Figure 10. Six switching angles as function of modulation
rate r, for the SHEPWM strategy to eliminate 5 harmonics
(5, 7, 11, 13 and 15).
(a)
(b)
(c)
Figure 11. The simple voltage VA and its spectrum of three-
phase five-level inverter controlled by for SHEPWM
strategy to eliminate 5 harmonics (5, 7, 11, 13 and 17). (a) r
= 0.6; (b) r = 0.8; (c) r =1.
easily be filtered. For The sinusoidal pulse width modu-
lation strategy with a one carrier, we have for m even
only the odd harmonics exist, for m odd, we have odd

N. O. CHERCHALI ET AL. 282
0.9 0.92 0.94 0.96
-6
-4
-2
0
2
4
6Ia & Irefa (A)
time (s)
0.9 0.92 0.94 0.96
-1
-0.5
0
0.5
1
time (s)
Ia-Irefa (A)
Ia Irefa (A)Ia-Irefa (A)
(a)
(b)
Figure 12. (a) reference and real currents and the dif-
ference between the two currents εA; (b) The simple voltage
VA and its spectrum of three-phase five-level inverter
controlled by the hysteresis current control (Δi = 0.5 A).
0.90.92 0.94 0.96
-6
-4
-2
0
2
4
6Ia & Irefa(A)
time (s)
0.9 0.92 0.94 0.96
-0.4
-0.2
0
0.2
0.4
time (s)
Ia-Ir e fa (A)
Irefa Ia ( A)Ia-Irefa (A )
(a)
(b)
Figure 13. (a) reference and real currents and the dif-
ference between the two currents εA; (b) The simple voltage
VA and its spectrum of three-phase five-level inverter
controlled byThe hysteresis current control (Δi = 0.1 A).
harmonics and even harmonics too. For the strategy
sinusoidal pulse width modulation four carriers it has
only even harmonics.
Figure 11 shows the existence of only odd harmonics
and the magnitudes of first eliminated har- monics are
null.
We note for the hysteresis current control is charac-
terized by hysteresis band i. From Figures 12 and 13 it
is observed that the hysteresis current control is charac-
terized by a variable frequency modulation. This change
will be even higher than the hysteresis value of (i) will
be low. The spectrum of the voltage VA, has even and
odd harmonics, the magnitudes of harmonic nearly neg-
ligible compared to that of the fundamental especially for
i = 0.1.
Figures 14 show the total harmonic distortion THD of
the voltage VA, and the magnitude of the fundamental
harmonic.
The characteristic of adjustment strategy for the
sinusoidal pulse width modulation strategy with a one
carrier is linear for r = 0 to 0.5, and 0.56 to 1 but for r =
0.5 to 0.56 it’s constant because of the condition (16).
And total harmonic distortion is decreasing function of r
(Figure 13(a)).
2
p
mrefk p
UV U
m
(16)
For The four carriers sinusoidal pulse width modu-
tion strategy the modulation ratio r are like for the
strategy with a one carrier, we have a linear adjustment
of the magnitude of the fundamental r = 0 to 1. The total
harmonic distortion THD decreases when r increases
(Figure 14(b)), this strategy is better than with a one
carrier.
The modulation ratio r of the SHEPWM strategy is
linear from 0.6 to r = 1.02 (Figure 14(c)) beyond this
interval the system of nonlinear equation has no
solutions after condition of angles (14). We note that the
THD decreases as r increases. And we see also the best
value for r which gives a low total harmonic distortion is
0.9 and r = 1.00
About The hysteresis current control, it is usefully
than other strategies, more it can be controlled in closed
loop, but we have to make an optimal control for low
values of range (I). And the output voltages are
asynchronous and no periodical.
5. Conclusions
In our work we presented and modeled the three-phase
five-level inverter NPC structure then we applied to it
different strategies: The sinusoidal pulse width modu-
lation strategy with a one carrier, The four carriers
sinusoidal pulse width modulation strategy, the selective
harmonic eliminated pulse width modulation method
SHEPWM strategy and at the end we saw The hysteresis
current control.
After this study, we can note the following:

N. O. CHERCHALI ET AL.283
(a)
(b)
(c)
Figure 14. THD results and fundamental harmonic; (a) The
strategy with a one carrier (m = 6); (b) The four carriers
sinusoidal pulsewidth modulation strategy (m = 6); (c) The
SHEPWM strategy to eliminate 5 harmonics (5, 7, 11, 13
and 17).
The four carriers sinusoidal pulse width modulation
strategy is more favorable than the sinusoidal pulse
width modulation strategy with a one carrier, and it can
be made with analog circuits.
Selective harmonic eliminated pulse width modula-
tion method SHEPWM strategy is favorable to other
control strategies in terms of number of switching
(commutation energy dissipation) and noise nuisance.
The hysteresis current control it perfectly follows the
current reference, it can be controlled in closed loop.
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