Int. J. of Recent Trends in Engineering & Technology, Vol. 11, June 2014
Simulation of Space Vector PWM for 3-Level Inverter Fed
Induction Motor in Overmodulation Region
1,3,4
R Linga Swamy1, R.Somanatham2, P.V.N. Prasad3 and G.Srinivas4
Department of Electrical engineering, University College of Engineering, Osmania University, Hyderabad,
AP,India.
Email: rlswamy@gmail.com, rsm2006@rediffmail.com,
2
EEE Department, C.V.S.R. College of Engineering, Hyderabad
Email: polaki@rediffmail.com
Abstract— This paper describes the simulation of an over modulation strategy of SVPWM of a three level
inverter fed induction motor drive that easily extends from the under modulation strategy compare to the
conventional implementation. In this, the SVPWM operation is analysed in three different regions,
undermodulation region, overmodulation region 1 and overmodulation region 2 and they have been
compared with their results. It also describes systematically the algorithm development, system analysis and
extensive evaluation study to validate the modulator performance. The modulator takes the command voltage
and angle information at the input from a MATLAB program and generates symmetrical PWM waves for
the three phases of a switching inverter that operates at 3.0 KHz switching frequency. A simulink model of
three phase Inverter and Induction motor is developed.The performance of an Induction motor drive has
been has been evaluated extensively by smoothly varying the voltage and frequency in the whole speed range
that covers both under modulation and over modulation regions and performance was found to be excellent
with the simulation studies.
Index Terms— Three-level NPC inverter ,Induction motor drive, SV PWM, Overmodulation,.
I. INTRODUCTION
The rapid development of the capacity and the switching frequency of power semiconductor devices and the
continuous advance of the power electronics technology have made many changes in static power converter systems
and industrial motor drive areas. Especially, the voltage source PWM inverters have been extending their application
area widely.
Three-level inverter topology being widely used in high voltage/ high power applications due to its high voltage
handling and good harmonic rejection capabilities with currently available power devices like GTOS. It is known
that the three-level inverter roughly has four times better in harmonics content compared with conventional twolevel topology having same number of devices and ratings. So far various PWM techniques controlling three- level
inverter have been studied and a good plenty of results are published such as modified two-level triangular carrier
modulation, cost function minimizing PWM and space vector. Space vector PWM of a three-level inverter is
considerably more complex than that of a two-level inverter because of large number of inverter switching states [1].
In addition, there is the problem of neutral point voltage balancing. Unfortunately, operation in the under modulation
range of SVM restricts the drive operation in constant torque region only with voltage modulation factor up to
90.7%. An over modulation strategy of SVM with modulation factor extending from 90.7% to near unity is essential
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if the drive is required to operate at extended speed including the field-weakening region in vector control with
higher torque and power characteristics.
II. SPACE VECTOR PWM OF 3-LEVEL INVERTER IN UNDER MODULATION REGION
The over modulation strategy of a three-level inverter to be described in the paper is somewhat hybrid in nature,
i.e., it incorporates the under modulation strategy in part of a cycle.
Figure 1. Three-level inverter induction motor drive with space vector PWM
The phase U, for example, is in state P (positive bus voltage) when the switches S1U and S2U are closed, whereas it
is in state N (negative bus voltage) when S3U and S4U are closed. At neutral point clamping, the phase is in state O
when either S2U or S3U conducts depending on positive or negative phase current polarity, respectively. For neutral
point voltage balancing, the average current injected at O should be zero. The SVM controller is indicated in the
control block diagram. It receives the voltage (V*qs= V*) and angle (θe* ) command signals at the input as shown and
generates the PWM pulses for the inverter. For a vector-controlled drive with synchronous current control [1], both
V*qs and V*ds signals are present and the unit vector signal (θe*) can be generated in feedback (for direct vector
control) or feed forward (for indirect vector control) manner.
As the frequency or speed command signal We* is gradually increased from zero, the SVM first operates in under
modulation region, and then smoothly transitions into over modulation region with linear voltage transfer
characteristic in the over modulation range until square-wave operation is attained. Of course, a three-level inverter
cannot operate in square-wave mode (modulation factor m = 1) because it will then loose the three level switching
characteristics. It should be mentioned here that for the line-side converter (or rectifier) in ac-dc-ac conversion, the
SVM algorithm should be restricted to under modulation region only. A three-level inverter is characterized by 33 =
27 switching states as indicated in Fig. 3.3 where each phase can have P, N or O state. There are 24 active states,
and the remaining three are zero states (PPP,OOO,NNN) that lie at the center of the hexagon. The area of the
hexagon can be divided into six sectors (A to F) and each sector has four regions (1 to 4) giving altogether 24
regions of operation. The command voltage (V* ) trajectory, given by circle, can expand from zero to that inscribed
in the large hexagon in the upper limit of the undermodulation range[3].
At this limit, the modulation factor m = 0.907, where m = V* / V1sw (V* command or reference voltage magnitude
and V1sw = peak value of phase fundamental voltage at square wave condition). Fig.2. shows a smaller circle
embracing the region 1 of all the sectors which is defined as undermodulation mode-1. The large circle beyond
region 1 that embraces regions 2, 3, and 4 of all the sectors is defined as undermodulation mode-2. In
undermodulation region, the nearest three inverter voltage vectors that coincide with the apexes of the triangle are
selected and the corresponding time segments are calculated to construct the PWM wave. For example, if V * is
located in region 3 of sector A as shown, the switching vectors V1 , V3 and V4 are selected and the corresponding
time segments Ta, Tb and Tc are calculated. These time segments are then distributed in a certain sequence in the
sampling period Ta) so that the PWM wave is symmetrical and the neutral point voltage remains balanced. The
transfer characteristic between the fundamental output voltage and the command voltage is inherently linear in the
whole undermodulation range[3].
III.THREE-LEVEL INVERTER TOPOLOGY AND SWITCHING STATES
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Fig.2 Shows the representation of the space voltage vectors for output voltage of three level inverter. According to
the magnitude of the voltage vectors, we divide the min to four groups; zero voltage vector (Vo), small voltage
vectors (V1, V4, V7, V10, V13, V16) middle voltage vectors(V3, V6, V9, V12 ,V15 , V18). Large voltage vector (V2, V5, V8,
V11, V14, V17). The zero voltage vector (ZVV) has three switching states, the middle voltage vector (MVV) has only
one and so does the large voltage vector (LVV).. It shows the space vector diagram of all switching states, where the
P, O, N represent terminal voltage respectively, that is Vdc/2, 0, -Vdc/2.
Figure 2. Space vector representation
Figure3 Voltage vector sector1
IV. VOLTAGE VECTOR AND ITS DURATION
Fig. 3.shows the triangle formed by the voltage vectors V0, V2and V5. This triangle is divided into four small
triangles 1, 2, 3 and 4. In the space voltage vector PWM, generally, output voltage vector is formed by its nearest three
vectors in order to minimize the harmonic components of the output voltage and the current .The duration of each vector
can be calculated by vector calculation. For instance, if the reference voltage vector falls into the triangle 3, the duration
of each voltage vector can be calculated by the following equations[4]:
V1 Ta+ V3 Tb+ V4Tc = V*Ts
(1)
Ta + Tb + T c = Ts
(2)
TABLE I. VOLTAGE VECTOR DURATION
Switching Pattern Generation Consider Minimum On/Off Time
Vs r = 0.8*vdc
K = (2*vsr)/(sqrt(3)*vdc)
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(3)
(4)
Figure 4. Switching pattern for undermodulation region
Fig 4. shows the hexagon diagram of showing the switching pattern of space vector pwm in undermodulation region
with modulation factor less than 0.9 with 60 number of samples operating in 24 regions having respective phase voltage
vectors and corresponding time segments Ta, Tb, Tc.
TABLE II. SWITCHING PATTERN FOR SPACE VECTOR OF 3 LEVEL INVERTER IN
UNDERMODULATION REGION
Region Samples
States
Switching
States
1
5-17-16-4
POO-PON-PNN-ONN
2
4-16-17-5
0NN-PNN-PON-POO
3
5-17-16-4
POO-PON-PNN-ONN
4
4-16-17-5
POO-PON-PNN-ONN
3
5
4-7-17-5
0NN-OON-PON-POO
4
6
6-18-17-7
PPO-PPN-PON-OON
7
7-17-18-6
OON-PON-PPN-PPO
8
6-18-17-7
PPO-PPN-PON-OON
9
7-17-18-6
OON-PON-PPN-PPO
10
6-18-17-7
PPO-PPN-PON-OON
2
The undermodulation mode ends with this switching pattern and by increase of reference voltage and frequency the space
vector pwm shifts towards the overmodulation region and operation.
V.INTORDUCTION TO OVERMODULATION
The zero-vector time decreases as the stator voltage vector amplitude increases. The sinusoidal output quantities
are retained when the zero-vectors are present in the space vector modulation[1]. This modulation mode is called
linear modulation. After this point, the overmodulation methods are needed. Overmodulation is used to increase the
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voltage output of the PWM controlled frequency converter. It is important to use the full frequency converter
voltage because, in using the full frequency converter voltage, it is possible to both reduce the cost and increase the
output power. Furthermore, an electric drive with high overmodulation performance is less sensitive to DC-link
voltage disturbances. A DC-linkvoltage sag may lead in an unintentional entering to the overmodulation region. The
DC-link sag is a result of the line voltage sag or fault conditions of electric drive. When smaller DC-link capacitors
are used, voltage sags caused by the full-wave rectifier bridge are present all the time. Under such conditions, a high
performance overmodulation method could maintain the drive performance as much as possible. The inverter
blanking time and minimum-pulse-width constraints could further reduce the linearity range. For reasons of
simplicity, the following study of overmodulation does not take into consideration the blanking time and minimumpulse-width limitations. The modulation index M is used to describe the voltage utilization of the modulator [2].
Here, similar to the reference of Holtz (1993), the modulation index is defined with the magnitude of the
fundamental voltages of the inverter output voltage V and the theoretical maximum voltage under six-step operation
Vref
=
Vdc
Figure 5. Space voltage vectors showing operation in overmodulation region I (0.907<m<0.952)
VI.SVPWM OVER MODULATION OPERATION IN MODE I
The inherently nonlinear operation in over modulation region starts when the reference voltage V * exceeds the
hexagon boundary. The SVM over modulation strategy of three-level inverter has some similarity with that of a two-level
inverter[6]. The principle of over modulation is similar in all the sectors, and therefore, we will highlight the operation for
sector A only. In over modulation mode-1, shown in Fig 6. for the sector A, V* crosses the hexagon side at two points. As
explained above, during mode 1 of overmodulation region, a significant part of operation occurs on the hexagon side in
the sections bc in region 2 and cd in region 4. The analytical expressions for time segments in these sections will now be
derived. Consider that the reference voltage V* is tracking the section bc in region 2 as indicated in Fig. 4. Here the sector
angle α is now replaced by the general trajectory angle θe . The following two equations should be valid for space vector
PWM:
V2 · Tc + V3 · Tb = V*·
(5)
Tb + Tc =
(6)
Where Ts = sampling time. The voltage V* can be resolved into component vectors VA and VB as shown in the figure.
From the geometry we can write
Sector A, Region 2:
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=
= 2 .V*
=
VA = V*
(7)
=
V* (8)
- VB
(9)
Substituting (7) and (8) in (9) and simplifying, we get:
VA = V2
(10)
Fig. 6. Derivation of time segments in regions 3 and 4 of sector A for the trajectory on the hexagon.
Since
⁄
=
⁄
we can write:
Tc =
*
(11)
Therefore, to establish, the vector has to be impressed for the time segment
Tb =
- Tc
(12)
as given by (12). Similar derivations were made for region 2 in all the six sectors. The resulting expressions are
summarized in the second column of Table 3.
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Figure 7. Hexagon diagram of svpwm of three level inverter showing the no. of samples allocation in overmodulation
region I
TABLE III
SWITCHING PATTERN FOR OVERMODULATION
REGION 1 WITH 60 NO. OF SAMPLES
Similar calculations were made for region 4 in all the sectors. The resulting expressions are summarized in the
third column of Table 4 where θe´ is substituted by general θe angle
TABLE IV ANALYTICAL EXPRESSIONS OF TIME SEGMENTS OF VOLTAGE VECTORS IN DIFFERENT
REGIONS AND SECTORS DURING HEXAGON TRACKING
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VII.SVPWM OVERMODULATION OPERATION IN MODE II
The overmodulation region-2 starts when V* or m increases further. The operation in this region, as shown in Fig 8. for
the sector A [2], V* crosses the hexagon side at two points.
Fig 8. Space voltage vectors showing operation in
overmodulation region II(0.907<m<0.952)
Fig 9. Phase Voltage Trajectory in Overmodulation region II
To compensate the loss of fundamental voltage, i.e., to track the output fundamental voltage with the reference
voltage[6], a modified reference voltage trajectory is selected that remains partly on the hexagon and partly on a
circle. The circular part of the trajectory, shown by the segments ab and de has larger radius Vm* (Vm* > V*) and
crosses the hexagon at angle θ, as shown in the Fig 9. The expression of , as function of crossover angle, can be
derived as [6]
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The Van Voltage wave is given by approximate linear segments for the hexagonal trajectory and sinusoidal
segments for the circular trajectory as shown in above figure. is characterized by partly holding the hexagon corner
vector for holding angle αh , and partly tracking the hexagon side (segments bc and cd) in every sector. During
holding angle, the machine phase voltages remains constant, whereas during hexagon tracking the voltages change
similar to that of mode-1 described above [2]. The angle αh increases with modulation factor until increases with
modulation factor until at the end of mode-2 ideal six-step or square-wave operation is attained when the modified
vector is held at hexagon corners for 60o , i.e., αh = 30o. Fig 10 shows the hexagon diagram of showing the
switching pattern of space vector pwm in overmodulation region with modulation factor more than 0.97 with 60
number of samples operating in 24 regions having respective phase voltage vectors and corresponding time
segments Ta, Tb, Tc.
Figure 10. Hexagon diagram of svpwm of three level inverter showing the no. of samples allocation in
overmodulation region II
TABLE V SWITCHING PATTERN FOR OVERMODULATION REGIONII WITH 60 NO. OF SAMPLES
VIII.SIMULINK IMPLIMENTATION
Fig11. shows the simulink model for space vector PWM for 3- level inverter fed induction motor in both
overmodulation and undermodulation regions. In this model the complete operation of space vector PWM in both the
regions takes place for 60 number of samples..All the simulink models uses the switching pulses generated from the
Matlab program. Matlab program have been developed to implement the proposed scheme. Programs are developed for
both the undermodulation and overmodulation regions for the 3- level inverter fed induction motor to attain the greater
speeds.
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iga
Van
igb
Vbn
igc
Vcn
IGa
v an
IGb
Te
v bn
IGc
N
v cn
Switching signals
from Program
implementing SVM
Te,N,flux
v dc
Input dc
vdc/2
voltage
Vzn
Tl
iabcs
INVERTER
Load
torque
Tl
INDUCTION
MOTOR
ia,ib.ic
Figure 11. Simulink diagram of 3-Level Inverter connected to Induction motor Load
Continuous
IX.SIMULATION RESULTS
pow ergui
The results in fig. 12 are obtained for SVPWM Inverter fed Induction motor in undermodulation region(fig12(a)),
Overmodulation region I(fig12(b)) and Overmodulation region II(fig12(c)).It is observed that output voltage and
speed increases in Overmodulation regions.
Figure 12(a). Electrical Torque and Speed (Vs) Time in undermodulation region
Fig 12(a) shows the simulated waveforms Torque and Speed for 3-Level inverter fed Induction motor in
undermodulation region with a load torque of 10Nm.It is observed that Steady state torque of 10Nm is
reached at 0.18S and steady state speed of 1440rmp is reached at 0.2S.
Figure 12(b). Machine line voltage and phase current in undermodulation region
Fig 12(b) shows the simulated waveforms line voltage and phase current for 3-Level inverter fed
Induction motor in undermodulation region.It is observed that Steady output voltage rms value is 201.3V.
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Figure 12(c). Electrical Torque and Speed (Vs) Time in overmodulation region I
Fig 12(c) shows the simulated waveforms Torque and Speed for 3-Level inverter fed Induction motor in
Overmodulation regionI with a load torque of 10Nm.It is observed that Steady state torque of 10Nm is reached at
0.18S and steady state speed of 1450rmp is reached which is greater than undermodulation region.
Figure12 (d). Machine line voltage and phase current in overmodulation region I
Fig 12(d) shows the simulated waveforms line voltage and phase current for 3-Level inverter fed Induction
motor in overmodulation regionI.It is observed that Steady output voltage rms value is 207.9V which is greater
than undermodulation region .
Figure 12(e). Electrical Torque and Speed (Vs) Time in overmodulation region II
Fig 12(e) shows the simulated waveforms Torque and Speed for 3-Level inverter fed Induction motor in
Overmodulation regionII with a load torque of 10Nm.It is observed that Steady state torque of 10Nm is reached at
0.18S and steady state speed of 1461rmp is reached which is greater than undermodulation region and
Overmodulation regionI.
Figure 12(f). Machine line voltage and phase currents in overmodulation region II
Fig 12(d) shows the simulated waveforms line voltage and phase current for 3-Level inverter fed Induction motor
in Overmodulation regionII.It is observed that Steady output voltage rms value is 229.5V which is greater than
undermodulation region and Overmodulation regionI.
.
TABLE VI PERFORMANCE EVALUATION
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CONCLUSIONS
Space vector pulse width modulation of three level inverter has established their importance in high power high
performance industrial drive applications.A new simple Space Vector PWM Algorithm for 3 level inverter fed induction
motor drive operation in Undermodulation and Overmodulation regions is simulated using MATLAB/Simulink.
When compared to three level inverter in undermodulation region, in Overmodulation region the number of
switching states are less therefore the switching losses are very less. The simulation results shows that Speed,Vrms
and Irms of the drive is increased in overmodulation region when compared to undermodulation region. Hence, it is
useful in applications particularly where large speeds are required instantly. The values obtained during the simulation
are shown in table 6.
REFERENCES
[1] B. K. Bose, Modern Power Electronics and AC Drives. Upper Saddle River, NJ: Prentice-Hall, 2002.
[2] Subrata K. Mondal, Bimal K. Bose, Valentin Oleschuk, and Joao O. P. Pinto,”Space vector pulse width
modulation of three level inverter extending operation into overmodulation region”, IEEE Transaction on Power
Electronics, Vol. 18, No. 2, March 2003
[3] M. Koyama, T. Fujii, R. Uchida, and T. Kawabata, “Space voltage vector based new PWM method for large
capacity three-level GTO inverter,” in Proc. IEEE IECON Conf., 1992, pp. 271–276.
[4] Y. H. Lee, B. S. Suh, and D. S. Hyun, “A novel PWM scheme for a three-level voltage source inverter with GTO
thyristors,” IEEE Trans. Ind. Applicat., vol. 32, pp. 260–268, Mar./Apr. 1996.
[5] S. K. Mondal, J. O. P. Pinto, and B. K. Bose, “A neural-network-based space vector PWM controller for a threelevel voltage-fed inverter induction motor drive,” IEEE Trans. Ind. Applicat., vol. 38, pp. 660–669, May/June 2002.
[6] J. O. P. Pinto, B. K. Bose, L. E. B. da Silva, and M. P. , “A neural network based space vector PWM controller
for voltage-fed inverter induction motor drive,” IEEE Trans. Ind. Applicat., vol. 36, pp.1628–36, Nov./Dec. 2000.
Mr.R.Linga Swamy received his B.Tech degree in Electrical and Electronics engineering from Gokaraju Rangaraju
institute of Engineering and Technology, Hyderabad in 2002 and the M.Tech degree in power electronics and drives
from NIT, Warangal in 2004. Presently he is working as an Assistant Professor in Department of electrical
engineering, University College of Engineering, Osmania University, Hyderabad, Andhra Pradesh. His areas of
Interest include Multilevel Inverters,Space vector PWM,Induction motor drives.
Dr.R.Somanatham received his B.E, M.Tech (IDC), and Ph.D, F.I.E from Department of Electrical Engineering,
University College of Engineering, osmania university.He received gold medal in M.E. programme. He worked as a
Professor in the Department of Electrical Engineering, Osmania University, Hyderabad. Presently he is serving as
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Professor and HOD in the EEE Department, C.V.S.R. College of Engineering, Hyderabad. His areas of Interest
include power electronics, industrial drive and solid state ac and dc drives.
Dr.P.V.N.Prasad graduated in Electrical and Electronics Engineering from Jawaharlal Nehru Technological
University Hyderabad in 1983 and received M.E. in Industrial Drives and Control from Osmania University,
Hyderabad in 1986. He obtained his Ph.D in 2002 from Osmania University. Presently he is serving as Professor in
the Department of Electrical Engineering, Osmania University, Hyderabad. His areas of Interest include Reliability
Engineering,Simulation of Power Electronic Drives. He is a member of Institute of Engineers (India) and Indian
Society of Technical Education.He is Recipient of Dr. Rajendra Prasad Memorial Prize.IE (I), 1993-94 for best
paper.
Mr G.Srinivas obtained the B.Tech degree in Electrical and Electronics engineering from , C.V.S.R. College of
Engineering, Hyderabad in 2006 and the received M.E. in Industrial Drives and Control from University College of
Engineering, Osmania University, Hyderabad in 2009.
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