2557
Vol. 5
Indian Journal of Science and Technology
No. 4 (Apr 2012)
ISSN: 0974- 6846
Digital simulation of two level inverter based on space vector pulse width modulation
1*
Snehasish Pal and Suvarun Dalapati
1
2
Department of Electrical Engineering, JIS College of Engineering, Kalyani, West Bengal-741233, India
Asst. General Manager (R & D), Stesalit Limited, Electronic Systems Division, Kolkata- 700091, India
snehasish_pal@yahoo.co.in*; suvarundalapati@yahoo.co.in
2
Abstract
Space Vector Pulse Width Modulation (SVPWM), one of the advanced computation based PWM techniques, has many
advantages over conventional carrier-based PWM methodologies. Recently, with the easy availability of
Microcontrollers and Digital Signal Processors, this technique is being widely used in industrial inverters. This paper
presents a simple model for a three-phase two level SVPWM inverter using MATLAB-Simulink software. The entire
model is based on only elementary Simulink blocks, and the use of advanced tool-box functions has been avoided.
Hence, the model can be used, understood and modified easily as per the need of the user. The inverter has been
divided into several sub-systems. Each such ‘sub-system-block’ is explained individually. Both linear and overmodulation-zone-controls have been included. The model operates successfully for various values of amplitude
modulation index.
Keywords: Space Vector Pulse Width Modulation, Two-level inverter, MATLAB-Simulink, Linear zone, Over-modulation
zone.
Introduction
(termed as ‘over-modulation zone-1’ and ‘overSVPWM technique based inverters have been a modulation zone-2’). Subsequently the mathematical
widely researched topic in the field of power electronics expressions, for deriving the SVPWM control in various
and machine drives over the last few years (Boost & zones, are also derived and presented. The blocks are
Ziogas, 1988; Bose, 2006). The technique enjoys several then combined together to synthesize the model of the full
advantages over conventional PWM techniques (e.g. SVPWM inverter. This inverter model is simulated in open
sine-triangle PWM). Some of its advantages include more loop conditions for a three phase star connected
effective utilization of DC bus voltage, optimum harmonic balanced inductive load. Some sample results for the
content for a wide load range, non-requirement of high inverter operation in open loop conditions for all the three
frequency carriers and the allied synchronization zones of operations are presented to validate the
problems etc. (Bose, 2006; Holtz, 1992). Recently, with correctness of the model.
the easy availability of DSP and Microcontrollers with The basic structure of the SVPWM inverter
high computational features, this technique is being
The essence of SVPWM technique can be
applied in various industrial inverters.
understood easily from any standard text book on power
MATLAB-Simulink based simulations have been electronics (Bose, 2006). The three phase balanced
accepted globally both in academic and research
institutes, as well as in industry to be a standard tool for
Fig.1. Six-switch inverter feeding its output to a three phase
simulating various complicated industrial systems
star connected inductive load (with floating neutral); the
source neutral point ‘N’ may be tapped by splitting the dc
(Ayasun & Karbeyaz, 2007). In the recent versions of
bus into two equal halves by equal capacitors
MATLAB-Simulink, the user has been provided with many
additional Simulink-Libraries and Models (in block form)
to help the modelling of several complicated systems
more easily (Hunt et al., 2006; Shaffer, 2007). However,
although the newer libraries / blocks ease the
development of models for simulating complicated
systems, the price to be paid is in terms of the time and
PC-resources (e.g. memory, CPU-speed etc.) required.
This paper presents a model for the three phase two
level SVPWM inverter in MATLAB-Simulink environment.
The model has been developed by using only basic
Simulink Library blocks, thereby reducing simulation time,
without compromising on the accuracy of the solution.
The model of the inverter comprises of several subsystems. In the following sections, the function of each
sub-system is explained with reference to the SVPWM
technique for linear and both the over-modulation zones
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windings of an induction motor, when fed with a balanced
three-phase sinusoidal voltage-set, will generate a
resultant space vector, which has a fixed amplitude and
rotates along a circular trajectory in space. The basic aim
of the SVPWM inverter is to generate such a ‘rotating
space-vector’.
No. 4 (Apr 2012)
ISSN: 0974- 6846
sector number n as inputs and calculates the time
durations t0, t7, (for applying the null vectors) and t1,t2 (for
applying active vectors) of a given sector. The ‘pulse
generator’ block takes these time-values and applies
suitable active and null vectors to the load.
Description of Constituent Blocks
This section is devoted toward describing each
building-block of the SVPWM Inverter model for the
various zones of inverter operation (i.e. linear, overmodulation-1 and over-modulation-2 zones). The
mathematical deductions for each block are also
presented in the corresponding section.
The ‘Ma-calculator’ block
In this paper the ‘amplitude-modulation index’, termed as
Ma, is calculated as follows:
V
Vr
V
Ma  r 
 r …………………….. (2)
Vn
 2 V  Vd
 DC 
3 
(where n = 1, 2, … 6).
The structure of the ‘Ma-calculator’ block is shown below
Fig. 2. Six-step operation of the three phase bridge
inverter of Fig.1, (a) three load phase waveforms and (b)
space vectors forming a hexagon (encircled digits show
sector numbers)
Fig. 4. (a) Ma-calculator block and (b) its internal structure
The
SVPWM
inverter
has
the
conventional
six-switch based bridge
structure as shown in Fig.1. The resultant
space-vector can be readily derived from the
load-phase voltages generated from the
inverter as follows:
Vs 
2
 van  avbn  a 2 vcn  ………………. (1)
3
(a)
Using equation (1), the resultant space
vectors for a six-step operation can be easily
derived to form the hexagon, as shown in
Fig.2. It may be noted that the six ‘active vectors’
connects the centre of the hexagon to the six vertices,
while the two ‘null-vectors’ are located at the hexagon
centre. This ‘space-vector-hexagon’ defines the area,
within which the resultant space vector will always lie.
The basic block diagram of the SVPWM inverter is
presented in Fig.3. The voltage and frequency are fed as
the reference signals. The ‘Ma & θ calculator block’
calculates the value of Ma and θ. Depending upon the
value of Ma, the inverter then must be given a set
trajectory, along which the space-vector rotates with
respect to the hexagon-centre (Bose, 2006). The
‘Trajectory Selector’ block calculates this trajectory and
modifies the value of Ma and θ as Mae and θsect
respectively. The ‘time-splitter’ block takes Mae, θsect and
Fig.3. Basic block diagram for the SVPWM inverter model
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(b)
in Fig.4.
The ‘theta sampler’ block
Depending upon the chosen switching frequency, the
inverter combines the various active and null vectors to
synthesize an ‘average-vector’ over one switching cycle
to match the given reference space vector. For computing
the time of applying the various fundamental vectors, the
knowledge of the value of θ is required. The value of θ
may be computed from the given value of switching and
output frequencies and is to be held constant during one
switching cycle. At the beginning of the next switching
cycle, the value of θ will have to be ‘refreshed’. The
‘theta-sampler’ block performs the above function. This
block is presented in Fig.5. It may be observed that the
‘Zero-Order-Hold’ block, as shown in Fig.5b, must have a
sampling frequency which is same as the switching
frequency of the inverter (chosen to be 6 kHz in this
case).
The ‘sector-number-generator’ block
The ‘Sector-Number-Generator’ block computes the
sector number from the given value of theta as input. The
sector number may be generated by noting the value of θ,
as shown in Table 1.
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Fig. 5. (a) Theta-sampler block and (b) its internal structure
(a)
(b)
Trajectory selector block-1 (for linear zone and overmodulation-zone-1)
Fig. 6. Original reference trajectory input to ‘trajectory
selector block-1’ (circle with light thick line) and
modified reference trajectory output from the same
block (circle with dark-narrow line) for linear zone of
operation (Ma is chosen as 0.8 in this case)
defines the trajectory to be followed by the inverter
output. Trajectory-selector-block-1 accomplishes this
function for the linear zone and the over-modulation
zone-1 of the inverter operation.
Linear zone
The ‘linear-zone’ for inverter-operation takes place
when the reference trajectory is a circle lying completely
within the hexagon. This scenario exists when the
computed value of Ma lies between 0 and 0.866. The
‘linear-zone-detector-block’ checks whether the computed
value of Ma lies within the range 0 – 0.866, or not. Once,
Ma lies within this range, the ‘trajectory-selector-block’
passes on the computed value of Ma and θ, which it
receives as input, directly to its output (Fig.6). Thus, in
this case, Ma = Mae.
Over-modulation zone-1
This zone exists when 0.866<Ma<0.9091. In this
zone, the ‘original-reference-trajectory’ is a circle, which
traverses outside the ‘space-vector-hexagon’. Thus, in
every sector of the hexagon, the ‘original-referencetrajectory’, defined by a circle, cuts the hexagon boundary
in two distinct points (Fig.7). However, it is not possible
for the inverter to follow this trajectory directly. To
compensate for this area, which is lost, the ‘trajectoryselector-block-1’ must select a modified trajectory. This
new trajectory is shown in Fig. 8. The modified trajectory
follows a circular path from angle 0 to α (within a sector)
The trajectory selector block-1 takes in the computed
value of Ma and θ as inputs. Based on these quantities, it
Fig. 8. Modified reference trajectory to
compensate for the area lost
Fig. 7. Original reference trajectory traversing
outside the space vector hexagon
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Fig. 9. Variation of Ma with α
No. 4 (Apr 2012)
ISSN: 0974- 6846
with a radius (r1) greater than the radius of the original
reference trajectory (r). It meets the hexagon boundary at
some angle α, follows the hexagon boundary up to the
angle    , after which it reverts to a circular

3

trajectory of radius r1 again. This circular trajectory is
followed till the end of the sector (at angle  ). The angle
3
Fig.10. Original reference trajectory input to
‘trajectory selector block-1’(circle with light thick
line) and modified reference trajectory output from
the same block (trajectory with dark-narrow line)
for over-modulationzone-1 of operation (Ma is
chosen as 0.9 in this case)
α, also called the ‘cross-over angle’ for the modified
reference trajectory, may be determined by areamatching principle. Thus, to determine the modified
trajectory for a value of Ma, which is received as input, the
controller should compute two quantities, namely: (a) the
value of α and (b) the value of r1 = Vov. The following
mathematical treatment provides the solution. Referring
to Fig.8, the actual area determined from the ‘original
reference trajectory’, per half-sector, is given by:
Aref 
 2
Vr ……………………………......................... (3)
12
Area traversed per half-sector by the ‘modified reference
trajectory’ is given by:
Amref 
 2 1 2


Vov  VDC tan     ………….... (4)
2
6
6

Thus, to satisfy the area-matching criterion, the above
two areas, given by Equations (3) and (4) must be
equated.
 2  2 1 2


Vr  Vov  VDC tan     …………… (5)
12
2
6
6

Again, from Fig. 8, it easily follows that:
Vov 
1


VDC sec     …………………........... (6)
3
6

Using the result of Equation (6) in Equation (5), and after
Fig.11(a) Trajectory selector block-1 (for linear zone and over-modulation zone-1, and (b) its internal structure
(b)
(a)
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Just as in the case of ‘trajectory-selector-block-1’, the
‘trajectory-selector-block-2’ also takes in the computed
value of Ma and θ as input and checks whether the value
of Ma lies within the range for over-modulation zone-2,
which is 0.9091<Ma<1. If the value lies within this range,
then the ‘trajectory-selector-block-2’ modifies the spacevector-reference trajectory suitably. If the value of Ma lies
below this range, then the value of Ma is either in the
linear zone or over-modulation-zone-1. In this case, the
computed trajectory of ‘trajectory-selector-block-1’ is
allowed to pass through. The principle of operation of this
block is explained in the next section.
Principle of operation
The control algorithm is modified as follows.
 For an output frequency required, the time by which
one sector is to be traversed, is determined.
 In every sector, for a certain time (determined by the
value of Ma), the modified reference space vector will lie
fixed at the starting edge of the sector (i.e. at V1 for
Fig. 12. Original and modified reference trajectories
for over-modulation-zone-2 (in case of sector 1)
Fig.13. Magnitudes of original reference and modified
reference signals, plotted with respect to time
sector-1, at V2 for sector-2 etc.).
 For the remainder of the time (for one sector) the
modified-reference-trajectory will move along the
boundary of the hexagon (in that sector) and will have
to reach the other edge (i.e. the finishing edge) of the
sector. The finishing edge of this sector (i.e. at V2 for
Fig.14. Angles of original reference and Modified
reference signals, plotted with respect to time
sector-1, at V3 for sector-2 etc.) will act as the starting
edge for the next sector.
 Thus, in this zone (over-modulation-zone-2), the value
of θ (which is input to the trajectory selector block) is to
be modified into  eff (which is to be output from the
trajectory selector block). The value of
some algebra, it follows that:
2 2





M a   1  tan 2       tan     ……(7)
9
6

6


For every value of α, Equation (7) gives one unique
value of Ma (negative value is not considered). Thus, a
look-up table may be formed, which will give us a value of
α for a given value of Ma. Using this look-up table, for
each value of Ma, the corresponding value of the crossover angle may be obtained. The nature of variation of Ma
for various value of α is shown in Fig.9. A typical result
from the ‘trajectory-selector-block-1’ is presented next in
Fig.10, corresponding to the operation in ‘overmodulation-zone-1’. It may be noted that by following the
modified trajectory, the inverter-operation now moves into
a non-linear zone. The block diagram and the internal
structure for the ‘trajectory-selector-block-1’ is presented
next in Fig.11(a) and Fig.11(b) respectively.
Trajectory selector block-2 (for over-modulation-zone-2)
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 eff will be used
to compute the value of θsect in the successive stages.
The case may be illustrated with the help of Fig.12,
where sector-1 has been taken as an example. Here, as
shown in Fig.13, if Ts be the time in which a sector is to
be traversed (this is determined by the choice of the
inverter output frequency, e.g. 50Hz / 60Hz), then for a
particular time Th, the modified-reference-trajectory must
stay at V1 (which forms the starting edge of the sector),
then move along the hexagon-boundary (straight line)
from V1 to V2 , within a time of  Ts  Th  . Fig.13 and
Fig.14 show the time plot for the original reference and
modified reference vector magnitudes and angles
respectively within one sector.
Table 1. Sector number generated by noting the value of θ
Range of θ
Sector Number
0  /3
1
 / 3    2 / 3
2
2 / 3    
3
    4 / 3
4
4 / 3    5 / 3
5
5 / 3    2
6
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Fig. 15 (a) Trajectory selector block for over-modulation-zone-2 and (b) internal structure
(a)
(b)
Fig.16. Combining vectors to achieve
a
resultant
vector;
a
1
t 

V
T 
1
1
and
Fig.17. Symmetrical pulse distribution
(centre-aligned mode)
sw
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Thus, as seen from the above discussion,
Table 2. various sectors and the corresponding vector sequence
to control the SVPWM inverter in the overSector
Vector Sequence
modulation-zone-2, the time Th must be
No.
first
determined.
The
following
1
V0 (t0/2) V1 (t1/2) V2 (t2/2) V7 (t7) V2 (t2/2) V1 (t1/2) V0 (t0/2)
2
V0 (t0/2) V3 (t1/2) V2 (t2/2) V7 (t7) V2 (t2/2) V3 (t1/2) V0 (t0/2)
mathematical treatment will derive a
3
V0 (t0/2) V3 (t1/2) V4 (t2/2) V7 (t7) V4 (t2/2) V3 (t1/2) V0 (t0/2)
formula for determining Th (or the
V0 (t0/2) V5 (t1/2) V4 (t2/2) V7 (t7) V4 (t2/2) V5 (t1/2) V0 (t0/2)
4
corresponding angle αh, also called the
5
V0 (t0/2) V5 (t1/2) V6 (t2/2) V7 (t7) V6 (t2/2) V5 (t1/2) V0 (t0/2)
‘holding-angle’).
6
V0 (t0/2) V1 (t1/2) V6 (t2/2) V7 (t7) V6 (t2/2) V1 (t1/2) V0 (t0/2)
As the ‘modified-reference-vector’
stays at one active vector location for a certain finite time The time splitter block ‘splits’ one switching period into
in every sector (of the space-vector-hexagon), the rate, at sub-intervals for applying the active and null vectors
which it will traverse to the other end of the same sector corresponding to that sector. Such vectors must be
will be higher than the output frequency. Let this modified applied in proper sequence to achieve centre-aligned
value of angular frequency be ω1 (ω1>2πfo). Thus, from pulse positioning (Fig.16). The time durations, for which
Fig.13 and Fig.14, the modified reference space vector the active vectors are to be applied, are given by:
t
can be defined as follows:
t1  2   M a cos  sect  Tsw ……………….. (13)
,

F t 
V
2
d

0  t  Th
3
Vd sec
2
Here,


6

 1  t  Th 
,
.. (8)
Th  t  Ts

3
1 Ts  Th  
Alternatively, in the range Th  t  Ts , F(t) may be defined
as:
F t  
3
2
1
Vd
sin



……….................... (9)
 1  t  Th 
3
Hence, by substituting z = t-Th, the actual area traversed
(in one sector) by the modified reference vector may be
calculated as follows:
Amref  Vd Th 
3
2
Ts  Th
Vd

0
dz



sin   1 z 
3
 ………………........ (10)
3 3
Vd  Ts  Th  ln 3
2
Again, area traversed in one sector by the original
reference is given by:
T
Aref  Vr o ………………….............................................. (11)
6
Equating the two areas, given by (10) and (11), the
following relationship between Ma and Th may be
obtained:
 Vd Th 
 To   T   3 3 ln 3   To  T  …………............. (12)
 h 

h 
6

 2
 6
Ma 
The MATLAB-Simulink model for the ‘trajectory-selectorblock-2’, which works in conjunction with ‘trajectoryselector-block-1’, is presented next in Fig.15.
Time-splitter block
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and
2
M aTsw sin  sect ……………… (14)
3
The time-durations for which the null vectors are to be
applied can be easily derived by using the following
relationship:
T   t1  t 2 
……………….. (15)
t 0  t 7  sw
2
Thus, for sector-1, the sequence for each vector (with
time-duration) may be as follows:
V0 (t0/2) V1 (t1/2) V2 (t2/2) V7 (t7) V2 (t2/2) V1
(t1/2) V0 (t0/2)………….. (16)
This gives rise to a pulse distribution, as shown in
Fig.17 (assuming that the state ‘1’ implies that the upper
switch of any leg is ON, while the state ‘0’ implies that the
lower switch of the same leg is ON). The above
procedure (of time distribution & symmetrical pulse
positioning) is to be followed for each sector individually.
The various sectors and the corresponding vector
sequence are given in Table 2.
Thus, it may be observed that the vector sequence is
of the ‘forward’ type in odd numbered sectors, while the
sequence is of the ‘reversed’ type for the even-numbered
sectors. Thus, the effective value of angle in a sector for
computing time distribution may be obtained as follows:
 effective 
t2 
1   1
n
    1 n 1  …………... (17)
   sect
3
.
2
Thus, the steps to be followed, for computing time in any
sector (for linear zone of operation), are as follows:
1. From the value of θ and the sector number,
compute θsect and θeffective using (17).
2. Using the value of Ma and θeffective, compute t1, t2, t7
and t0 using (13) – (15).
3. Split up these times symmetrically among the
corresponding active and null vectors to get centrealigned pulses
For over-modulation zones 1 or 2, (13) and (14) reduces
to the following form:
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However, the reference frequency command may be
positive / negative. However, since a negative referencefrequency implies a change in phase-sequence of the
output PWM waveform, the same is achieved by using
the ‘direction-reverser-block’, as shown in Fig.19.
The overall block diagram of the three phase
2 sin  effective
SVPWM
inverter with all the constituent blocks, as
t2  Tsw
………......
described above, is presented in Fig.20. The ‘space
3 cos  effective  sin  effective
vector display block’ is not a part of the standard inverter,
but is kept for display purpose only.
(19)
Results
t0  t7  0 ………………............ (20)
and
To test the effectiveness of this model, it has been
Pulse generator block
simulated in MATLAB-Simulink environment for various
conditions. In this section, the various results
Table 3. Three different inverter-legs, by taking one state (out of three) at
from this SVPWM Inverter-Model will be
a time from each cell of Table 2
displayed and explained. The various parameter
Vector States for corresponding time durations
Sector
values, used for simulation is presented in TableNo.
t0/2 t1/2 t2/2
t7/2
t7/2 t2/2
t1/2
t0/2
4. Initially, a reference is set to yield a load phase
1
000 100 110 111
111 110 100 000
000
voltage of 220V (amplitude) from this inverter.
2
000 010 110 111
111 110 010 000
000
Thus, the inverter operates in the linear zone.
3
000 010 011 111
111 011 010 000
000
4
000 001 011 111
111 011 001 000
000
Hence, in this case, the Ma-trajectory (as input by
5
000 001 101 111
111 101 001 000
000
the user) matches the computed Ma-trajectory, as
6
000 100 101 111
111 101 100 000
000
shown in Fig.21. As happens in case of linear
Various ‘switching states’ represent the inverter zone of operation, with V/f start, the trajectories are
output for different sectors. The computed values of time- having circular shape, gradually expanding in radii to
durations for each state is compared with a fixed reach a steady state value. The time-plot of the inverter
frequency saw-tooth waveform and the state-table line voltage and load phase voltage are presented in
(shown in Table-3) is utilised to output the pulses to the Fig.22 and Fig.23 respectively. The amplitude of load
load. The sector number input determines the row to be current, for this set value of load voltage, can be
selected. Thus, in each sector, the cells of one particular calculated to be 11.81A at 50Hz. The load-current-spacerow are selected in sequence, while the row changes vector trajectory and the actual load currents are
whenever the space vector is to move from one sector to presented in Fig.24 and Fig.25 respectively. Fig.25a
another. As the saw-tooth waveform has a negative shows three load phase currents together (w.r.t the same
gradient for a very short duration in each switching cycle, set of axes), while Fig.25b shows one load phase voltage
this information (sign of gradient) is used for re-setting the and the corresponding load phase current. As in the case
states to ‘000’ at the end of every switching cycle. Re- for R-L loads, the load-current clearly lags the
setting duration being very short as compared to other corresponding load-voltage.
durations, its effect on the overall pulse pattern is
The same model is now used again and the
negligible. From Table 3, three separate look-up tables reference value (of phase voltage amplitude) is set at
have been generated for three different inverter-legs, by 330V (over-modulation zone-1) and 350V (overtaking one state (out of three) at a time from each cell of modulation zone-2), keeping the DC bus voltage fixed.
Table 2. The pulse-generator block details are presented The corresponding results for reference and actual space
in Fig.18.
vector trajectories and load current are presented in
Fig.26 and 27 respectively. Fig.28 shows the comparison
Table 4. Values for simulation
between the FFT plots for a standard Sine-PWM inverter
Sl.
Parameter
Value / Type
and a space vector PWM inverter. As seen, the Space
No.
Vector PWM inverter shows a more evenly distributed
1.
DC bus voltage
560V
harmonic pattern.
Output phase voltage (set as
2.
220V
reference)
Conclusion
3.
Switching strategy
SVPWM
In this paper, a MATLAB-Simulink model for a three
4.
Switching / Sampling freq.
6 kHz
phase SVPWM Inverter has been presented. The model
5.
O/P frequency (rated)
50Hz
is based on elementary MATLAB-Simulink functional
6.
Type of load
Resistive-inductive
blocks only, and thus provides a medium for quick and
7.
Load value
R =10Ω, L=50mH
easy simulation for several cycles of the output
Direction reverser block
frequency. It can be easily incorporated in larger
All the computations for the previous sections have ‘MATLAB-Simulink’ models for power-electronics and
been completed by using positive values of θ only. machine drives simulations.
 3 cos  effective  sin  effective 
t1  Tsw 
 …………..... (18)
3
cos


sin


effective
effective 



Research article
Indian Society for Education and Environment (iSee)



“Two level inverter”
http://www.indjst.org
S.Pal & S.Dalapati
Indian J.Sci.Technol.
2565
Vol. 5
Indian Journal of Science and Technology
No. 4 (Apr 2012)
ISSN: 0974- 6846
Fig. 18. (a) Pulse generator block (left) and (b) internal structure (right)
(b)
(a)
Fig. 19. (a) Direction-reverser block (left) and (b) internal structure (right)
(b)
(a)
Fig. 20. Detailed internal structure (left) and overall block diagram (right) of the SVPWM inverter
(a)
Research article
Indian Society for Education and Environment (iSee)
(b)
“Two level inverter”
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S.Pal & S.Dalapati
Indian J.Sci.Technol.
2566
Vol. 5
Indian Journal of Science and Technology
Fig. 21. User-defined Ma-trajectory (thin dark line) and
inverter-computed Ma-trajectory (thick grey line) for the
inverter, operating in the linear zone with V/f start;
the steady-state circular
No. 4 (Apr 2012)
ISSN: 0974- 6846
Fig. 24. Load current space vector plot for the
inverter delivering an output phase voltage
of 220V (amplitude), by operating in the linear zone
Fig. 25a. Load phase currents for the
inverter operating in the linear zone
Fig. 22. Inverter output line voltage (VRY) for
the inverter operating in the linear-zone
Fig. 23. Load phase voltages for the inverter operating in the linear zone
Research article
Indian Society for Education and Environment (iSee)
“Two level inverter”
http://www.indjst.org
S.Pal & S.Dalapati
Indian J.Sci.Technol.
2567
Vol. 5
Indian Journal of Science and Technology
No. 4 (Apr 2012)
ISSN: 0974- 6846
Fig. 25b. One load phase voltage and corresponding load phase current for the inverter
operating in linear zone
Fig. 26a. User-defined Ma-trajectory (thin dark line)
and inverter-computed Ma-trajectory(thick grey line)
for the inverter, operating in over-modulation zone-1
Fig. 27a. User-defined Ma-trajectory (thin dark line)
and inverter-computed Ma-trajectory (thick grey line)
for the inverter, operating in over-modulation zone-2
Research article
Indian Society for Education and Environment (iSee)
Fig. 26b. Load phase currents for the inverter
operating in over-modulation zone-1
Fig. 27b. Load phase currents for the inverter
operating in over-modulation zone-2
“Two level inverter”
http://www.indjst.org
S.Pal & S.Dalapati
Indian J.Sci.Technol.
2568
Vol. 5
Indian Journal of Science and Technology
No. 4 (Apr 2012)
ISSN: 0974- 6846
5. Kang DW, Lee YH, Suh BS, Choi CH, and Hyun DS
(2003) An improved carrier-based SVPWM method
using leg-voltage redundancies in generalized
cascaded multilevel inverter topology. IEEE Transact.
Power Elect. 18(1), 180-187.
6. Boost MA and Ziogas PD (1988) State-of-the-art
carrier PWM techniques: A critical evaluation. IEEE
Transact. on Indus. Appl. 24(2) March/April.
7. Ayasun S and Karbeyaz G (2007) DC-Motor speed
control methods using MATLAB/Simulink and their
integration into undergraduate courses. Wiley
Periodicals. pp: 347–354.
8. Hunt BR, Lipsman RL, Rosenberg JM, Coombes KR,
Osborn JE and Stuck JG (2006) A guide to MATLAB
for beginners and experienced users. Cambridge
University Press.
9. Shaffer R (2007) Fundamentals of power electronics
with MATLAB. Thomson Learning Inc.
Fig. 28a. Fourier spectrum for Sine-PWM inverter
Fig. 28b. Fourier spectrum for SVPWM inverter
The model can operate in all the zones for an SVPWM
inverter, namely linear-zone, over-modulation-zone-1,
and over-modulation-zone-2. The performance of this
inverter-model is checked upon a balanced three phase
resistive-inductive load for the various zones in open loop
mode. The results follow the well-known trends of
SVPWM inverters.
References
1. Bose BK (2006) Power electronics and motor drives:
Advances and trends. Academic Press, Elsevier
Publ.
2. Holtz J (1992) Pulse width modulation- A survey,
IEEE Transact. Indus. Elect. 39(5), 410-420.
3. Mondal SK, Bose BK, Oleschuk V and Pinto JOP
(2003) Space vector pulse width modulation of threelevel inverter extending operation into over
modulation region. IEEE Transact. Power Elect.
18(2), 604–611.
4. Zhou KZ and Wang D (2002) Relationship between
space-vector modulation and three-phase carrierbased PWM: A comprehensive analysis. IEEE
Transact. Indus. Elect. 49(1), 186–196.
Research article
Indian Society for Education and Environment (iSee)
“Two level inverter”
http://www.indjst.org
S.Pal & S.Dalapati
Indian J.Sci.Technol.