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154
Chapter 5
Decoupled PWM Algorithm Based Open-End Winding Induction Motor
Drive
5.1 Introduction:
A simple generalized PWM algorithm has been presented in the
previous chapter for a diode-clamped multilevel inverter fed
DTC-IM
drive. Nowadays, in medium and high power drive applications,
the
open-end winding induction motor drives are becoming popular due
to
their numerous advantages. This chapter presents a
simplified
decoupled PWM algorithm for open-end winding induction motor
drive. In the proposed method, the open-end winding induction
motor
fed by two 2-level inverters at either end which, produces space
vector
locations, identical to those of a conventional 3-level
inverter. The
proposed PWM algorithm does not employ any look-up tables and
time
consuming task of sector identification. The proposed algorithm
has
been developed by using the concept of imaginary switching
times,
which are proportional to the instantaneous phase voltages.
Thus, the
proposed algorithm reduces the complexity when compared with
the
conventional SV approach.
5.2 Open-End Winding Induction Motor Drive:
Fig.5.1 shows the basic open-end winding induction motor
drive
operated with a single power supply. The symbols AOV , BOV and
COV
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155
denote the pole voltages of the inverter-1. Similarly, the
symbols AOV ,
BOV and COV denote the pole voltages of inverter-2. The space
vector
locations from individual inverters are shown in Fig. 5.2. The
numbers
1 to 8 denote the states assumed by inverter-1 and the numbers
1
through 8 denote the states assumed by inverter-2 (Fig.
5.2).
Fig.5.1 The primitive open-end winding induction motor
drive.
Fig. 5.2 Space vector locations of inverter-1 (Left) and
inverter-2 (Right).
Table 5.1 summarizes the switching state of the switching
devices for both the inverters in all the states. In Table 5.1,
+
indicates that the top switch in a leg of a given inverter is
turned on
2(++-)
1(+--)
3(-+-)
4(-++)
5(--+) 6(+-+)
7(+++) 8(---)
2(++-) 3(-+-)
1(+--) 4(-++)
5(--+) 6(+-+)
7(+++) 8(---)
Vdc/2 Vdc/2
A B
C C B
A O
Open-End wdg.
Induction Motor S5l
S2l S6l S4l
S1l S3l S1
S4 S6 S2
S3 S5
Inverter 1 Inverter 2
Vdc/4
Vdc/4
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156
and - indicates that the bottom switch in a leg of a given
inverter is
turned on. As each inverter is capable of assuming 8 states
independently of the other, a total of 64 space vector
combinations are
possible with this circuit configuration. The space vector
locations for
all space vector combinations of the two inverters are shown in
Fig.
5.3. In Fig.5.3, |OA| represents the DC-link voltage of
individual
inverters, and is equal to 2dcV while |OG| represents the
DC-link
voltage of an equivalent single inverter drive, and is equal to
dcV .
Fig. 5.3 Resultant space vector combinations in the
dual-inverter scheme.
Fig.5.1 shows the basic open-end winding induction motor
drive. It cannot be operated with a single power supply, due to
the
presence of zero-sequence voltages (common-mode voltages).
Consequently, a high zero-sequence current would flow through
the
27 28 75
85 16
34
76
21 45
38
86 37
11
44
22, 77
33, 78
66, 88
55, 87
18 17
65
74
84
83 12
67 54
68
73 57
43
61 82
72
58
71 47
48
56 32
81
(53, 62)
A
BC
D
E F
G
H
I J K
L
M
N
O
P Q R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
(52)
(63)
(13, 64) S
(14)
(15, 24)
(25) (35, 26) (36)
(31, 46)
(41)
(51, 42)
23
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157
motor phase windings, which is deleterious to the switching
devices
and the motor itself. To suppress the zero-sequence components
in
the motor phases, each inverter is operated with an isolated
dc-power
supply as shown in Fig. 5.4.
Table 5.1 Switching states of the individual inverters.
State of inverter 1
Switches Turned ON
State of inverter 2
Switches Turned ON
1 (+--) S6, S1, S2 1 (+--) S6, S1, S2
2 (++-) S1, S2, S3 2 (++-) S1, S2, S3
3 (-+-) S2, S3, S4 3 (-+-) S2, S3, S4
4 (-++) S3, S4, S5 4 (-++) S3, S4, S5
5 (--+) S4, S5, S6 5 (--+) S4, S5, S6
6 (+-+) S5, S6, S1 6 (+-+) S5, S6, S1
7 (+++) S1, S3, S5 7 (+++) S1, S3, S5
8 (---) S2, S4, S6 8 (---) S2, S4, S6
Fig. 5.4 The open-end winding induction motor drive with two
isolated power supplies.
Vdc/4
Vdc/4
A B
C C B
A O
Open-End wdg.
Induction Motor S5l
S2l S6l S4l
S1l S3l S1
S4 S6 S2
S3 S5
Inverter 1 Inverter 2
Vdc/4
Vdc/4
O
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158
From the Fig.5.4, when isolated DC power supplies are used
for
individual inverters, the zero-sequence current cannot flow as
it is
denied a path. Consequently, the zero-sequence voltage
appears
across the points O and O'. The zero-sequence voltage resulting
from
each of the 64 space vector combinations is reproduced in Table
5.2.
Table-5.2: Zero sequence voltage contributions in the difference
of the pole-voltages of the individual inverters.
2dcV 3dcV 6dcV 0 6dcV 3dcV 2dcV
8-7 8-4
8-6
8-2
5-7
3-7
1-7
8-5, 8-3
5-4, 3-4
8-1, 5-6
5-2, 3-6
3-2, 4-7
1-4, 1-6
1-2, 6-7
2-7
8-8, 5-5
5-3, 3-5
3-3, 4-4
5-1, 3-1
4-6, 4-2,
1-5, 1-3
6-4, 2-4
1-1, 6-6
6-2, 2-6
2-2, 7-7
5-8, 3-8
4-5, 4-3
1-8, 6-5
2-5, 6-3
2-3, 7-4
4-1, 6-1
2-1, 7-6
7-2
4-8
6-8
2-8
7-5
7-3
7-1
7-8
In Fig. 5.5, the vector OT represents the reference vector (also
called
the reference sample), with its tip situated in sector-7 (Fig.
5.3). This
vector is to be synthesized in the average sense by switching
the space
vector combinations situated in the closest proximity (the
combinations situated at the vertices A, G and H in the present
case)
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159
using the space vector modulation technique. In the work
reported in
reference [87], the reference vector OT is transformed to OT in
the
core hexagon ABCDEF by using an appropriate coordinate
transformation, which shifts the point A to point O.
Fig. 5.5: Resolution of the reference voltage space vector in
the middle and outer sectors.
In the core hexagon, the switching timings of the active
vectors
OA, OB and the switching time of the null vector situated at O
to
synthesize the transformed reference vector OT are evaluated.
The
switching algorithm described in reference [80] is employed
to
evaluate these timings. These timings are then employed to
produce
the actual reference vector OT situated in sector-7 by
switching
1
V
V
W
W
T T
A-Ph axis A
BC
D
E F
G
H
I J K
L
M
N
O
P Q R
S
B-Ph axis
C-Ph axis
U U
7
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160
amongst the switching combinations available at the vertices A,
G and
H. The latter step requires a lookup table in which the space
vector
combinations available at each space vector location are stored.
Thus,
it is evident that with this switching algorithm, the
controller
negotiates a considerable computational burden primarily because
of
sector identification and coordinate transformation. Also, there
is a
need requirement for look-up tables, enhancing the memory
requirement. Further, the zero-sequence voltage in the
difference of
the respective pole voltages of individual inverters (which is
dropped
across the points O and O in Fig. 5.4) is also high with this
PWM
scheme.
5.3 Proposed Decoupled PWM Algorithm:
The proposed PWM strategy is based on the fact that the
reference voltage space vector refV can be synthesized with two
equal
and opposite components 2/refV and 2/refV , by subtracting
the
latter component from the former. It is also based on the
observation
that the effect of applying a vector with inverter-1 while
inverter-2
assumes a null state is the same as that of applying the
opposite
vector with inverter-2 while inverter-1 assumes a null state.
Fig. 5.6
shows the method of this PWM strategy. It is worth noting that
the
phase axes of the motor viewed with reference to individual
inverters
are in phase opposition.
In Fig.5.6, the vector OT represents the actual reference
voltage
space vector that is to be synthesized from the dual-inverter
system
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161
and is given by refV . This vector is resolved into two equal
and
opposite components OT1 ( )2/refV and OT2 ( )+ 01802/refV . The
vector OT1 is synthesized by inverter-1 in the average sense by
switching amongst the states (8-1-2-7) while the vector OT2
is
reconstructed by inverter-2 in the average sense by switching
amongst
the states (8-5-4-7).
Fig. 5.6 The proposed decoupled PWM strategy.
The simplified switching algorithm, which is described in
chapter-4 for the classical case of a 2-level inverter feeding
an
ordinary induction motor is extended for the dual-inverter
system to
compute the switching timings for individual inverters. The
proposed
algorithm uses only the instantaneous phase reference voltages
and is
B-ph axis
A-ph axis
J o
T
C-ph axis
4'
2'
J
T1
A-ph axis
7',8'
6' 5'
3'
1' o
T1
A-ph axis 7,8
6 5
3
1 o
2
4 J
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162
based on the concept of effective time as follows:
In the proposed decoupled PWM algorithm, when the reference
voltage
vector falls in the first sector of inverter-1, the imaginary
switching
time which is proportional to the a-phase ( anT ) has a maximum
value,
the imaginary switching time which is proportional to the
c-phase
( cnT ) has a minimum value and the imaginary switching time
which is
proportional to the b-phase ( bnT ) is neither minimum nor
maximum
switching time. Thus, in general to calculate the active
vector
switching times, the maximum and minimum values of imaginary
switching times are calculated in every sampling time as given
in (5.1)
(5.2).
),,(max cnbnan TTTMaxT = (5.1)
),,(min cnbnan TTTMinT = (5.2)
The effective time effT can be defined as the time difference
between
maxT and minT and can be given as in (5.3).
minmax TTTeff = (5.3)
The effective time means the duration in which the effective
voltage is supplied to the machine terminals. In the actual
switching
instants, there is one degree of freedom that the effective time
can be
located anywhere within one sampling interval. To generate
actual
switching pattern which preserves the effective time, the
zero
sequence time is subjoined to the phase voltage time. In order
to
locate the effective time in centre of the sampling interval,
the zero
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163
sequence voltage has to be symmetrically distributed at the
beginning
and end of one sampling period. Therefore, the actual switching
times
for each inverter leg can be simply obtained by the time
shifting
operation as below.
offsetcsgc
offsetbsgb
offsetasga
TTT
TTT
TTT
+=
+=
+=
(5.4)
To distribute zero voltage symmetrically during one sampling
period, the offset time offsetT is achieved using a simple
sorting
algorithm. The zero voltage vector time duration can be
calculated as
given in (5.5).
effszero TTT = (5.5)
And, 2/min zerooffset TTT + (5.6)
Therefore, min2/ TTT zerooffset = (5.7)
In order to generate symmetrical switching pulse pattern
within
two sampling intervals, when the switching sequence is ON
sequence,
the actual switching time will be replaced by the subtraction
value
with the sampling time as fallows.
gcgbgasgcgbga TTT ,,,, = (5.8)
As described above, the effective time implies the applied time
of a
certain active vector. Therefore, with the effective vector
concept, the
actual switching time can be obtained directly from the
stationary
frame reference voltage without sector identification, effective
time
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164
calculation and recombination. the similar procedure is adopted
for
inverter-2 also.
In the context of a dual inverter drive, there exist two sets
of
phase switching times, one for each inverter. The timings gbga
TT , and
gcT correspond to inverter-1 while the timings '' , gbga TT
and
'gcT
correspond to inverter-2. The instantaneous reference phase
voltages
**, ba VV and*cV correspond to the actual reference space vector
refV of
the dual-inverter system. As individual inverters operate with
the
references 2/refV and 2/refV respectively, it follows that
the
corresponding phase references are given by 2/,2/ ** ba VV and
2/*cV
for inverter-1 and 2/,2/ ** ba VV and 2/*cV for inverter-2.
These
references are then employed to determine the phase
switching
timings of each inverter using the aforementioned switching
algorithm. Thus, both inverters are operated with the same
sequence
so that the null vector combinations are 88 and 77. From Table
5.1,
it may be noted that these two combinations result in the
zero-
sequence voltage that is zero. If one inverter is operated with
on-
sequence and the other with off-sequence, the null vector
combinations would be 87 or 78. From Table 5.2 it is evident
that
the zero-sequence voltage of the difference of the pole-voltages
is
maximum for these two combinations. It is interesting to note
that
this zero-sequence voltage is much lesser with this algorithm
than the
lookup table approach used in [83]. This is because the
combinations
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165
87 and 78are used extensively with that approach [83]. The merit
of
the decoupled control is that there is no computational burden
on the
controller and is therefore amenable to be used with slower
controllers
(processors) and possibly the reduced zero-sequence voltage in
the
difference of pole-voltages. However, in this approach, both
inverters
are to be switched.
The conventional d-q model of a normal 3-phase induction
motor is modified to compute the motor phase current of the
open-end
winding induction motor drive as shown in Fig. 5.7.
Fig. 5.7 d-q model of an open-end winding induction motor.
The inputs for this model are the PWM signals of the
individual
inverters and their DC link voltages. The pole voltages of
the
individual inverters are then computed. Subtracting the pole
voltages
Vcn
Vbn
Van
V00'
+
+
+
-
-
+
+
+
V'a0
V'b0
V'c0
-
-
-
+
+
+
Vc0
Vb0
Va0
Inverter-1
Inverter-2
-
Induction
Motor
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166
of inverter-2 from those of inverter-1, the difference of pole
voltages is
obtained. If the individual inverters are operated off isolated
DC power
supplies, the zero-sequence content of the difference in pole
voltages
is subtracted as shown in Fig. 5.7, to obtain the actual motor
phase
voltage. It may be noted that the zero-sequence voltage, in this
case,
appears across the points O and O'. The actual motor phase
voltages
thus computed are impressed onto the conventional d-q model
of
induction motor to compute the motor phase currents.
5.4 Results and Discussions:
Matlab-Simulink based simulation studies have been carried
out to validate the proposed decoupled based direct torque
controlled
induction motor drive. Various conditions such as starting,
steady
state, step change in load and speed reversal are simulated.
The
simulation parameters and specifications of induction motor used
in
this thesis are given in Appendix - I. The average switching
frequency
of the inverter is taken as 3 kHz. For the simulation, the
reference flux
is taken as 1wb and starting torque is limited to 40 N-m.
The
simulation results for proposed decoupled PWM algorithms
based
DTC-IM drive are shown in from Fig 5.8 to Fig 5.21.
Fig 5.8 and Fig 5.9 show the no-load starting transients of
speed,
currents, torque, flux and phase and line voltages for
proposed
decoupled PWM algorithm based DTC-IM drive. The no-load
steady
state plots of speed, torque, stator currents, flux, phase and
line
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167
voltages at 1200 rpm are given in Fig 5.10-Fig.5.11. The
harmonic
distortion in the steady state stator current along with THD
value is
shown in Fig 5.12. From Fig 5.10 to Fig 5.12, it can be observed
that
the steady state ripple in torque, flux and current is very
less
compared to conventional DTC. Also, the proposed decoupled
PWM
algorithm based DTC provides constant switching frequency of
the
inverter. The locus of the stator flux is given in Fig 5.14.
From which it
can be observed that the locus is almost is a circle of constant
radius.
The transients in speed, torque, currents and flux during the
step
change in load torque and corresponding phase and line voltages
are
shown in Fig. 5.15-Fig.5.16. Also, the transients in speed,
torque,
currents, flux, and voltages during the speed reversals (from
+1200
rpm to -1200 rpm and from -1200 rpm to +1200 rpm) are shown
from
Fig. 5.17 to Fig. 5.20. The four-quadrant speed-torque
characteristic
of the proposed drive is shown in Fig. 5.21.
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Fig. 5.8 Starting transients of speed, torque, stator currents
and stator flux for proposed decoupled PWM based DTC-IM drive.
Fig. 5.9 Starting transients in phase and line voltages for
proposed decoupled PWM based DTC-IM drive.
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169
Fig. 5.10 Steady state plots of speed, torque, stator currents
and stator flux for proposed decoupled PWM based DTC-IM drive
at
1200 rpm.
Fig. 5.11 The phase and line voltages for proposed decoupled
PWM based DTC-IM drive during the steady state.
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170
Fig. 5.12 Harmonic Spectrum of stator current along with
THD.
Fig. 5.13 Harmonic Spectrum of stator voltage along with
THD.
Fig. 5.14 Locus of stator flux in proposed decoupled PWM
based
DTC-IM drive.
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171
Fig. 5.15 Transients in speed, torque, stator currents and
stator flux during step change in load: a 30 N-m load is applied at
0.5 s
and removed at 0.6 s.
Fig. 5.16 The phase and line voltages during a step change in
load torque: a 30 N-m load torque is applied at 0.5 s and removed
at
0.6 s.
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172
Fig. 5.17 Transients in speed, torque, stator currents and
stator flux during speed reversal: speed is changed from +1200 rpm
to
-1200 rpm at 0.7 s.
Fig. 5.18 The phase and line voltage variations during the speed
reversal (speed is changed from +1200 rpm to -1200 rpm at
0.7s).
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173
Fig. 5.19 Transients in speed, torque, stator currents and
stator flux during speed reversal: speed is changed from -1200 rpm
to
+1200 rpm at 1.35 s.
Fig. 5.20 The phase and line voltage variations during the
speed
reversal (speed is changed from -1200 rpm to +1200 rpm at
1.35s).
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174
Fig. 5.21 The torque and speed characteristics in four
quadrants
for proposed decoupled PWM based DTC-IM drive.
5.5 Summary:
A simple decoupled PWM algorithm has been presented in this
chapter for direct torque controlled open-end winding induction
motor
drive. The proposed algorithm has been developed by using
the
concept of imaginary switching times. The proposed algorithm
generates the voltages similar to the three-level inverter. To
validate
the proposed algorithm. The numerical simulation studies have
been
carried out and results are presented. From the simulation
results, it
can be observed that the proposed algorithm gives reduced
harmonic
distortion when compared with the two-level inverter fed
drive.