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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
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
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
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
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)
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
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
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
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
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
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
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
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
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.
168
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.
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.
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.
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.
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).
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).
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.