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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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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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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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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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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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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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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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

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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

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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.

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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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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.