direct torque control of induction motor - shodhganga : a...

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Chapter – 3

Direct Torque Control of Induction Motor

3.1 Introduction:

In recent years, the research has been focused to find out

different solutions for the induction motor control having the features

of precise and quick torque response and reduction of the complexity

of field oriented control. The direct torque control (DTC) technique has

been recognized as the viable solution to achieve these requirements.

The DTC based induction motor drives were developed and presented

more than two decades ago by I.Takahashi and M. Depenbrock.

However, at present, ABB is the only industrial company who has

introduced a commercially available direct torque controlled induction

motor drive. This technique is based on the space vector approach,

where the torque and flux of an induction motor can be directly and

independently controlled without any coordination transformation.

Though the DTC gives fast transient response, it gives large steady

state ripples and variable switching frequency of the inverter.

To reduce the steady state ripples and to get constant switching

frequency of the inverter, space vector PWM algorithm has been used

for DTC. However, the SVPWM algorithm also gives more harmonic

distortion. To reduce the harmonic distortion further, multilevel

inverters have been used in the literature. This chapter presents the

46

principles of DTC and SVPWM algorithms. Finally, a simplified

SVPWM algorithm has been proposed for three level inverter based

direct torque controlled induction motor drive.

3.2 Direct Torque Control of Induction Motor Drive:

3.2.1 Principle of DTC:

The electromagnetic torque of a three-phase induction motor can

be written as [2, 4]

ηψψσ

sin22

3sr

rs

me

LL

LPT = (3.1)

where η is the angle between the stator flux linkage space vector ( sψ )

and rotor flux linkage space vector ( rψ ), as shown in Fig. 3.1 and σ is

the leakage coefficient given by

−=

rs

m

LL

L2

1σ .

Fig. 3.1 sψ movement relative to rψ under influence of voltage

vectors.

The expression given in (3.1) is valid for both the steady state

and transient state conditions. In steady state both the stator flux and

rotor flux moves with the same angular velocity. The rotor flux lags

the stator flux by torque angle. But during transients these two

η rψ

sψ

sd

sq

Movement with active

forward vector

Movement with active

backward vector

Stops with zero vectors

Rotates continuously

47

vectors do not have the same velocity. From (3.1), it is clear that the

motor torque can be varied by varying the rotor or stator flux linkage

vectors. The magnitude of the stator flux is normally kept constant.

The rotor time constant of a standard squirrel-cage induction machine

is very large, thus the rotor flux linkage changes very slowly compared

to the stator flux linkage [2-4, 21]. So assuming both to be constant, it

follows from (3.1) that torque can be rapidly changed by changing ‘η ’

in the required direction. This is the essence of “Direct Torque

Control”. During a short transient, the rotor flux is almost unchanged,

thus rapid changes of electromagnetic torque can be produced by

rotating the stator flux in the required direction according to the

demanded torque. However, the stator flux linkage space vector can

be changed by the stator voltages.

If for simplicity it is assumed that the stator ohmic drops can be

neglected, then dt

dV s

sψ

= , so the inverter voltage directly impresses

the stator flux. For a short time t∆ , when the voltage vector is applied,

tVss ∆=∆ψ . Thus, the stator flux linkage space vector moves by sψ∆

in the direction of the stator voltage space vector at a speed

proportional to magnitude of voltage space vector (i.e. dc link voltage).

By selecting step-by-step the appropriate stator voltage vector, it is

then possible to change the stator flux in the required direction.

Decoupled control of the torque and stator flux is achieved by acting

on the radial and tangential components of the stator flux linkage

48

vector in the locus. These two components are directly proportional to

the components of the stator voltage vector in the same directions [4].

Thus, for the torque production, the angle η plays a very

important role. By assuming a slow motion of the rotor flux linkage

space vector, if a forward active voltage vector is applied then it causes

rapid movement of sψ and torque increases with ‘η ’. On the other

hand, when a zero voltage vector is used, the stator flux vector sψ

becomes stationary and the electromagnetic torque will decrease,

since rψ continues to move forward and the angle ‘η ’ decreases. If the

duration of zero voltage space vector is sufficiently long, then the rotor

flux linkage space vector will overtake the stator flux linkage space

vector, the angle ‘η ’ will change its sign and the torque will also

change its direction. Thus, it is possible to change the speed of stator

flux linkage space vector by changing the ratio between the zero and

non-zero voltage vectors. It is important to note that the duration of

zero voltage vectors has a direct effect on torque oscillations.

By considering the three-phase, two-level, six pulse voltage

source inverter (VSI), there are six non-zero active voltage space

vectors and two zero voltage space vectors as shown in Fig. 3.2. The

six active voltage space vectors can be represented as

( )[ ] 6,...,2,13

1exp3

2=−= k kjVV dck

π (3.2)

49

Fig. 3.2 Inverter voltage space vectors.

Depending on the position of stator flux linkage space vector, it

is possible to switch the appropriate voltage vectors to control both

stator flux and torque. As an example if stator flux linkage space

vector is in sector I as shown in Fig. 3.3, then voltage vectors 2V and

6V can increase the stator flux and 3V and 5V can decrease the stator

flux. Similarly 2V and 3V can increase the torque and 5V and 6V can

decrease the torque. Similarly the suitable voltage vectors can be

selected for other sectors. Thus, as depicted in the Fig. 3.3, when the

stator flux amplitude has to be increased, a voltage vector, phase

shifted by an angle larger than 90o with respect to existing stator flux

linkage space vector ( sψ ) is applied. In contrast, if stator flux

amplitude has to be reduced, a voltage vector, phase shifted by an

angle less than 90o will be applied. Similarly, by applying suitable

voltage space vector in the direction of rotation of stator flux, torque

)111(7V

)100(1V

)101(6V )001(5V

)011(4V

)010(3V )110(2V

)000(0V

Sector I

50

( eT ) can be increased and by applying the voltage space vector, which

is opposite to the direction of rotation of stator flux, eT can be

reduced.

Fig. 3.3 selection of suitable voltage space vector in sector I (-300 to +300).

3.2.2 Conventional DTC Block Diagram:

The Fig. 3.4 shows the block diagram of conventional direct

torque controlled induction motor drive. There are two hysteresis

control loops, one for the control of torque and other for the control of

stator flux. The flux controller controls the machine operating flux to

maintain the magnitude of the operating flux at the rated value till the

rated speed. Torque control loop maintains the torque close to the

torque demand. Based on the outputs of these controllers and the

instantaneous position of stator flux vector, a proper voltage space

vector is selected.

Sector 1

d

q

sψ

TI)(FI, 2V TI)(FD, 3V

TD)(FD, 5V TD)(FI, 6V

rω

51

Fig. 3.4 Block diagram of conventional DTC.

3.2.2.1 Optimum Switching Vector Selection:

Based on the outputs of hysteresis controllers and position of

the stator flux vector, the optimum switching table will be

constructed. This gives the optimum selection of the switching voltage

space vectors for all the possible stator flux linkage space vector

positions. In conventional DTC (CDTC), the stator flux linkage and

torque errors are restricted within their respective hysteresis bands,

which are sψ∆2 and eT∆2 wide respectively. If a stator flux increase

is require then 1=ψS ; if a stator flux decrease is required then

0=ψS . The digitized output signals of the two level flux hysteresis

controller are defined as,

If sss ψψψ ∆−≤ * then 1=ψS

If sss ψψψ ∆+≥ * then 0=ψS

Adaptive

Motor Model 3 2

IM

PI + _

_

_

+

+

*eT

*sψ

eT

sψ

sψ∆

eT∆ Optimal

Switching

Table

Sector

Calculation

Vds, Vqs

Calculation

Reference

Speed

Motor

Speed

52

If a torque increase is required then 1=TS , if a torque decrease is

require then 1−=TS , and if no change in the torque is required then

0=TS . The digitized output signals of the three level torque

hysteresis controller for the anticlockwise rotation or forward rotation

can be defined as,

If eee TTT ∆≥−* then 1=TS

If *ee TT ≥ then 0=TS

And for clockwise rotation or backward rotation

If eee TTT ∆−≤−* then 1−=TS

If *ee TT ≤ then 0=TS

Depending upon the ψS , TS and the position of the stator flux

linkage space vector, the suitable switching voltage vector is

determined from the lookup table, which is given in Table 3.1.

Table 3.1 Optimum voltage switching vector lookup table.

ψS TS Sector I

-30o to 30o

Sector II

30o to 90o

Sector III

90o to 150o

Sector IV

150o to 210o

Sector V

210o to 270o

Sector VI

270o to 330o

1

1 2V 3V 4V 5V 6V 1V

0 7V 0V 7V 0V 7V 0V

-1 6V 1V 2V 3V 4V 5V

0

1 3V 4V 5V 6V 1V 2V

0 0V 7V 0V 7V 0V 7V

-1 5V 6V 1V 2V 3V 4V

53

3.2.2.2 Adaptive Motor Model:

The adaptive motor model [29-31] is responsible for generating

four internal feedback signals, which are

• Stator flux

• Electromagnetic torque

• Rotor speed

• Stator flux linkages phasor angle (in radians).

The first two values are critical for the proper operation of DTC.

The stator flux and the torque outputs of the adaptive motor model

are identical with that of actual values. The stator flux, torque and

stator flux linkages phasor angle can be estimated by using (3.3) –

(3.5).

dtiRV ssss )( −= ∫ψ (3.3)

[ ]qsdsdsqse iiP

T ψψ −=22

3 (3.4)

= −

ds

qsTan

ψ

ψθ 1 rad (3.5)

The speed of the induction motor can be estimated by using

various algorithms as reported in the literature. Since the rotor speed

is calculated with in this model, there is no need to feedback any shaft

speed or position with tachometers or encoders. This is a significant

advance over all other AC drive technology.

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3.2.3 Results and Discussions:

To validate the conventional direct torque controlled induction

motor drive several numerical simulations have been carried out by

using Matlab/Simulink. The simulation parameters and specifications

of induction motor used in this thesis are given in Appendix - I. For

the simulation studies, the reference flux is taken as 1wb and starting

torque is limited to 40 N-m. Various conditions such as starting,

steady state, step change in load and speed reversal are simulated.

The results for conventional direct torque controlled induction motor

drive are shown in Fig 3.5 to Fig 3.17.

Fig 3.5 starting transients of speed, torque, stator currents and

stator flux for CDTC-IM drive.

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Fig 3.5 shows the starting transients of speed, torque, currents

and stator flux for conventional DTC (CDTC) based induction motor

drive. the starting transients in phase and line voltages are shown in

Fig 3.6.

Fig. 3.6 Starting transients in phase and line voltages of CDTC-

IM drive.

Fig. 3.7 shows the steady state plots of speed, torque, stator

currents and stator flux of CDTC based IM drive. Fig. 3.8 gives the

phase and line voltages of CDTC based IM drive during the steady

state. The total harmonic distortion (THD) of the line current is shown

in Fig. 3.9. From Fig. 3.7 to Fig. 3.9, it can be observed that the CDTC

algorithm gives large steady state ripples in torque, current and stator

flux. Moreover, it can observe that the CDTC gives variable switching

frequency operation of the inverter. The THD of line current is also

quite high for CDTC based IM drive. The locus of the stator flux is

shown in Fig. 3.10, which is following a circular locus with constant

radius.

56

Fig 3.7 steady state plots of speed, torque, stator currents and

stator flux for CDTC based IM drive at 1200 rpm.

Fig 3.8 the phase and line voltages for CDTC based IM drive

during the steady state.

57

Fig 3.9 Harmonic Spectrum of stator current along with THD.

Fig 3.10 locus of stator flux in CDTC based IM drive.

The transients in speed, torque, currents and flux during the

step change in load torque (a load torque of 30 N-m is applied at 0.5s

and removed at 0.6s) are shown in Fig. 3.11. The magnitude of the

stator flux is same even though the torque command has changed.

from which, it can be observed that the CDTC gives decoupled control

of torque and flux. The phase and line voltages are shown in Fig. 3.12

during the step change in load torque.

58

3.11 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. 3.12 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.

59

The transients in speed, torque, stator currents, stator flux,

phase and line voltages during the speed reversals (from +1200 rpm to

-1200 rpm and from -1200 rpm to +1200 rpm) are shown from Fig

3.13 to Fig 3.16. From Fig 3.17, it can be observed that the CDTC

based IM drive gives good performance in all the four quadrants.

From the above simulation results, it can be observed that the

CDTC gives fast transient response with increased ripple in torque,

flux and currents.

Fig 3.13 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.

60

Fig. 3.14 the phase and line voltage variations during the speed

reversal (speed is changed from +1200 rpm to -1200 rpm at 0.7s).

Fig 3.15 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.

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Fig. 3.16 the phase and line voltage variations during the speed

reversal (speed is changed from -1200 rpm to +1200 rpm at 1.35s).

Fig 3.17 the torque and speed characteristics in four quadrants

for CDTC based IM drive.

3.2.4 Summary:

As the name suggests, DTC controls the motor torque and flux

directly. Also, DTC is simple and gives fast dynamic response. Despite

its simplicity, it gives more steady state ripple in torque, flux and

current. From the simulation results the same can be inferred.

62

3.3 Space Vector Pulsewidth Modulation Algorithm Based DTC:

3.3.1 SVPWM Algorithm:

In recent years voltage source inverter (VSI) is widely used to

generate variable voltage, variable frequency, 3-phase ac required for

variable speed ac drives. The ac voltage is defined by two

characteristics, namely amplitude and frequency. Hence, it is

essential to work out an algorithm that permits control over both of

these quantities. Pulse width modulation (PWM) controls the average

output voltage over a sufficiently small period called sampling period,

by producing pulses of variable duty-cycle.

Every leg of a three-phase VSI can be represented using a

single-pole double-throw (SPDT) switch as shown in Fig. 3.18. Every

terminal of the induction motor will be connected to the pole of one of

the inverter legs, and thereby, either to the positive dc bus or the

negative dc bus. Thus every one of the three pole voltages

( aoV , boV and coV ), measured with respect to the dc bus centre (o), is

either dcV5.0+ or dcV5.0− at any instant.

Fig. 3.18 Three-phase voltage source inverter.

a b c + + +

- - -

dcV5.0+

o

dcV5.0−

63

In Fig 3.18, the a-phase and c-phase are shown connected to

the positive dc bus, while b-phase is connected to the negative dc bus.

This state can be designated as +-+ or 101. Thus, every phase of a

three-phase VSI can be connected either to the positive or the negative

dc bus. Hence, the three phases together can have 23 or 8

combinations of switching states. To designate the switching states

code numbers 0 to 7 are used and these switching states are shown in

Fig. 3.19. In case of the switching states --- (V0) and +++ (V7), all the

three poles are connected to the same dc bus, effectively shorting the

induction motor and resulting in no transfer of power between the dc

bus and induction motor. These two states are called ‘zero voltage

vectors’ or ‘zero states’. In case of the other switching states, power

gets transferred between the dc bus and induction motor. These states

(1, 2…6) are called ‘active voltage vectors’ or ‘active states’.

Fig. 3.19 Possible switching states of the inverter.

V0 (- - -) V1 (+ - -) V2 (+ + -) V3 (- + -)

V7 (+ + +) V6 (+ - +) V5 (- - +) V4 (- + +)

64

For a given set of inverter pole voltages (Vao, Vbo, Vco), the vector

components (Vd, Vq) in the stationary reference frame are found by the

forward Clarke transform as

++= 3

4

3

2

3

2ππ

j

co

j

boaos eVeVVV (3.6)

The relationship between the phase voltages anV , bnV , cnV and

the pole voltages aoV , boV and coV is given by:

nocnconobnbonoanao VVVVVVVVV +=+=+= ;; (3.7)

Since 0=++ cnbnan VVV ,

3

)( coboaono

VVVV

++= (3.8)

where noV is the common mode voltage.

From (3.6) and (3.7) it is evident that the phase voltages anV ,

bnV , cnV also result in the same space vector sV . The space vector sV

can also be resolved into two rectangular components namely dV and

qV . It is customary to place the q-axis along the a-phase axis of the

induction motor. The relationship between dV , qV and the

instantaneous phase voltages anV , bnV , cnV can be given by the

conventional three-phase to two-phase transformation as follows:

−

−−

=

cn

bn

an

d

q

V

V

V

V

V

2

3

2

30

2

1

2

11

3

2 (3.9)

65

The set of balanced three-phase voltages can be represented in

the stationary reference frame by a space vector of constant

magnitude, equal to the amplitude of the voltages, and rotating with

angular speed fπω 2= . The space vector locations for the switching

states may be evaluated using (3.6). Then, all the possible switching

states of an inverter may be depicted as voltage space vectors as

shown in Fig. 3.20. The space vector locations for a two-level inverter

form the vertices of a regular hexagon, forming six symmetrical

sectors as shown in Fig. 3.20.

Fig. 3.20 Voltage space vectors produced by an inverter.

From (3.6), it is easily shown that the active voltage vectors or

active states can be represented as

6 ..., 1,2, k where 3

2 3)1(

==−

πkj

dck eVV (3.10)

A combination of switching states can be utilized, while

maintaining the volt-second balance to generate a given sample in an

Vref

V1 (+ - -)

V2 (+ + -) V3 (- + -)

V4 (- ++)

V5 (- - +) V6 (+ - +)

V0 (- - -)

V7 (+ ++)

α

I

II

III

IV

V

VI

q

d

T1

T2

66

average sense during a subcycle. This combination of switching

states, which generate a sample, is termed as a ‘switching sequence’.

This does not mean that any arbitrary set of active vectors and zero

vectors can be applied maintaining the volt-second balance to

generate a PWM waveform. There are certain restrictions, which need

to be imposed so as to generate a PWM waveform, which results in

minimum harmonic distortion.

A well-designed PWM algorithm is one where there are no pulses

of opposite polarity in the line-to-line voltage waveforms, that is, a

line-to-line voltage must be either dcV+ or 0 and must not be dcV− at

any instant in the positive half-cycle, the existence of which would

lead to large ripple currents. Further, the simultaneous switching of

two phases must be avoided to utilize the available switching

frequency of the inverter efficiently. Hence, when the reference voltage

vector is within a given sector, the active states that can be applied

are only those two, namely x and y, whose vectors form the

boundaries of that sector as shown in Fig. 3.21. The application of any

other active states, results in a pulse of opposite polarity. The zero

state, which is closer to x or just one switch away, can be referred to

as zx. The other zero state, which is closer to y, can be referred to as

zy. The active and zero states that can be applied for each sector are

given in Table 3.2.

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Fig 3.21 Active and zero states in a sector.

The voltage vector refV in Fig. 3.20 represents the reference

voltage space vector or sample, corresponding to the desired value of

the fundamental components for the output phase voltages. It is

obtained by substituting the instantaneous values of the reference

phase voltages, sampled at regular time intervals in (3.6)

Table 3.2 Active states and zero states for each sector.

Rθ Sector x y zx zy

0-60 I 1 2 0 7

60-120 II 2 3 7 0

120-180 III 3 4 0 7

180-240 IV 4 5 7 0

240-300 V 5 6 0 7

300-360 VI 6 1 7 0

But, there is no direct way to generate the sample and hence

the sample can be reproduced in the average sense. The reference

vector is sampled at equal intervals of time, sT referred to as subcycle

or sampling time period. Different voltage vectors that can be

produced by the inverter are applied over different durations with in a

Vref

x

y

α zx

Zy

68

subcycle such that the average vector produced over the subcycle is

equal to the sampled value of the reference vector, both in terms of

magnitude and angle. It has been established that the vectors to be

used to generate any sample are the zero vectors and the two active

vectors forming the boundary of the sector in which the sample lies.

As all the six sectors are symmetrical, here the discussion is

limited to sector-I only. Let 1T and 2T be the durations for which the

active states 1 and 2 are to be applied respectively in a given sampling

time period sT . Let zT be the total duration for which the zero states

are to be applied. From the principle of volt-time balance 1T , 2T and

zT can be calculated as:

zdcdcsref TTVTVTV *0*603

2*0

3

2* 21 +°∠+°∠=°∠α (3.11)

( )

( ) 2

1

*60sin60cos3

2

*3

2*sincos

TjV

TVTjV

oodc

dcsref

+

+=+ αα

(3.12)

by equating the real and imaginary parts, we get

21 *60cos3

2*

3

2*cos TVTVTV o

dcdcsref +=α (3.13)

2*60sin3

2*sin TVTV o

dcsref =α (3.14)

from (3.13) and (3.14)

( ) so

i TMT )60sin(32

1 απ

−= (3.15)

( ) sin32

2 si TMT απ

= (3.16)

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where ‘ iM ’ is the modulation index, given by dc

iV

M2

Vrefπ=

To keep the switching frequency constant, the remainder of the

time is spent on the zero states, that is

21 TTTT sZ −−= (3.17)

In the SVPWM strategy, the total zero voltage vector time is

equally distributed between V0 and V7. Further, in this method, the

zero voltage vector time is distributed symmetrically at the start and

end of the subcycle in a symmetrical manner. Moreover, to minimize

the switching frequency of the inverter, it is desirable that switching

should take place in one phase of the inverter only for a transition

from one state to another. Thus, SVPWM uses 0127-7210 in sector-I,

0327-7230 in sector-II and so on. Fig. 3.22 depicts a typical switching

sequence when the sample is situated in sector-I.

Fig. 3.22 Gating signal generation using SVPWM scheme in sector-I.

gaT gaT

gbT gbT

gcT gcT

On sequence

Off sequence Ts Ts

2

zT

2

zT

2

zT

2

zT 1T 1T 2T 2T

70

In Fig.3.22, the symbols gaT , gbT and gcT respectively denote the

time duration for which the top switch in each phase leg is turned on,

from which, it can be seen that the chopping frequency of each phase

of the inverter is equal to half of the sampling frequency. Table-3.3

depicts the switching sequence for all the sectors. One of the

important advantages of the SVPWM over the sine-triangle PWM is

that it gives nearly 15% more output voltage compared to the later,

while still remaining in modulation.

Table 3.3 Switching sequences in all the sectors for SVPWM.

Sector number On-sequence Off-sequence

1 0-1-2-7 7-2-1-0

2 0-3-2-7 7-2-3-0

3 0-3-4-7 7-4-3-0

4 0-5-4-7 7-4-5-0

5 0-5-6-7 7-6-5-0

6 0-1-6-7 7-6-1-0

3.3.2 Proposed SVPWM Based DTC:

The reference voltage space vector can be constructed in many

ways. But, to reduce the complexity of the algorithm, in this thesis,

the required reference voltage vector, to control the torque and flux

cycle-by-cycle basis is constructed by using the errors between the

reference d-axis and q-axis stator fluxes and d-axis and q-axis

estimated stator fluxes sampled from the previous cycle. The block

71

diagram of the proposed SVPWM based DTC is as shown in Fig. 3.23.

From Fig. 3.23, it is seen that the proposed SVPWM based DTC

scheme retains all the advantages of the CDTC, such as no co-

ordinate transformation, robust to motor parameters, etc. However a

space vector modulator is used to generate the pulses for the inverter,

therefore the complexity is increased in comparison with the CDTC

method.

In the proposed method, the position of the reference stator flux

vector *sψ is derived by the addition of slip speed and actual rotor

speed. The actual synchronous speed of the stator flux vector sψ is

calculated from the adaptive motor model.

Fig. 3.23 Block diagram of proposed SVPWM based DTC.

Adaptive Motor Model 3

2

IM

Vds, Vqs

Calculation

Reference

Voltage Vector Calculator

Speed

+ _

+ _

∗

eT

eT

∫slω

+

∗dsV

rω Ref speed

eθ

sψ

*

sψ

+

eω

dcV

*

qsV

S V P W M

SMC PI

72

After each sampling interval, actual stator flux vector sψ is

corrected by the error and it tries to attain the reference flux space

vector *sψ . Thus the flux error is minimized in each sampling interval.

The d-axis and q-axis components of the reference voltage vector can

be obtained as follows:

Reference values of the d-axis and q- axis stator fluxes and actual

values of the d-axis and q-axis stator fluxes are compared in the

reference voltage vector calculator block and hence the errors in the d-

axis and q-axis stator flux vectors are obtained as in (3.18)-(3.19).

ψψψ dsdsds −=∆ * (3.18)

ψψψ qsqsqs −=∆ * (3.19)

The knowledge of flux error and stator ohmic drop allows the

determination of appropriate reference voltage space vectors as given

in (3.20)-(3.21).

TiRV

s

dsdssds

ψ∆+=* (3.20)

T

iRVs

qsqssqs

ψ∆+=* (3.21)

Where, Ts is the duration of subcycle or sampling period and it is a

half of period of the switching frequency. This implies that the torque

and flux are controlled twice per switching cycle. Further, these d-q

components of the reference voltage vector are fed to the SVPWM

block from which, the actual switching times for each inverter leg are

calculated.

73


Matlab-Simulink based simulation studies have been carried

out to validate the proposed SVPWM algorithm 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 simulated results are shown in Fig 3.24 to Fig 3.36.

Fig. 3.24 simulation results of SVPWM based DTC: starting

transients.

74

Fig 3.24 shows the no-load starting transients of speed,

currents, torque and flux. Fig. 3.25 shows the starting transients in

phase and line voltages for SVPWM algorithm based DTC-IM drive.

Fig. 3.25 starting transients in phase and line voltages for

SVPWM algorithm based DTC drive.

The no-load steady state plots of speed, torque, stator currents,

flux, phase and line voltages at 1200 rpm are given in Fig 3.26-

Fig.3.27. The harmonic distortion in the steady state stator current

along with THD value is shown in Fig 3.28. From Fig 3.26 to Fig 3.28,

it can be observed that the steady state ripple in torque, flux and

current is very less compared to CDTC. Also, the proposed SVPWM

based DTC provides constant switching frequency of the inverter.

Moreover, with the SVPWM based DTC, the speed fluctuations can

also be reduced. The locus of the stator flux is given in Fig 3.29. From

which it can be observed that the locus is almost is a circle of

constant radius.

75

Fig. 3.26 Simulation results of SVPWM based DTC: steady-state

plots at 1200 rpm.

Fig. 3.27 the phase and line voltages of SVPWM based DTC drive

during the steady state operation.

76

Fig. 3.28 Harmonic Spectrum of stator current along with THD

for SVPWM based DTC-IM drive.

Fig. 3.29 locus of stator flux in SVPWM based DTC-IM drive.

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. 3.30-Fig. 3.31. 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. 3.32 to Fig. 3.35. the four-quadrant speed-torque characteristic of

the proposed drive is shown in Fig. 3.36.

77

3.30 transients during step change in load torque (a 30 N-m load

torque is applied at 0.5 s and removed at 0.6s).

3.31 the phase and line voltages of SVPWM based DTC during step

change in load torque (a 30 N-m load torque is applied at 0.5 s and removed at 0.6s).

78

Fig. 3.32 transients in speed, torque, current and flux during

speed reversal (speed is changed from +1200 rpm to -1200 rpm at 0.7 s).

Fig. 3.33 transients in phase and line voltages during speed

reversal (speed is changed from +1200 rpm to -1200 rpm at 0.7 s).

79

Fig. 3.34 transients in speed, torque, current and flux during

speed reversal (speed is changed from -1200 rpm to +1200 rpm at 1.35 s).


reversal (speed is changed from -1200 rpm to 1200 rpm at 1.35 s).

80

Fig. 3.36 Speed-torque characteristic of SVPWM based DTC drive

in four-quadrants.

3.3.4 Summary:

The steady state ripples of stator current, torque and flux are

very high in CDTC. Also, the presence of hysteresis controllers in

CDTC strategy produces variable switching frequency operation of the

PWM inverter. In order to improve the performance of CDTC in terms

of ripples, in this section SVPWM algorithm based on reference voltage

vector calculator which utilizes the stator flux components as control

variables has been used for DTC. The proposed algorithm enables the

operation at constant switching frequency. By comparing the

reference values of d-axis and q-axis stator flux with estimated stator

fluxes, the errors in d-axis and q-axis stator flux are obtained. The

knowledge of these errors allows the determination of voltage space

vector which the VSI has to apply to the induction motor during the

81

next sampling time period. Then the required voltage space vector is

synthesized by means of SVPWM algorithm to generate the gating

signals for the VSI. The numerical simulations at different operating

conditions have been carried out and the results prove the validity of

the proposed algorithm.

3.4 Three-Level NPC Inverter Based DTC Drive:

The inverters with voltage levels three or more referred as

multilevel inverters in the literature. The general structure of the

multilevel inverters is to synthesize a near sinusoidal voltage from

several levels of the DC voltages, typically obtained from capacitor

voltage sources. The multilevel inverters can be classified into three

types:

1. Diode clamped multilevel inverter

2. Flying capacitor clamped multilevel inverter

3. Cascade capacitor multilevel inverter

This section focuses on diode clamped three level inverter only.

3.4.1 Diode clamped Three Level Inverter:

The three level diode clamp inverter is also called neutral point

clamped (NPC) inverter. The NPC configuration was first proposed by

Nabae, Takahashi in 1981. Fig. 3.37 shows the power circuit of a 3-

phase, three level NPC inverter. Node 'o' indicates the negative bus

and 'm' is the midpoint of the dc bus. Switches (SR1, S’R2) of phase R,

(SY1; S’Y2) of phase Y and (SB1; S’B2) of phase B are the main devices

operating as modulating switches for the PWM. SR2, S’R1, SY2, S’Y1, SB2

82

and S’B1 are the auxiliary switches to clamp the output voltage to the

midpoint (node m) together with the diodes DR1, DR2, DY1, DY2, DB1,

and DB2.

Fig 3.37 Three level diode clamp inverter.

3.4.2 Principle of Operation:

Assume the dc rail 0 is the reference point of the output phase

voltage. To produce a stair case output voltage, consider only R-phase

leg of the three level inverter. The steps to synthesize the three- level

voltages are as follows:

Dz2

Dz1

Dy2

Dy1

Dr2

Dr1

S̸

y1 S/r1

o

c

n

c

p

S̸

r2 S̸

y2 S̸

b2

S̸

b1

Sb2 Sy2 Sr2

Sr1 Sy1 sb1

Phase R Phase Y Phase B

Vdc/2

Vdc/2

83

� For an output voltage level VRo =Vdc/2, turn on all upper-half

switches SR1 through SR2.

� For an output voltage level VRo =0, turn on the middle switches

S’R1 and SR2

� For an output voltage level VRo= -Vdc/2, turn on the lower half

switches S’R1 and SR2.

� State condition SR =1 then SR1 and SR2 are ON and S’R1 and

S’R2 are off and DR1 and DR2 are off.

� State condition SR=0 then the switches SR1and SR2 are off and

SR2 and S’R1 are ON and DR1 and DR2 will conduct depending on

the polarity of the load current.

� State condition SR=-1 then the switches SR1 and SR2 are off and

S’R1 and S’R2 are ON and DR1 and DR2 are off.

Table 3.4 shows the switch status and corresponding pole

voltage of R-phase.

Table 3.4 Switch status, definition of state and pole voltage

Switch status State Pole voltage

SR1=ON,SR2=ON,

S’R1=OFF,SR2’=OFF,

DR1=OFF, DR2=OFF

SR=+1

VRm = Vdc/2

SR1=OFF,SR1=ON,

S’R1=ON,S’R2=OFF,

DR1 or DR2 will conduct depending

on the polarity of the load current.

SR = 0

VRm = 0

SR1=OFF,SR2=OFF, S’R1=ON,

S’R2=ON, DR1=OFF,DR2=OFF

SR = -1

VRm= -Vdc/2

84

Thus a neutral point clamped pulse width modulation (PWM)

inverter composed of main switching devices which operate as

switches for PWM and auxiliary switching devices to clamp the output

terminal voltage to the neutral point potential.

3.4.3 Simplified SVPWM Algorithm for 3-Level NPC Inverter:

3.4.3.1 Space Vector's Plot:

the functional equivalent of 3-phase three level voltage source

inverter is shown in Fig. 3.38, in which every leg of the inverter is a

single pole triple throw (SPTT) switch.

Fig. 3.38 Function equivalent of three level VSI.

Every terminal of the load is connected to the pole of the

inverter legs, and thereby, depending upon the position of the pole,

the pole voltage is clamped to positive or zero or negative dc bus. Thus

every pole of the three pole voltages (VRO, VYO and VBO), measured

with respect to the DC bus center (m), is 2

DCV+ or 0 or

2

DCV− at any

instant. In Fig.3.38, the R-phase is shown connected to the positive

bus, while Y is clamped to neutral and B-phase is connected to the

negative bus. This state is designated as 1 0 -1. As every phase can be

m

B Y R

V

dc

2

V

dc

2

85

connected to the positive or the zero or the negative bus, the three

phases together can have 33 or 27 combinations of switching states.

In case of the states 000, -1 -1 -1 and 1 1 1, all the three poles are

connected to the same bus , effectively shorting the load and resulting

in no transfer of power between the DC bus and load. These three

states are called ‘zero states’. In case of the other states, power gets

transferred between the DC bus and load. These states are called

‘active states’.

Space vectors are plotted by normalizing the phase voltages

along α-β axis by knowing the switching instants which takes the

values 1 or 0. When R pole is connected to positive then

011 elsem a = and when it is connected to zero then

012 elsem a = similarly when R pole is connected to negative DC

bus then 013 elsem a = . Similarly for other poles Y and B. The line

voltages VRY, VYB, VBR are calculated from the (3.22) as follows:

( )

( )

( )32

2

2

131

3131

3131

mammmVdc

V

mmmmVdc

V

mmmmV

V

accBR

bcbbYB

bbaadc

RY

+−−=

+−−=

+−−=

(3.22)

And phase voltages are obtained as

( ) ( ) ( )YBBRBNRYYBYNBRRYRN VVV VVV VVV −=−=−=3

1;

3

1;

3

1(3.23)

To plot the 27 switching states using the phase voltages involves

complex procedure so, these phase voltages are converted to new

86

references α–β axis as stated before. The magnitudes of βοαο VV , are

obtained as follows:

−=

BN

YN

RN

V

V

V

V

V

V

0002

3

2

30

002

3

οο

βο

αο

(3.24)

Fig. 3.39 space vectors of three level inverter.

From the above matrix the values of αοV and βοV are obtained for all

the 27 switching states and are as shown in the Table 3.5. All the

V0

V5(-1-10)

V1(0-1-1)

V1(100) V7(1-1-1)

V8(10-1)V2(00-1)

V2(110)

V9(11-1)V10(01-1) V11(-11-1)

V3(-10-1)

V3(010)

V12(-110)

V13(-111) V4(011)

V4(-100)

V14(-101)

V15(-1-11)

V5(001)

V16(0-11)

V17(1-11)

V6(101)

V6(0-10)V18(1-10)

P-axis

Β-axis

87

points ( αV , βV ) obtained above are plotted in α–β plane as shown in

the Fig 3.39.

Table 3.5 states and voltages.

s.no states RYV YBV BRV RNV YNV BNV αV βV

1 -1 -1 -1 0 0 0 0 0 0 0 0

2 -1 -1 0 0 -V/2 V/2 -V/6 -V/6 V/3 -V/4 -0.433V

3 -1 -1 1 0 -V V -V/3 -V/3 2V/3 V/2 -0.866V

4 -1 1 -1 -V V 0 -V/3 2V/3 -V/3 -V/2 0.866V

5 -1 1 0 -V V/2 V/2 -V/2 V/2 0 -.75V 0.433V

6 -1 1 1 -V 0 V -2V/3 V/3 V/3 -V 0

7 -1 0 -1 -V/2 Vdc/2 0 -V/6 V/3 -V/6 -.25V 0.433V

8 -1 0 0 -V/2 0 V/2- -V/3 V/6 V/6 -0.5V 0

9 -1 0 1 -V/2 -V/2 V -V/2 0 V/2 -.75V -0.433V

10 0 -1 -1 V/2 0 -V/2 V/3 -V/6 -V/6 V/2 0

11 0 -1 0 V/2 -V/2 0 V/6 -V/3 V/6 0.25V -0.433V

12 0 -1 1 V/2 -V V/2 0 -V/2 V/2 0 -0.866V

13 0 1 -1 -V/2 V -V/2 0 V/2 -V/2 0 0.866V

14 0 1 0 -V/2 V/2 0 -V/6 V/3 -V/6 -.25V 0.433V

15 0 1 1 -V/2 0 V/2 -V/3 V/3 V/6 -V/2 0

16 0 0 -1 0 V/2 -V/2 V/6 V/6 -V/3 0.25V 0.433V

17 0 0 0 0 0 0 0 0 0 0 0

18 0 0 1 0 -V/2 V/2 -V/6 -V/6 V/3 -.25V -0.433V

19 1 -1 -1 V 0 -V 2V/3 -V/3 -V/3 V 0

20 1 -1 0 V -V/2 -V/2 V/2 -V/2 0 0.75V -0.433V

21 1 -1 1 V -V 0 V/3 -2V/3 V/3 V/2 -0.866V

22 1 0 -1 V/2 V/2 -V V/2 0 -V/2 0.75V 0.433V

23 1 0 0 V/2 0 -V/2 V/3 -V/6 -V/6 V/2 0

24 1 0 1 V/2 -V/2 0 V/6 -V/3 V/6 0.25V -0.433V

25 1 1 -1 0 V -V V/3 V/3 -2V/3 V/2 0.866V

26 1 1 0 0 V/2 -V/2 V/6 V/6 -V/3 0.25V 0.433V

27 1 1 1 0 0 0 0 0 0 0 0

.

88

Table 3.6 space vectors groups and states.

Groups Vectors Magnitude 1 pu

= dcV

STATES

Zero vector

0V

0 P.U

(0 0 0), (1 1 1) and (-1 -1 -1)

Small vectors

6

5

4

3

2

1

V

V

V

V

V

V

0.5 P.U

(1 0 0) (0 -1 -1) (1 1 0) (0 0 -1)

(0 1 0) (-10 -1)

(-10 0) (0 1 1 )

(-1 -1 0) (0 01)

(0 -1 0) (1 0 1)

Medium vectors

18

16

14

12

10

8

V

V

V

V

V

V

0.866 P.U

(1 0 -1) (0 1 -1) (-1 1 0) (-1 0 1) (0 -1 1) (1 -1 0)

Large vectors

17

15

13

11

9

7

V

V

V

V

V

V

1 P.U

(1 -1 -1) (1 1 -1) (-1 1 -1) (-1 1 1 ) (-1 -1 1) ( 1 -1 1)

3.4.3.2 Simplified Approach for SVPWM Algorithm:

The symmetry in the space vectors can be exploited to simplify

the task of volt-second balance. above task. In the proposed approach,

the entire space vector plane is divided into six sectors Z1, Z2, Z3, Z4,

89

Z5 and Z6 as shown in Fig 3.40. The sector definition is different from

the sector definition usually followed for two level inverters. From the

following discussion it will be clear that this sector definition will lead

to symmetry and hence helps in simplifying the algorithm.

All the six sectors are symmetric and each of the sectors is

associated with seven vectors. The vectors associated with each of the

sectors can now be viewed as a set of seven vectors with

corresponding small vector at the center.

Fig 3.40 Space vectors of three level inverter with sector and sub

sector definition.

All the vectors associated with the given sector Z1, can be

mapped to a set of seven fictitious vectors with V1 as the center. This

is illustrated in Fig. 3.41.

90

(a) Vectors of sector 1.

(b) Mapping of vectors of sector 1 to fictitious vectors.

Fig. 3.41 Mapping of vectors of sector 1 to fictitious vectors.

The fictitious vectors are similar to those of two level inverters.

The vector ZV'

forms the origin and its magnitude is always zero and

for a given sector this vector is similar to the zero vector of two level

inverters. The three nearest vectors can be identified as XV'

, YV'

and ZV'

as shown in Fig. 3.41. The polar forms of rV'

, XV'

, YV'

and ZV'

are

calculated from the voltage relations (3.28).

V/r

V/zx=V1(100)

V/zy=V1(0-1-1)

V/x=V0(000)

V/x=V18(1-10) V

/y=V2(0-10)

V/y=V7(1-1-1)

V/y=V2(00-1)

d- axis

q- axis

V/x=V8(10-1)

Vr

11

12

13

14

15

16

Vr

Vzx=V1(100)

Vzy=V1(0-1-1)

Vx=V0(000)

Vx=V18(1-10) Vy=V2(0-10)

Vy=V7(1-1-1)

Vy=V2(00-1)

d- axis

q- axis

Vx=V8(10-1)

11

12

13

14

15

16

91

131

131

131

131

VeVV

VeVV

VeVV

VeVV

zjzz

zjyy

zjxx

zjrr

−=

−=

−=

−=

−

−

−

−

/)('

/)('

/)('

/)('

π

π

π

π

(3.28)

Let x

T and y

T be the durations for which the active states x and

y are to be applied respectively. Let zT be the total duration for which

the zero states are to be applied. From the principle of volt-time

balancex

T , y

T and zT can be calculated as:

yxsz

yyxxsr

yyxxsr

TTTT

TVTVTV

TVTVTV

−−=

+=

+=

'''

'''

βββ

ααα

(3.29)

To keep the switching frequency constant, the remainder of the

time is spent on the zero state.

3.4.4 Simplified SVPWM algorithm based 3-Level Inverter Fed

DTC Drive:

To reduce the complexity of the algorithm, in this thesis, the

required reference voltage vector, to control the torque and flux cycle-

by-cycle basis is constructed by using the errors between the

reference d-axis and q-axis stator fluxes and d-axis and q-axis

estimated stator fluxes sampled from the previous cycle. The block

diagram of the proposed SVPWM based DTC is as shown in Fig. 3.42.

From Fig. 3.42, it is seen that the proposed SVPWM based DTC

scheme retains all the advantages of the CDTC, such as no co-

ordinate transformation, robust to motor parameters, etc. However a

92

space vector modulator is used to generate the pulses for the inverter,

therefore the complexity is increased in comparison with the CDTC

method.

Fig. 3.42 Block diagram of proposed SVPWM based DTC.

In the proposed method, the position of the reference stator flux

vector *sψ is derived by the addition of slip speed and actual rotor

speed. The actual synchronous speed of the stator flux vector sψ is

calculated from the adaptive motor model. After each sampling

interval, actual stator flux vector sψ is corrected by the error and it

tries to attain the reference flux space vector *sψ . Thus the flux error

is minimized in each sampling interval. The d-axis and q-axis

components of the reference voltage vector can be obtained as follows:

Adaptive Motor Model 3

2

IM

Vds, Vqs

Calculation

Reference Voltage

Vector

Calculator

Speed

+ _

+ _

∗eT

eT

∫slω

+

∗dsV

rω Ref speed

eθ

sψ

*

sψ

+

eω

dcV

*

qsV

S V P W M

SMC PI

93

Reference values of the d-axis and q- axis stator fluxes and actual

values of the d-axis and q-axis stator fluxes are compared in the

reference voltage vector calculator block and hence the errors in the d-

axis and q-axis stator flux vectors are obtained as in (3.30)-(3.31).

ψψψ dsdsds −=∆ * (3.30)

ψψψ qsqsqs −=∆ * (3.31)

The knowledge of flux error and stator ohmic drop allows the

determination of appropriate reference voltage space vectors as given

in (3.32)-(3.33).

TiRV

s

dsdssds

ψ∆+=* (3.32)

T

iRVs

qsqssqs

ψ∆+=* (3.33)

Where, Ts is the duration of subcycle or sampling period and it is a

half of period of the switching frequency. This implies that the torque

and flux are controlled twice per switching cycle. Further, these d-q

components of the reference voltage vector are fed to the SVPWM

block from which, the actual switching times for each inverter leg are

calculated.


Matlab-Simulink based simulation studies have been carried

out to validate the proposed simplified SVPWM algorithm based three-

level inverter fed 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

94

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 simulated results are shown

in Fig 3.43 to Fig 3.55.

Fig 3.43 and Fig 3.44 show the no-load starting transients of

speed, currents, torque, flux and voltages. The no-load steady state

plots of speed, currents, torque, flux and voltages at 1200 rpm are

given in Fig 3.45-Fig. 3.46. The harmonic distortion in the steady

state stator current along with THD is shown in Fig 3.47. From Fig

3.45 and Fig 3.47, it can be observed that the steady state ripple in

torque, flux and current is very less compared to 2 level SVPWMDTC.

Also, the proposed SVPWM based DTC provides constant switching

frequency of the inverter. The locus of the stator flux is shown in Fig.

3.48.

95

Fig. 3.43starting transients in speed, torque, currents and flux for simplified SVPWM algorithm based 3-level inverter fed DTC-IM.

Fig. 3.44starting transients in phase and line voltages for simplified SVPWM algorithm based 3-level inverter fed DTC-IM.

96

Fig. 3.45 Steady state plots of speed, torque, currents and flux for

simplified SVPWM algorithm based 3-level inverter fed DTC-IM.

Fig. 3.46 Steady state plots of phase and line voltages for


97

Fig. 3.47 Harmonic spectra of steady state line current for


Fig. 3.48 Locus of stator flux for simplified SVPWM algorithm

based 3-level inverter fed DTC-IM.

Fig 3.49 and Fig. 3.50 shows the transients in speed, torque,

currents, flux and voltages during the step change in load torque.

from which it can be observed that, even though there is a change in

torque, the flux is constant, which proves the decoupling control of

induction motor.

98

Fig. 3.49 transients during step change in load for simplified

SVPWM algorithm based 3-level inverter fed DTC-IM: a 30 N-m load is applied at 0.5 sec.

Fig. 3.50 phase and line voltages during a step change in load for simplified SVPWM algorithm based 3-level inverter fed DTC-IM: a

30 N-m load is applied at 0.5 sec.

99

The transients in speed, torque and currents during the speed

reversals (from +1200 rpm to -1200 rpm and from -1200 rpm to

+1200 rpm) are shown from Fig. 3.51 to Fig. 3.54. Fig 3.55 shows the

four-quadrant operation of drive.

Fig. 3.51 transients in speed, torque, currents and flux during speed reversal for simplified SVPWM algorithm based 3-level

inverter fed DTC-IM (speed is changed from 1200 rpm to -1200 rpm at 0.7 s).

100


reversal for simplified SVPWM algorithm based 3-level inverter fed DTC-IM (speed is changed from 1200rpm to -1200rpm at

0.7s).

Fig. 3.53 transients in speed, torque, currents and flux during speed reversal for simplified SVPWM algorithm based 3-level

inverter fed DTC-IM (speed is changed from -1200 rpm to +1200 rpm at 1.35 s).

101


reversal for simplified SVPWM algorithm based 3-level inverter fed DTC-IM (speed is changed from -1200rpm to +1200rpm at

1.35s).

Fig. 3.55 Four-quadrant operation of proposed simplified SVPWM

algorithm based 3-level inverter fed induction motor drive.

102

3.4.6 Summary:

The steady state ripples of stator current, torque and flux are

reduced by 3 level SVPWM compared to 2 level SVPWM algorithm. In

this section 3 level SVPWM algorithm based on reference voltage

vector calculator which utilizes the stator flux components as control

variables has been used for DTC. The proposed algorithm enables the

operation at constant switching frequency. By comparing the

reference values of d-axis and q-axis stator flux with estimated stator

fluxes, the errors in d-axis and q-axis stator flux are obtained. The

knowledge of these errors allows the determination of voltage space

vector which the VSI has to apply to the induction motor during the

next sampling time period. Then the required voltage space vector is

synthesized by means of SVPWM algorithm to generate the gating

signals for the VSI. The numerical simulations at different operating

conditions have been carried out and the results prove the validity of

the proposed control algorithm.

direct torque control of induction motor - shodhganga : a...

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