a simple method of torque ripple reduction for direct torque control of pwm inverter-fed induction...

8/12/2019 A Simple Method of Torque Ripple Reduction for Direct Torque Control of Pwm Inverter-fed Induction Machine Driv

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for several motor operating points, to show theimproved steady state operation as compared toconventional DTC.

2. DIRECT TORQUE CONTROL

The basic model of the classical DTC inductionmotor scheme is shown in Figure 1. It consists oftorque and stator flux estimators, torque and fluxhysteresis comparators, a switching table and avoltage source inverter (VSI). The configuration ismuch simpler than that of the FOC system whereframe transformation, rotor position or speed sensorsare required. The basic idea of DTC is to choose the

best voltage vector in order to control both stator fluxand electromagnetic torque of machinesimultaneously [1].At each sample time, the two stator currents i SA and

iSBand DC-bus voltage UDCare sampled.

T

CBA SSS ,,

+

+

*s

*T

( )6,...,2,1kS

1

1

0

1

1

S

( )7,...,1,0su

Figure 1: Block diagram of the conventional DTC

The components of the stator voltage spacevector in the stationary reference frame are calculatedas shown in (1) and (2) [3].

=

23

2 CBADCs

SSSUu (1)

33

2 CBDCs

SSUu

= (2)

where: CBA SSS ,, denote the inverter

switching states, in which ( )CBAiSi ,,1 == , if theupper leg switch is on and 0=iS , if the upper legswitch is off.The components of the stator current spacevector are calculated using equations (3) and (4),supposing the motor has the star connection.

sAs ii = (3)

3

2 sBsAs

ii

i

+

= (4)

Using the equations (1) (4) and the statorresistance, the components of the stator fluxare calculated in (5) and (6):

( )dtiRu ssss

= (5)

( )dtiRu ssss = (6)The circular trajectory of stator flux is divided intosix symmetrical sections (S1 S6) referred to invertervoltage vectors, as shown in Figure 2. The components of the stator flux are used to determinethe sector in which the flux vector are located.Then using equations (3) (6), the magnitude of thestator flux and electromagnetic torque are calculatedin (7) and (8).

sss22

+= (7)

( ) sssse iiPT = 23

(8)

where: P is the number of pole pairsRs is the Stator resistance.

The calculated magnitude of stator flux andelectromagnetic torque are compared with theirreference values in their corresponding hysteresiscomparators, as are shown in Figure 1. Finally, theoutputs of the comparators and the number of sectorat which the stator flux space vector is located arefed to a switching table to select an appropriateinverter voltage vector [3]. As shown in Figure 2,eight switching combinations can be selected in atwo-level voltage source inverter, two of whichdetermine zero voltage vectors and the othersgenerate six equally spaced voltage vectors havingthe same amplitude.

)100(1u

)110(2u)010(3u

)011(4u

)001(5u )101(6u

)000(0u)111(7u

Figure 2: The inverter voltage vectors and the stator

flux sectors

The selected voltage vector will be applied to theinduction motor at the end of the sample time.

148

Annals of the University of Craiova, Electrical Engineering series, No. 30, 2006_________________________________________________________________________________________________


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3. TORQUE RIPPLE REDUCTION

In conventional DTC, the voltage vector selection isbased on the torque and flux errors, but small andlarge errors are not distinguished by the hysteresis

controllers. The voltage vectors are applied for theentire sample period, even for small errors, resultinglarge torque overshoots in steady-state regime.The proposed method for torque ripple reduction,

presented in this paper, consists in the modulation ofthe nonzero voltage vector duration over a sampling

period, according to the torque and stator flux errors,using simmetric PWM. The nonzero voltage vectorsare selected using a switching table, like in classicalDTC. The null vectors are automatically inserted byusing PWM, so they are no more needed in theswitching table. Consequently, in the proposedcontrol scheme, shown in Figure 3, simple

comparators, with no hysteresis, are used. A dutyratio calculator and a PWM block have been added tothe classical scheme.

T

CBA SSS ,,

+

+

*s

*T

S ( )6,...,2,1kS

1

1

1

1

( )6,...,1su

Figure 3: Block diagram of the proposed control

Every sample time, one of the six nonzero voltagevectors are selected from the switching table, and it isapplied to the inverter using simmetric PWMswitching strategy. The PWM period is considerredequal to the control sample period.To apply to the inverter the selected voltage vector(denoting the corresponding inverter switching states

iS , CBAi ,,= ), with a given duty ratio, it wasadopted the following method: for 0=iS , the pulseduty ratio of the corresponding inverter leg takes zerovalue, otherwise it takes the calculated value. Thecalculation procedure of the duty ratio is presented

below.In order to preserve the very good dynamic responseof the classical DTC, the proposed method forreducing the torque ripple is applied only when theactual torque value is located in a proximity zone,arround the reference value. This zone, whose widthis denoted by TZ , is similar to the torque hysteresis

band of the classical DTC torque comparator. In

other words, only for torque errors between TZ and

TZ the voltage duty ratio is modified, otherwise it is

kept at 100%.For a preliminar approach, the duty ratio was taken

equal to the normalized torque error which meansthe ratio of the torque error, T , to the zone width,

TZ as shown in (9).

1=T

TT

Z

(9)

where:T

T

Z

is the normalized value of the

torque error

T is the duty ratio corresponding tothe torque error.

This first approach was tested and it was revealedthat if only the torque error is taken into account,small values of the duty ratio conduce to stator fluxdecrease at low frequencies, when the voltage dropon the stator resistance becomes significant. The fluxdecrease determines the torque decrease, whichconsequently enlarges the duty cycle. However, thiscompensation is slow, generating flux oscillations. Inorder to avoid the flux decrease at low frequencies,the method was improved by taking into account alsothe flux error, which is normalized in the samemanner as the torque error. The duty ratiocorresponding to the flux error is considerred as aratio of the rest of the sampling period, ( )T1 , as inequation (10).

( )TF

FZ

F

= 1 (10)

where:F

F

Z

is the normalized value of the flux

error

F is the duty ratio corresponding tothe flux error.

The final value of the duty ratio, which takes into

account both errors is calculated in (11), so that itwill be a fractionar value.

11

+=+=

T

T

FT

TFT

ZZZ

F

(11)

In Figure 4 is represented the duty ratio as function

of normalized torque errorT

T

Z

, for different

constant values of normalized flux errorF

F

Z

(characteristics (a), (b) and (c)). The duty ratio islimitted to a minimum value,

min , in order to

consider the maximum inverter switching frequency.

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T

T

Z

min

Figure 4: The characteristics of duty ratio ( ) for:

(a)( )

0=

aF

F

Z, (b)

( )

0

bF

F

Z, (c)

( ) ( )bF

F

cF

F

ZZ

>

Every sample time, the duty ratio is calculated usingthe algorithm presented in Figure 5.

FT +=

TT Z


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0 0.1 0.2 0.3 0.4

0

2

4

6

8

10

time [s]

Torque[N

m]

(a)

0 0.1 0.2 0.3 0.4-10

-7.5

-5

-2.5

0

2.5

5

7.5

10

time [s]

Statorcurrent[A]

(b )

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time [s]

Statorflux[Wb]

(c)

Figure 7: Classic DTC, at 1000 rpm: (a) torque,

(b) stator current, (c) stator flux magnitude

In order to adequately illustrate the comparisonbetween the conventional DTC and DTC withproposed improvement scheme, the torque and fluxhysteresis bands widths were set (by trial and error)so that the torque and flux ripple to be as low as

possible in conventional DTC:

nT THB = 11.0 and nF FHB = 04.0

where: THB is the torque hysteresis band width

nT is the motor rated torque,

respectively: FHB is the flux hysteresis band width

nF is the rated flux.

In Figure 8 and 9 are shown the results obtained byDTC using the proposed solution for torque ripplereduction, for low and respectively high frequency.The voltage duty ratio is related to both the torqueand flux errors, according to equation (11).

The zone widths TZ and FZ , introduced by theproposed method, were set to nT1.0 and nF1.0 respectively.

0 0.1 0.2 0.3 0.4-2

0

2

4

6

8

10

time [s]

Torque[Nm]

(a)

0 0.1 0.2 0.3 0.4-10

-7.5

-5

-2.5

0

2.5

5

7.5

10

time [s]

Stato

rcurrent[A]

(b)

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time [s]

Statorflux[Wb]

(c)

Figure 8: DTC with voltage control using the proposedmethod, at 100 rpm: (a) torque, (b) stator current, (c)

stator flux magnitude

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0 0.1 0.2 0.3 0.4-2

0

2

4

6

8

10

time [s]

Torque[Nm]

(a)

0 0.1 0.2 0.3 0.4-10

-7.5

-5

-2.5

0

2.5

5

7.5

10

time [s]

Statorcurrent[A]

(b )

0 0.1 0.2 0.3 0.40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time [s]

Statorflux[Wb]

(c)

Figure 9: DTC with voltage control using the proposedmethod, at 1000 rpm: (a) torque, (b) stator current, (c)

stator flux magnitude

The results show an important reduction of torque,current and flux ripple obtained when the proposedsolution is used, comparing with the conventionalDTC.

5. CONCLUSIONS

This paper presents a cost-effective solution forreducing the torque ripple in conventional DirectTorque Control, while preserving the dynamic

response and structural simplicity of this controlscheme.The solution proposed uses PWM control of thevoltage vector with duty ratio determined using asimple algorithm based on torque and flux errors.The results show that not only the torque ripple wasreduced, but also the stator current and flux ripples.Compared with other methods for reducing the torqueripple in DTC, like [5] and [6], the proposed methodis much simpler and does not need additional motor

parameters or knowledge of the rotor speed.Taking into account that today many microcontrollersand DSP offer PWM interfaces, the proposed method

can be very easily implemented on them, adding verylittle computation effort to the classical DTC controlalgorithm.

References

[1] I. Takahashi, T. Noguchi, A new quick-responseand highefficiency control strategy of aninduction motor, IEEE Trans. Ind. Applicat., vol.IA-22, Sept./Oct. 1986, pp. 820827.

[2] P. Tiitinen, M. Surandra, The next generationmotor control method, DTC direct torque control,Proc. Int. Conf. on Power Electron., Drives andEnergy System for Industrial Growth, N. Delhi,1996, pp. 3743.

[3] P. Vas, Sensorless Vector and Direct TorqueControl. New York: Oxford University Press,1998.

[4] D. Casadei, G. Serra, A. Tani, Implementation ofa direct control algorithm for induction motorsbased on discrete space vector modulation, IEEETrans. Power Electron., vol. 15, no. 4, July 2000,

pp. 769 777.

[5] J. Kang, S. Sul, New direct torque control ofinduction motor for minimum torque ripple and

constant switching frequency, IEEE Trans. Ind.Applicat., vol. 35, Sept./Oct. 1999, pp. 10761082.

[6] L. Romeral, A. Arias, E. Aldabas, M. G. Jayne,Novel Direct Torque Control (DTC) Scheme WithFuzzy Adaptive Torque-Ripple Reduction, IEEETrans. Ind. Applicat., vol. 50, June 2003, pp. 487492.

[7] S.V.Paurc, M.Covrig, S.Velicu, K.Gavros,Simulation of the dynamics of an eccentricpresser driven by an induction motor using DirectTorque Control, Adv. Topics in ElectricalEngineering, ATTE, nov.2004, pp. II - 102-109.

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a simple method of torque ripple reduction for direct torque control of pwm inverter-fed induction...

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