An Improvement in Dynamic Response of a Direct Torque Controlled Induction Motor Using

Sector Advancing Technique

Narasimham PVRL1, Sarma AVRS2, Vargilkumar E3

1Department of Electrical & Electronics Engg. Gudlavalleru Engineering College, Gudlavalleru-521 356, India. 2 Department of Electrical Engg. Osmania University, Hyderabad, A.P., India.

3 Department of Electrical & Electronics Engg. Gudlavalleru Engineering College, Gudlavalleru-521 356, India.

Abstract--- Among all the speed control techniques for induction motor drives, Direct Torque Control (DTC) method is simple and efficient because DTC is independent of machine rotor parameters and free from d-q transformation. Modern DTC based drives are equipped with estimators, observers, and machine intelligence systems to improve the dynamics and efficiency of the drive. This paper is aimed to focus on Sector Advancing Technique (SAT) for reducing the response time of the drive for a known torque command. Simulation studies are carried out using MATLAB/SIMULINK and results of DTC with SAT over conventional DTC are presented. Keywords— Induction Machine, Direct Torque Control, Stator flux, Torque ripple.

I INTRODUCTION The DTC method is one of the most recently

researched induction motor control method proposed by Japanese and German researchers [1, 2]. In DTC it is possible to control directly the stator flux and the torque by selecting appropriate inverter state. The main feature of this method of control is decoupled control of flux and torque without the need of coordinate transformation and inner current regulation loops. This scheme consists of a DTC controller, torque and flux estimator and a Voltage Source Inverter (VSI). It does not need pulse width modulator and position encoder, which results in fast dynamic response.

The DTC has a drawback of having inherent torque and flux ripple. This has been the topic of research for the last few years to reduce the ripple and to improve the performance of DTC of induction machines [3-7]. The major indicator of quality of dynamic response of a DTC is response time to the torque command. In this paper reduction of response time is realized by using the Sector Advancing Technique (SAT) to a conventional DTC [4] controlled induction motor drive. The basic principle of Sector Advancing Technique, mathematical equations, simulink model , simulation results and their comparison with the conventional method and conclusions are given in subsequent sections.

II DYNAMIC EQUATIONS OF INDUCTION MOTOR The dynamic T- model of induction machine in the

stator reference frame with motor variables expressed in vector form is given in Fig.1.

Fig. 1 T-model of Induction Motor

The voltage equations of stator and rotor are given by

)2...(0

)1...(

rrrr

ssss

wjpiR

piRV

λλ

λ

−+=

+=

Symbol ‘p’ denotes the differential operator d/dt. Lls is stator leakage inductance Lm is magnetizing inductance, Llr is rotor leakage inductance. Ls = Lls+Lm is stator inductance and Lr = Llr+Lm is rotor inductance. The dynamic model allows derivation of voltage-current equation of induction motor. Using the space vectors, the equation can be written as

[ ] [ ][ ] [ ][ ] )3....(iBvAdt

id+=

)5....(][][

)4....(][][T

qrdrqsds

Tqrdrqsds

vvvvv

iiiiiwhere

=

=

)6...(

0000

0000

1][ 2

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−−

−−

=

sm

sm

mr

mr

m

LLLL

LLLL

LA

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22

00

00

02

0

02

0

2 )7...(1][

mrs

srmsmsrs

rssrmsms

mrmrrsm

mrmrmr

LLLL

LRLLwLRLLwLLwLRLLwLR

LRLLwLRLwLLwLRLwrL

LB

−=

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

−−−−

−−−−

=

σ

σ

The stator and rotor flux are related to stator and rotor currents as

)8...(⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

r

s

rm

ms

r

s

ii

LLLL

λλ

The stator flux is given by

)9....(ssss iRV

dtd

−=λ

While the rotor flux in the squirrel cage induction motor satisfies the relation

)10....(0 rrrr iRjw

dtd

−= λλ

The developed torque ‘TM’ can be expressed in several forms, one such form is

)11....()(23

2dsqsqsdsM iiPT λλ −=

III BASICS OF DIRECT TORQUE CONTROL

The torque developed by in an induction motor can be written as

)13....()sin(23

2

)12...(.)Im(23

2

2

*2

srrsm

rsm

M

LLP

LLPT

θλλ

λλ

σ

σ

=

=

Here θsr denotes the angle between the stator flux and rotor flux. and is called as torque angle. The torque can be controlled by adjusting this angle. The magnitude of stator flux λs, a measure of intensity of magnetic field in the motor is directly dependent on the stator voltage. The same stator voltage can also be employed to control θsr there by controlling the torque developed. The stator flux can be estimated as

)14....()0()(0

s

t

ssss dtiRV λλ +−= ∫

From Fig.1, it is observed that the derivative of stator flux reacts instantly to changes in the stator voltage, the respective two space vectors are separated by in the circuit by the stator resistance Rs only.

However, the vector derivative of rotor flux ‘рλr’ is separated from that of stator flux by stator and rotor leakage inductances. Therefore the reaction of rotor flux vector to stator voltage is somewhat sluggish in comparison with that of stator flux vector.

In Fig.2 at a certain instant t, the initial vectors of stator and rotor are denoted by λs(t) and λr(t) respectively. After a time Δt, the new stator voltage vector λs(t+Δt) differs from λs in both magnitude and direction. As time Δt is very small the changes in rotor flux has been negligible. The stator flux has increased and torque angle θsr has been reduced by Δ θsr. Thus, appropriate selection of inverter states allows adjustments of both the strength of magnetic field of motor and developed torque.

The basic premises and principles of the direct torque control methods can be formulated as follows. (1) Stator flux is a time integral of stator EMF. Therefore its magnitude strongly depends on the stator voltage. (2) Developed torque is proportional to the sine of angle between the stator and rotor flux vectors. (3) Reaction of rotor flux to changes in stator voltage is slower than that of stator flux.

Consequently both the magnitude of stator flux and developed torque can be directly controlled by proper selection of space vectors of stator voltage i.e., selection of inverter states. Specifically, (1) Non zero voltage vectors whose misalignment with the stator flux vector does not exceed ±900 cause flux to increase. (2) Non zero voltage vectors whose misalignment with the stator flux vector exceeds ±900 cause flux to decrease. (3) Zero states V0 and V7 practically do not affect the vector of stator flux which stops moving. (4) The developed torque can be controlled by selecting such inverter state, where the stator flux vector is accelerated, stopped or decelerated.

Th The kth voltage vector is given by

Vk=Vdc vkje Θ

... (15)

Where Vdc denotes the dc input voltage of the inverter. )16....(3/)1( π−=Θ kvk .

Figure 2 Effect of Voltage Vector on Stator Flux and Torque

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TABLE 2 Selection of Voltage State based on Flux and

Torque Errors

Figure 3 Indication of sectors

The d-q plane is divided into six wide vectors designated 1 through 6 and centered on corresponding voltage vectors as given in Fig. 3.

A stator flux vector λs is said to be associated with the voltage vector Vk when it passes through the sector k. Impacts of individual voltage vectors on stator flux and developed torque are listed in Table 1 . Vk Vk+1 Vk+2 Vk+3 Vk+4 Vk+5 Vz

λ ↑↑ ↑ ↓ ↓↓ ↓ ↑ — TM ? ↑ ↑ ? ↓ ↓ ↓

The impact of vectors Vk and Vk+3 on the developed torque is ambiguous because it depends on whether the flux vector is leading or lagging the voltage vector in question. The zero vector Vz does not affect the flux but reduces the torque, because the vector of rotor flux gains on the stopped stator flux .

IV BLOCK DIAGRAM OF BASIC DTC SCHEME

The basic block diagram of the DTC drive system is shown in Fig. 4. The DC link voltage Vdc and two stator currents ia and ib are measured and space vectors Vs and is of stator voltage and current are determined in the voltage and current synthesizer. Based on Vs and Is , the stator flux vector λs of the stator flux is compared with the reference value λs* and TM is compared with the reference torque TM* in the torque control loop.

The flux and torque errors bλ and bT are applied to respective hysteresis controllers. The flux controller output signal can assume the values 0 and 1 and that of torque controller can assume the values of -1 , 0 ,1 as given in figure(5) . Selection of inverter state is based on values of -1, 0, and 1. Selection of inverter state is based tion are provided in Table2.

Flux error

Torque error θ1 θ 2 θ 3 θ 4 θ 5 θ 6

bλ=1 bT = 1 bT =0

bT = -1

V2 V7 V6

V3 V0 V1

V4 V7 V2

V5 V0 V3

V6 V7 V4

V1 V0 V5

bλ=0 bT = 1 bT =0 bT =-1

V3 V0 V5

V4 V7 V6

V5 V0 V1

V6 V7 V2

V7 V0 V3

V1 V7 V4

From table2 and Fig.6 , it can be observed that

five cases are distinguished in selection of the state of the inverter. (1) Both flux and torque are to be decreased. (2) The flux is to be decreased but the torque is to be increased. (3) The flux and torque are to be increased. (4) The flux is to increased and the torque to be decreased. (5) The torque error is within the tolerance range.

Case (5) calls for such a zero state that minimizes the number of switching. It is stated in the literature that as the width of hysteresis loop is reduced, the ripple in the flux and torque reduces and switching frequency increases.

λ s(t)

Figure 6 Effect of Stator Voltage Vector on Torque and Flux

TABLE 1 Influence of Voltage State on Stator flux and Torque

Figure 4 Basic DTC scheme

Figure 5 Hysteresis Controllers

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V IMPLEMENTATION OF SECTOR ADVANCING TECHNIQUE

Various improvements of the basic scheme described often involving Space Vector Modulation Technique (SVM), Fuzzy Logic Controllers; Machine Intelligence Systems are used to improve the flux waveform, ripple free torque, dynamics and efficiency of the drive and to enhance the quality of stator currents in the motor. Sector advancing technique is employed for reducing the response time of the drive to the torque command. This time is often used as a major indicator of quality of the dynamic performance of the drive.

In a DTC, a vector of inverter voltage used in one sector of the vector plane to decrease the stator flux is employed in next sector when the flux is to be increased. With such a control the trajectory of stator flux control vector forms a piecewise linear approximation of a circle as given in Fig.7. In the proposed Sector Advancing Technique (SAT), for rapid changes in torque command, the line separating the two sectors is shifted back by an angle α radians. Due to this there is an advancement of a sector by an angle α at that boundary region and the inverter applies vector states of next sector into the present sector. As the linear speed of the stator flux vector along its trajectory is constant and equals the dc supply voltage of the inverter, the voltage vector takes a shortcut. It arrives at a new location in a shorter time than if it traveled along the regular trajectory as shown in Fig.8 The acceleration of stator flux vector results in a rapid increase of the torque, because that vector quickly moves away from the rotor flux vector. The greater the sector shift α, the greater the torque increase.

VI SIMULATION RESULTS

To validate the proposed sector advancement technique, simulations have been carried out by using MATLAB/SIMULINK, with the following machine parameters.

Rated power 1.5kW, 4 pole, Rs = 8.49Ω Rr = 7.65Ω, Ls = 0.5253 H Lr = 0.5253H Lm=0.5015H J=0.02 kg-m2. The reference torque is taken as 20 N-m and reference flux as 1 unit.

The simulation model is given in Fig. 9. The locus of flux in Conventional DTC (CDTC) and with 300 angle advancement in sector 2 of SAT in DTC (SATDTC) is shown in Fig.10

The variation of torque with time of CDTC and SATDTC are given in Fig.11 and Fig. 12. It is observed that the time taken by DTC to reach a load torque of 5N-m is 0.45s where as that in SATDTC it is 0.422s (approximately 6.22% improvement) which proves that there is an improvement in the dynamic response with sector angle advancement. The variation of rotor speed in both the schemes is shown in Fig.13 and in Fig.14. The time to reach final speed in CDTC is 0.5s and in proposed scheme it is 0.45s. The steady speed of SATDTC is observed to be slightly higher value with more ripple content as compared to CDTC. The stator currents are shown in Fig. 15 and Fig.16

Figure 8 Selection of voltage vectors in SATDTC

Figure 7 Selection of voltage vectors in CDTC

Figure 10 Locus of Flux in CDTC and SATDTC

Figure 9 Simulink Models of CDTC and SATDTC

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Studies have been made on response time, torque ripple, speed, flux ripple, steady currents by varying the sector angle advancement from 00 to 600. It is observed that the ripple content increases with increase in advancement of angle in a sector. Even though studies are made with SAT in sector 2, it can be extended to all other sectors also. But it is preferred to adopt the SAT in one sector at a time rather than applying SAT in more than one sector at a time, to keep the ripple in torque and flux and currents at lower values.

VII CONCLUSIONS

In this paper, Sector Advancement Technique (SAT) has been proposed to improve the dynamic response of a Direct Torque Controlled induction motor. Simulation studies shows that the improvement in dynamic response is 6.22% in SATDTC as compared to CDTC for the induction motor with parameters listed above. The ripple in torque and flux are increased in SATDTC as compared to CDTC. The toque ripple and flux ripple can be minimized by using well defined techniques.

Figure 11 Developed torque in CDTC

Figure 12 Developed torque in SATDTC

Figure 13 Rotor speed in CDTC

Figure 14 Rotor speed in SATDTC

Figure 15 Stator currents in CDTC

Figure 16 Stator currents in SATDTC

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VIII REFERENCES

1. I.Takahashi and T. Noguchi , “A new quick response and

high efficiency control strategy of an induction motor “, IEEE Trans. Indus. Appl. Vol.22, no.5pp 820-827, 1986.

2. M. Depenbrock ,”Direct Self Control (DSC) of inverter fed induction machine”, IEEE Trans. Power Electronics , Vol. no. 3 , pp 420-429,1988.

3. I. Tahahashi and Y. Ohmori, “High –Performance direct torque control of induction motor ‘IEEE Tran. Indus. Appl. Vol. 25, pp 257-264, 1989.

4. A.H.Trzynadlowski, “Control of induction motors” Academic Press.

5. B.K.Bose , “ Modern Power Electronics and AC Drives”, Pearson Education, India 2003.

6. G.R. Selmon “Modelling of induction machines for electric Drives”, IEEE Tran. Ind. Appl. Vol 25 No.6 pp 1126-1130, 1989.

7. I.Takahashi and T. Nouguchi,”Take a look back upon the past decade of direct torque control”, Proc.IEEE – IECON 97 , 23rd International Conference, Vol2, pp546-551, 1997.

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