IEEE Xplore Download2353

8/23/2019 IEEE Xplore Download2353

1/7

778 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 53, NO. 3, JUNE 2006

Direct Torque Control of an Induction MotorUsing a Single Current Sensor

Manuele Bertoluzzo, Giuseppe Buja, Fellow, IEEE, and Roberto Menis, Member, IEEE

AbstractA novel scheme for the direct torque control (DTC)of an induction motor (IM) is proposed, which uses a single sensorof current inserted in the inverter dc link. The rationale behindthe proposal is to develop a low-cost but high performance IMdrive. The scheme exploits a simple and robust algorithm to re-construct the stator currents needed to estimate the motor flux andtorque. The algorithm operates in two stages: first, it predicts thestator currents from a model of the motor and then adjusts theprediction on the basis of the sensed dc-link current. Experimentalresults are given to demonstrate the ability of the scheme inreproducing the performance of a traditional DTC IM drive.

Index TermsDirect torque control (DTC), induction motor

(IM), sensor count reduction.

I. INTRODUCTION

AN induction motor (IM) drive controlled with the direct

torque control (DTC) technique exhibits performance

similar to a field-oriented drive despite the simpler structure

[1][3]. In fact, a DTC scheme accomplishes the closed-loop

control of the stator flux magnitude and the electromagnetic

torque of the motor without the intermediary of any current loop

or shaft sensor. To this end, the DTC scheme senses the stator

currents and the dc-link voltage and processes them, together

with the states of the inverter switches, to estimate the actualvalues of the controlled variables.

The hardware of a DTC scheme could further be reduced

by using only one sensor of current and by inserting it in the

inverter dc link. The aim of this paper is to develop and to

test such a solution. For this purpose, a suitable algorithm for

the reconstruction of the stator currents is devised, and the

performance of the resulting drive is evaluated.

The issue of reconstructing the output currents of an inverter

from the current in the dc link has been dealt with by a num-

ber of papers [4][7]. However, they are focused on inverters

modulated with the space-vector (SV) technique, and no paper,

apart from [8], is concerned with DTC. Furthermore, Habetler

and Divan [8] limit themselves in considering a resonant dc-linkinverter oscillating at high frequency; and hence, the solution

arranged there is not applicable to standard DTC-operated

inverters.

Manuscript received March 8, 2004; revised January 5, 2006. Abstractpublished on the Internet March 18, 2006.

M. Bertoluzzo and G. Buja are with the Department of ElectricalEngineering, University of Padova, 35131 Padova, Italy (e-mail: [email protected]; [email protected]).

R. Menis is with the Department of Electrotechnics, Electronics and Com-puter Science, University of Trieste, 34127 Trieste, Italy (e-mail: [email protected]).

Digital Object Identifier 10.1109/TIE.2006.874415

In detail, this paper is organized as follows. Section II

reviews the operation of a traditional DTC scheme. Section III

presents the proposed DTC scheme with a single current sensor.

Section IV sets forth the algorithm to reconstruct the stator cur-

rents. Section V analyzes the performance of the novel scheme

by experiments. Section VI concludes the paper.

II. DTC OPERATION

The block diagram of an IM drive controlled with the tra-

ditional DTC scheme is drawn in Fig. 1. The drive is equippedwith two sensors of current inserted in the stator phases and one

sensor of voltage connected across the dc link. The inputs to the

drive are the references s and for the stator flux magnitude

and the motor torque, respectively. Their actual values are

estimated in the feedback path by help of the following blocks:

1) stator current SV calculator; 2) stator voltage SV calculator;

and 3) flux and torque estimator. In this paper, the SV represen-

tation is obtained by an amplitude-invariant transformation of

the three-phase variables into a two-axis stationary frame d, qwith the axis d aligned along the phase a of the stator.

The stator current SV calculator computes the SV is of thestator current by

is =2

3

ias + ibse

j 23 + icse

j 43

(1)

where ias and ibs are the sensed stator currents, and ics isdetermined as

ics = (ias + ibs) (2)

because the motor has no neutral connection.

The stator voltage SV calculator computes the SV vs of thevoltage applied to the motor by

vs =23Vdc

Sa + Sbe

j 23 + Sce

j 43

(3)

where Vdc is the inverter dc-link voltage, and Sa, Sb, and Sc arethe states of the upper switches of the inverter (S= 1 meansswitch closed and S= 0 means switch open).

The eight voltage SVs generated by the inverter are drawn in

Fig. 2. They are marked with a subscript from 0 to 7 and are

labeled with the switch states (Sa, Sb, Sc). SVs 16 are termedactive inverter voltage vectors, whereas SVs 0 and 7 are termed

zero-inverter-voltage vectors.

The flux and torque estimator determines at first the stator

flux SV s

by integrating the IM stator voltage equation, which

0278-0046/$20.00 2006 IEEE


2/7

BERTOLUZZO et al.: DIRECT TORQUE CONTROL OF AN INDUCTION MOTOR USING A SINGLE CURRENT SENSOR 779

Fig. 1. Conventional DTC IM drive.

Fig. 2. Inverter voltage SVs and stator flux regions.

is given as

vs = Rsis +dsdt

(4)

i.e., by

s =

(vs Rsis)dt (5)

where Rs is the stator resistance. Then, from (5), the followingvariables are estimated:

1) stator flux magnitude, by

s =2ds +

2qs (6)

2) motor torque, by

=3

2p(iqsds idsqs) (7)

3) 60 region (or sextant) r of the stationary plane wherethe stator flux vector lies, by manipulating the d andq components of s as illustrated in [1]. In Fig. 2, thesextants are distinguished by a circled number, and theirboundaries are given by the dashed-line radii.

The DTC scheme develops its control action by means of

the three blocks placed in the forward path in Fig. 1, namely:1) flux controller; 2) torque controller; and 3) inverter voltage

Fig. 3. (a) Flux and (b) torque controllers.

TABLE IINVERTER VOLTAGE SV SELECTION TABLE FOR THE

STATOR FLU X SV IN REGION 1

selector. The controllers are of hysteresis type as shown inFig. 3, where h is the flux hysteresis band, h is the torquehysteresis band, and is the offset of the torque hysteresisband. The comparators are entered by the flux e

sand torque

e errors and deliver the control signals v

sand v, which

represent the digitized voltage demands required to keep theerrors within the hysteresis bands of the controllers.

The inverter voltage selector decides, by help of a table,which one among the eight voltage SVs generated by theinverter fulfills the control demands and applies it to the motor.

Decision depends on the region spanned by the stator flux SV.As an example, in region 1, Table I is used.

It can be easily realized that the three-level torque compara-tor together with the selection rules in Table I has a number ofmerits. Let the motor operate in steady state so that the torqueerrors are smaller than . For positive errors (and clockwisemotor rotation), the active vectors V2 or V3 are applied to themotor, whereas for negative errors, they are applied the zerovectors V0 or V7. The choice between the two zero vectors isdictated by the demand of having a low switching count. Underthese circumstances, the switching rate of the inverter is keptat a minimum. Instead, when the torque reference undergoesa large step-down change, ensuing for instance from a sudden

request of speed reversal, the torque error is greater than ,and the active vectors V5 and V6 are applied to the motor in


3/7


Fig. 4. Single-current-sensor DTC IM drive.

place of the zero ones, thus speeding up the torque responseand endowing the drive with speed-reversal capabilities.

III. SINGLE CURRENT SENSOR DTC SCHEME

The proposed DTC scheme is drawn in Fig. 4. The schemesenses the inverter dc-link current only and goes back to thestator currents by means of a reconstruction algorithm. Thealgorithm is incorporated in the flux and torque estimator andutilizes the sensed current, the switch states (Sa, Sb, Sc), andthe stator flux SV estimated in the previous sampling interval.

In addition to the two sensors of current in the stator phases,most of the traditional DTC IM drives mount an additionalcurrent sensor in the dc link for fault protection. With theproposed scheme, only the sensor in the dc link is still used andis committed for both the protection and the estimation task. It

is worth to note that the hardware of the resulting drive is thesame as that of a voltage-to-frequency (V/F) drive.

IV. STATOR CURRENT RECONSTRUCTION

The reconstruction algorithm works in two stages. In the firststage, the stator currents are predicted, whereas in the secondstage, the predicted values are adjusted in accordance with thesensed dc-link current. The stator current reconstruction as wellas the flux and torque estimation and the DTC control run indiscrete time.

A. Prediction Stage

The prediction stage relies on the dynamics of the statorcurrent. A model of them can be found from the stator voltage(4) and the flux relationship, which is defined as

s = sr + Ls is (8)

where sr is the rotor flux SV referred to the stator with theratio Lm/Lr, and Ls is the stator transient inductance. Sub-stitution of (8) into (4) gives

vs = Rs is + Ls dis

dt+ esr (9)

Fig. 5. IM equivalent circuit.

where esr is the SV of the back electromotive force (EMF)behind the stator transient inductance, which is given as

esr =dsrdt. (10)

The three-phase equivalent circuit associated to (9) is drawnin Fig. 5.

Rearranging (9) yields

disdt

=1

Ls

vs Rsis

dsrdt

. (11)

Compared with the stator flux, the dynamics of the rotor fluxare much more sluggish [9]. Then, the change in the magnitudeof the rotor flux SV within a sampling interval is negligible, andthe time rate ofsr can be simplified, i.e.,

dsrdt

= jsrsr (12)

where sr

is the angular frequency of sr. Such a frequencycan be calculated as the derivative of the spatial position

sr

ofsr, i.e., as

sr =dsrdt. (13)


4/7


TABLE IIDC-LIN K IN-SERIES STATOR PHASE CURRENT VERSUS

INVERTER UPPER-SWITCH STATES

By (12), (11) becomes

disdt

=1

Ls(vs Rsis j

srsr). (14)

Discrete integration of (14) gives the prediction of current atthe instant k as a function of the variables at the instant (k 1).Being the behavior of the rotor flux smooth, discretization of(14) can be simply carried out by means of the rectangular rule.The resulting equation is

ips(k) = is(k1) +TsLs

vs(k1)Rs is(k1)j

sr(k1)sr(k1)

(15)

where superscript p denotes predicted current, Ts is the sam-pling period, vs(k 1) is the inverter voltage SV selected at theinstant (k 1) and applied over the actual sampling interval,and

sr(k 1) and sr(k 1) are calculated respectively by

the following equations derived from (13) and (8):

sr

(k 1) =

sr(k 1)

sr(k 2)

Ts(16)

sr(k 1) = s(k 1) Lsis(k 1). (17)

B. Adjustment Stage

When the inverter applies an active voltage SV to the motor,there is always one stator phase that is connected in series tothe dc-link rail of the inverter, either to the positive or to thenegative polarity, whereas the other two phases are connectedin parallel to the opposite polarity. The in-series phase can beeasily identified from the states of the upper switches of theinverter, and the current flowing in this phase is either equal oropposite to the dc-link current as illustrated in Table II. Whenthe inverter applies a zero-voltage SV, the motor terminals areshorted and the dc-link current is zero.

The adjustment stage takes advantage of Table II to enhancethe reconstruction of the stator currents. In this stage, thepredicted current of the dc-link in-series phase is discardedand is replaced with the sensed dc-link current. Because ofthe modeling and processing errors in the prediction stage, thepredicted value may differ from the sensed current. This impliesthat the current of one or both of the other two stator phases alsodiffers from their actual value. To keep the sum of the statorcurrents at zero and, at the same time, to improve the overallreconstruction of current, the deviation detected for the currentof the in-series phase is split between the other two phases.Of course, the adjustment stage is not executed when a zero-voltage SV is applied to the motor.

Splitting is done in a straightforward manner by dividing thecurrent deviation into two equal parts. When, for instance, the

in-series phase is a, the equations of the adjustment stage areas follows:

ia(k) = ima (k)

ia(k) = ima (k) i

pa(k)

ib(k) = ipb(k) i

a(k)2

ic(k) = ipc(k)

ia(k)

2(18)

where superscriptm denotes measured current.The equal-split policy would be correct to the extent that the

equivalent circuits of the two phases have the same behavior.Because the element that differentiates the two circuits is theback EMF, this policy is fairly precise at low speed, when theback EMF behind the stator transient inductance is less thanthe voltage drop across the stator impedance. On the other hand,

at low speed, there is a great number of zero-inverter-voltageSVs applied to the motor, which does not allow the frequentadjustment of the prediction, and the current reconstructionbecomes inaccurate because of the propagation of the errorsin the prediction stage. The equal-split policy, instead, is quiteinaccurate at high speed, but the great number of active invertervoltage SVs applied to the motor permits the frequent adjust-ment of the stator currents, thus overriding the errors introducedby the inaccurate split.

To cope with the reconstruction errors at low speed, the offset of the torque controller hysteresis band is gradually shrunkas the angular speed of the rotor flux diminishes. Then, fornegative torque errors, active inverter voltage SVs (i.e., V5 or V6

for the stator flux in region 1) are applied to the motor in placeof the zero-inverter-voltage SVs for an increasing number ofsampling intervals, and this enables a more frequent adjustmentof the current prediction. For the drive described in the nextsection, satisfactory operation has been achieved by linearlydecreasing from h to 0, with the decrease that starts at 25%of the rated motor frequency and reaches 0 at about 15% of it.When = 0, only active voltage SVs are applied to the motor,and the adjustment of current is carried out at every samplinginterval.

V. EXPERIMENTAL RESULTS

A DTC IM drive arranged as in Fig. 2 has been set upand tested. The experimental rig is illustrated in Fig. 6. Thecontrol program is implemented in the digital signal processor(DSP) board and cycles every 50 s. The basic functionscarried out by the control program are listed as follows:1) acquisition of the signals coming from the sensors of currentand voltage in the dc link; 2) processing of the signals by meansof the reconstruction, estimation, and control algorithms; and3) command of the inverter switches. The flowchart of thecontrol program is drawn in Fig. 7. Data on the rig devices arelisted in the Appendix.

The stator flux magnitude, the motor torque, and the actual

and reconstructed stator currents are downloaded by the DSP tothe oscilloscope for display purposes. The personal computer


5/7


Fig. 6. Experimental rig.

Fig. 7. Flowchart of the single-sensor DTC control program.

in the rig is employed for editing the control program andcommanding the drive.

Several tests have been executed on the DTC IM drive toevaluate its static and dynamic performance. The results ofthree significant tests are reported here. In all the tests, the

motor is operated at rated stator flux. In the first test, the torquereference is solicited with a square wave, switching from plus tominus half the rated torque while the motor is running at 75% ofthe rated speed. The period of the square wave is short enoughto keep the motor speed nearly constant. The second test is areplica of the first one but with the motor running at 10% of therated speed.

The motor torque, the stator flux magnitude, and the ac-tual stator currents obtained with the first test are plotted inFig. 8(a)(c), respectively. The reconstructed values of current,if reported in Fig. 8(c), would be indistinguishable from theactual ones. To highlight the difference, a portion of currentand the respective reconstructed value are magnified and plotted

in Fig. 8(d). The quantities obtained with the second test areplotted in Fig. 9(a)(d). The results of the two tests show the

Fig. 8. Experimental results at 75% of the rated speed.

Fig. 9. Experimental results at 10% of the rated speed.

excellent behavior of the drive both in steady state and duringtransients. In particular, the torque response is fast and theflux regulation is accurate, closely reproducing the performance

exhibited by a traditional DTC scheme. The plots of Figs. 8(d)and 9(d), in turn, demonstrate that the reconstruction algorithmis effective in tracking the stator current accurately both at highspeed and low speed.

The adjustment stage makes the reconstruction of the statorcurrents somewhat robust against a mismatch in the modelparameters because it exerts a compensating action for thedeviation arising in the prediction stage. This feature has beenverified by carrying out the preceding tests with a mismatch of30% in the value ofLs employed to predict the currents. Therelevant plot of current and that of the respective reconstructedvalue are given in Fig. 10(a) and (b), respectively, at 75% and10% of the rated motor speed. Comparison of the outcomes

with those in Figs. 8(d) and 9(d) is evidence of the robustnessof the reconstruction algorithm.


6/7


Fig. 10. Experimental results with Ls mismatch.

VI. CONCLUSION

This paper has presented a novel DTC scheme for IM drives,based on the use of a single sensor of current inserted in theinverter dc link. The scheme reconstructs the stator currentsneeded to estimate the stator flux magnitude and the motortorque, by means of an algorithm that at first predicts the cur-

rents of the phases and then adjusts them by taking advantage ofthe sensed dc-link current. Prediction is carried out by means ofa suitable model of the motor, whereas adjustment is operatedby setting the current of the stator phase in series with the dclink at the sensed value and by altering the predicted values ofcurrent of the other two phases by half the detected deviation inthe current of the dc-link in-series phase.

The performance of a DTC IM drive arranged with the novelscheme has been then experimented. The results have shownthe excellent performance of the drive, nearly identical to thatachievable with the traditional DTC scheme. On the other hand,the novel scheme requires an additional computation burdenand the knowledge of the stator transient inductance. As provenin this paper, the latter inconvenience is eased by the robustnessof the reconstruction algorithm that allows the usage of a roughestimate of the inductance.

APPENDIX

The data on the experimental rig are as follows.DTC Torque controller hysteresis band: 5% of

the rated torque; flux controller hysteresisband: 2% of the rated stator flux; samplinginterval: 50 s.

IM Rated power: 3 kW; line-to-line voltage:

380 V; phase current: 7.3 A; frequency:50 Hz; speed: 1410 r/min; power factor:0.82; efficiency: 76%; pole pairs: 2; sta-tor resistance: 1.95 ; rotor resistance:1.66 ; total leakage inductance: 21 mH;stator inductance: 243 mH; rotor induc-tance: 244 mH; magnetizing inductance:233 mH.

Inverter Voltage source inverter supplied by a530-V dc supply. The switching frequencyof the inverter varies from 1.5 to 3 kHz inthe operation range.

DSP board TMS320F240 DSP evaluation module.

Signal conditioner Antialiasing filters and circuits for adapt-ing the signal level.

REFERENCES

[1] I. Takahashi and T. Noguchi, A new quick-response and high-efficiencycontrol strategy of an induction motor, IEEE Trans. Ind. Appl., vol. IA-22,no. 5, pp. 820827, Sep./Oct. 1986.

[2] M. Depenbrok, Direct self-control (DSC) of inverter-fed induction ma-chine, IEEE Trans. Power Electron., vol. 3, no. 4, pp. 420429, Oct. 1988.

[3] G. Buja and M. Kazmierkowski, Direct torque control of PWM inverter-fed AC motorsA survey, IEEE Trans. Ind. Electron., vol. 51, no. 4,pp. 744757, Aug. 2004.

[4] T. C. Green and B. W. Williams, Derivation of motor line-current wave-forms from the DC-link current of an inverter, Proc. Inst. Electr. Eng.,vol. 136, no. 4, pt. B, pp. 196204, Jul. 1989.

[5] F. Petruzziello, G. Joos, and P. D. Ziogas, Some implementation aspectsof line current reconstruction in three-phase PWM inverter, in Proc. IEEE

IECON, 1990, pp. 11491154.[6] J. F. Moynihan, R. C. Kavanagh, M. G. Egan, and J. M. D. Murphy,

Indirect phase current detection for field oriented control of a permanentmagnet synchronous motor drive, in Proc. EPE, 1991, pp. 641646.

[7] W. C. Lee, T. K. Lee, and D. S. Hyun, Comparison of single-sensor currentcontrol in the DC link for three-phase voltage-source PWM converters,

IEEE Trans. Ind. Electron., vol. 48, no. 3, pp. 491505, Jun. 2001.[8] T. G. Habetler andD. M. Divan, Control strategies fordirect torque control

using discrete pulse modulation, IEEE Trans. Ind. Appl., vol. 27, no. 5,pp. 893901, Sep./Oct. 1991.

[9] M. Bertoluzzo, G. Buja, and R. Menis, Analytical formulation of the directcontrol of induction motor drives, in Proc. IEEE Int. Symp. Ind. Electron.,1999, pp. 1420.

Manuele Bertoluzzo received the M.S. degree inelectronic engineering and the Ph.D. degree in indus-trial electronics and computer science from the Uni-versity of Padova, Padova, Italy, in 1993 and 1997,respectively.

From 1998 to 2000, he was a member of theresearch and development division of an electricaldrive factory. In 2000, he joined the Department ofElectrical Engineering, University of Padova, as aResearcher in the Scientific Disciplines Group and

carried out research in the fields of electric convert-ers, machines, and drives. He is currently involved in the analysis and designof control systems and communication networks for power electronics andautomotive systems.

Giuseppe Buja (M78SM84F95) received theLaurea degree in electronic engineering (with hon-ors) from the University of Padova, Padova, Italy,in 1970.

Upon graduation, he joined the Engineering Fac-ulty of the University of Padova. Since 1986, he hasbeen a Full Professor of power electronics, first atthe University of Trieste, Trieste, Italy, and then atthe University of Padova. He has carried out research

in the fields of static converters, electric drives, andindustrialautomation. He has authored or coauthored

more than 150 papers published in refereed journals and international con-ference proceedings. He has started the Laboratory of Electric Drives at theUniversity of Trieste and the Laboratory of Industrial Automation at theUniversity of Padova, the latter of which he is currently the Head. He hasdirected several research projects granted by the university and by privatecompanies. He has served as the Coordinator of the Ph.D. course in electricalengineering at the University of Padova.

Prof. Buja has served the IEEE in several capacities, including as theGeneral Chairman of the 20th Annual Conference of the IEEE IndustrialElectronics Society (IEEE IECON94) and as an Associate Editor of the IEEETRANSACTIONS ON INDUSTRIAL ELECTRONICS. He was a cofounder ofthe International Symposium on Diagnostics for Electric Machines, PowerElectronics and Drives (SDEMPED). Currently, he is a Senior Member of theAdministrative Committee of the IEEE Industrial Electronics Society, a Voted

Member of the Executive Council of the Association on Power Electronics andMotion Control (PEMC), and an Associate Editor of the International Journalof Electrical Engineering in Transportation.


7/7


Roberto Menis (S76M92) was born in Osoppo,Udine, Italy. He received the Laurea degree in elec-tronic engineering from the University of Trieste,Trieste, Italy, in 1982.

From 1982 to 1984, he was a member of the tech-nical staff of an aeronautic industrial company. In1984, he joined the Department of Electrotechnics,Electronics, and Computer Science, University of

Trieste, where he is currently an Associate Professorof electric drives and the Head of the Electric DrivesLaboratory. His research interests are in the field of

electric machines and drives, which include modeling and identification ofac machines, control of synchronous generators for diesel-alternator groups,control of ac and direct current motors, and industry applications of the drives.

Documents

IEEE Xplore Download2353