Direct Torque Control of Induction Motors with Stator Flux ...

ISSN 0005—1144ATKAAF 48(3—4), 85—98 (2007)

Dubravko Krušelj, Josip Ungarov, Vladimir Siladi

Direct Torque Control of Induction Motors with Stator FluxCorrection Applied to the Low-floor Tramcars

UDK 621.313.33:629.43IFAC 5.7.2

Original scientific paper

The paper presents a modified direct torque control (DTC) method of an induction motor, which is ap-plied in the main drive of the low-floor tramcars series TMK2200 manufactured by the Croatian consortiumCROTRAM — Končar d.d., TŽV Gredelj d.d. and Đuro Đaković d.d. The modification consists in the correc-tion of stator flux vector by means of appropriate stator current component. Simplicity of the basic DTC ismaintained because the only required machine parameter is stator resistance, yet the method enables stableoperation in the whole speed range (including standstill). In comparison with other DTC schemes, the pro-posed method is more reliable because the rotor parameters are not used and the rotor quantities are not cal-culated. The method has been fully verified through exploitation of vehicles, and the simulation results arecompared with the experiments on the laboratory model of the drive.

Key words: tramcar, induction motor, direct torque control, estimation

1 INTRODUCTION

The most important task of induction motor vec-tor control in tramcars is to ensure required trac-tion and braking characteristics. Also, it has to in-sure safe and reliable operation and comfortabledrive. Generally, tramcar drives have very wideregulation range regarding speed and load. For ex-ample, in tramcars series TMK2200 at maximumspeed of 70 km/h, motor speed is 250 % of ratedvalue (the vehicle has to be tested also at 10 %higher speed, i.e. 77 km/h) and in some operationregimes motor load is 230 % of rated one. The re-

quired traction and braking characteristics are pre-sented in Figures 1 and 2. Figure 1 shows dia-grams of the tractive effort (F) vs. vehicle speed(v) and figure 2 shows diagrams of the normalizedtorque of induction motor (M/Mn) vs. normalizedspeed of the motor (n/nn), where Mn and nn arerated torque and motor speed, respectively.

With regard to such a wide speed and torquerange in which induction motor operates, it is de-sirable to choose very simple and reliable vectorcontrol method which uses as less as possible ma-chine parameters. It is especially desirable to com-

AUTOMATIKA 48(2007) 3—4, 85—98 85

Fig. 1 Tractive effort diagram of tramcar series TMK2200Fig. 2 Traction and braking torques of induction motor in

tramcar series TMK2200

kruselj:clanak master.qxd 7.12.2007 7:00 Page 85

pletely avoid usage of rotor parameters becausethey are very machine temperature and load de-pendent and they can not be measured during ope-ration. Such a method is the DTC method that hasits basics in [1, 2, 3]. It has electromagnetic torqueand stator flux regulation loops, hysteresis regula-tors and it does not require any current regulatorsand related coordinate transformations. The torqueand stator flux are estimated only from measuredstator quantities and stator resistance parameter.

A method described in [1, 2] is so called directself-control (DSC). It is aimed firstly for highpower drives with very low switching frequency,for instance electric locomotives [4, 5, 6]. An in-teresting fact is that in these papers more complexregulation algorithm is used in the low speed range(from standstill up to approximately 20—30 % ratedspeed as is mentioned in [7]). This algorithm re-quires knowledge of magnetizing inductance, sta-tor leakage inductance, rotor leakage inductanceand rotor resistance, so, all machine parameters areused. The reason for this is minimum thyristorconduction interval (the voltage that is smallenough can not be supplied to the motor). In [6]is only mentioned, without any explanation, thatthe use of more complex model for stator flux esti-mation is necessary at low speeds. The DTC met-hod for drives which are not limited with switch-ing frequency is presented in [3]. On the basis de-scribed in this paper, after approximately 10 years,whole series of inverters are developed and com-mercialized ([8, 9, 10]). But the problem with sta-ble operation at low speeds still was not solved.In [3] is mentioned, to be quoted: »… integratorscause some drift and operation errors at low-ve-locity regions. The reason for this is that the oper-ation of integrators can not be done perfectly atzero velocity because of no induced electromotiveforce in the motor, so that control of Ψ1 (statorflux) might be unstable when R1 (stator resistance)deviates from the correct value. These problemsare negligible at relatively high velocities such asabove 2 Hz.« Therefore, the stator flux is at lowspeeds estimated by means of stator inductance,main inductance and stator and rotor currents. In[8] is emphasized that stator flux estimation insuch a way (with current correction feedback), tobe quoted: »… highly improves the stator flux esti-mate, especially at low speed.«, but it was not ex-plicitly mentioned up to which speed and frequen-cy this feedback should be used and does it or notdepend on motor load.

In this paper we present a modification of thedirect torque control method based on the statorflux correction. The method is extension of our

previous work presented in [11, 12]. The methodreveals all characteristics of the basic DTC methodbut it insures stable and reliable operation in thewhole speed region, including start-up from stand-still. The modification of the stator flux is madeby means of appropriate component of the statorcurrent. In this way, the rotor parameters are notused and the rotor quantities do not have to be cal-culated.

The paper is organised as follows: the secondsection presents the related work in the field, thethird section presents the basic DTC method andproposed modifications and the forth section givesresults of simulation and experimental testing.

2 RELATED WORK ON DIRECT TORQUE CONTROL

The basic DTC method introduced in [3] be-came the most researched vector control of induc-tion motors in the middle nineties of last century.There are a lot of papers which analyze some DTCaspects and most important of them are brieflyanalysed below.

Apart from the basic DTC principle, some deri-vations are summarized in [7]. A DTC methodwhich uses switching table, the DSC method, andthe DTC method with constant switching frequen-cy are described in detail. The method with switch-ing table is defined as a basic, and it is pointedout that many modifications of the basic DTCscheme are aimed at improving starting conditionsand very low speed operation, torque ripple reduc-tion, noise level attenuation, improving overloadcondition, increasing the number of available vol-tage vectors, switching frequency control and rotorflux control.

The DTC method and field-oriented vector con-trol (FOC) are compared in [13]. Simplicity of thebasic DTC scheme is emphasized because it doesnot use PI regulators, coordinate transformations,current regulators and special timers for PWM sig-nals. But the DTC presents some disadvantages:difficulty to control torque and stator flux at verylow speed, high current and torque ripples, vari-able switching behaviour, high noise level and lackof direct current control.

In [14] is described a DTC method which usescombination of so called voltage model and cur-rent model for stator flux estimation. Furthermore,an additional carrier signal (500 Hz, square wave)is delivered to torque comparator input. This in-jected signal improves the waveform of stator fluxand current and guarantees a robust start and ope-ration at zero speed region.

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Direct Torque Control of Induction Motors... D. Krušelj, J. Ungarov, V. Siladi


A method described in [15, 16] uses rotor fluxvector as a regulation quantity instead of statorflux vector. The rotor flux is estimated by meansof stator voltages and currents, all machine para-meters and difference between estimated and refe-rence rotor flux value. The proposed flux estima-tor uses complex gain which is function of theworking conditions. It is also pointed out that thestator resistance errors and current sensor offsetssignificantly degrade the drive behaviour in thelow speed range.

In order to minimize torque oscillations, torquechanges when zero voltage vector is supplied tothe motor are analyzed in [17]. Although the basicDTC scheme with hysteresis torque and flux com-parators is used, in the whole speed range theswitching frequency is maintained constant, andthe stator flux vector and the rotor flux vector haveto be estimated. So, all machine parameters mustbe known.

During the start-up and at low speeds the basicDTC method causes demagnetisation phenomena.A new algorithm for avoiding this phenomenon ispresented in [18]. Not only the torque, but also thestator flux is kept between hysteresis bands. Onlyextensive simulations prove effectiveness of theproposed method.

As a result of the uneven voltage vector contri-bution to the control of torque and stator flux in adirect torque controlled induction machine, the sta-tor flux magnitude drops particularly when ma-chine is running at low speed. A simple strategywhich rotates the basic DTC switching sector ispresented in [19]. Thereby, stator flux drops arereduced and also current waveform is improved.

In [20] is emphasized that the delay in feedbacksignals (inherent to every digital system) causesthat neither the torque error nor the stator fluxerror can be restricted within hysteresis bands.Decreasing the width of hysteresis bands can in-crease the switching frequency only to some level.The method proposed in the paper introduces adithering technique by superposing triangular wa-ves with high frequency and minute amplitude onthe torque and the flux error. As a result, the torqueripple, the stator flux ripple and the acoustic noiseare significantly reduced.

The influence of the torque and flux hysteresisbands to the switching frequency is analyzed in[21]. The switching frequency can be predictedfrom machine parameters, operating conditions andsampling time and it can be limited in order notto excess allowed value. With proposed method, it

is also possible to improve current harmonics ofinduction motor.

The duty-cycle control scheme is proposed in[22]. The method equals the average torque andthe lower torque hysteresis limit and reduces thevariation in switching frequency. Torque ripplesare also reduced, especially in the low speed re-gion.

The novel DTC technique which apply voltagevector not for the whole sampling period but onlyfor the time interval needed by the torque to reachthe upper (or lower) limit of the hysteresis band ispresented in [23]. By this approach, the controlsystem emulates the operation of a torque hystere-sis controller of analog type since the applicationtime of the inverter voltage vector is dictated bythe allowed torque excursion and not by the sam-pling period. The torque ripples are considerablyreduced by predicting the motor torque one sam-pling period ahead.

A new direct torque and flux control based onspace-vector modulation is introduced in [24]. Theproposed strategy reduces the acoustical noise, thetorque and the current ripples. The switching fre-quency is constant and controllable. But the met-hod is more complex than basic one, it uses fourPI regulators with different proportional and inte-gral gains (some of them are dependent on opera-tion conditions) and all machine parameters haveto be known. A similar method is proposed in [25].Instead of hysteresis regulators and switching tab-le, PI regulators are used for the torque and thestator flux control, and the switching frequency isconstant. The basic DTC method and its combina-tion with the space-vector modulation are com-pared in [26]. The combination also uses PI regu-lators.

Although a method in [27] is described as thedirect torque control with constant switching fre-quency, a lot of modification can be observed. Themethod does not use hysteresis regulators and thereference value of the stator flux vector is calcu-lated by means of the reference value of the torqueand the rotor flux. The method also utilizes coor-dinate transformation and space-vector modulationtechnique. It is emphasized that the inverter dead--time compensation highly improves the drive per-formance, especially at low speeds.

A sort of discrete space-vector modulation is in-troduced in [28]. Using a standard voltage-sourceinverter topology, the number of voltage vectorscan be increased by subdividing the cycle periodin three equal time intervals. In comparison with

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D. Krušelj, J. Ungarov, V. Siladi Direct Torque Control of Induction Motors...


the basic DTC scheme, the torque and current rip-ple are significantly reduced but the control algo-rithm is more complex.

The similar approach is used in [29]. Two novelswitching techniques are proposed: in the first, thenonzero and zero voltage vectors are applied to themotor, each of them half a sampling period, andin the second technique, the complex plane is divi-ded in 12 sectors and two nonzero voltage vectorsare used during the sampling period, also each halfa sampling period.

The method described in [30] is based on a vari-able duty cycle. The appropriate voltage vector isnot applied for the whole sampling period, and itsduration is calculated according to the machineelectromotive force.

In spite of torque hysteresis regulator, the useof PI regulator, two comparators and two triangu-lar waveform generators is proposed in [31]. Theproposed controller replaces the three-level hys-teresis comparator and is capable of reducing thetorque ripple and maintaining a constant switchingfrequency.

In the drives with the speed control, it is possi-ble to correct the stator flux with the speed error.The method, which is especially effective in thelow speed region, is presented in [32].

The switching characteristics of the DTC are as-sessed in [33]. The dependencies of the switchingfrequency on the supply angular frequency, invert-er dc link voltage and the sampling period are an-alyzed. All theoretical results are confirmed bysimulations and experiments on three different mo-tors.

3 PROPOSED DIRECT TORQUE CONTROL METHOD FOR TRAMCAR MAIN DRIVE

From all listed papers one can conclude whatare the main disadvantages of the basic DTC met-hod (the method with possible change of switch-ing state only in predefined time period and withthe use of adequate switching table):— the difficulties with the torque and the flux con-

trol in the low speed range are emphasized al-most in all listed papers, without the explicitexplanation what is the reason for such a be-haviour of the drive and from which speed theDTC method operates stable and reliable;

— the variable switching frequency increases thetorque pulsations, the current ripples and thenoise level, and the dependence of the switch-ing frequency is in some drives undesirable;

— sometimes is the fact that the inverter currentscannot be directly controlled very big disadvan-tage;

— for some drives it is undesirable that the aver-age value of the torque does not match the ref-erence value.

Which undesirable characteristics that are afore-mentioned have an important and significant influ-ence on the tramcar operation? The torque and theflux control in the low speed range are very im-portant because traffic conditions make the start-up from standstill practically the most frequenttramcar operation state. Regardless of the positionof the drive controller, and hence regardless of thereference value of the torque, a comfortable startwithout any oscillations and undesirable jerks is tobe achieved.

The variable switching frequency is not big dis-advantage. Namely, total losses that are dissipatedon the semiconductor module consist of switchingand conducting losses. Switching losses depend onswitching frequency and on currents and conduct-ing losses depend only on currents, i.e. on the load.So, it is possible to control the switching frequen-cy with the change of the hysteresis bands, in orderto decrease it in the low speed range (the maxi-mum torque references are bigger) and vice versaat higher speeds. From the point of noise, the vari-able switching frequency is actually desirable, be-cause the drive in that case reveals the characteri-stics of the white noise. If a DTC method withconstant switching frequency has to be applied,with regard to the IGBT components that are usedand with regard to the available space in the vehi-cle, the switching frequency should not exceed ap-proximately 2,5 kHz. Therefore, in all methods thatuse some kind of combination between the DTCand the space-vector modulation, the switching pe-riod has to be approximately 400 µs or more. Thisperiod is too long period for good and reliable con-trol (in the most drives that were analyzed in thelisted papers the sampling periods are up to 200 µs,so, the switching frequencies are 5 kHz or more).

A direct current control is desirable in order toavoid overcurrents during operation. However,with limitation of the maximum traction and brak-ing torques, avoidance of fast changes of statorflux reference value and its appropriate adjustmentto the speed and dc link voltage, it is possible tocontrol the currents indirectly. Therefore, the sta-ble operation in the whole speed region and at allconditions can be achieved without any overcur-rents. The mismatch between the average and thereference torque value practically does not have

88 AUTOMATIKA 48(2007) 3—4, 85—98



any influence, because the torque needed for ac-celeration or deceleration of the vehicle is set bythe driver.

Therefore, it can be concluded that the basicDTC is appropriate vector control method for thetramcar main drive and generally for the driveswith very wide regulation range regarding speedand load. However, the stable and reliable drive inthe low speed region has to be achieved. It is alsodesirable to avoid control schemes which use rotorquantities and rotor parameters (this would addi-tionally increase the unreliability and the uncer-tainty of the drive), and to avoid the use of diffe-rent control algorithms in the low and in the highspeed range (this approach is more complex andmakes the analysis of the drive during operationmore difficult).

3.1 Basic direct torque control method

In the DTC method an electromagnetic torqueand a stator flux vector are regulated quantities.The stator flux vector is defined with phase valu-es, [34, 35]:

(1)

Ψsi (i = 1, 2, 3) is the phase stator flux of themotor and can be calculated according to:

(2)

usi is motor phase voltage and is defined withdc link voltage, switching state applied in observedtime interval and with voltage drops on semicon-ductors. Rs is motor phase stator resistance and isiis motor phase stator current.

The developed electromagnetic torque (the tor-que in the air-gap) can be calculated from estima-ted fluxes and measured currents:

(3)

where p is the number of pole pairs of the motor.The torque and the stator flux can be regulated

by means of an appropriate voltage vector, i.e. withadequate switching state. It is possible to applytotal eight combination which result with six non--zero voltage vectors and with two zero voltagevectors (in this case the voltages of the motor aredetermined with the voltage drops on a semicon-ductors). The stator voltage vector is defined ana-logous to (1):

m p i ielm s s s s= −3 1 2 2 1( )Ψ Ψ

Ψsi si s siu R i t= −∫ ( )d .

r

r rΨ Ψ Ψ Ψ

Ψ Ψs s s

js

j

s s

e e

j

= + + =

= +1 2

23

3

43

π π

Re( ) Im( ).

(4)

and is presented in the complex plane for afore-mentioned combination in Figure 3. In figure is alsomarked a division of the complex plane into six sec-tors (sextants), 30º around every voltage vector.

The stator voltage vector is a discrete quantity.It can have only six discrete values with a moduledetermined mostly with the dc link voltage andone value at which the module is approximatelyzero. On the other hand, the stator flux vector is acontinuous quantity, whose module and positioncan be influenced by appropriate control of invert-er switching state. If the module of the stator fluxvector is at some speed constant, the currents andall fluxes in the machine will be nearly sinusoidal,and the torque change can be very fast due to apossible fast change of the angle between the sta-tor and rotor flux vector ([3]). In such a way, themachine torque is controlled directly and the valueand frequency of the fundamental component ofinverter output voltage are controlled indirectly.

A position of the stator flux vector has to becalculated in the DTC method, i.e. it has to be de-termined in which sector the stator flux vector lies.Furthermore, the hysteresis torque and flux regu-lators are used. If one designates τ as an output ofthe torque regulator and φ as an output of the fluxregulator, and if 1 means that the regulated quan-tities are bellow lower hysteresis boundary (the re-ference value minus hysteresis width) and 0 means

r r ru u u e u e u j us s s

js

js s= + + = +1 2

23

3

43

π π

Re( ) Im( )

AUTOMATIKA 48(2007) 3—4, 85—98 89


Fig. 3 Stator voltage vectors in complex plane


that the regulated quantities are above higher hy-steresis boundary (the reference value plus hyste-resis width), the control algorithm of inverterswitching state will be defined. This algorithm ispresented in Table 1, [3, 36]. The table is validonly for one direction regarding speed (counter--clockwise to the figure 3), and for the oppositespeed direction the switching state table should bedefined completely analogously.

are determined with dc link voltage and with volta-ge drops on semiconductors, are used for the sta-tor flux estimation. The dc link voltage is a measu-red quantity and, like in the stator currents, thereis a small difference between real value and corre-sponding value in the DSP. The voltage drops onsemiconductors have great influence on the driveoperation, especially in the low speed range (a zerovoltage vector is applied for a relatively long timeperiod and the motor voltages are defined directlywith the voltage drops on semiconductors). There-fore, they have to be taken into account for stableoperation. For the stator flux estimation, the statorcurrents and the stator flux resistance are alsoused. There are aforementioned errors in currents,and the value of resistance can be corrected thro-ugh winding temperature using thermal transdu-cers.

A consequence of the stator flux estimation inthe described way is a difference between real flu-xes in the machine and the fluxes calculated inDSP. The electromagnetic torque, the module andthe position of the stator flux vector are calculatedfrom estimated values of the stator flux. So, in thecase of mismatches of the fluxes, wrong inverterswitching state, i.e. wrong voltage vector could beapplied. The torque and stator flux reference val-ues would not be maintained and the drive couldbecome unstable. But, if there are torque oscilla-tions, and if the machine fluxes are not sinusoidaland have dc components (although there are notoscillations in estimated torque and stator fluxescalculated in DSP are sinusoidal), the machine cur-rents will not also be sinusoidal or will have dccomponents. The question is how to use informa-tion contained in the currents?

For this purpose, in Figure 4 the stator currentvector and stator flux vector are presented.An angle between them is designated with ∆ϕ and has positive values in a traction mode and nega-tive values in the braking mode. Namely, the de-veloped electromagnetic torque in (3) can be de-fined in terms of:

(5)

It is possible to divide the stator current vectorinto a component that is collinear with the sta-tor flux vector and a component that is perpen-dicular to it. is also the component which crea-tes the torque:

(6)m p ielm s sM= 23

r rΨ .

risM

risM

risΨ

m p ielm s s= 23

r rΨ sin( ).∆ϕ

ris

rΨs

90 AUTOMATIKA 48(2007) 3—4, 85—98


Table 1 Direct torque control switching state table

Sector 1 2 3 4 5 6

τ = 0φ = 0

φ = 1

τ = 1φ = 0

φ = 1r

U1r

U6r

U5r

U4r

U3r

U2

rU2

rU1

rU6

rU5

rU4

rU3

r rU U7 6,

r rU U0 5,

r rU U7 4,

r rU U0 3,

r rU U7 2,

r rU U0 1,

rU7

rU0

rU0

rU7

rU0

There are two non-zero voltage vectors in Table1, denoted with and . The only differencebetween them is that for the first voltage vector allall three upper IGBT switches in the inverter andfor the second all three lower switches are used.Two voltage vectors are also combined in the casewhen the torque decrease and the flux increase arerequired (τ = 0 and φ = 1). The non-zero voltagevector is used in the low speed region, [34], be-cause use of the zero voltage vector in a large timeperiod can cause a demagnetisation of the ma-chine, especially in breaking mode.

3.2 Modification of the basic direct torque control method

The basic idea of stator flux correction is to usestator currents in an appropriate manner. Namely,both the stator currents and the stator fluxes areconsequences of the supplied voltages. They dis-tinguish in the fact that the currents are measuredand the fluxes are estimated quantities. The diffe-rences between motor currents and their correspon-ding values in DSP are small due to current trans-ducers errors, a low-pass filtering, which is neces-sary, and due to errors in A/D conversion. On theother hand, the differences between the real fluxesin the machine and the corresponding estimatedvalues in the DSP could be large. The main rea-son for this is a calculation of the phase fluxes ac-cording to (2) with some numerical methods andwith an integration time typically couple of tensmicroseconds or more, and the use of integer arith-metics. Furthermore, the machine voltages, which

rU0

rU1


Although the is stator current component, itcan be analyzed as a vector with its real and imagi-nary part:

(7)

Because the vectors and are collinear, areal part of the stator flux vector and a currentcomponent isΨa, and an imaginary part of and a current component isΨa, in the case of correctcontrol and stable drive operation, must be sinu-soidal and must be in phase. This fact is used forthe stator flux correction. It is enough to comparethe instantaneous values of the real and imaginaryparts of the vectors and (with adequatescaling) and the difference (also with scaling) toadd to the fluxes calculated according to (2):

(8)

(9)

ki is scalar with a dimension of an inductance,is the corrected stator flux vector, and kΨ is

scalar. Then, by means of the vector compo-nents, the torque is calculated according to (3) and the switching states are determined according tothe switching table 1.

Although an estimated angle , which vector closes with the real axis (figure 4), is used for cal-culation of the real and imaginary component ofthe vector , and which could be different fromthe real machine angle, the use of the stator cur-rent vector for calculation of an angle ∆ϕ and amodule of the vector , in some way gives infor-

risΨ

risΨ

α rΨ s

rΨsc

rΨsc

∆

∆

r r r

r r r

Ψ Ψ

Ψ Ψ Ψ

Ψ

Ψ

s i s s

sc s s

k i

k

= −

= + .

rΨs

risΨ

rΨs

rΨs

rΨs

risΨ

ri i jis s a s bΨ Ψ Ψ= + .

risΨ

mation about the drive contained in the stator cur-rents. Any stator currents distortion and deviationfrom a sinusoidal waveform will result with non-collinearity of real vectors and , accordingto (8) an adequate flux correction will be done, andthe real and imaginary components of vectorsand will force to be in phase. In the case of asinusoidal supply, the vector calculated ac-cording to (8) would be a vector collinear with thestator flux vector , and the corrected stator fluxvector calculated according to (9), would diffe-rentiate from the vector only regarding modu-les. But, with correct choosing of the scalars ki and kΨ , it is possible to obtain that the difference be-tween modules of the vectors and is verysmall, and that the drive operation is completelystable in the whole speed range and at all condi-tions.

4 SIMULATION AND EXPERIMENTAL RESULTS

4.1 Laboratory model of tramcar drive

The drive assembled in the laboratory consistsof components that are in tramcars: IGBT (1200A, 1700 V) inverter in the three phase bridge con-nection and two induction motor which are con-nected in parallel. The data and parameters of trac-tion motor are given in Table 2:

rΨs

rΨsc

rΨs

∆r

Ψs

risΨ

rΨs

rΨs

risΨ

rΨs

rΨsc

AUTOMATIKA 48(2007) 3—4, 85—98 91


Fig. 4 Stator current vector and stator flux vector in complex plane

Data Parameters

Type V6AOJ Stator 0,044 Ω205-04 resistance

Connection star Stator leakage 0,263 mH

Power 65 kW inductance

Voltage 320 V Magnetizing 8,90 mHCurrent 150 A inductance

Frequency 58 Hz Rotor 0,025 Ωresistance

Pole pairs 2 Rotor leakage 0,350 mH

Speed 1705 min−1 inductance

Table 2 Data and parameters of tramcar induction motor

The dc link voltage in experiments was equalto the rated value of tramcar supply network in thecity of Zagreb (600 V). A load-machine is dc mo-tor that enables setting of operation steady-stateswith regard to motor speed and load and is alsoused as a high inertia for dynamic tests. The con-


trol algorithm is executed with the digital signalprocessor (DSP) TMS320F240 and the samplingtime is 80 µs. The hysteresis bands are settled insuch a way that the switching frequency is in rangefrom 1,5 kHz to 2,5 kHz range.

In simulation model both voltage drops on semi-conductors and inverter dead-time is taken into ac-count. The motor is described in rotor flux coordi-nate system, and is adapted to a voltage source in-verter, [35, 36]. For numerical calculation of dif-ferential equations an integration time constant is100 ns. On the other hand, for calculation of thestator fluxes according to (2), the torque accord-ing to (3) and for determination of the switchingstate, the 80 µs time period is used. Integer arith-metics, low-pass filtering of the stator currents anddc link voltage and their A/D conversion are alsoused.

4.2 Simulation and experimental results

For a presentation of measured results, the datawhich are in the DSP software and are availablethrough D/A outputs are used. The measured quan-tities are: the estimated torque, the inverter cur-rent, the estimated phase stator flux and the cur-rent component of the vector which is in thephase with the measured flux (according to Figure4). The operation and stability of the drive are alsoadditionally controlled with direct measurement ofthe torque on the shaft (the torque transducer wasused) and with the speed measurement (combina-tion of a speed sensor and a toothed wheel wasused).

The above described correction method is first-ly verified in steady-state for rated operating point(motor speed 1705 min−1 and an average value ofthe torque for each motor 364 Nm). Figures 5 and6 present simulation and experimental results. Thescalar ki in (8) was 2 mH (module of product for rated values was about 30 % of vector modu-le), and kΨ in (9) was 7 ⋅10−4. Therefore, the diffe-rence in the vector module and its correctedquantity is practically negligible. These are al-so values of the scalars ki and kΨ that are used inthe whole tramcar operation range (Figure 2).

Since the basic DTC method has most difficul-ties in the low speed region, the next experimentwas done at 5 % of rated speed, also with rated

rΨsc

rΨs

rΨs

k ii srΨ

risΨ

load. Figures 7 and 8 show simulation and experi-mental results with the same scalars ki and kΨ likein the experiment at rated steady-state point. It isevident from the pictures that the currents are sinu-soidal and that the drive operates stable.

An influence of the correction method is ana-lyzed at the same operating point (5 % of ratedspeed and rated load), but with amounts of scalarski and kΨ which are 10 times smaller then in theprevious experiment. Figures 9 and 10 present re-sults. Even though there are no oscillations in thetorque, and the estimated stator flux is sinusoidal,it can be noted that the inverter current has dccomponent (a duration of plus and minus half-pe-riod are uneven) and, like the current componentof vector in phase with measured flux, devia-tes from sinusoidal waveform. Consequently, therewere oscillations in motor torque (the torque onthe shaft). It is interesting to point out that at thisspeed the drive operation without correction prac-tically was not possible, i.e. the basic DTC methodcould not be applied. Namely, the torque oscilla-tions were very large, the motor currents werestrongly distorted and the steady-state operationwas impossible.

For verification of the applied method, a start-upfrom standstill was done. A dc load machine wasused only as a high inertia, and therefore, it isachieved that time duration of the starting wassimilar to starting duration on the vehicle. Afterinitial dc magnetisation, approximately maximumtorque is set. The reference value of the torque ischanged with predefined change of rate in orderto limit the drive jerk.

Figure 11 presents experimental results withamounts of scalars ki i kΨ that are adjusted on thevehicle, and Figure 12 presents results with thevalues which are 10 times smaller. In both casesthere are no oscillations in the estimated torques,and the estimated fluxes are sinusoidal. But, in theexperiment depicted in Figure 11, there are no os-cillations in the torque on the shaft and the cur-rents are completely sinusoidal. However, in Fi-gure 12 there is again a deviation of the currentsfrom sinusoidal waveform and their strong distor-tion, accompanied with significant oscillations inthe torque on the shaft and in the speed. The start--up of the vehicle in such a way would be veryuncomfortable with high jerks; actually, it wouldbe completely unacceptable.

risΨ

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AUTOMATIKA 48(2007) 3—4, 85—98 93


Fig. 5 Estimated torque and inverter current at rated speed and at rated load; use of correction method with ki and kΨ like on the vehicle

Fig. 6 Estimated stator flux and component of at rated speed and rated load; use of correction method with ki and kΨ like on the vehicle

risΨ

kruselj:clanak master.qxd 7.12.2007 7:00 3

94 AUTOMATIKA 48(2007) 3—4, 85—98


Fig. 7 Estimated torque and inverter current at 5 % of rated speed and rated load; use of correction method with ki and kΨ like on the vehicle

Fig. 8 Estimated stator flux and component of at 5 % of rated speed and rated load; useof correction method with ki and kΨ like on the vehicle

risΨ


AUTOMATIKA 48(2007) 3—4, 85—98 95


Fig. 9 Estimated torque and inverter current at 5 % of rated speed and rated load; use of cor-rection method with ki and kΨ 10 times smaller than on the vehicle

Fig. 10 Estimated stator flux and component of at 5 % of rated speed and rated load;use of correction method with ki and kΨ 10 times smaller than on the vehicle

risΨ


96 AUTOMATIKA 48(2007) 3—4, 85—98


Fig. 11 Estimated torque, inverter current, estimated stator flux and component of ;start-up of drive; use of correction method with ki and kΨ like on the vehicle; experimental

results

risΨ

Fig. 12 Estimated torque, inverter current, estimated stator flux and component of ; start--up of drive; use of correction method with ki and kΨ 10 times smaller than on the vehicle;

experimental results

risΨ


5 CONCLUSION

One of the main tramcar drive characteristic isvery wide regulation range regarding speed andtorque, as well as often starting from standstill.Vector control of tramcar induction motor has tofulfil all regulation requests and insure stable andreliable operation. In the low-floor tramcars seriesTMK2200 a DTC method was applied. The met-hod is very suitable for tramcar drives because ituses only stator parameters and stator quantities.But, the basic DTC method can not be used in thelow speed region (a stable drive operation withoutsome modification can not be achieved withoutsome modification). Therefore, the basic methodis modified with the correction of the stator fluxvector by means of an appropriate stator currentcomponent. With the correction, the oscillations inthe torque and current ripples at low speeds areeliminated, and the comfortable start-up is achie-ved without deterioration of any basic DTC cha-racteristics. In such a way, an use of rotor param-eters is avoid, there is no need for calculation ofrotor quantities, and the only one control algorithmis used in the whole speed range. The drive opera-tion is, consequently, simpler and more reliable.

The method is verified with the experiments onthe laboratory model of the drive and during vehi-cles exploitation (some vehicles are running morethan two years).

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AUTOMATIKA 48(2007) 3—4, 85—98 97



Izravno upravljanje momentom asinkronih motora s korekcijom statorskog toka primijenjeno naniskopodnim tramvajima. U članku je prezentirana modificirana metoda izravnog upravljanja momentomasinkronih motora, primijenjena u glavnom pogonu niskopodnih tramvaja serije TMK2200 koje proizvodihrvatski konzorcij CROTRAM — Končar d.d., TŽV Gredelj d.d. i Đuro Đaković d.d. Modifikacija se sastoji ukorekciji vektora statorskog toka pomoću odgovarajuće komponente statorske struje. Jednostavnost izvornemetode je zadržana budući da je jedini parametar stroja kojeg je potrebno poznavati otpor statorskog namota,s time da je osiguran stabilan rad u čitavom području brzina vrtnje uključujući i mirovanje. U usporedbi s osta-lim varijantama izravnog upravljanja momentom, predložena metoda je pouzdanija jer se ne koriste rotorskiparametri niti se računaju rotorske veličine. Metoda je u potpunosti provjerena tijekom eksploatacije vozila, asimulacijski rezultati su usporeeni s eksperimentalnima na modelu pogona u laboratoriju.

Klju~ne rije~i: tramvaj, asinkroni motor, izravno upravljanje momentom, estimacija

AUTHOR’S ADDRESS

Dubravko KrušeljJosip UngarovVladimir SiladiKončar — Electrical Engineering Institute, Inc.Fallerovo šetalište 22, pp 202, HR-10 002 Zagreb, Croatiae-mail: [email protected]

[email protected]@koncar-institut.hr

Received: 2007-09-12

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