Induction motors for crane applicationsR.M. Crowder and G.A. Smith

Indexing terms: Induction motors, Velocity control, Controllers, Cranes,Hoists

Abstract: The paper describes a control system for 4-quadrant operation of induction motors with character-istics suitable for crane hoist duty. The control system is based on a combination of stator-voltage controland rotor chopping. A thyristor stator-voltage regulator is used to provide a means of motor-speed closed-loop control. The regulator automatically reverses the phase rotation for plug braking or provides d.c. to thestator for injection braking as determined by load conditions. The rotor chopper operates with a duty cyclethat is a predetermined function of rotor speed. Analysis of the chopper action in the rotor is used to deter-mine the optimum function required to develop the maximum possible torque per stator ampere over theoperating speed range. Different control functions are found to be necessary for motoring and d.c.-injectionmodes of operation. Analysis of the system and experimental results are presented showing successful4-quadrant operation.

List of symbols

a = firing-angle delay|3 = turn-off angle\ = rotor-chopper duty cycle, on time/cycle timeT = cycle time of the rotor chopper0 = phase angle for machine winding

a; = supply frequency, rad/sLi = stator-leakage inductance referred to the rotorLi = rotor-leakage inductanceR = external-rotor resistance

R i = stator-winding resistance referred to the rotorR2 = rotor-winding resistanceVdc = rotor-chopper d.c. voltage

E = r.m.s. rotor voltage per phase at standstillIdc = rotor-chopper d.c. current

Irms = rotor-chopper r.m.s. currentMs = motor torque in synchronous watts

s = slipn = motor speed, rev/s

1 Introduction

The. hoist drive on a crane is difficult to realise as it mustoperate smoothly over a wide speed range to raise or lowerthe hook at controlled speeds irrespective of the load. Whenlifting, the drive must provide motoring torque with a rela-tively flat speed/torque characteristic to prevent excessivespeed change from heavy-load to light-hook conditions. Inaddition, when lowering, the drive torque can be motoringor braking depending upon whether the load torque exceedsthe mechanical friction of the hoist mechanism. A situationcan be found when, on releasing the mechanical brake, themotor must provide a motoring torque to exceed friction,but as soon as the load torque exceeds the running frictionthe motor must change to a braking mode. Thus 4-quadrantoperation of the motor is required.

2 Combined stator-rotor control system

A method for controlling a slip-ring induction motor toprovide high torque in all four quadrants of operation isshown in Fig. 1. Thyristor controls are applied to both thestator and rotor of the machine.

Paper T479P, first received 28th August and in revised from 7thOctober 1979Dr. Crowder is with Leicestershire Power Electronics Limited, Unit2, Manor Drive, Sileby, Leicestershire, England and Dr. Smith iswith the Department of Engineering, University of Leicester,Leicester, LEI 7RH, England.

194

A stator-voltage regulator controls the speed of theinduction motor to the demanded value by closed-loopcontrol. The regulator thyristors can be selected to provideboth forward and reverse rotation of the motor. Brakingtorque can be developed by either d.c. injection or phasereversal.

The stator-voltage regulator also operates within the limitof full-load rated current of the motor. Although the voltageregulator is capable of controlling the motor at any setspeed throughout the speed range the large stator currentsand power loss at high slip values would place a severerestriction on the drive.

3 -phase voltageregulator rotor choppern

Rfl v

chopperfiring

circuits

voltageregulator

firingcircuits

functiongenerator J

speeddemand

Fig. 1 Combined stator-rotor control system

quadrant 2 quadrant 1

d.c.injection plug, torque

X max

speed

quadrant 3 -torque quadrant A

Fig. 2 Four-quadrant characteristics

Quadrant 1 — MotoringQuadrant 2 — BrakingQuadrant 3 — MotoringQuadrant 4 — Braking

ELECTRIC POWER APPLICATIONS, DECEMBER 1979, Vol. 2, No. 6

0140-1327/79/060194 + 05 $01-50/0

Mode

Forward motoringReverse motoringD.C. braking

Table 1 : Thyristor operation

Thyristors operating

171

2 38 94 6

4108

559

66

To achieve a high value of torque at all speeds the rotorresistance must be changed to suit the desired operatingspeed. This is achieved by controlling the duty cycle X ofthe chopper in the rotor circuit as a predetermined functionof motor speed; the function being such that maximumpossible torque is available at all speeds within the limitationof rated motor current. The resultant 4-quadrant character-istics are shown in Fig. 2. It should be noted that the func-tion relating duty cycle X to speed is different in the motor-ing and braking regions. The characteristics show thatd.c.-injection braking will not give high braking torquebelow speed Nx, and so to operate at low speeds with anoverhauling load, plug braking, by phase reversal, must beused.

3 Steady-state analysis of the stator-regulator

A simplified diagram of the regulator and delta-wound statorof the induction motor is shown in Fig. 3. To fully describethe operation of the regulator the voltages across themachine windings have to be examined. There are twodistinct types of wave form present. Mode-1 operation occurswhen the current is discontinuous and only two thyristorsconduct at any time. Mode-2 operation occurs when thecurrent is continuous and there are either two or threethryistors conducting.

3.1 Conduction mode 1

The thyristors are fired in pairs with a delay angle a shownin Fig. 4 for thyristors 5 and 2 operating during the halfcycle sin (cot — 4ir/3). With an inductive load, current willcontinue to flow after reversal of the applied voltage andthe thyristors revert to their off state when the current iszero at angle j3.

The limit of mode 1 occurs when the waveform is nolonger discontinuous, i.e. when a = 0: — TT/3. At this point ais defined as a t . Note that the Hne4o4ine voltage willappear across winding 1 for conduction of thyristors 5and 2 during the half cycles of Fsin (cot — 4n/3), but only

Fig. 3 Stator-voltage regulator

half the line-to-line voltage will appear across winding 1during half cycles of V sin wf and V sin (cor — 2TT/3).

To calculate the voltage and current harmonics it isnecessary to determine the value of |3 for specific values ofa and phase angle 0. An analytic technique was used asdescribed by Shepherd1 which determines that

sin (fi — 0) — sin (a — 0) exp [— cot 0(0 — a)] = 0

Where 0 = tan~lcoL/R for the machine winding. Angle j3can be found by an iterative solution.

5-2 1-4 1-6thyristors fired

3 6 3 2 52

Fig. 5 Voltage across winding 1: mode 2 operation

3.2 Conduction mode 2

The voltage across winding 1 for this mode of operation isshown in Fig. 5. At some arbitrary instant X current flowsthrough thyristor 5 to the combination of winding 1, inparallel with the series connection of windings 3 and 2, andreturns to the supply via. thyristor 2. At instant Y thyristor4 is fired and, as three thyristors are conducting, full line-to-line voltage appears across all windings. As the voltage atthe cathode of thyristor 4 is more negative than that at thecathode of thyristor 2, the current through winding 2reduces and then increases in a reverse sense until it is equalto the current in winding 1. The current through thyristor 2will then be zero and it will turn off at point Z. Thus,thyristor 5 conducts over the range a. to j3 and, provided (3can be found for given values of a, then the waveformacross each winding can be fully specified.

The technique used to determine j3 was to assume a valuefor /3 which then permits the voltage waveform across wind-ings 1 and 2 to be represented, by regular piecewise func-tions.2 A numerical integration technique3 was then usedto calculate the harmonic coefficients in the Fourier seriesrepresenting the voltage across windings 1 and 2. Using asingle-phase equivalent circuit model for the inductionmotor the effective impedence of each winding was foundand used to calculate the currents in windings 1 and 2 usinga current harmonic summation method.4 If the twocurrents sum to zero then the current to thyristor 2 would

Fig. 4 Voltage across winding 1: mode 1 operation

18 19 20 21 22 23 24 25 26 27 2-8 2-9

o.radFig. 6 Relationship between firing angle a and turn-off angle 0o Experimental locked rotorx Calculated locked rotor

ELECTRIC POWER APPLICATIONS, DECEMBER 1979, Vol. 2, No. 6 195

be zero corresponding to turn off showing that the assumedvalue for j3 at the turn-off point was correct. If the currentsdo not sum to zero the procedure is repeated for differentvalues of 0 until a zero is achieved. Fig. 6 shows the com-parison of calculated and experimentally observed resultsfor j3 as a function of a for a locked-rotor condition.

3.3 Torque/speed characteristics

The voltage analysis gave information on the harmoniccontent of the applied voltage to the machine windings. Asthe contribution to motor torque decreased significantlyas the order of harmonic increased, only the fundamentalcomponent was considered for prediction of motor torque.

The motor operates under speed control by regulatingthe stator voltage but with an overriding control limitingthe stator current to a prescribed maximum value. To cal-culate the maximum torque available at a given slip, theappropriate winding parameters in the model are used todetermine the a/0 relationship, thus allowing calculation ofthe fundamental total r.m.s. voltage ratio. The total r.m.s.stator current can then be calculated and a value of a foundthat just maintains the current at the rated maximum value.The fundamental component of voltage for this value of ais then used to determine the motor torque from the single-phase model. In this way torque/speed characteristics canbe predicted allowing for harmonics and the current limitingaction of the control system.

4 Control of the induction motor by rotor-currentchopping

It is evident that the desired torque-speed characteristics,providing essentially constant torque at all speeds, cannotbe realised by the stator voltage regulator alone. The peakof the torque-speed characteristic can be moved to thedesired operating speed by changing the rotor resistance.This can be accomplished by connecting the rotor to a 3-phase bridge rectifier with resistance load and thyristorchopper, as shown in Fig. 7. A d.c. equivalent circuit isshown in Fig. 8.

From conventional theory the value for Vdc, allowing foroverlap is

where

Vdc = sE0

3SCJ

n (1)

thyristorchopper

Fig. 7 Rotor-chopper circuit

idc^rms 2 s R l 2R,

sE,,

Fig. 8 D.C.-equivalent circuit

196

Eo =

The output torque, in synchronous watts, is given by

rotor-circuit copper lossMs = (2)

VdcIdc-2sRlI7r

= \E0-3-f(Ll+L2)\Idc-2R1Prms (3)

The chopper current consists of an exponential rise and fallcorresponding to the 'on' and 'off states of the chopper(see Appendix 9). Detailed analysis of the rotor-choppercircuit5"7 can then be used to determine Idc and Irms foreach value of slip and substituted into eqn. 3 to give thepredicted torque. Theoretical and experimental results forthe torque-speed characteristic were taken and gave goodagreement.

4.1 External rotor resistance, R

The value of the external rotor resistance controls the shapeof the complete operating envelope of the motor. The dutycycle of the chopper will have operating limits Xj and X2

which will be a function of the chopper design. The chopperused had a minimum value Xj of 0-2, i.e. the chopper wason for a minimum of 20% of the operating cycle time of2-5 mS. Torque is a function of slip, external rotor resist-ance R, and duty cycle X with all other parameters heldconstant. The developed torque and motor current can bedetermined from eqns. 11 and 3 for a range of values of/?with X = X-i and s = 1. Thus a value for R was determinedto give the maximum possible standstill torque within therated value of motor current. Ideally the chopper shouldhave maximum value X2 of 1-0, i.e. effectively short circuit-ing the rotor terminals for operations near synchronousspeed. The chopper used had a value X2 of 0-8 which limitedhigh speed performance.

4.2 Func tion genera tor

The function generator is used to produce a relationshipbetween the speed of the motor and the duty cycle of thechopper such that the machine can, within its current-rating

09

0 8

07

06

05

03

02

0-1

usableoperatingrange

ai 02 03 04 05 0 6 07 0 8 09 10speed, p.u.

Fig. 9 Rotor-chopper control function

ELECTRIC POWER APPLICATIONS, DECEMBER 1979, Vol. 2, No. 6

limits, produce maximum possible torque at that speed.Using the previously determined external rotor resistance,values for the duty cycle X were calculated which just gaverated motor current at each of a range of operating speeds.The function relating duty cycle to speed is shown inFig. 9. During d.c.-injection braking, a low value of rotorresistance is required near standstill, but a high value ofresistance is needed at low slip speeds. The duty-cyclefunction during braking operation is, approximately, themotoring function inverted with respect to speed.

The functions were linearised and electronically gener-ated to control the duty cycle with the appropriate func-tion being automatically selected for motoring or brakingoperation.

speeddemand servo

forward

f

rectifier

Fig. 10 Block diagram of control system

5 Control system operation

A block diagram of the electronic controls required toprovide 4-quadrant operation of the system is shown in Fig.10. The pulse circuits to the stator regulator reduce thefiring-delay angle as the positive input to them increases.

When the system is operating in the forward (hoisting)mode, i.e. quadrant 1, the negative speed reference will begreater than the positive feedback from the tachogeneratorand the output of AI will be positive. A positive voltage atA1 selects the motoring function for the rotor chopper andthe forward motoring thyristors in the stator regulator.

If the negative reference is reduced slowly towards zero,the motor will slow down with the output from A1 stillbeing positive, but of a smaller value. If, however, thedemand signal is quickly reduced towards zero the outputof A\ will change polarity. A negative voltage at A\ selectsthe braking function for the rotor chopper and the d.c.braking thyristors in the stator regulator. The drive willthen be operating in quadrant 4. The electronic rectifierensures that the pulse circuits still see a positive input givinga phase advance and therefore increasing d.c. injection forincreasing speed error.

Consider the hoist drive lifting a load at a speed veryclose to standstill. If the demanded speed is reduced, themotoring torque will eventually become insufficient to holdthe load which will start falling. The change in tachogener-ator polarity will increase the output of A1 positively andthe system will be operating in the plug-braking mode, i.e.in quadrant 2. If the demand is further reduced and reversedthe load will fall at an increasing, but controlled, speed. Ata predetermined lowering speed, when plug braking becomesless effective, a detector changes the a.c. regulator to thed.c.-braking mode and selects the braking function for therotor chopper. Thus the drive is lowering with a brakingtorque in quadrant 2.

If it is required to lower a lightly loaded hook thatcannot overhaul the drive then the speed demand must bereversed causing amplifier^ 1 tochange polarity. The negativepolarity of A\ together with a reverse-speed demand isdetected, and changes the a.c. regulator to the reverse-motoring mode. The electronic rectifier ensures an increas-ing phase advance for increased speed demand and the loadis driven down in quadrant 3.

6 Experimental results

Laboratory tests were carried out with the drive systemoperating in all four quadrants. The torque-speed character-istics obtained are shown in Fig. 11. The curves show maxi-mum possible torque up to the limit of rated motor current.The limited range of duty cycle of the chopper can be seenparticularly as a loss of performance near synchronousspeed in quadrants 1 and 3. The changeover from plugbraking to d.c.-injection braking in quadrants 2 and 4 wasoptimised at speeds greater than anticipated because thesuperior plug-braking performance caused by the highstray-load losses of the test machine. Predicted performanceof the system agreed well with experimental results exceptin the regions where the stray load losses had a noticeableeffect.

quadrant 2plug braking

torque,Nm

:2000 }i0O0optimum changeover

\ between plug and"1

sdynamic braking _

quadrant 3-3

effect of stray quadrantiload loss

1000 2000 3000speed, rev per min

quadrant A

Fig. 11 Speed/torque characteristics of the 4-quadrant controller

The characteristics of the 4-quadrant controller are suit-able for a hoist drive and are close to the operating require-ments, although the speed range at which full-load torque isavailable is limited by the design of the rotor chopper.

A linearised model of the controller and motor was usedto predict the dynamic behaviour of the system to smallperturbations in speed demand. The predictions comparedvery favourably with experimental results but a moredetailed analysis would be necessary to include disconti-nuities and nonlinearities for operation through the fourquadrants.

7 Conclusions

A system for combining the control of a stator-voltage regu-lator and a rotor chopper for an induction motor has beenanalysed and experimental results show that stable4-quadrant operation suitable for hoist applications ispossible. The speed range of the practical system wasrestricted by the limited range of the rotor chopper usedin the tests. The speed range could be extended by improv-ing the chopper design. Plug braking torques on the testequipment were high due to stray losses; however, thetechnique of automatic changeover to d.c.-injection brakingwas implemented and found effective. The disadvantages of

ELECTRIC POWER APPLICATIONS, DECEMBER 1979, Vol. 2, No. 6 197

the system are the complexity of stator/rotor control andthe energy losses dissipated in the machine and in theexternal rotor resistance.

Before such a system could be implemented industrially,detailed consideration would be required into the safetyimplications of equipment failure. Application of brakesand removal of power would have to be automaticallyinitiated by monitoring appropriate parameters, i.e. speederror. The system, however, does provide a solution to the4-quadrant operation of induction motors for crane-hoistdrives.

in Fig. 7 in which, neglecting ripple, the instantaneousvoltage may be assumed to be sE0 • The current waveformat the rectifier output of the rotor chopper is shown inFig. 12. The current consists of two exponential curves.

During the rise period

(4)

8 References

J SHEPHERD, W.: 'Steady state analysis of the series resistanceinductance circuit controlled by silicon controlled rectifiers,IEEE Trans., 1965, IGA-2, pp. 259

2 GUPTA, S.C., BAYLESS, J.R., and PEIKARI, B.: 'Circuitanalysis with computer application to problem solving' (IntextEducational, 1972)

3 DORN,W.,andMcCRAKEN,D.: 'Numerical method with Fortrancase studies' (Wiley, 1972)

4 TAKEUCHI, T.J.: 'Theory of s.c.r. circuits and application tomotor control' (Tokyo Electrical Engineering College Press,1968)

5 SEN, P.C., and MA, K.H.: 'Rotor chopper control for inductionmotor drive: TRC strategy', IEEE Trans., 1975, IA-11, pp.43-49

6 WANI, N.S., and RAMAMOORTY, M.: 'Chopper controlled slip-ring induction motor', ibid., 1977, IECI-24, pp. 153-161

7 SEN, P.C., and MA, K.H.: 'Constant torque operation of induc-tion motors using chopper in rotor circuit', ibid., 1978, IA-14pp. 408-414

9 Appendix: Analysis of the rotor chopper

At the relatively high chopping rate, the analysis can bebased upon a typical instantaneous current path as shown

where

R3 = 2(&Rx +R2) and Tx =

When t = XT, i(t) = I2 hence

sE0 (sE0 \h = -^--\ — "A exp [-^X

K3 \ K3 I

During the fall period

_ sEQ ( SE0

where

R4 = R3+R and T2 =

(5)

(6)

sE0

-X)]

-exp [-T2(\ -X)T]

-fO = (l-\)T,i(t) = h, so

sE0 (sE0 \h = — ~ T T - ^ exp [~

exp

(7)

Substitution gives

|-\)T]\

R3

and

h

i ( t )A

sE0

1 - e x p [-

. on ^|^—off

1 - e x p [-[

1-exp [-T2(\ -\)T] exp [-(9)

The mean value Idc and the r.m.s. value / r m s can beobtained from

1 rXT 1 rd -1 J0 1 JKT

i2dt

and

A T

XT 1/2

(10)

(11)

Fig. 12 Rectified current waveform

The values of Idc and / r m s can then be used in eqn. 3 tocalculate the output torque for which the motor r.m.s.current will be given from eqn. 11.

198 ELECTRIC POWER APPLICATIONS, DECEMBER 1979, Vol. 2, No. 6