Computing and Measuring Dynamic Characteristics of the Induction Motor

7/26/2019 Computing and Measuring Dynamic Characteristics of the Induction Motor

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Abstract

-- This paper contains computing and measuringresults of start-up, step load, braking and reversingperformance of the induction motor. Computing of dynamicstates was carried out using idealized mathematical model ofthe induction motor. In order to obtain comparative results,measuring of the dynamic characteristics of the inductionmotor was carried out with U/f power converter. The load ofthe induction motor is realized with eddy current brake. Theresults of computing and measuring are presented andcompared.

Index Terms -- dynamic characteristics, induction motor,reversing, step load, start-up, U/f power converter

NOMENCLATURE

Lm – mutual inductance (stator/rotor) L s – stator windings inductance Lr – rotor windings inductance R s – stator windings resistance R s – rotor windings resistanceT L – torque load

J – torque inertiaV – voltage

f – frequency p – pair pole

n – speed s – slipω – electrical angular speedω m – mechanical angular speed

Ψ – flux linkageσ – total dissipation factor

I. I NTRODUCTION

Induction motors are the most frequently used type ofmotor today, and they are the work backbone of the industry.In comparison to other types of motors they have manyadvantages. The most significant ones are simple design,

which leads to less required maintenance, and low cost of production. Electrical drives with inverter supplied inductionmotor require more detailed research. Drives with inverterfed squirrel cage motors are capable of achieving wide speedranges, but nonsinusoidal voltage from the inverter leads tosome undesirable consequences: higher losses in copper andiron, longer duration of transient states, oscillations of theelectromagnetic torque on the shaft, and increased noise.

A. Bosović is with Public Enterprise Elektroprivreda of Bosnia and

Herzegovina, Sarajevo, Bosna and Herzegovina (e-mail:[email protected])

Š. Mašić and S. Smaka are with University of Sarajevo, Faculty ofElectrical Engineering, 71000 Sarajevo, Bosnia and Herzegovina (e-mail:[email protected] and [email protected])

II. MATHEMATICAL MODEL OF THE INDUCTION MOTOR

Mathematical model of the induction motor for dynamiccharacteristics calculation is given in the "dq" coordinates,which rotate with the angular speed ω k [1]. Themathematical model is based upon the assumptions: B-Hcurve of the iron is linear, the air gap is slotless and

bilaterally cylindrical, the winding distribution in the air gapis continuous and sinusoidal, and iron losses are neglected.

In the form suitable for numerical integration, it consistsof the following equations:

sd s s m

d sd rd k sd s s r

d R R L

V dt L L L

Ψ Ψ Ψ ω Ψ

σ σ = − − +

sq s s mq sq rq k sq

s s r

d R R LV

dt L L L

Ψ Ψ Ψ ω Ψ

σ σ = − + −

( )rd r mr rd sd k m rq

r s r

d R L R p

dt L L L

Ψ Ψ Ψ ω ω Ψ

σ σ = − + − −

( )rq r mr

rq sq k m rd r s r

d R L R p

dt L L L

Ψ Ψ Ψ ω ω Ψ

σ σ = − + + −

( )3 1

2m m L

sq rd sd rq s r

d L T p

dt J L L J

ω Ψ Ψ Ψ Ψ

σ = − −

V d and V q components for three-phase sinusoidal voltagesupplied to the stator of the motor are:

( ) ( )cos cos 2d max k max k V V t V f t ω ω π ω = − = −

( ) ( )sin sin 2q max k max k V V t V f t ω ω π ω = − = −

Equivalent circuit of the induction motor is shown on Fig. 1.

Fig. 1. Equivalent circuit of induction motor

The parameters of the equivalent circuit of the inductionmotor are obtained from no load and blocked rotor tests. Theinductances L s and Lr in mathematical model are:

= + s m s L L Lσ

= +r m r L L Lσ

The rotor quantities are referred on the stator side.

Computing and Measuring DynamicCharacteristics of the Induction Motor

A. Bosović, Š. Mašić, S. Smaka



III. DYNAMIC CHARACTERISTICS - COMPUTING

The calculations of the dynamic characteristics of theinduction motor were made with the mathematical model in"dq" coordinates, rotating with the angular speed ω k = 0 forthree-phase sinusoidal voltage.

Stator voltage components V d and V q are:

( )cos 2d maxV V f t π =

( )sin 2q maxV V f t π =

and they are calculated at each integration step. Numerical integration of differential equations of the

mathematical model was made by Runge-Kutta IV ordermethod, with constant integration step length.

The calculation of dynamic performance of the inductionmotor was made with the full load torque and rotor inertia of

both the motor and the eddy current brake. The simulation of power converter in mathematical model was carried out verysimply through V / f = const ratio.

Start-up

Speed, torque and stator current during start-up of themotor, obtained by mathematical model for V / f =110/25 and220/50, are given on Fig. 2 to Fig. 5 respectively.

0 1 2 3 4 5Time (s)

0

400

800

1200

1600

S p e e d ( r p m )

50 Hz

25 Hz

Fig. 2. Speed during start-up of the motor

0 1 2 3 4 5Time (s)

-40

0

40

80

120

T o r q u e ( N m ) 50 Hz25 Hz

Fig. 3. Torque during start-up of the motor

0 1 2 3 4 5Time (s)

0

10

20

30

40

50

C u r r e n t ( A )

50 Hz

25 Hz

Fig. 4. Stator current during start-up of the motor

0 400 800 1200 1600Speed (rpm)

-40

0

40

80

120

T o r q u e ( N m )

25 Hz50 Hz

Fig. 5. Torque-speed characteristic during start-up of the motor

B. Step load

Step load transient was carried out by sudden change ofload torque from no load torque to full (nominal) torque ofthe motor, in the moment when motor speed was constant.Fig. 6 to Fig. 8 shows speed, torque and RMS value of stator

phase current during step load for V / f =110/25 and 220/50.

0 2 4 6 8 10Time (s)

0

400

800

1200

1600

S p e e d ( r p m )

25 Hz

50 Hz

Fig. 6. Speed during step load

0 2 4 6 8 10Time (s)

-40

0

40

80

120

160

T o r q u e ( N m )

25 Hz

50 Hz

Fig. 7. Torque during step load

0 2 4 6 8 10Time (s)

0

10

20

30

40

50

C u r r e n t ( A )

25 Hz

50 Hz

Fig. 8. Stator current during step load



C. Dynamic braking and reversing

Calculation of the dynamic braking and reversingtransient was done by simulating by exchange of terminalsof two stator phase during full load torque.

Speed, torque and stator current during dynamic brakingand reversing are given on Fig. 9 to Fig. 11.

0 4 8 12 16 20Time (s)

-2000

-1000

0

1000

2000

S p e e d ( r e v / m i n ) 25 Hz

50 Hz

Fig. 9. Speed during braking and reversing

0 4 8 12 16 20

Time (s)

-80

-40

0

40

80

120

160

T o r q u e ( N m )

25 Hz

50 Hz

Fig. 10. Torque during braking and reversing

0 4 8 12 16 20Time (s)

0

10

20

30

40

50

S t a t o r c u r r e n t ( A )

25 Hz

50 Hz

Fig. 11. Stator current during braking and reversing

IV. DYNAMIC CHARACTERISTICS - MEASURING

Dynamic performance of the 4 kW induction motor wastested. The motor was controlled by ABB power converter(model ACS-800). The communication with converter wasrealized via PCMCIA card, with optical cable as theconnection between computer and power converter.Computer program Drive Window (ver. 2.0), developed byABB, enabled simple and effective adjustment of the motor

parameters and graph drawing of the motor variables.For three dynamic states mentioned, three variables weremonitored and plotted on the graphs: speed of the motorshaft, electromagnetic torque, and RMS value of stator phasecurrent.

All three mentioned variables are plotted on all of thegraphs, and they reached their stationary values inasymptotic transition.

Unit for speed used was revolutions per minute (rpm),electromagnetic torque was calculated in percentages ofnominal torque (%), while the current was measured in amps(A). The load of the motor was given by eddy current brake.Since some of the variables on the graphs are scaled, their

real values are shown on the vertical graph cursor, which is plotted on every graph. Signs used for all the graphs are:• [1] Speed;• [2] RMS stator phase current;• [3] Electromagnetic torque.

The first dynamic state monitored is start-up of the motor.Reference speed given was 1428 rpm, with the full torqueload on the motor shaft. Value of the electromagnetic torquein stationary state, which is required to compensate full loadtorque, is 100 %. The current needed for the motor to

produce that torque is 9,12 A.Fig. 12 shows all three variables, during start-up of the

motor with full load, plotted on the graphs with scalingfactor 1. Limits for torque and stator current, imposed by

power converter, were respectively 300 % of nominal torqueand 24 A.

Fig. 12. Measured speed, torque and stator current during start-up

As we can see it is inconvenient to plot all of these threevariables on the same graph with scaling factor 1, so for thisresearch, variables were plotted on the graphs with differentscaling factors. Scaled characteristics during start-up areshown on Fig 13. Only speed is plotted with the scalingfactor 1, while motor torque and stator current are plotted

with scaling factors of 55 and 2 respectively.

Fig. 13. Measured speed, torque and stator current during start up(scaled current and torque; scaled factor 55 and 2 respectively)

0 1 0 .0 2 0 .0 3 0 . 00

3 0 0

6 0 0

9 0 0

1 2 0 0

1 5 0 0

1 4 2 8 . 1 [ 1 ]

9 . 1 2 4 8 6 [ 2 ] 1 0 0 . 6 0 1 [ 3 ]

Time (s)

Monitor

0 1 0 .0 2 0 .0 3 0 . 00

3 0 0

6 0 0

9 0 0

1 2 0 0

1 5 0 0

1 4 2 7 . 5 2 [ 1 ]

5 0 8 . 7 7 5 [ 2 ]

2 0 2 . 0 8 9 [ 3 ]

Time (s)

Monitor



Fig. 14 shows scaled characteristics during step load.

Fig. 14. Measured speed, torque and stator current during step load(scaled current and torque; scaled factor 55 and 2 respectively)

It can be noticed that closed-loop control implemented in power converter enable the same speed of rotation as beforestep load.

Counter-current braking was the third dynamic statemonitored. Fig. 15 shows scaled characteristics for brakingand reversing dynamic states.

Fig. 15. Speed, torque and stator current during braking and reversing(scaled current and torque; scaled factor 55 and 2 respectively)

It can be notice that motor produced negative torque tostop the motor shaft from spinning. Counter-current brakingstopped the motor in the shortest time period possible. Inquasistatic state at the end of reversing, torque has almostthe same value as the torque at the end of the start-up. It isequal to full torque of the motor (100 %) at the speed of

1430 rpm.Comparison of the results between computed andmeasured speed was made for start-up transient and aregiven and shown on Fig. 16.

0 4 8 12Time (s)

0

400

800

1200

1600

S p e e d ( r p m )

computed

measured

Fig. 16. Compared results for speed between computation and measurement

Experimental setup with tested motor, power converter,eddy current brake with control unit, and PC are shown onFig. 17.

Fig. 17. Experimental setup

V. CONCLUSIONS

A procedure for computing and measuring the dynamiccharacteristics of the induction motor has been presented.The computed method was based on idealized mathematicalmodel in stationary "dq" system coordinates. Start-up, stepload, dynamic braking and reversing states were simulatedfor tested motor for various ratios between supply voltageand frequency.

Differences between computed and measuredcharacteristics are longer transient time in dynamic states.

These are caused by limits on torque and phase current of themotor imposed by U/f power converter.

The mathematical model represents the dynamic states ofthe induction motor with good accuracy.

VI. APPENDIX

A. The induction motor used for this research was three- phase slip ring induction motor with nominal data:4 kW; 1410 rpm; Δ / Y; 220/380 V; 50 Hz; 15,2/8,8 A;cosϕ = 0,83; inertia moment: 0,14 kgm2.

Parameters of equivalent circuit:R 1 = 1,025 Ω; R 2 = 1,78 Ω; X1σ = 2,817 Ω; X2σ = 2,817 Ω;

Xm = 36,77 Ω; R Fe = 460 Ω.

B. ABB power converter: Type: ACS-800Input: 3~ 380 - 415 V ± 10% V; 4,7 A; 48 - 63 Hz.Output: 3~ 0-Uinput; 5,1 A; 0-300 Hz.

C. Eddy current brake unit: Type: LPS 800 LKMax. brake moment: 800 Nm; max. speed: 4500 rpm;inertia moment: 0,5 kgm2.

VII. ACKNOWLEDGMENT

The authors would like to thank F. Mehmedović fromABB Melbourne, Australia, and ABB Oy, Finland, for helpwith preparing experimental setup.

0 1 0 . 0 2 0 .0 3 0 .00

3 0 0

6 0 0

9 0 0

1 2 0 0

1 5 0 0 1 4 3 0 . 0 5 [ 1 ]

5 2 5 . 3 1 7 [ 2 ]

2 1 5 . 7 2 6 [ 3 ]

Time (s)

Monitor

10.0 20.0 30.0

-1600

-800

0

80 0

1600

-1426.02 [1]

546.643 [2]

-216.474 [3]Time (s)

Monitor



VIII. R EFERENCES [1] Chee-Mun Ong, Dynamic Simulation of Electric Machinery, Prentice

Hall, 1998.[2] A. Bosović , " Dynamic performance of induction motor supplied from

U/f converter ABB-ACS 800" – Diploma Dissertation, Faculty ofElectrical Engineering Sarajevo, 2009.

[3] Drive Window 2 User's manual , ABB DriveWare, 2006.[4] Technical Guide No.1 Direct Torque Control, ABB, 1999.[5] ABB industrial drives ACS 800 catalog, drive modules, 0.55 to 2240

kW , ABB, 20

[6] Firmware manual ACS 800 Standard Application Program 7.x, ABB2003.

[7] Hardware Manual ACS 800-01 drives (0.55 to 110 kW), ABB, 2002.

IX. BIOGRAPHIES Adnan Bosović was born in Sarajevo in 1987, where he finished his primaryand secondary education. He was awarded both times with the title of the beststudent in the generation. He graduated at the University of Sarajevo, Facultyof Electrical Engineering, and Department for Electrical Power Engineering in2009 with the highest average score of grades. He is currently working for Mr.Sci. diploma at the same department.

From 2010 he is an employee of the Public Enterprise Elektroprivreda ofBosnia and Herzegovina, Department for Strategic Development.

Šemsudin Mašić graduated from University of Sarajevo 1974, receivedM.S. degree from University of Zagreb 1982 and Ph.D. degree fromUniversity of Sarajevo 1992. After completing his graduate studies, he became an Assistant in Department of Power Engineering at the Faculty ofElectrical Engineering, University of Sarajevo. Since 1982 he is ResearchFellow at the Institute for Automatic and Computer Science and at theElectrical Power Institute by Energoinvest Company, Sarajevo. His researchinterests are in the areas of electric machines and drives, especiallynumerical analysis of magnetic fields, mathematical models and measuringcharacteristics of electric machines and electrical drives in traffic systems.

He is now Full Professor, Head of Department of Electrical Machines andDrives. Dr Mašić is senior member of IEEE. Currently, he is the Chairmanof the A1 Study Committee of Cigré section of Bosnia and Herzegovina.

Senad Smaka was born on 1969 in Sarajevo, Bosnia and Herzegovina. Hegraduated from the Faculty of Electrical Engineering at University ofSarajevo in 1996. From 2000 he works as teaching assistant on Departmentof Power Engineering of Faculty of Electrical Engineering in Sarajevo. Hereceived M.S. degree in electrical engineering from the Faculty of ElectricalEngineering and Computing at University of Zagreb in 2004. He iscurrently working toward the Ph.D. degree in electrical engineering. Hisresearch interests include HEVs, modeling and numerical analysis ofelectrical machines and drives. He is member of IEEE.

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Computing and Measuring Dynamic Characteristics of the Induction Motor