Speed Estimation of Induction Motors with Rotor Slot Harmonics

5th International Scientific Conference on Energy and Climate Change

Alfred PJETRIYmer LUGAYmer LUGAMyrteza BRANESHIMyrteza BRANESHIAstrit BARDHIAstrit BARDHI

11-12 October 2012, Athens Greece

Rotor Speed Monitoring in Induction Motors

Conventional Techniques (Mechanical Speed Sensor )

Mathematical Model of IM (MRAS)

Rotor Slot Harmonics SENSORLESS

Conventional Techniques

D.C. Tachogenerators

A.C. Tachogenerators

Encoders

Resolvers

Increase the cost of control system

Gives errors because of mounting

Vibration

Ingress of contaminant

Reduces the system reliability

Sensorlees Techniques

Mathematical Model of IM (MRAS)

Rotor Slot Harmonics

Mathematical Model Sensorlees TechniquesDisadvantages

Nonlinearity of Magnetic Circuit

Rotor and Stator Resistance Variation with Temperature

Air Gap Flux of Induction Machines

1 1

5 1

7 1

1, 1

1, 1

1, 1

1, 1

ˆ, cos

ˆ cos 5

ˆ cos 7

ˆ cos

ˆ cos

ˆ cos

ˆ cos

s s

s s

r r m

r r m

t p t

p t

p t

Z p t

Z p t

Z p t s t

Z p t s t

1 1

5 1

7 1

1, 1

1, 1

1, 1

1, 1

ˆ, cos

ˆ cos 5

ˆ cos 7

ˆ cos

ˆ cos

ˆ cos

ˆ cos

s s

s s

r r m

r r m

t p t

p t

p t

Z p t

Z p t

Z p t s t

Z p t s t

Air Gap Flux of Induction Machines

1 1

5 1

7 1

1, 1

1, 1

1, 1

1, 1

ˆ, cos

ˆ cos 5

ˆ cos 7

ˆ cos

ˆ cos

ˆ cos

ˆ cos

s s

s s

r r m

r r m

t p t

p t

p t

Z p t

Z p t

Z p t s t

Z p t s t

Air Gap Flux of Induction Machines

1 1

5 1 7 1

11,

11,

11,

11,

ˆˆ cos

ˆ ˆcos 5 cos 7

ˆ+ cos

ˆ cos

ˆ cos

ˆ cos

sA

ss

ss

r mr

r mr

u U p tt

U p t U p t

U Z p t

U Z p t

U Z p t s t

U Z p t s t

E.m.f. induced in stator winding.

Analysis of Rotor Slot Harmonics.

1 1

1 1

2 1

1 2

1= 1 2cos 2( 1)

2 3

cos 1

11 2cos 2( 1)

2 3

cos 1

s sA sB sC

r rr

r rr h

r rr

r rr h

u u u u

Z Zk

p p

Z Zt f

p p

Z Zk

p p

Z Zt f

p p

1 1

1 1

2 1

1 2

1= 1 2cos 2( 1)

2 3

cos 1

11 2cos 2( 1)

2 3

cos 1

s sA sB sC

r rr

r rr h

r rr

r rr h

u u u u

Z Zk

p p

Z Zt f

p p

Z Zk

p p

Z Zt f

p p

Analysis of Rotor Slot Harmonics.

Signal Measurement for Rotor Slot HarmonicsusA

usB

usC

B C

O

A

O¢

R

R

R

Oscilloscope

us signal

Fundamental frequency of voltage signal su

1

11r

s

Z sf f

p

Induction Motor Rotor Speed in RPM

1

1

60 1s

r

ffn

Z f

Eksperimental Setup Stand

Experimental Results

Measured

1492 rpm

Estimated1490 rpm

Measured

1469 rpm

Estimated1466 rpm

Experimental Results

Measured

1430 rpm

Estimated1431 rpm

Experimental Results

COMPARISON OF MEASURED AND ESTIMATED SPEED

Nr.fs

[Hz]f1

[Hz]nestimated

[rpm]nmeasured

[rpm]Error[%]

1 1192 50 1490 1492 0.1342 1185 50 1480 1477 0.2033 1174 50 1466 1469 0.2034 1168 50 1458 1454 0.2755 1162 50 1450 1450 06 1155 50 1441 1442 0.0697 1147 50 1431 1430 0.0708 1137 50 1418 1418 09 1131 50 1410 1408 0.142

P[kW]

n[rpm]

U[V]

I[A]

cos f1

[HZ]

3 1430 380 6.9 0.82 50

INDUCTION MOTOR RATED DATA

Number of rotor slots Zr=46

CONCLUSIONS Does not need mechanical sensor

Maintenance free

It is not affected by environment

Do not depend of motor parameters

Simple and robust method

THANK YOU