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