This document discusses three-phase induction motors. It begins by listing advantages such as being widely used, cheap, easy to maintain, and having fewer mechanical parts than other machines. Problems discussed include grounding faults causing insulation breakdown, isolation failures between coils, and broken rotor bars affecting torque. Methods of motor maintenance like corrective, preventive, and predictive are introduced. Parameter estimation techniques involving time-domain, frequency-domain, using motor construction data, or based on steady-state models are summarized. Finally, recursive least squares estimation is described as a method to determine electrical and mechanical parameters in real-time using motor voltage, current and speed measurements.

2. 1-Three phase induction motor.
Advantages Problems
 It is the center of majority of
the industrial production
process.
 Cheap.
 Small size.
 Easy maintenance.
 Mechinical parts is less than
other machines.

3. Problems in stator
Grounding.
occures resulting
breakdown insulation
between phase and ground
,this lead to short circuit.
I=V/R
Isolation.
Isolation
Benfits problems

4. Benfits.
It aims current loop.
Ia=Ib=Ic
R=ρL/A
At constant(ρ,A)
RαL
Th=(Rh/Rc)(K+Tc)-
k
RαT
T L R
Problem of isolation.
Break down
insulation
Reasons Types
Increasing
voltage
Increasing
current

5. Types
Turn to turn.
Coil to coil.
L R I
Currents not
equal.
Phase to phase.
Phase to ground.

6. Problems in rotor. Rotor resistance.
 Torque depend on rotor
resistance.
 TαRr/s
 At broken bar
 This effect on torque.

7. Induction Motor Models
Steady-state model. Dynamic model

8. where:
p=d/dt Ls=Lls+Lm Lr=Llr+Lm
   
    

























































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













r
r
s
s
r
r
r
r
e
m
m
r
e
r
r
e
r
r
m
r
e
m
m
m
e
s
s
s
e
m
e
m
s
e
s
s
s
s
i
i
i
i
p
L
R
L
p
L
L
L
p
L
R
L
p
L
p
L
L
p
L
R
L
L
p
L
L
p
L
R
V
V


















0
0
)
(
2
3
r
s
r
s
m
p
e i
i
i
i
L
P
T 


 

m
m
m
m
l
e f
dt
d
J
T
T 




p
r
m
P

 

9. Mathmietical model of I.M
Stator:
 Vαs=(Rs+pLs) iαs-wLs iβs+pLm iαr-wLm iβr (1)
 Vβs=wLs iαs +(Rs+pLs) iβs +wLm iαr +pLm iβr (2)
 Rotor
 0=Lmp iαs-(w-wr)Lm iβs +(Rr+Lrp) iαr-(w-wr)Lr iβr (3)
 0=(w-wr)Lmiαs +Lmp iβs+(w-wr)Lr iαr+(Rr+Lrp) iβr (4)
Where:
P=d/dt Ls=Lls+Lm Lr=Llr+Lm

10. Solving
At occurs
breakdown
isolation .
L R I
We can from
mointoring current
and voltage for
protection of motor.
2-Maintenance.
Maintenance
Predictive
maintenance
Corrective
maintenance
Preventive
maintenance

11. Corrective maintenance Preventive maintenance
Concept
Repair of equipment to back
to original operation
condition.
It occurs after problem.
Concept.
Regular examination of
equipment for defects by
means of PM checklist and
sensory perception.
Examples:
1-Lubrication.
2-Filters.
3-Testing.

12. Predicative maintenance
 Concept.
Regular examination of
equipment to determine
what corrective actions
should be performed with
best timing.
OR
Predictive maintenance
monitors the performance
and condition of equipment
and condition of
equipment or system to
detect degradation.
Examples
Vibration mointoring.
Oil analysis.
Signature analysis of
voltage and current.
Performance testing.
Visual inspection.
Predicative maintenance is
the best method

13. 3-Parameters
estimation
Concept Types
Time
domain
parameter
estimation
Frequency
domain
parameter
estimation
Parameter
calculation
from motor
construction
data
Parameter
estimation based
on steady – state
motor model.
Real-time
parameter
estimation

14. Concept
This method is used to
mointoring parameters of
machine and its performance
.
Types of paramrters:
1-Electrical parameters.
Rs,Ls,Lm,Rr,Lr,Rcore
2-Mechinical parameters
Moment of inertia.
Real-time parameter
estimation.
 This type is used to tune the
controllers of induction motor
drive.
 This requires real-time
parameter estimation
technique.
 Using simplified I.M models.
 this is fast enough to
continuously update.

15. Parameter calculation
from motor construction
data.
 This method requires
adetailes knowledge of the
machines construction ,
such as
material parameters.
 It is the most accurate.
 It is the most cost.
 It based on field
calculation method.
 Such as: the finite element
method
Parameter estimation
based on steady-state
motor model.
 This method requires
available data(V,I,speed).
 This method based on I.M
steady-state equations.
 This is the most common
type of parameter estimation
.
 Such as:
1- RLS
2-MRAS

16. Frequency –domain
parameter estimation.
This method based on
measurements that are
performed at stand still.
In facts ,stand still tests
are not common
industry practice.
Time-domain parameter
estimation.
This method performed
and modl parameters are
adjusted to match the
measurements.
 Not all parameters can
be observed using
measurements
quantities
This method is costly.
The required data not
available.

17. 4-Parameters estimation using RLS Algorithm

 Advantages:
 Requirements data is available.
Stator voltages , Stator currents, speed.
 Can determination full parameters at the same
time.
 Good accurty.
Fast response.

18. Mathematical model of RLS Algorithm.
From dynamic model of I.M Vαr=0 Vβr=0
We will operate at constant speed w=0
   
    










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r
r
s
s
r
r
r
r
m
m
r
r
r
r
r
m
r
m
m
s
s
m
s
s
s
s
i
i
i
i
p
L
R
L
p
L
L
L
p
L
R
L
p
L
p
L
p
L
R
p
L
p
L
R
V
V










0
0
0
0
0
0

19. Mathmatical model of RLS Algorithm
 Stator
• Vαs=(Rs+ p Ls) iαs + p Lm iαr (5)
• Vβs=(Rs+ p Ls) iβs +p Lm iβr (6)
 Rotor:
• 0=Lm p iαs+wr Lm iβs +(Rr+Lr p) iαr+wr Lr iβr (7)
• 0= -wr Lmiαs +Lm p iβs-wr Lr iαr+(Rr+Lr p) iβr (8)
Where:
P=d/dt Ls=Lls+Lm Lr=Llr+Lm

20. a
R L R L
j
a
L R
T
j
b
L
b
L
T
j
s r r s
s
r
o
r s
s r
r
r
s
o
r
s r
r
1
1
1
1



 







 













Where:
 Ls = Lm + Lls and Lr = Lm + Llr
 s = Ls Lr - Lm
2
is a leakage coefficient.
 Vs=Vsα+j Vsβ
 is=isα+j isβ
Where:
 Vsα , Vsβ are the -axis and -
axis stator voltage components
in the stationary reference frame
.
 isα, isβ are the corresponding
currents.
s
o
s
s
o
s
s
V
b
dt
dV
b
i
a
dt
di
a
dt
i
d



 1
1
2
2
The coefficients of above equation are
functions of the machine parameters and
the rotor speed (wr) , and given by:
From(7),(8) , we can obtion:
iαr, iβr afunction iαs, iβs.
Then the time derivatives

21. From above equations,we can obtion:
 Where:
 Y(t) is the measurements.
 X(t) is the regression matrix.
 Θ(t) is the unknown parameters.
   
t
t
x
t
y 

)
(


















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
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
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


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



s
s
r
s
s
r
s
s
s
s
r
s
s
r
s
s
s
r
s
s
r
s
V
V
dt
dV
i
i
dt
di
V
V
dt
dV
i
i
dt
di
dt
di
dt
i
d
dt
di
dt
i
d


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
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
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
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
2
2
2
2

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













5
4
3
2
1






22. We have two matrix:
First matrix.
Second matrix.















 s
s
r
s
s
r
s
s
s
r
s
V
V
dt
dV
i
i
dt
di
dt
di
dt
i
d











2
2














 s
s
r
s
s
r
s
s
s
r
s
V
V
dt
dV
i
i
dt
di
dt
di
dt
i
d











2
2
















5
4
3
2
1





















5
4
3
2
1






23. Clarke Transformation.
ls
s
r
r
r
L
R
R
L
R 



1

r
ls
s
r
L
L
R
R


2

ls
s
L
R

3

ls
L
1
4 

r
ls
r
L
L
R

5


24. t
V
V e
s
s 
 cos

)
cos( 

 t
i
i e
s
s 

)
sin( 

 t
i
i e
s
s 

)
sin(
/ 


 t
i
dt
di e
s
e
s 


)
cos(
/ 

 t
i
dt
di e
s
e
s 


t
V
V e
s
s 
 sin


25.  
   
 





















5
4
3
2
1











 




 s
s
e
r
s
r
s
s
e
s
e
r
e V
V
i
i
i
i
From the first matrix ,we can
obtion these yield.
 
 
s
e
r
e i
t
y 


 

)
(
 
 
s
s
e
r
s
r
s
s
e V
V
i
i
i
t
x 



 


 



)
(

26. Flow chart of RLS
Algorithm
start
Inputs Vs ,Is,
speed (measured)
Clarke transformation
From equatios : obtion
Y(t) x(t)
Y’(t)=x(t)*theta(t-1)
ԑ=Y(t)-Y’(t)
From equation : obtion P(t) (covariance matrix)
Theta(t) =theta(t-1)+p(t)x(m) ԑ(t)
Outputs Electrical parameters
Rs Rr Lls Lr

27. The following steps describe the RLS algorithm used
to estimate the unknown vector (θ)
 Set the initial value of the estimated parameter and covariance
matrix P.
 covariance matrix P is assumed to be diagonal matrix with large
postive numbers.
 Compute estimate y’.
y’(k)=x(t)*θ(t-1)
 Compute the estimation error of y(t).
ԑ=y(t)-y’(t)
 Compute the estimation covariance matrix at t















)
(
)
1
(
)
(
)
1
(
)
(
)
(
)
1
(
)
1
(
1
)
(
t
x
t
P
t
x
t
P
t
x
t
x
t
P
t
P
t
P T
T



28.  The forgetting α=0.999 is used to track the time variation of the
unknown parameters.
 Compute the estimation veator θ’ at instant t.
θ’(t)=θ’(t-1)+p(t)x(t)ԑ(t)
 Repeat these steps until apreset minimum error ԑ(t) is reached.
 By estimating vectors θ’ ,the electrical parameters can be easily
deduced by using the following equations.
4
3
ˆ
ˆ
ˆ



s
R
4
ˆ
1
ˆ


ls
L










 3
1
3
1
5
ˆ
ˆ
ˆ
ˆ
ˆ
1
ˆ 




r
L










 3
1
3
2
4
ˆ
ˆ
ˆ
ˆ
ˆ
1
ˆ 




r
R

29. 5-Expermintial and simulation results of parameters.
The test motor was a 10 H.P, 220 V, 50 Hz, delta connected,
. The rated current per phase was 15 A at 1450 rpm.
The next table illustrates the estimated mean values of
electrical motor parameters obtained using the RLS
algorithm and those obtained experimentally (standard
tests). The third row shows the percentage error results. It
can be noted that it is possible to estimate all electrical
parameters with good precision (estimation errors between
2-5 %). These errors are small and tolerated to get good
parameters estimation.

30. Electrical parameters Rs(Ω) Lls(H) Rr(Ω) Lr
Expermintal 0.512 0.0051 0.174 0.1122
Estimated 0.5044 0.004899 0.1701 0.1070
%│ Error │ 1.437 3.9 2.24 4.6

31. Stator resistance estimation.

32. Expermintial and Estimated values of stator
resistance.

33. Rotor resistance estimation.

34. Expermintial and Estimated values of rotor
resistance.

35. Stator leakage inductance estimation.

36. Expermintial and Estimated values of stator leakage
inductance.

37. Rotor self inductance
estimation.

38. Expermintial and Estimated values of rotor self inductance.

39. Discussion 6- performance of I.M at
Steady-State operation.
 From above figures, we
notice:
 fast convergence time.
 Small estimation errors in
steady-state.
 Motor Performance include on:
 Input current.
 Input power.
 Output power.
 Losses power.
 Efficiency.
 Speed.
 Power factor.
 We compare between
motor performance
depend on :
 Expermintial parameters.
 Estimation parameters.

40. Expermintal results.
Motor torque(N.m) 0.25 F.l 0.5 F.l 0.75 F.l F.l 1.1 F.L
Speed rpm 1488 1475 1462 1448 1442
Input current (A) 6.874 8.964 11.73 14.88 16.16
Input power (KW) 2.051 4.141 6.267 8.43 9.273
Output power(KW) 2.025 4.016 5.97 7.884 8.609
Efficiency 98.74 96.97 95.27 93.52 92.84
Losses(KW) 0.02578 0.1253 0.2966 0.5459 0.6642
Slip 0.008159 0.01662 0.02546 0.0347 0.038
Power factor 0.44 0.688 0.79 0.85 0.86

41. Estimation results.
Motor torque(N.m) 0.25 F.l 0.5 F.l 0.75 F.l F.l 1.1 F.L
Speed rpm 1488 1476 1463 1450 1444
Input current (A) 6.876 8.946 11.69 14.8 16.07
Input power (KW) 2.05 4.139 6.263 8.423 9.264
Output power(KW) 2.026 4.019 5.976 7.895 8.622
Efficiency 98.82 97.08 95.42 93.73 93.07
Losses 0.02411 0.1208 0.2869 0.5279 0.642
Slip 0.007875 0.01603 0.02469 0.0334 0.03702
Power factor 0.437 0.689 0.8 0.854 0.865

42. Relation between Torque and speed at
different loads.

43. Relation between Torque and current at
different loads.

44. Relation between Torque and input power at
different loads.

45. Relation between Torque and losses power at
different loads.

46. Relation between Torque and power factor at
different loads.

47. Relation between Torque and efficiency at
different loads.

48. 7-Conclusion
 An identification methodology based on the RLS algorithm was
successfully applied in this work to identify induction motor electrical
parameters, without saturation effect and skin effect ,harmonic and
temperature .
 The identification algorithm should be executed when the system is in
steady state operation.
 predicative maintenance includes on :
 Electrical parameters
 Mechinical parameters
 Mechinical parameters plays important role in predicative
maintenance.
such as : estimation load torque to known Tl<Te or not.

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