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8/12/2019 Computational Analysis of 3-Dimensional Transient Heat Conduction in the Stator of an Induction Motor during Re
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Computational Analysis of 3-Dimensional Transient
Heat Conduction in the Stator of an Induction Motor
during Reactor Starting using Finite Element Method
A. K. Naskar1and D. Sarkar
2
1Seacom Engineering College, Howrah, IndiaEmail: naskar73@gmail.com
2
Bengal Engineering & Science University, Howrah, IndiaEmail: debasissrkr@yahoo.co.in
Abstract In developing electric motors in general and induction motors in particular
temperature limit is a key factor affecting the efficiency of the overall design. Sinceconventional loading of induction motors is often expensive, the estimation of temperaturerise by tools of mathematical modeling becomes increasingly important. Excepting for
providing a more accurate representation of the problem, the proposed model can alsoreduce computing costs. The paper develops a three-dimensional transient thermal model in
polar co-ordinates using finite element formulation and arch shaped elements. Atemperature-time method is employed to evaluate the distribution of loss in various parts ofthe machine. Using these loss distributions as an input for finite element analysis, more
accurate temperature distributions can be obtained. The model is applied to predict thetemperature rise in the stator of a squirrel cage 7.5 kW totally enclosed fan-cooled induction
motor. The temperature distribution has been determined considering convection from the
back of core surface, outer air gap surface and annular end surface of a totally enclosedstructure.
Index Terms FEM, Induction Motor, Thermal Analysis, Design Performance, Transients
I.INTRODUCTION
Considering the extended use of squirrel cage induction machine in industrial or domestic applications both
as motor and generator, the improvement of the energy efficiency of this electromechanical energy converterrepresents a continuous challenge for the design engineers, any achievements in this area meaning importantenergy savings for the world economy. Thus to design a reliable and economical motor, accurate prediction
of temperature distribution within the motor and effective use of the coolant for carrying away the heat
generated in the iron and copper are important to designers[18].
Traditionally, thermal studies of electrical machines have been carried out by analytical techniques, or by
thermal network method [1], [8]. These techniques are useful when approximations to thermal circuit
parameters and geometry are accepted. Numerical techniques based on finite element methods [5],[7] and[10]-[20] are more suitable for analysis of complex system. Rajagopal, M.S, Kulkarni, D.B, Seetharamu,K.N,and Ashwathnarayana P. A [4], [6] have carried out two-dimensional steady state and transient thermal
DOI: 02.PEIE.2014.5.14 Association of Computer Electronics and Electrical Engineers, 2014
Proc. of Int. Conf. onAdvances in Power Electronics and Instrumentation Engineering, PEIE
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analysis of TEFC machines using FEM. Compared to the finite difference method, the finite element method
can easily handle complicated boundary configurations and discontinuities in material properties.
The finite element method was first introduced for the steady state thermal analysis of the stator cores oflarge turbine-generators by Armor and Chari [2]. However, their works are restricted to core packages far
from the ends and they do not consider the influence of the stator coil heat. Sarkar and Bhattacharya [9] alsodescribed a method based on arch-shaped finite elements with explicitly derived solution matrices for
determining the thermal field of induction motors.In this paper, the finite element method is used for predicting the temperature distribution in the stator of an
induction motor using arch-shaped finite elements with explicitly derived solution matrices. A 100-element
three-dimensional slice of armature iron, together with copper winding bounded by planes at mid-slot, mid-tooth and mid-package, are used for solution to a transient stator heating problem, and this defines the scope
of this technique. The model is applied to one squirrel cage TEFC machine of 7.5 KW and the temperaturesobtained are found to be within the permissible limit in terms of overall temperature rise computed from the
resulting loss density distribution.
II.POLYPHASE INDUCTION MOTOR MODEL AND BOUNDARY CONDITIONS
The details of the induction motor are shown in Fig. 1. In this analysis, the 3-dimensional slice of core ironand winding has been chosen for modeling the problem and the geometry is bounded by planes passingthrough the mid-tooth, the mid-slot and the package centre. This is shown in Fig.2, taken from the shaded
region A of Fig.1. The temperature distribution is assumed symmetrical across these three planes, with theheat flux normal to the three surfaces being zero. From the other three boundary surfaces, heat is transferred
by convection to the surrounding gas. It is convected to the air-gap gas from the teeth, to the back of core gasfrom the yoke iron, and to the core end gas from the annular end surface of core. The boundary conditions
may be written in terms of nT / , the temperature gradient normal to the surface.
Axial centre of package 0=pn
T
(1)
Mid-slot surface 0=Sn
T
(2)
Mid-tooth surface 0=tn
T
(3)
Air-gap surface ( )GA
rAG
n
TVTTh
= (4)
Annular end surface of core ( )D
zDn
TVTTh
= (5)
Back-of-core surface, ( )BC
rBCn
TVTTh
= (6)
A. Finite Element Formulation
The governing differential equation for transient heat conduction is expressed in the general form as
0~1
2
2
2
2
2 =+++
t
TCPQ
Z
TV
T
r
V
r
TrV
rrmmzr
(7)
To find the solution of (7) together with the boundary and initial conditions by Galerkins weighted residualapproach, we first express the approximate behaviour of the nodal temperature within each elementaccording to equation (8). Since substitution of this approximation into the original differential equation and
boundary conditions results in some error called a residual, the method of weighted residual requires that theintegral of the projection of the residual on a set of weighting functions is zero over the solution region.
The approximate behaviour of the potential function within each element is prescribed in terms of their nodalvalues and some weighting functions N1, N2 such that
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Fig.1. Half sectional end & sectional elevation of a 7.5 kW squirrel cage induction motor
Fig. 2. Slice of core iron & winding bounded by planes at mid-slot, mid-tooth and mid-package
ii
mi
TNT =
=....2,1
(8)
The required equation governing the behaviour of an element is given by the expression:
0~
)()()(
2
)(
=
+
+
+
dvolt
TCPQ
z
TV
z
T
r
V
r
TV
rN
e
mm
e
z
ee
ri
vol
(9)
Integrating all the terms through integration by parts, the equation takes the form
rdzddrr
N
r
TV
dzdrNr
TVdrdzdr
r
TV
rN
ie
r
D
i
e
r
S
e
ri
D
e
ee
)(
)()(
)(
)(2
)(
=
rdzddrr
N
r
TVdNn
r
TV i
e
r
D
ir
e
r
See
.
)()(
)()(2
= (10)
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( ) ( )( )( )
( ) ( )( )( )abab
N
ab
abN
B
A
/14
11/
/14
11/
++
=
+
=
( ) ( )( )( )
( ) ( )( )( )abab
N
ab
abN
F
E
/14
11/
/14
11/
+
=
=
( ) ( )( )( )
( ) ( )( )( )ab
N
abN
D
C
/14
111
/14111
+=
++=
( ) ( )( )( )
( ) ( )( )( )ab
N
abN
H
G
/14
111
/14111
=
+=
(13)
It is seen that the shape functions satisfy the following conditions:
(a) That at any given vertex A the corresponding shape function NAhas a value of unity, and the othershape functions NB, NC, ,have a zero value at this vertex. Thus at node j, Nj = 1 but Ni= 0 , i
j .(b) The value of the potential varies linearly between any two adjacent nodes on the element edges.
(c) The value of the potential function in each element is determined by the order of the finite element.The order of the element is the order of polynomial of the spatial co-ordinates that describes the
potential within the element. The potential varies as a cubic function of the spatial co-ordinates onthe faces and within the element.
C. Approximate Numeric Form
According to Galerkins weighted residual approach, the weighting functions are chosen to be the same as
the shape functions. Substituting (12) and (13) into (10), gives
{ }[ ] +
+
+
+
=
V
ii
emm
e
i
e
z
e
i
ee
i
e
r
V
dVNTNTNt
CPNQ
z
T
Tz
TV
dVT
T
T
r
V
r
T
Tr
TV
0
)()()(
)()(
2
)()(
2][22
0
{ }
)()(
)(2
e
ii
e
S
dNThNTNhe
for i = A, B,., H (14)These equations, when evaluated lead to the matrix equation
[ ] [ ] [ ] [ ] [ ][ ] [ ] [ ][ ] [ ] [ ]CTHTZR SRTSTSSSSS ++=++++ 0 (15)
III.DISCRETIZED MODEL FOR FEM APPLICATION
The stator of an induction motor, under transient conditions is designed to maintain all temperatures belowclass A insulation limits of 105
oC hot spot. The hottest spot is generally in the copper coils. Thermal
conductivity of copper and insulation in the slot are taken together for simplification of calculation [2].
In the case of transient stator heating caused by reactor starting, the transient analysis procedure is able toprovide an estimate of the temperatures throughout the volume of the stator at an interval of time required to
bring the motor from rest to rated speed by providing reduced voltage and current during the starting periodand as the motor has reached a sufficiently high speed near to the operating speed, rated voltage and current
are provided by short circuiting the reactors during the starting action of the induction motor.Assuming that the machine is at rest with its stator winding at normal ambient temperature, respective
voltage and current are injected to the stator winding of the machines. The temperatures within the volume of
the stator are calculated at all nodal points for a period of time required for the reactor starting action.
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In this analysis, because of symmetry, the 3-dimensional slice of core iron and winding, chosen for modeling
the problem are divided into arch shaped finite elements as shown in fig 5.
Fig.5. Slice of core iron & winding bounded by planes of mid-slot & mid-tooth divided into arch shaped Finite Elements
IV.CALCULATION OF HEAT LOSSES
Heat losses in the tooth and yoke of the core are based on calculated magnetic flux densities (0.97 wb / m2
and 1.293 wb/m2 respectively) in these regions. Tooth flux lines are predominantly radial and yoke flux lines
are predominantly circumferential. The grain orientation of the core punching differs in these two directions
and therefore influences the heating for a given flux density. Copper losses in the winding are determinedfrom the length as well as the area required for the conductors in the slot.
Iron loss of stator core per unit volume = 0.0000388 W/mm3.Iron loss of stator teeth per unit volume= 0.0000392 W/mm
3.
A. Stator copper loss
In reactor starting of the induction motor, the equivalent circuit of which is shown in Fig.6, we are interested
to calculate the temperature distribution in the stator during the starting period. For the purpose of starting we
will take the starting voltage at 50% of full voltage to start with and calculations will be done on that voltagetill the reactor acts as impedance in the motor circuit. Finally, the temperature distribution within the stator
due to reduced voltage reactor starting are calculated by splitting the entire slip range (i.e. from s=1 to full
load slip s=0.04) into small intervals.
Fig.6. Equivalent Circuit of Induction Motor
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x1=8.15;Ic=0.176 Amp; r1=2.04;Im=2.41Amp
0425.0;415;39.2 1/2
=== sVVr
To calculate winding impedance of the reactor
Voltage across the reactor is=415/3 V
The stator winding current per phase during starting = )15.843.4(
4155.0
j+
= 22.37A.
Line current = 22.37 3 =38.75A, which is the output current of the reactor. From VA balancing the inputcurrent of the reactor is=38.75/2 =19.38A and 50% of total impedance of the reactor will be
=415/(319.382)= 6.18 To calculate stator current at starting when reactor is connected in the circuit from s=1.0 to s=0.2,
At start s=1.0
Resistance of the circuit= (+
/s) = (2.04+2.39/1) =4.43
Reactance in the circuit (x1) =8.15
Impedance of the circuit (z1) = (4.43)2+ (8.15)
2=9.3
As the stator is delta connected and 50% of full voltage is applied across the stator winding, the stator current
at s=1 will beI1=415/ (9.3+6.18)=415/15.48 =26.85ATo calculate stator current at different slips when motor is directly connected to the supply from slip s=0.2 to
full load slip s=0.0425,
At slip s=0.2Resistance of the circuit= r1+r
2/s = (2.04+2.39/0.2)= 13.99
When full voltage is provided across the stator winding by short-circuiting the reactors, the stator current at s= 0.2 will beI1=415/ (13.99+j8.15) =25.63A
The stator currents, stator copper losses and the time required for starting action at different slips are
calculated and tabulated as shown in Table I.
TABLEI.THE DIFFERENT VALUES OF STATOR CURRENT,STATOR COPPER LOSS /SLOT /UNIT VOLUME AND TIME REQUIRED FOR
STARTING ACTION AT DIFFERENT SLIPS IN REACTOR STARTING
B. Convective heat transfer co-efficient [2,8]
Three separate values of convection heat transfer co-efficient have been taken for the cylindrical curvedsurface over the stator frame and the cylindrical air gap surface and the annular end surfaces. The natural
convection heat transfer co-efficient on cylindrical curved surface over the stator frame is taken as h=5.25w/m
2 oC.
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The heat transfer co-efficient on forced convection for turbulent flow in cylindrical air gap surface is taken as
h=60.16 w/m2 o
C. The heat transfer co-efficient on forced convection for turbulent flow in annular end
surface is taken as,h= 34.67W / m2oC.
C. Thermal constants [3,9]
For a transient problem in three-dimensions, the following properties are taken for each different element
material as shown in Table II.
TABLE II. TYPICAL SET OF MATERIAL PROPERTIESFOR INDUCTION MOTOR STATOR
V.RESULTS AND DISCUSSIONS
Since the hottest spots are found to be in the stator copper as envisaged from the calculated temperatures for
the three-dimensional structure during the reactor starting period as shown in Table III, the temperaturevariation with time in each node of copper is taken as an index to understand the temperature profile duringthe transient. It is to be noted that the temperature is found to be maximum at the nodes pertaining to copper
in the axis of symmetry. The temperature rise is steady at different stator currents under the reactor starting
region at different slips from s = 1 to s = 0.2. It is also to be noted that under DOL run the motor has reached
a steady speed under full load condition and as such there is a slight decrease of hot spot temperaturespersisting across the axis of symmetry after the reactors are shorted.As a consequence, the temperature variation with time at hottest spots has been depicted in graphs as shown
in Fig. 7to investigate the magnitude of the temperature variation with time at different nodal points alongthe stator copper winding.
TABLE III.SOLUTION FOR THREE DIMENSIONAL STRUCTURE
Magnetic Steel Wedge Copper &Insulation
Vr 33.070 2.007
V 0.8260 1.062
VZ 2.874 358.267
Pm 7.86120 8.9684
Cm 523.589 385.361
NodeNos.
InitialTemperature
Temperatures exceeding 440
C in 1st
time step with convection in three dimensional structure of totally enclosed machinefor different stator current during Reactor starting.
Q=0.0
03257
I=26.8
5Amp
Startingtime=4.2
9secs
Q=0.0
031967
I=26.6
Amp
Startingtime=3.8
8secs
Q=0.0
03125
I=26.3
Amp
Startingtime=3.4
8secs
Q=0.0
0303065
I=25.9
Amp
Startingtime=3.0
9secs
Q=0.0
029148
I=25.4
Amp
Startingtime=2.7
02secs
Q=0.0
027563
I=24.7
Amp
Startingtime=2.3
3secs
Q=0.0
025078
I=23.5
6Amp
Startingtime=1.9
9secs
Q=0.0
0213725
I=21.7
5Amp
Startingtime=1.7secs
Q=0.0
0296779
I=25.6
3Amp
Startingtime=1.1
975
Q=0.0
0105249
I=15.2
6Amp
Startingtime=1.2
22secs
31 400C 44.563
0C
47.6950C
49.9060C
51.4880C
52.6100C
53.3680C
53.7990C
53.9250C
54.4270C
53.9820C
67 400C 44.567
0C
47.7070C
49.9330C
51.5310C
52.6700C
53.4430C
53.8870C
54.0230C
54.5330C
54.0950C
103 400C 44.587
0
C
47.7810
C
50.0730
C
51.7370
C
52.9350
C
53.7580
C
54.2440
C
54.4150
C
54.9460
C
54.5310
C137 400C 44.061
0C
47.0990C
49.4660C
51.3200C
52.7530C
53.8190C
54.5440C
54.9500C
55.5840C
55.4030C
138 400C 44.014
0C
47.1120C
49.5500C
51.4580C
52.9240C
54.0070C
54.7390C
55.1480C
55.7610C
55.5970C
139 400C 44.7410C
48.0920C
50.5320C
52.3220C
53.6220C
54.5240C
55.0670C
55.2760C
55.8420C
55.4370C
175 400C 44.408
0C
47.6680C
50.1050C
51.9250C
53.2650C
54.2100C
54.8020C
55.0680C
55.6210C
55.3120C
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Fig.7. Corresponding Temperatures vs Time
VI.CONCLUSIONS
The numerical models using finite element method developed in this paper referring to a 7.5 kW induction
motor proved to be accurate offering useful results for engineers involved in the design of electric machines.The results based on the proposed method show close agreement for totally enclosed machines with
calculated heat transfer coefficients at the back of core surface, air-gap surface and annular end surface of the
stator winding. This analysis gives the designers a better idea of where the hot spot is and how the heat iscarried away at the outer surfaces with the help of both conduction and convection modes of heat transfer, the
magnitude of which is determined in terms of coefficients usually derived from machine parameters.
VII.APPENDIX
A.Formulation Of The Heat Convection Matrix On Cylindrical Curved Surface
The heat convection term in (13) for i = A is
[ ]{ } dsNTNh ie
S e
)(
)(2
( ) dsNNTNNTNTh HAHBABAAS
e+++=
2
)(2
(16)
Now performing the integration in non-dimensional notation
dsNh A2
( ) ( ))(
16
1122
1
1
1
1dvcda
vh
+=
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( ) ( ) dvvdcha
+=1
1
1
1
2211
16
cha9
4= (17)
dsNNh BA ( ) ( ) ( ) ( ) )(
4
11
4
111
1
1
1dvcda
vvh
++
+=
( ) ( ) ddvvcha +=1
1
1
1
22 1116
cha9
2= (18)
Evaluating the other terms, we obtain
[ ]
=
0
00
00
00
00000
000000
0000
0000
94
92
94
929194
91
92
92
94
cahSH (19)
B.On annular end surface
By performing the integration over (
,v) space,
dsNh AS
e
2
)(2
( ) ( )( )
)(/14
1/2
221
1
1
1dvcda
ab
vabh
=
( )
+
=
2
2
4
4
2
2
23
2
124
1
/13
2
a
b
a
b
a
b
ab
ha (20)
dsNNh BA ( ) ( )
( ))(
/14
1/2
221
/
1
1dvcda
ab
vabh
ab
=
( )
+
=
3
4
23
2
124
1
/142
2
4
4
2
2
a
b
a
b
a
b
ab
ha
( )
+
=
2
2
4
4
2
2
23
2
124
1
/13 a
b
a
b
a
b
ab
ha (21)
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[ ]
[( )
]
[( )
]
[( )
]
[( )
]
[( )
]
[( )
]
[( )
]
[( )
]
[( )
]
[( )
]
+
+
+
+
+
+
+
+
+
+
=
0
00
000
0000
0000
)23
2
412
1(
/13
2
0000
)23
2
412
1(
/13
)23
2
412
1(
/13
2
0000
)66
1212
1(
/13
2
)66
1212
1(
/13
2
)23
2
124
1(
/13
2
0000
)6
6
1212
1(
/13
2
)6
6
1212
1(
/13
)
23
2
124
1(
/13
)
23
2
124
1(
/13
2
2
2
3
3
4
4
2
2
2
2
3
3
4
4
2
2
2
2
3
3
4
4
2
2
3
3
4
4
2
2
3
3
4
4
2
2
2
2
4
4
2
2
3
3
4
4
2
2
3
3
4
4
2
2
2
2
4
4
2
2
2
2
4
4
2
2
SYM
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
a
b
a
b
a
b
ab
ha
SH
(22)
C.Heat Convection Vector On cylindrical curved surface
From (13), the first term of the heat convection vector
( )( ) dvcdavThdsNThee
s
A
S
+=
)(2
)(2
4
112
( )( ) dvdvcaTh
114
1
1+
=
( ) ( )dvvdcaTh
114
1
1
1
1+
=
caTh = (23)Evaluating the other terms, we obtain
=
0
0
1
1
0
0
1
1
][ caThsC
(24)
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D.On annular end surface
The first term of the heat convection on ( ,v) space
( )( )( ) dvcdaab vabTh
dsNTh
ab
A
S e
=1
/
1
1
2
/121/
)(2
( ) ( )
=1
1
1
/
22
1/12
dvvda
b
ab
aTh
ab
( )
+
=
3
32
623
1
/1 a
b
a
b
ab
aTh (25)
Evaluating the other terms, we obtain
( )
+
+
+
+
=
0
0
0
0236
1236
1623
1623
1
/1][
2
2
3
3
2
2
3
3
3
3
3
3
2
a
b
a
ba
b
a
ba
b
a
ba
b
a
b
ab
aThs C
(26)
VIII.LIST OF SYMBOLS
Vr, Vand Vz Thermal conductivities in the radial,Circumferential and axial directions
Pm Material density,
Cm Material specific heat
T Potential function (Temperature)V Medium permeability (Thermal conductivity) watt /m
oC
q Flux (heat flux) watt / mm2.
Q Forcing function (Heat source)
T Surface temperature
TAG Air-gap gas temperature
TBC Back of core gas temperature
n Outward normal vector to the bounding curve TD Core-end gas temperature.
d Differential arc length along the boundary
[SR], [S] and [SZ] Symmetric co-efficient matrices (thermal stiffness matrices)[SH] Heat convection matrix.[T] Column vector of unknown temperatures.
[R] Forcing function (heat source) vector.[ST] Column vector of heat convection.
[SC] Column vector heat convection.
[T0] Column vector of unknown (previous point in time) temperatures.
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REFERENCES
[1] G. M. Rosenberry, Jr., The transient stalled temperature rise of cast aluminum squirrel-cage rotors for inductionmotors, AIEE Trans., vol. PAS-74, Oct. 1955.
[2] Armor, A.F., and Chari, M. V. K., Heat flow in the stator core of large turbine generators by the method of three-dimensional finite elements, Part-I: Analysis by Scalar potential formulation: Part - II: Temperature distribution inthe stator iron, IEEE Trans,Vol. PAS-95, No. 5, pp.1648-1668, September 1976.
[3] Armor, A. F., Transient Three Dimensional Finite Element Analysis of Heat Flow in Turbine-Generator Rotors,IEEE Transactions on Power Apparatus and Systems, Vol. PAS 99, No.3 May/June. 1980.
[4] Rajagopal,M.S.,Kulkarni,D.B.,Seetharamu,K.N.,and shwathnarayana P.A.,Axi-symmetric steady state thermalanalysis of totally enclosed fan cooled induction motors using FEM, 2 ndNat Conf.on CAD/CAM,19-20 Aug,1994.
[5] A. Bousbaine, W. FLow, and M. McCormick, Novel approach to the measurement of iron and stray losses ininduction motors, IEE Proc. Electr. Power Appl., vol. 143, no. 1, pp. 7886, 1996.
[6] Rajagopal,M.S., Seetharamu,K.N .and Ashwathnarayana.P.A., Transient thermal analysis of induction Motors ,IEEE Trans ,Energyconversion, Vol.13, No.1,March1998.
[7] Hwang, C.C., Wu, S. S. and. Jiang,Y. H., Novel Approach to the Solution of Temperature Distribution in theStator of an Induction Motor, IEEE Trans. on energy conversion, Vol. 15, No. 4, December 2000.
[8] O.I. Okoro, Steady and Transient states Thermal Analysis of a 7.5 KW Squirrel cage Induction Machine at RatedLoad Operation, IEEE Trans. Energy Convers., Vol. 20, no. 4, pp. 730-736, Dec. 2005.
[9] Sarkar, D., Bhattacharya, N.K. Approximate analysis of transient heat conduction in an induction motor duringstar-delta starting, in Proc. IEEE Int. Conf. on industrial technology (ICIT 2006), Dec., PP.1601-1606.
[10]Nerg, J ., Thermal Modeling of a High-Speed Solid-Rotor Induction Motor Proceedings of the 5th WSEASInternational Conference on Applications of Electrical Engineering, Prague, Czech Republic, March 12-14, 2006(pp90-95).
[11] Ruoho S., Dlala E., Arkkio A., Comparison of demagnetization models for finite-element analysis of permanentmagnet synchronous machines, IEEE Transactions on Magnetics 43 (2007) 11, pp. 39643968
[12] Islam J., Pippuri J., Perho J., Arkkio A., Time-harmonic finite-element analysis of eddy currents in the form-woundstator winding of a cage induction motor, IET Electric Power Applications 1 (2007) 5, pp. 839846.
[13] Lin R., Arkkio A., 3-D finite element analysis of magnetic forces on stator end-windings of an induction machine,IEEE Transactions on Magnetics 44 (2008) 11, Part 2, pp. 40454048.
[14] E. Dlala, "Comparison of models for estimating magnetic core losses in electrical machines using the finite-elementmethod", IEEE Transactions on Magnetics, 45(2):716-725, Feb. 2009.
[15] Ruoho S., Santa-Nokki T., Kolehmainen J., Arkkio A., Modeling magnet length within 2d finite-element analysisof electric machines, IEEE Transactions on Magnetics 45 (2009) 8, pp. 3114-3120.
[16] Pippuri J.E., Belahcen A., Dlala E., Arkkio A., Inclusion of eddy currents in laminations in two-dimensional finiteelement analysis, IEEE Transactions on Magnetics 46 (2010) 8, pp. 29152918.
[17]Nannan Zhao, Zhu, Z.Q., Weiguo Liu., Thermal analysis and comparison of permanent magnet motor andgenerator, International Conference on Electrical Machines and Systems (ICEMS), pp. 1 5. 2011.
[18] Hai Xia Xia; Lin Li; Jing Jing Du; Lei Liu.,Analysis and calculation of the 3D rotor temperature field of agenerator-motor, International Conference on Electrical Machines and Systems (ICEMS), 2011, pp.1 4.
[19] Ganesh B. Kumbhar, Satish M. Mahajan., Analysis of short circuit and inrush transients in a current transformerusing a field-circuit coupled FE formulation, IJEPES- Volume 33, Issue 8, Pages 13611367, October 2011.
[20] B.L. Rajalakshmi Samaga, K.P. Vittal.,Comprehensive study of mixed eccentricity fault diagnosis in inductionmotors using signature analysis, IJEPES- Volume 35, Pages 180-185, 2012.
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