i Digitally Signed by: Content manager’s Name DN : CN = Webmaster’s name O = University of Nigeria, Nsukka OU = Innovation Centre Agboeze Irene E. ENGINEERING ELECTRICAL ENGINEERING THERMAL MODELLING OF INDUCTION MACHINE USING THE LUMPED PARAMETER MODEL OTI, STEPHEN EJIOFOR OTI, STEPHEN EJIOFOR OTI, STEPHEN EJIOFOR OTI, STEPHEN EJIOFOR REG. NO: PG/PH.D/07/42465 REG. NO: PG/PH.D/07/42465 REG. NO: PG/PH.D/07/42465 REG. NO: PG/PH.D/07/42465
161
Embed
OTI, STEPHEN EJIOFOR REG. NO: PG/PH.D/07/42465 STEPHEN_0.pdf · Equivalent Circuit of the AC induction Machine 75 Figure 5.2. Simplified Equivalent Circuit of the AC induction Machine
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
i
Digitally Signed by: Content manager’s Name
DN : CN = Webmaster’s name
O = University of Nigeria, Nsukka
OU = Innovation Centre
Agboeze Irene E.
ENGINEERING
ELECTRICAL ENGINEERING
THERMAL MODELLING OF INDUCTION
MACHINE USING THE LUMPED PARAMETER
MODEL
OTI, STEPHEN EJIOFOROTI, STEPHEN EJIOFOROTI, STEPHEN EJIOFOROTI, STEPHEN EJIOFOR
THERMAL MODELLING OF INDUCTION THERMAL MODELLING OF INDUCTION THERMAL MODELLING OF INDUCTION THERMAL MODELLING OF INDUCTION MMMMACHINE ACHINE ACHINE ACHINE
USING THE LUMPED PARAMETER MODELUSING THE LUMPED PARAMETER MODELUSING THE LUMPED PARAMETER MODELUSING THE LUMPED PARAMETER MODEL....
BYBYBYBY
OTI, STEPHEN EJIOFOROTI, STEPHEN EJIOFOROTI, STEPHEN EJIOFOROTI, STEPHEN EJIOFOR
(Ph.D) DEGREE IN ELECTRICAL ENGINEERING DEPARTMENT,
UNIVERSITY OF NIGERIA, NSUKKA
BY
OTI, STEPHEN EJIOFOR
REG. NO: PG/Ph.D/07/42465
UNDER THE SUPERVISION
OF
ENGR. PROF. M. U. AGU & ENGR. PROF. E. C. EJIOGU
DEPARTMENT OF ELECTRICAL ENGINEERING
UNIVERSITY OF NIGERIA, NSUKKA
DECEMBER, 2014.
iv
TITLE PAGE
THERMAL MODELLING OF INDUCTION MACHINE USING THERMAL MODELLING OF INDUCTION MACHINE USING THERMAL MODELLING OF INDUCTION MACHINE USING THERMAL MODELLING OF INDUCTION MACHINE USING
THE LUMPED PARAMETER MODELTHE LUMPED PARAMETER MODELTHE LUMPED PARAMETER MODELTHE LUMPED PARAMETER MODEL
v
APPROVAL PAGE
THERMAL MODELLING OF INDUCTION MACHINE USING THE
LUMPED PARAMETER MODEL
By
Oti, Stephen Ejiofor. Reg. No: PG/Ph.D/07/42465
DECEMBER, 2014
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE AWARD OF DOCTOR OF PHILOSOPHY
(Ph.D) DEGREE IN ELECTRICAL ENGINEERING DEPARTMENT,
UNIVERSITY OF NIGERIA, NSUKKA
Oti, Stephen Ejiofor: Signature……………. Date…………
(Student)
Certified by:
Engr. Prof. M.U. Agu Signature……………..Date………….
(Supervisor I)
Engr. Prof. E. C. Ejiogu Signature………………Date………...
(Supervisor II)
Accepted by:
Engr. Prof. E. C. Ejiogu Signature……………..Date………...
(Head of Department)
Engr. Prof. E.S. Obe Signature……………..Date………...
(PG Faculty Rep.)
Engr. Prof. O. I. Okoro Signature………………Date………..
(External Examiner)
vi
CERTIFICATION PAGE
I hereby certify that the work which is being presented in this thesis entitled,
“Thermal Modelling of Induction Machine Using the Lumped Parameter Model”, in
partial fulfillment of the requirements for the award of Doctor of Philosophy (Ph.D)
Degree (Electric Machines & Drives) in the Department of Electrical Engineering,
University of Nigeria, Nsukka is an authentic record of the research carried out under
the supervision of Engr. Prof. M.U. Agu and Engr. Prof. E. C. Ejiogu except where
due reference has been made in the work. Therefore, opinions and assertions
contained herein are those of the authors as they are indicated on the reference pages.
The work embodied in this thesis has not been submitted for the award of any degree
of any other University.
Oti, Stephen Ejiofor: Signature……………. Date…………
(Student)
This is to certify that the above statement made by the candidate is correct and true to
the best of my knowledge.
Engr. Prof. M.U. Agu Signature……………..Date………….
(Supervisor I)
Engr. Prof. E. C. Ejiogu Signature………………Date………..
(Supervisor II)
Accepted by:
Engr. Prof. E. C. Ejiogu Signature……………..Date………...
(Head of Department)
Engr. Prof. E.S. Obe Signature……………..Date………...
(PG Faculty Rep.)
Engr. Prof. O. I. Okoro Signature………………Date………..
(External Examiner)
vii
DEDICATION
To godfathers that have the fear of God in them.
viii
ACKNOWLEDGEMENT
I am heartily thankful to my supervisors, Engr. Prof. M.U. Agu and Engr.
Prof. E.C. Ejiogu whose encouragement, guidance and support enabled
me to develop an understanding of the subject.
I would like to express my profound gratitude to Ven. Prof. T.C.
Madueme, Prof. L.U. Anih and Dr. B.O. Anyaka for their warm advice
and useful contributions, all towards making this work a success.
At the early stage of this work, and all the way from Germany, Dr. E.S.
Obe (now Professor) bombarded me with journal materials that I had
more than I needed. This similar feat was repeated of recent by Engr.
Chukwuemeka Awah who travelled out for his doctoral programme. May
God reward you abundantly.
I owe my deepest gratitude to Professor O.I. Okoro, who has been with
me physically and spiritually since the inception of this work, if it gives a
farmer joy as the planted seeds sprout, how much is expected of men
builder in the person of Prof. Okoro?
I am indebted to many of my colleagues: Engrs. Nwosu, Nnadi, Odeh,
Ogbuka, Mbunwe and Ani who have shared with me or supported me in
one way or the other to make or mar me. May God bless all of them.
It is an honour for me to thank the men at the laboratory unit- Mr.
Okafors, Okoro, Abula, Azu , Eze and Chi for their usual cooperation.
Emeka Omeje is also remembered for his prompt response when his
attention is needed by me. Many thanks to my friends: Hacco, Chika,
Okpoko, Chibuzo, Steve Agada, Alex, Simon, Ejor, Moses, Emma
Obollor, Amoke and Engr. Agbo of Mechanical Engineering.
At this juncture, I have to thank my people; brother Mike, sister Uche,
Uncle Emma, Amara and Princess for enduring with us until now that
God has chosen, and to Him be the Glory.
Lastly, I offer my regards and blessings to all of those who supported me
in any respect during the completion of the project.
ix
Abstract
Temperature rise is of much concern in the short and long term
operations of induction machine, the most useful industrial work icon.
This work examines induction machines mean temperatures at the
different core parts of the machine. The system’s thermal network is
developed, the algebraic and differential equations for the proposed
models are solved so as to ascertain the thermal performances of the
machine under steady and transient conditions. The lumped parameter
thermal method is used to estimate the temperature rise in induction
machine. This method is achieved using thermal resistances, thermal
capacitances and power losses. To analyze the thermal process, the
7.5kW machine is divided geometrically into a number of lumped
components, each component having a bulk thermal storage and heat
generation and interconnections to adjacent components through a
linear mesh of thermal impedances. The lumped parameters are derived
entirely from dimensional information, the thermal properties of the
materials used in the design, and constant heat transfer coefficients.
The thermal circuit in steady-state condition consists of thermal
resistances and heat sources connected between the components nodes
while for transient analysis, the thermal capacitances were used
additionally to take into account the change in internal energy of the
body with time. In the course of the simulation using MATLAB, the
response curves showing the predicted temperature rise for the
induction machine core parts were obtained. To find out the effect of
the decretization level on the symmetry, the two different thermal
models, the SIM and the LIM models having eleven and thirteen nodes
respectively were considered and the results from the two models were
compared. The resulting predicted temperature values together with
other results obtained in this work provide useful information to
designers and industries on the thermal characteristics of the induction
machine.
x
TABLE OF CONTENTS
Title page ………………………………………………………....…………….....….iii
Figure 3.1: Illustration of Fourier’s Conduction Law 15
Figure 3.2: Illustration of Newton’s law of cooling 16
Figure 3.3: Simplified diagram for the illustration of thermal and
electrical resistance relationship 26
Figure 3.4: Simplified diagram for further illustration of thermal and
electrical equivalent resistance 27
Figure 4.1: Heat transfer mechanism in squirrel cage IM 28
Figure 4.2: General cylindrical component 28
Figure 4.3: Conductive Thermal circuit- An annulus ring 29
Figure 4.4: Three terminal networks of the axial and radial networks 30
Figure 4.5: The combination of axial and radial networks for a symme-
trically distributed temp about the central radial plane. 32
Figure 4.6: Squirrel Cage Induction Machine Construction 36
Figure 4.7: The geometry of High Speed Induction Machine 36
Figure 4.8: The geometry of Induction Machine rotor teeth 38
Figure 4.9: Squirrel Cage Rotor 41
Figure 4.10: Thermal network model for the Induction machine 43
Figure 4.11: Thermal resistance of air-gap between insulation and iron 45
Figure 4.12: Thermal resistance between the stator iron and the yoke 47
Figure 4.13: Thermal resistance between stator iron and end-winding 49
Figure 4.14: Thermal resistance between Rotor Bar and end ring 50
Figure 4.15: Thermal capacitance for Stator Lamination 56
Figure 4.16: Thermal capacitance for stator iron 57
Figure 4.17: Thermal capacitances for end winding 59
Figure 4.18: Thermal capacitances for rotor iron 61
Figure 4.19: Thermal capacitances for the Rotor bar 63
Figure 4.20: Thermal Capacitance for the Various Rotor-Bar Sections 64
xiv
Figure 4.21: Thermal capacitances for the End rings 65
Figure 5.1. Equivalent Circuit of the AC induction Machine 75
Figure 5.2. Simplified Equivalent Circuit of the AC induction Machine 75
Figure 5.3. IEEE Equivalent Circuit of the AC induction Machine 76
Figure 5.4. Bar chart for loss segregation of 10HP induction machine 82
Figure 5.5. Graph of Torque-Speed characteristics for 10HP IM 83
Figure 5.6. Power against speed for 10HP induction machine 83
Figure 5.7. Stator current against Speed for 10HP IM 84
Figure 5.8. Graph of Torque-Slip characteristics for 10HP IM 84
Figure 5.9. Power factor against speed for 10HP IM 85
Figure 6.1:Transient Thermal model of SCIM with lumped parameter 91
Figure 6.2:Steady State Thermal model of SCIM with lumped parameter 91
Figure 6.3:Thermal network model for the SCIM (SIM Half Model) 95
Figure 6.4:Thermal network model for the SCIM (LIM Full Model) 97
Figure 6.5: Percentage difference in component steady state temperature for the half and full SIM model 107 Figure 6.6: Percentage difference in component steady state temperature for the half and full LIM model 107
Figure 6.7:Response curve for the predicted temp-(SIM Half Model) 108
Figure 6.8: Response curve for the predicted temp-(SIM Half Model contd.)109
Figure 6.9: Graph for predicted temp and symmetry-(SIM Full Model) 110
Figure 6.10:Response curve for predicted steady state temp for LIM 111
Figure 6.11:Response curve for predicted temp - (LIM Model contd.) 112
Figure 6.12: Graph for predicted steady state temp rise for LIM contd. 113
Figure 6.13: Curves to show symmetry in end-ring of LIM model 114
Figure 6.14: Graph for predicted temp and symmetry-(LIM Full Model) 115
xv
LIST OF TABLES
Table 3.1: Thermal conductivities of some materials at room conditions 15
Table 3.2: Emissivity of some materials at 300K 19
where ar = radius of the shaft , ck = conductivity of the core material
L = distance between adjacent elements and br = radius of the bottom of rotor slots.
In light of the descriptions given so far on the machine, an equivalent
circuit representing some core parts is given in the figure below. Table
4.1 showing some geometric values and dimensions for the machine
parts is also presented.
43
11
C4
C2
C1
R35 P5
R810
R511
End-ring
P8
R10a
Өc
P12
R312
R1213
C12 Stator teeth
P13
Rotor teeth
C13
R713
R79
Rotor Iron
Rotor bar
(winding)
End-ring
End-winding
End-winding
Frame
Stator lamination
Stator winding
Ambient
P1
R12
P2
Өa
R11c
Өb
R1b
R23
P3
P4 10
C8
C5
C3
P6
R67
P7
R78
R911
P9
C6
R26
R34 R410
C7
C9
44
Table 4.1 MACHINE GEOMETRIC / DIMENSIONAL DATA [29, 30, 33]
Machine elements Values Height of slot 16.9 mm Width of slot 7.76 mm Length of air-gap between slot teeth and insulation 0.1 mm Thickness of insulation 0.2 mm Area of conductor at the end-winding 40.38 mm2 Length of end-winding connection 216.79 mm Height of stator iron teeth 17.5 mm Number of rotor slots 28 Outer radius of stator 100 mm Inner radius of stator 62.5 mm Base of rotor slot 4.06 mm Slot-die ratio 1:12 Thickness of slot insulation 0.3 mm Inner radius of rotor 15 mm Height of end-ring 13.2 mm Width of end-ring 4.4 mm Copper winding cross section in slots 40.38 mm2 Iron core length 170 mm Total slot length 239 mm Length of rotor bar for sectioning 12.144 mm Mean roughness of air-gap 3e-7 m Air- gap length between stator core and lamination 0.7 mm Width of bar 3.86 mm Area of insulation 2570.4 cm2 Thickness of air 0.001mm Radius of end-ring 2.03 mm Height of rotor bar 13.7 mm Length of frame 250 mm Radius of frame 135 mm Number of end-caps 40 Number of rotor slots 28 Coil pitch 12 Diameter of wire 0.71mm Height of end-ring 13.2mm
Figure 4.10: Thermal network model for the Induction machine
45
4.5 CALCULATION OF THERMAL RESISTANCES
4.5.1 Thermal resistance of the air-gap between insulation and stator iron
Perimeter of the air-layer similar to that of the insulation
Pair ≅ 2 (16.9) + 7.76 ≅ 42mm per slot
Area of air-layer is also similar to area of insulation
Aair = Ains = Pair.L ; where L = stator core length = 170mm
Aair = 42 x 170 = 7140mm2
Total area = Aair –T = Aair x Ns . where Ns = number of stator slots = 36
Aair –T = 7140 x 36 = 257040mm2
Aair –T = 2570.4cm2 = Ains-T
R23a = Tairair
airsslot
Axk −
−
δ where sslot is stator slot
Width of end-ring 4.4mm Length of half-turn of stator winding 39.667 mm Equivalent stacking factor for rotor and stator 0.95 Permeability of free space -710 x 4π H/m
Temperature coefficient of copper at 200C 0.0039 /K
Number of turns in the stator winding 174
Specific heat capacity KkgJCcu ./385= , KkgJC fe ./460= , KkgJCC frameendR ./960==
C3 Thermal capacitance of stator winding 423.388 423.388 C4 End-windingR thermal capacitance 539.92 539.92 C5 Thermal capacitance of rotor iron 3204.08 3204.08 C6 Rotor bar thermal capacitance 408.267 408.267 C7 Thermal capacitance of end-ringR 218.785 218.785 *C8 Thermal capacitance of ambient air 1006 1006
69
C9 Thermal capacitance of end-ringL 218.785 C10 Thermal capacitance of ambient air 1006 C11 Thermal capacitance of end-windingL 539.92
*C12 Thermal capacitance of the stator teeth 341.33 *C13 Rotor teeth thermal capacitance 871.566 Thermal Resistances
(K/W)
(K/W)
*R1b between ambient and frame 0.0416 0.0416 R12 between frame and stator lamination 15.44e-3 15.44e-3 R23 between stator lamination and stator winding 35.58e-3 35.58e-3
R25 between stator lamination and rotor iron 0.131 0.131 R34 between stator winding and end-winding 0.1751 0.1751 *R48 of the end-winding 1.886 1.886 R56 between rotor bar (winding) and rotor iron 4.115e-3 4.115e-3 R67 between rotor bar and end-ring 0.1055 0.1055 R78 of the end-ring 0.932 0.932
R8c for ambient air 0.015 0.015 * R713 rotor bar and rotor teeth 0.002703 *R312 between stator teeth and stator winding 0.02245 *R1213 between stator teeth and rotor teeth 0.12576
CHAPTER FIVE
LOSSES IN INDUCTION MACHINE
5.1 DETERMINATION OF LOSSES IN INDUCTION MOTORS
Power losses that occur during the transfer of power from the electrical
supply to mechanical load give rise to the heating of the induction
machines. Some of the loss components were described in [72] under
iron losses, copper losses, harmonic losses, stray load losses and
mechanical losses.
70
There are five main losses that occur in an induction machine and these
are identified as follows:
1. Stator copper losses that occur as a result of the current flowing in the
stator.
2. Core losses linked to the magnetic flux in the machine, which is
independent of the load.
3. Stray load losses that vary with the driven load.
4. Rotor copper losses.
5. Friction and windage (rotational) losses that occur in the bearings
and ventilation ducts.
5.1.1 Stator and Rotor I2R Losses
These losses are major losses and typically account for 55% to 60% of
the total losses. I2R losses are heating losses resulting from current
passing through stator and rotor conductors. I2R losses are the function of
a conductor resistance, the square of current. This is one of the major
harmonic losses, a resistive loss of the rotor expressed as:
8158.91*%5.3=ROTaLP W 285.562= ……………………………………………… (5.34)
5.4 SEGREGATION AND ANALYSIS OF THE IM LOSSES The estimated losses are summarized in table (5.2) below and presented
in the following bar and pie charts for ease of understanding.
TABLE 5.2: Loss Segregation Obtained from Calculation
Losses Segregation Calculated Value (W)
Input Power (Pin) 8159.2
83
Stator Copper Loss 400.8250
Rotor Copper Loss 302.0875
Stator Core loss 235.0474
Friction and Windage Losses 50.5247
Stray Losses (PstrayIEEE-12B Standard) 163.1840
Total Losses (Watts) 1151.7
Output Power (Pout) 6968.5
1 2 3 4 50
50
100
150
200
250
300
350
400
450
Class of Losses
Losses
([w
atts]
)
1- STAcuL2- ROTcuL3- STAcore4- STRieee5- FRIwin
Figure 5.4. Bar chart representing loss segregation of 10HP induction machine
5.5 PERFORMANCE CHARACTERISTIC OF THE 10HP INDUCTION MACHINE
When the parameters of table 5.1 are further used for the equivalent
circuit of figure 5.1, steady state performance curves are generated as
indicated in figures 5.5 to 5.9.
84
0 500 1000 15000
20
40
60
80
100
120
140
160
180Torque vs speed curve for IM
Speed in RPM
Torq
ue in N
-m
Figure 5.5. Torque against speed characteristics for the 10HP induction machine
0 500 1000 15000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
4Power vs speed curve for IM
Speed in RPM
Pow
er in
watts
Figure 5.6. Power against speed characteristics for the 10HP induction machine
85
0 500 1000 15000
10
20
30
40
50
60
70stator current vs speed curve for IM
Speed in RPM
sta
tor
cu
rre
nt
in A
mp
ere
s
Figure 5.7. Stator current against Speed for 10HP induction machine
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
20
40
60
80
100
120
140
160
180Torque vs slip curve for IM
Torq
ue in N
-m
Slip in p.u.
Figure 5.8. Graph showing the Torque-Slip characteristics for 10HP induction machine
86
0 500 1000 15000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Power factor vs speed curve for IM
Speed in RPM
pow
er
facto
r
Figure 5.9. Graph of Power factor against Speed characteristics for the 10HP IM
The starting current for an induction motor is several times the running
current and the starting power factor is much lower than the power factor
at rated speed. Both of these features tend to cause the supply voltage to
dip during start-up and can cause problems for adjacent equipment. The
torque-speed/slip characteristic of this induction motor is shown in figures
(5.5 and 5.8) above along with mechanical load torque. The rated torque
is usually slightly smaller than the starting torque so that loads can be
started when rated load is applied. The curve has a definite maximum
value which can only be supplied for a very brief period since the motor
will overheat if it is allowed to stay longer.
87
In figure (5.7), the response of current to the speed is plotted. The starting
current is several times larger than the rated current since the back emf
induced by Faraday’s law grows smaller as the rotor speed decreases.
Whenever a squirrel-cage induction motor is started, the electrical system
experiences a current surge while the mechanical system experiences
torque surge. With line voltage applied to the machine, the current can be
anywhere from four to ten times the machine’s full load current. The
magnitude of the torque (turning force) that the driven equipment sees
can be above 200% of the machine’s full load torque [89]. These
wastages of power due to losses account for a reduced internal and
thermal efficiency of the machine [90, 91]. The associated current and
torque surges can be reduced substantially by reducing the voltage
supplied to the machine during starting as one of the most noticeable
effects of full voltage starting is the dimming or flickering of light during
starting.
5.6.1 Motor Efficiency /Losses
The difference - watts loss is due to electrical losses plus those due to
friction and windage. Even though higher horsepower motors are typically
more efficient, their losses are significant and should not be ignored. In
fact, according to [94] higher horsepower motors offer the greatest
savings potential for the least analysis effort, since just one motor can
save more energy than several smaller motors.
5.6.2 Determination of Motor Efficiency
Every AC motor has five components of watts losses which are the
reasons for its inefficiency. Watts losses are converted into heat which is
88
dissipated by the motor frame aided by internal or external fans. Stator
and rotor RI 2 losses are caused by current flowing through the motor
winding and are proportional to the current squared times the winding
resistance ( RI 2 ). Iron losses are mainly confined to the laminated core of
the stator and rotor and can be reduced by utilizing steels with low core
loss characteristics found in high grade silicon steel. Friction and windage
loss is due to all sources of friction and air movement in the motor and
may be appreciable in large high-speed or totally enclosed fan-cooled
motors. The stray load loss is due mainly to high frequency flux pulsations
caused by design and manufacturing variations.
5.6.3 Improving Efficiency by Minimizing Watts Losses Improvements
in motor efficiency can be achieved without compromising motor
performance at higher cost within the limits of existing design and
manufacturing technology. The formula for efficiency in equation (5.47)
shows that any improvement in motor efficiency must be the result of
reducing watts losses. In terms of the existing state of electric motor
technology, a reduction in watts losses can be achieved in various ways.
All of these changes to reduce motor losses are possible with existing
motor design and manufacturing technology. They would, however,
require additional materials and/or the use of higher quality materials and
improved manufacturing processes resulting in increased motor cost. In
summary, we can say that reduced losses imply improved efficiency.
89
Table 5.3: Efficiency improvement schemes [94]
Watts Loss Area Efficiency Improvement 1 Iron Use of thinner gauge, lower loss core steel
reduces eddy current losses. Longer core adds more steel to the design, which reduces losses due to lower operating flux densities.
2 Stator RI 2 Use of more copper and larger conductors increases cross sectional area of stator windings. This lowers resistance ( R ) of the windings and reduces losses due to current flow ( I ).
3 Rotor RI 2 Use of larger rotor conductor bars increases size of cross section, lowering conductor resistance ( R ) and losses due to current flow ( I ).
4 Friction/ Windage Use of low loss fan design reduces losses due to air movement.
5 Stray Load Loss Use of optimized design and strict quality control procedures minimizes stray load losses.
5.7 THE EFFECTS OF TEMPERATURE
Temperature effect in induction machine has a very important influence in
the assessment of the machines performance. Many works could not
consider the effects due to the difficulty encountered in the measurements.
This difficulty according to [95] is due to the strong coupling between the
electrical and thermal phenomena inherent in the machine. Attempts at
modelling it by the variation of the stator and rotor equivalent resistances
as a function of their average temperatures which were measured directly
90
using a microprocessor-based data acquisition apparatus was carried out
in [77]. The measured resistance mR at the test temperature tT is
corrected to a specified temperature sT as follows;
It is observed that contrary to the research results of some authors, the
machine does not have a uniform increase in temperature in some of the
core parts. The larger the machine, the more the difference in
temperature meaning reduced asymmetry effect.
The transient and steady state models are analyzed. Tabular and
graphical results from the steady and transient states simulation are
presented leading to a clearer comparison of results obtained. Some
discrepancies as may be noticed in this work are likely coming from the
neglect of radiation effect cum errors due to assumptions and
approximations.
121
In conclusion, this work can appropriately be employed to predict the
temperature distribution in induction machine especially when used for
wind energy generation. The results obtained here provide useful
information in area of machine design and thermal characteristics of the
induction machine.
7.2 RECOMMENDATION
The thermal lumped model that has been developed gives a good
estimation of the machine temperature but there is more work that can be
done to further improve the model, some of which are:
• Setting up an equivalent electrical model for loss calculation. The loss
calculation for the lumped circuit model has been partly based on the estimated
data. Setting up a separate electrical circuit for loss calculation based on
geometrical data will give the free will of estimating the temperature on
theoretical machine design with much ease.
• Accounting for the Cooling characteristics. The frame to ambient thermal
resistance has been decided based on measured data, giving an empirical
relation as the cooling characteristics were not available, future work needs to
take the cooling characteristic into consideration so as to make the model
functional for a realistic range of temperature condition.
• Calculation of the thermal losses in a FEM simulation program and validating
the model through finite element method FEM calculations is likely to give a
more sound result.
Generally, temperatures variations should be given considerable
importance in the design and protection of our machines. A data base
should be produced from several generated thermal results for predictive
122
purposes. This will go a long way in the improvement of loadability
schedules especially in wind energy generation schemes.
REFERENCES
[1] F. Marignetti, I. Cornelia Vese, R. Di Stefano, M. Radulescu, “Thermal analysis of a permanent-magnet Tubular machine”, Annals of the University of Craiova, Electrical Engineering series, Vol.1, No. 30, 2006. [2] A. Boglietti, A. Cavagnino and D. A. Staton, “TEFC Induction Motors Thermal Model: A parameter Sensitivity Analysis“, IEEE Transactions on Industrial Applications, Vol. 41, no. 3, pp. 756-763, May/Jun. 2005. [3] A. Boglietti, A. Cavagnino and D. A. Staton, “Thermal Analysis of TEFC Induction Motors”, 2003 IAS Annual Meeting, ,Salt Lake City, USA, Vol. 2, pp. 849-856, 12 – 16 October 2003. [4] D. A. Staton and E. So, “Determination of optimal Thermal Parameters for Brushless Permanent Magnet Motor Design”, IEEE Transactions on Energy Conversion , Vol. 1, pp. 41-49, 1998. [5] X. Ding , M. Bhattacharya and C. Mi , “Simplified Thermal Model of PM Motors in Hybrid Vehicle Applications Taking into Account Eddy Current Loss in Magnets”, Journal of Asian Electric Vehicles, Volume 8, Number 1, pp.1337, June 2010.
[6] L. Sang-Bin, T.G. Habetler, G. Ronald and J. D. Gritter, “An Evaluation of Model-Based Stator Resistance Estimation for Induction Motor Stator Winding Temperature Monitoring”, IEEE Transactions on Energy Conversion, Vol.17, No.1 pp. 7-15, March 2002. [7] P.C. Krause and C.H. Thomas, “Simulation of symmetrical Induction machines,” IEEE Transactions PAS-84, Vol.11, pp.1038-1053, 1965. [8] S.J. Pickering, D. Lampard, M. Shanel,: “Modelling Ventilation and Cooling of Rotors of Salient Pole Machines,” IEEE International
123
Electric machines and Drives Conference (IEMDC), pp. 806-808, June 2001. [9] C.M. Liao, C.L. Chen, T. Katcher,: “Thermal Management of AC Induction Motors Using Computational Fluid Dynamic Modelling,” International Conference (IEMD ’99) Electric machines and Drives, pp. 189-191, May 1999. [10] O.I. Okoro,: “Simplified Thermal Analysis of Asynchronous Machine”,Journal of ASTM International, Vol.2, No.1, pp. 1- 20, January 2005. [11] P.H. Mellor, D. Roberts, D.R. Turner, “Lumped parameter model For electrical machines of TEFC design”, IEEE Proceedings-B, Vol.138, No.5, pp. 205-218, September 1991. [12] M.R. Feyzi and A.M. Parker, “Heating in deep-bar rotor cages”, IEEE Proceedings on Electrical Power Applications, Vol.144, No.4, pp. 271-276, July 1997. [13] J.P. Batos, M.F. Cabreira, N. Sadowski and S.R. Aruda, “A Thermal analysis of induction motors using a weak coupled modeling”, IEEE Transactions on Magnetics, Vol.33, No.2, pp. 1714- 1717, March 1997. [14] P.H. Mellor, D. Roberts, D.R. Turner, “Real time prediction of temperatures in an induction motor using a microprocessor” IEEE Transactions on Electric Machines and Power system,Vol.13, pp. 333-352, September 1988. [15] O.I. Okoro, “Steady and transient states thermal analysis of induction machine at blocked rotor operation”, European transactions on electrical power,16: pp. 109-120, October 2006. [16] Z.J. Liu, D. Howe, P.H. Mellor and M.K. Jenkins, “Analysis of permanent magnet machines”, Sixth International Conference, pp. 359 - 364, September 1993.
124
[17] Z.W. Vilar, D. Patterson and R.A. Dougal, “Thermal Analysis of a Single-Sided Axial Flux Permanent Magnet Motor”, IECON Industrial Electronic Society, p.5, 2005. [18] P.H. Mellor, D. Roberts and D.R. Turner: “Microprocessor based induction motor thermal protection”, 2nd International conference on electrical machines, design and applications. IEEE conference publication 254, pp. 16-20, 1985. [19] D. Roberts,:‘The application of an induction motor thermal model to motor protection and other functions’, PhD thesis, University of Liverpool, 1986. [20] S.T. Scowby , R.T. Dobson , and M.J. Kamper, “Thermal modeling of an axial flux permanent magnet machine”, Applied Thermal Engineering, Vol. 24, pp. 193-207, 2004. [21] C.H.Lim, G. Airoldi, J.R. Bumby, R.G. Dominy, G.I.Ingram, K. Mahkamov, N.L. Brown, A. Mebarki and M. Shanel, “Experimental and CFD verifications of the 2D lumped parameter thermal modelling of single-sided slotted axial flux generator”, International Journal of Thermal Science, Vol. 9, pp.1-29, 2009. [22] J. Saari, ‘Thermal modelling of high speed induction machines’, Acta Polytechnic Scandinavia. Electrical Engineering series No. 82, Helsinki, pp. 1-69, May 1995. [23] C.R. Soderberg: ‘Steady flow of heat in large turbine generators’ AIEE Transactions, Vol.50, No.1, pp.782-802, June 1931. [24] J.J. Bates and A. Tustin: “Temperature rises in electrical machines as related to the properties of thermal networks”, The Proceedings of IEEE, Part A, Vol.103, No.1, pp. 471-482, April 1956. [25] R.L. Kotnik, “An Equivalent thermal circuit for non-ventilated induction motors”, AIEE Transactions , Vol.3A, No.73, pp. 1604 -1609, 1954. [26] M. Kaltenbatcher and J. Saari: ‘An asymmetric thermal model for totally enclosed fan-cooled induction motors’ Laboratory of
125
Electromechanics Report(38), University of Technology Helsinki, Espoo, Finland, pp.1-107,1992. [27] J. Mukosieji: “Problems of thermal resistance measurement of thermal networks of electric machines”, 3rd International conference on electrical machines and drives, London, UK, pp.199 – 202,16-18 November 1987. [28] J. Mukosieji: “Equivalent thermal network of totally-enclosed induction motors”, International conference on electrical machines and drives, Lausanne, Switzerland, Vol.2, pp. 679-682, 18-21, September 1984. [29] G. Kylander,:“Thermal modelling of small cage induction motors” Technical Report no 265, Chalmers University of Technology, Gothenburg, Sweden, p. 113, 1995. [30] O.I. Okoro., ‘Dynamic and thermal modelling of induction machine with non linear effects’, Ph.D. Thesis, University of Kassel Press,Germany, September 2002. [31] O.I. Okoro, “Dynamic modelling and simulation of synchronous generator for wind energy generation using matlab”, Global Journal of Engineering Research, Nigeria, Vol.3, No.1&2, pp. 71-78, 2004. [32] O.I. Okoro, Bernd Weidemann, Olorunfemi Ojo, “An efficient thermal model for induction machines”, Proceedings of IEEE Transactions on Industry and Energy conversion, Vol.5, No.4, pp. 2477-2484, 2004.
[33] O.I. Okoro, “ Thermal analysis of Asynchronous Machine”, Journal of ASTM International, Vol.2, No.1, pp.1-20 January 2005. [34] O.I. Okoro, E. Edward, P. Govender and W. Awuma “Electrical and thermal analysis of asynchronous machine for wind energy generation”, Proceeding on Domestic Use of Energy Conference, Cape town,Southern Africa, pp. 145 -152, 2006.
126
[35] E.O. Nwangwu, O.I. Okoro and S.E. Oti, “A Review of the Application of Lumped Parameters and Finite Element Methods in the Thermal Analysis of Electric Machines”, Proceedings of ESPTAE 2008, National Conference, University of Nigeria, Nsukka, pp. 149-159,June, 2008. [36] O.I. Okoro, “Steady and transient states thermal analysis of a 7.5-kW Squirrel-Cage induction machine at rated load operation”. IEEE transactions on Energy Conversion, Vol.20, No.4, pp.110 - 119, December 2005. [37] O.I. Okoro, “Rectangular and circular shaped rotor bar modeling for skin effect”, Journal of Science, Engineering and Technology, Vol.12, No.1, pp. 5898 - 5909, 2005. [38] A.F. Armor and M.V.K. Chari: “Heat flow in the stator core of large turbine generators, by the method of three dimensional finite-element, Part 11:Temperature in the stator core”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-95, No.5, pp. 1657- 1668, September/October 1976. [39] A.F. Armor and M.V.K. Chari: “Heat flow in the stator core of large turbine generators, by the method of three-dimensional finite-element, Part 1:Analysis by scalar potential formulation”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS- 95, No.5, pp. 1648-1656, September/October 1976. [40] A.F. Armor, “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, pp. 934- 946, May/June 1980. [41] C. Alain, C. Espanet and N. Wavre, “BLDC Motor Stator and Rotor Iron Losses and Thermal Behaviour Based on Lumped Schemes and 3-D FEM Analysis”, IEEE Transactions on Industry Applications,Vol. 39, No.5, pp. 1314-1322, September/October 2003. [42] S. Doi, K. Ito and S. Nonaka : “Three-dimensional thermal analysis stator end-core for large turbine-generators using flow
127
visualization results” IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No.7, pp.1856-1862, July 1985. [43] J. Roger and G. Jimenez: “The finite element method application to the study of the temperature distribution inside electric rotating machine”, International conference on electrical machines, Manchester, U.K., Vol.3, pp. 976-980, 15-17 September 1992. [44] V.K. Garg and J. Raymond: “Magneto-thermal coupled analysis of canned induction motor”, IEEE Transactions on Energy Conversion, Vol.5, No.1, pp. 110-114, March 1990. [45] V. Hatziathanassiou, J. Xypteras and G. Archontoulakis,: “Electrical-thermal coupled calculation of an asynchronous machine” Archive fur Elektrotechnik 77, pp.117-122, 1994. [46] C.E. Tindall and S. Brankin: “Loss at source thermal modelling in salient pole alternators using 3-dimensional finite difference techniques” IEEE Transactions on Magnetics, Vol.24, No.1, pp. 278-281, January 1988. [47] M. Chertkov and A. Shenkman, “Determination of heat state of normal load induction motors by a no-load test run”, IEEE Transactions on Electric Machines and Power System,Vol.21,No.1, pp. 356-369, 1993. [48] D.J. Tilak Siyambalapitiya, P.G. McLarean and P. P. Acarnley, “A rotor condition monitor for squirrel-cage induction machines”, IEEE Transactions on Industry Applications, Vol.1A-23, No.2, pp. 334-339, Mar./April 1987. [49] J.T. Boys and M.J. Miles, “Empirical thermal model for inverter-driven cage induction machines” IEEE Proceedings on Electric Power Applications,Vol.141,No.6, pp. 360-372, November 1994. [50] A.L. Shenkman, M. Chertkov, “Experimental method for synthesis of generalized thermal circuit of polyphase induction motors”, IEEE Transactions on Energy conversion, Vol.15, No.3, pp. 264-268, September 2000.
128
[51] K.A. Stroud, Engineering Mathematics, Palgrave Publishers, New York, 5th edition, pp. 1031-1094, 2001. [52] A. Y. Cengel, M. A. Boles, Michael A. Boles, Numerical methods in heat conduction; McGraw-Hill, London W.I., 1998. [53] H.J. Smith, J.W. Harris, Basic Thermodynamics for Engineers; Mac-Donald & co publishers Ltd London, 1963. [54] A. Y. Cengel, M. A. Boles, Thermodynamics: An Engineering approach; Third edition, McGraw-Hill, W.I. New York, 1998. [55] M. J. Movan, H. N. Shapiro, Fundamentals of Engineering Thermo- dynamics; John Wiley & sons inc New York, 1992. [56] D. Sarkar, P.K. Mukherjee and S.K. Sen,: “Use of 3-dimensional finite elements for computation of temperature distribution in the stator of an induction motor” IEEE Proceedings-B, Vol.138, No. 2, pp. 79-81, March 1991. [57] J.P. Batos, M.F.R.R. Cabreira,N. Sadowski, and S.R. Aruda, “A thermal analysis of induction motors using a weak coupled modeling”, IEEE Transactions on Magnetics, Vol.33, No.2, pp. 1714-1717, March 1997. [58] M.N. Ozisik, Heat transfer-A basic approach, McGraw-Hill book company, New York, 1985. [59] “Fundamentals of heat and mass transfer”, Wiley company, New York, 1990. [60] F.J. Gieras, R. Wang, M. J. Kamper, Axial flux permanent magnet brushless machines. 2nd edition, Springler publisher, 2008. [61] http://www.wikipedia./wiki/Reynolds/HRS Spiratude 2009, last accessed on 28/10/2014. [62] C. Mejuto, M. Mueller, M. Shanel, A. Mebarki, M. Reekie, D. Staton, “Improved Synchronous Machine Thermal Modelling”,
129
Proceedings of the international conference on Electrical Machines , paper ID 182 ,2008. [63] A. Bosbaine, M. McCormick, W.F. Low, “In-Situ determination of thermal coefficients for electrical machines”, IEEE Transactions on Energy Conversion, Vol.10, No.3, pp. 385-391, September 1995. [64] R. Glises, R. Bernard, D. Chamagne, J.M. Kauffmann, “Equivalent thermal conductivities for twisted flat windings”, J.Phisique III,France, vol.6, pp. 1389-1401, October 1996. [65] G. Swift, T.S. Molinski and W. Lehn, “A fundamental approach to transformer thermal modelling”,Part1, IEEE Transactions on Power delivery, Vol.16, No.2, pp. 51, April 2001. [66] K.S. Ball, B. Farouk, V.C. Dixit, “An Experimental study of heat transfer in a vertical annulus with a rotating cylinder”, International journal of Heat Transfer, Volume 104, No. 1. pp. 631-636, 1982. [67] D. Roberts, ‘The Application of an induction motor thermal model to motor protection and other functions’ Ph.D. Research Report, University of Liverpool, pp. 1 – 107, 1986. [68] G.L. Taylor, “Distribution of velocity and temperature between concentric cylinders”, Proceedings of Royal Society, 159 part A, pp. 546 – 578, 1935. [69] C. Gazley,“Heat transfer characteristics of rotating and axial flow between concentric cylinders”, Transactions of ASME,Vol.1, No.1, pp. 79 – 89,1958. [70] G.F. Luke, “The cooling of Electric machines”, Transactions of AIEE, 45, pp. 1278 – 1288, 1923. [71] I. Mori and W. Nakayami:, “Forced convective heat transfer in a straight pipe rotating about a parallel axis”, International Journal of heat mass transfer, 10, pp. 1179 – 1194, 1923.
130
[72] S.C. Peak and J.L. Oldenkamp: “A study of system losses in a transistorized inverter-induction motor drive system”, IEEE transactions, Vol.1A-21, No.1, pp. 248 – 258, 1985. [73] ‘Heat transfer and fluid flow data book’ (General Electric), 1969. [74] K.M. Becker and J. Kaye, “Measurement of diabatic flow in an annulus with an inner rotating cylinder” Journal of Heat transfer 84, pp. 97 – 105, 1962. [75] H. Aoki, H. Nohira and H. Arai, “Convective heat transfer in an annulus with an inner rotating cylinder”, Bulletin of JSME 10, pp. 523 – 532, 1967. [76] I.J. Perez and J.G Kassakian: “A stationary thermal model for smooth air-gap rotating electric machines”, Transactions of Electric Machines and Electromechanics,Vol. 3, pp. 285-303, 1979. [77] J.J. Germishuizen, A Jöckel and M.J. Kamper, “Numerical calculation of iron-and pulsation Losses on induction machines with open stator Slots”, University of Stellenbosch, South Africa. Vol. 4, No.2, June 1984. [78] M.R. Udayagiri and T.A. Lipo, ‘Simulation of Inverter fed Induction motors including core-losses’, Research Report 88-30, University of Wisconsin-Madison, January 1988.
[79] Rakesh Parekh “AC Induction Motor Fundamentals”, Microchip Techno- logy Inc, USA, Document AN887, pp.1-22, 2003. [80] R. Beguenane and M.E.H. Benbouzid, “Induction motor thermal monitoring by means of rotor resistance identification”, IEEE Transactions on Energy conversion, Vol.14, No.3, p. 71, September 1999. [81] R. L. Nailen, Stray load loss: What it’s all about, Electrical Apparatus, August 1997. [82] F. Taegen and R. Walezak, “Experimental verification of stray losses in cage induction motors under no-load, full-load and reverse
131
rotation test conditions”, Archiv für Elektrotechnik 70, pp.255-263, (1987). [83] A. Binder; CAD and dynamics of Electric Machines, unpublished lecture note, Institut fur Elekrische Energiewandlung, Technische Universitat Darmstadt, Germany, pages 2/73-2/74, 2009. [84] J. D. Kueck, J.R. Gray, R.C. Driver, and J. Hsu, “Assessment of Available Methods for Evaluating In-Service Motor Efficiency”, Oak Ridge National Laboratory, ORNL/TM-13237, Tennessee, 1996 [85] P.C. Sen, Principles of Electric Machines and Power Electronics, John Wiley and Sons, New-York, pp. 227-247, 1997. [ 86] IEEE Standard Test Procedure for Polyphase Induction Motors and Generators, IEEE Standard 112-2004, Nov. 2004.
[87] I. Daut, K. Anayet, M. Irwanto, N. Gomesh, M. Muzhar, M. Asri and Syatirah, Parameters Calculation of 5 HP AC Induction Motor, Proceedings of International Conference on Applications and Design in Mechanical Engineering (ICADME), Batu Ferringhi, Penang, Malaysia,pp.12B1-12B4, 11 – 13 October 2009.
[88] J. Hsu, J. D. Kueck, M. Olszewski, D. A. Casada, P.J. Otaduy, and L. M. Tolbert, “Comparison of Induction Motor Field Efficiency Evaluation Methods”, IEEE Trans. Industry Applications, Vol. 34, no.1, pp. 117-125, Jan/Feb 1998. [89] D. Square, “Reduced voltage starting of low voltage three phase squirrel cage IM”, Bulletin No. 8600PD9201, Raleigh, N.C, USA, pp.1-16, June 1992. [90] R. Beguenane and M.E.H. Benbouzid, “Induction motor thermal monitoring by means of rotor resistance identification”, IEEE Transactions on Energy conversion, Vol.14, No.3, page 71, September 1999. [91] A. Bosbaine, M. McCormick, W.F. Low, “In-Situ determination of thermal coefficients for electrical machines”, IEEE Transactions on Energy Conversion, Vol.10, No.3, pp.385-391, September 1995.
132
[92] H. Köfler, ‘Stray Load Losses in Induction Machines: A Review of experimental measuring Methods and a critical Performance Evaluation,’ University of Graz, Austria, Electro technical, Vol. 7, pp. 55-61, (1986). [93] A. A. Jimoh, R.D. Findlay, M. Poloujadoff, “Stray Losses in Induction machines: Part I, Definition, Origin and Measurement, Part II, Calculation and Reduction”, IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, N0.6, pp. 1500-1512, June 1985. [94] http://www.efficiency/reliance.com/mtr/b7087, last accessed on 28/10/14. [95] R. Glises, A. Miraoui, J.M. Kauffmann, “Thermal modeling for an induction motor”, J.Phisique III, Vol.2, No.2 pp. 1849-1859, September 1993. [96] A. Benjan, Heat transfer dynamics, Wiley, New York, 1993. [97] A. Di Gerlando and I. Vistoli, “Improved thermal modelling of induction motors for design purposes”, IEEE Proceedings on Magnetics, pp. 381 – 386, 1994. [98] Krause, P.C., O. Wasynczuk, and S.D. Sudhoff, Analysis of Electric Machinery, IEEE Press, 2002. [99] O.I. Okoro, Introduction to Matlab/Simulink for Engineers and Scientists, 2nd edition, John Jacob’s Classic Publishers Ltd, Enugu, Nigeria, January 2008. [100] Learning Matlab 7 User’s guide, Students’ version: The Mathworks inc, Natic, December 2005. [101] S.E. Lyshevski, Engineering and Scientific computations using Matlab, John Wiley & Sons Inc. Publications, New-Jersey, 2003.
133
APPENDIX
Program data
Program-A: Thermal network model for the squirrel cage induction machine (11n), HALF OF SIM MODEL --Considered global R1b R12 R34 R25 C1 C2 C3 C4 P1 P2 P3 x0 t0 tf tspan xb global C5 C6 C7 C8 R8c R48 R67 R78 R56 R23 global P4 P5 P6 P7 P8 xc Thermal Differential equations Theta(1)=(1/C1)*(P1-(x(1)-xb)/R1b-(x(1)-x(2))/R12); Theta(2)=(1/C2)*(P2-(x(2)-x(1))/R12-(x(2)-x(3))/R23-(x(2)-x(5))/R25); Theta(3)=(1/C3)*(P3-(x(3)-x(2))/R23-(x(3)-x(4))/R34); Theta(4)=(1/C4)*(P4-(x(4)-x(8))/R48-(x(4)-x(3))/R34); Theta(5)=(1/C5)*(P5-(x(5)-x(2))/R25-(x(5)-x(6))/R56); Theta(6)=(1/C6)*(P6-(x(6)-x(7))/R67-(x(6)-x(5))/R56); Theta(7)=(1/C7)*(P7-(x(7)-x(8))/R78-(x(7)-x(6))/R67); Theta(8)=(1/C8)*(P8-(x(8)-x(4))/R48-(x(8)-x(7))/R78-(x(8)-xc)/R8c); global R1b R12 R34 R25 C1 C2 C3 C4 P1 P2 P3 x0 t0 tf tspan xb global C5 C6 C7 C8 R8c R48 R56 R78 R67 R23 global P4 P5 P6 P7 P8 xc Initial temperature x0=[20]; Thermal Capacitances C1=18446.55; C2=4450.625; C3=423.388; C4=539.92; C5=3204.08; C6=408.267; C7=218.785; C8=1006;
134
Heat Losses PfeT=292.196; Ks=0.975; P2=(Ks*PfeT); P3=384.27824; P4=84.35376; P5=(1-Ks)*PfeT; P6=72.503; P7=111.04; Thermal resistances R1b=0.0416; R12=15.44e-3; R23=35.58e-3; R25=0.131; R34=0.1751; R48=1.886; R56=4.115e-3; R67=0.1055; R78=0.932; R8c=0.015; xb=20; xc=20; t0=0.0; tinterval=0.5; tf=7560; tspan=t0:tinterval:tf; figure(1); plot(t/60,x(:,2),'r'); grid on hold on plot(t/60,x(:,3),'b'); plot(t/60,x(:,4),'g'); plot(t/60,x(:,6),'c'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated Load') legend('Stator lamination','Stator winding','End winding','Rotor winding') figure(2); plot(t/60,x(:,5),'r'); grid on hold on plot(t/60,x(:,7),'g'); plot(t/60,x(:,1),'b');
135
xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated load') legend('Rotor iron','End Ring','Frame') display('computed steady-state temperatures')
Program-B: Thermal network model for the squirrel cage induction machine
plot(t/60,x(:,4),'g'); plot(t/60,x(:,6),'c'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated Load') legend('Stator lamination','Stator winding','End winding','Rotor winding') figure(2); plot(t/60,x(:,5),'r'); grid on hold on plot(t/60,x(:,7),'g'); plot(t/60,x(:,1),'b'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated load') legend('Rotor iron','End Ring','Frame') figure(3); plot(t/60,x(:,9),'r'); grid on hold on plot(t/60,x(:,11),'b'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated load') legend('End ringL','End windingL') display('computed steady-state temperatures')
Program-C: Thermal network model for the squirrel cage induction IM (13n), Half (LHS) of the LIM model --Considered
function Theta=oti3(t,x) global R1b R12 R34 R25 C1 C2 C3 C4 P1 P2 P3 x0 t0 tf tspan xb global C5 C6 C7 C8 R8c R48 R67 R78 R56 R23 global P4 P5 P6 P7 P8 xc Thermal Differential equations
R67=0.1055; R78=0.932; R8c=0.015; xb=20; xc=20; t0=0.0; tinterval=0.5; tf=7560; tspan=t0:tinterval:tf; figure(1); plot(t/60,x(:,2),'r'); grid on hold on plot(t/60,x(:,3),'b'); plot(t/60,x(:,4),'g'); plot(t/60,x(:,6),'c'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated Load') legend('Stator lamination','Stator winding','End winding','Rotor winding') figure(2); plot(t/60,x(:,5),'r'); grid on hold on plot(t/60,x(:,7),'g'); plot(t/60,x(:,1),'b'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated load') legend('Rotor iron','End Ring','Frame') display('computed steady-state temperatures')
Program-D: Thermal network model for the squirrel cage induction IM (13n), Complete LIM model –Considered global R1b R12 R34 R25 C1 C2 C3 C4 P1 P2 P3 x0 t0 tf tspan xb xa xc global C8 C9 C10 C11 C12 R69 R910 R1011 R10a R311 R8c R48 R67 R78 global P4 P5 P6 P7 P8 P9 P10 P11 xc R56 R23
P9=P7 P11=P4 P12=68.113 P13=93.445 Thermal resistances R1b=0.0416; R12=15.44e-3; R23=35.58e-3; R25=0.131; R34=0.1751; R48=1.886; R56=4.115e-3; R67=0.1055; R78=0.932; R8c=0.015; R69=67 R910=R78 R1011=R48 R10a=R8c R311=R34 R613=0.002703 R312=0.02245 R1213=0.12576 xb=20; xc=20; xa=20; t0=0.0; tinterval=0.5; tf=7560; tspan=t0:tinterval:tf; figure(1); plot(t/60,x(:,2),'r'); grid on hold on plot(t/60,x(:,3),'b'); plot(t/60,x(:,4),'g'); plot(t/60,x(:,6),'c'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated Load') legend('Stator lamination','Stator winding','End winding','Rotor winding') figure(2); plot(t/60,x(:,5),'r');
142
grid on hold on plot(t/60,x(:,7),'g'); plot(t/60,x(:,1),'b'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated load') legend('Rotor iron','End Ring','Frame') figure(3); plot(t/60,x(:,9),'r'); grid on hold on plot(t/60,x(:,11),'b'); plot(t/60,x(:,12),'g'); plot(t/60,x(:,13),'c'); xlabel('Time[Mins]') ylabel('Temperature rise[°C]') title('Graph of temperature rise against time at rated load') legend('End ringR','End windingR','Stator teeth','Rotor teeth') display('computed steady-state temperatures')