IM design course.pptx

Introductory Course on Design of Three-Phase Induction Motors
Ali Jamali Fard
https://ComProgExpert.com

Course objective
Pout 1HP  0.75kW
Speed 1500RPM
OSDmax 125mm
Lstk,max  70mm
Vt  400V
d  72.1%
PFd  0.8
Induction Motor
https://ComProgExpert.com Introductory Course on Design of Three-Phase Induction Motors 2

Motor Nameplate

IE efficiency classes

IEC standard frame
IEC 60072-1

Main dimensions
A 125mm B 100mm

Main dimensions
A 125mm
B 100mm

Outer stator diameter
A 125mm

Shaft height (frame size)

Stack length

Analytic Design
Developing electromagnetic design core in Excel

Classification of design variables
Design Variables
Independent
Fixed
Adjusted by
Designer
Dependent
Direct
Dependent
Indirect
Dependent
Pout ,OSDmax
av
p

B ,ar 
Lstk
out
m
T


Pout
wst , Ntc , KgRotor

Electromagnetic design procedure
Electromagnetic Design
Fixed Independents Direct Dependents
Independents Adjusted by Designer Indirect Dependents
Convergence logic
sw
Bav
 ar


J


 :
Eff
:
KgAPs
 OSD





av
av sw
:
KgAPs  f Bav ,ac, Jsw ,...

OSD  f (B ,ac,ar,...)

Eff  f B ,ac, J ,...





The aim in this section

Direct Dependents: output torque
P
m
Tout  out
Rated output torque
Rated output power
Rated mechanical speed

m  2 RPS
RPS 
RPM
60

Direct Dependents: slip & rotor frequency
s
RPM
RPM  RPM
s  s
slip
Rated rotor speed
Synchronous speed
fr  s fs
s
RPM 
120 fs
p

Calculation of input power (Volt-Ampere)
in
d

P 
Pout
Desired efficiency
d
Pout
Sin 
 cos

Desired power factor
in in
Q  S  1 cos
2
Input reactive power
Input Volt-Ampere
Input real power

Direct Dependents: terminal & phase current
t
P
3V cos()
It  in
Terminal current
3
ph
I
 It
 
I
 t


Phase current

Direct Dependents: phase voltage
3
 Vt
ph
V  

 V
 t

Direct Dependents: coil current
c
I 
Iph
p
N
Number of parallel paths

Direct Dependents: coil voltage
ph
p
V
N

Vc  Ncpph
Number of coils per phase
Number of parallel paths
Coil voltage
 2m
 Ns
cpph
N  N
 s
Double layer winding
Single layer winding

 m
Number of phases

Output equation: input KVA
Input KVA  Sin  3Vph  Iph
ph
emf
ph
E
V
 
Phase back-EMF
Lower than 1: Motor operation
Higher than 1: Generator operation
in
ph
emf

S  3
Eph
 I

Output equation: phase back-EMF
Number of effective turns per phase
Rated frequency of supply Pole flux
Winding factor

Calculation of the number of Ntph and Ntc (initial guess)

1
tph tc cpph
p
N  N  N
N
Number of turns per coil

Calculation of the winding factor
kW  kd kp kskew
Distribution factor Skew factor
Pitch factor

Distribution factor
Ns
m p
q 
Number of stator slots per pole per phase
 
2
u
s
N
Stator slot pitch angle

Pitch factor
Short pitching is a method of reduction of air gap
harmonics in a double layer winding

Pitch factor

Ns
Q
y
p
Pole pitch

Skew factor

Skew angle
s
s
sq
sin 

 s  
sin

 p 2 
k 

Rotor skew angle

Output equation: input KVA
av
B
DL

pp
D
ac 
32 Ntc  Ncpph  Ic
Magnetic loading Electrical loading

Output equation: output coefficient
w
P 1.112
k  B a 
out
 

d cos

d
out
P
1.112
k  B ac cos

 
w av

out
P  G D2
Lrps
w av d
emf
1.112
k  B ac cos

G 
Output coefficient Rotor volume
Revolutions per second

Magnetic loading

Electric loading

Calculation of main dimensions
P
D2
L 
p
ar 
L
p
 
D
p
Aspect ratio
Pole pitch
p D2
L
D  3
ar 

Total flux & pole flux
total av
  B DL
Flux under one pole
p
 

Total air gap flux

Stator lamination geometry
sy
w
wst1
bs2
bs0
hs0
hs1
D
OSD
wst2
bs1 hs2
wst
w
 
wst 2
st1

Calculation of width of the stator tooth
st,max  Bst  wst1  Lki
Width of stator tooth at tip
wst2  wst  wst1
Width of stator tooth at tail
Iron insulation factor

Maximum stator tooth flux

Maximum stator tooth flux
 
st,max
2
Ns
Ns
r
D
d L


B.ds  B  
   
2 2 2
r p av
B  B cos(
p
) 
B cos(
p
)
st,max
p
 s   s 
p
 2N   2N 
 
Bav DL
sin
 p 
 sin
 p 

Calculation of width of stator yoke
2
p
sy
 B wsy  Lki
Width of stator yoke
Maximum flux in stator yoke
wsy

Calculation of the stator slot dimensions
s1
s
wst1 /2 
b  2

tan/ N  D
 h  h  
s  2 s0 s1 
 cos/ N 
 
 
D
y  tan/ Ns x
wst1
bs1

Calculation of the number of Ntph and Ntc (initial guess)
tph
N 
w
Eph
4.44 f k p
Number of turns per coil

1
tph tc cpph
p
N  N  N
N

Calculation of the slot area
Copper area of coil arm
cAca  Ntc cAsc
cAca
kf
gAca  Fill factor
Gross area of coil arm
gAca
Nps  3
Copper area of single conductor
cAsc

Fill factor of the benchmark motor?

Calculation of cAsc (initial guess)
Jsw
cAsc 
Ic
Maximum current density in stator winding
Coil current (RMS)
After Calculation of the cAsc we should update it with SWG or AWG table
Jsw  cAsc  cAca  K f  gAca  gAss  hs2 ,bs2 

Calculation of the stator slot depth
  s0
 h  hs1  h
2
 
/ 2 

 

 
 D




s2 s
bs1  bs2 
b  2 tan 
w
b b
hs2
s
s
N
 
2

Ntc Ntph p L
p
  B
p,old
p,new
old
L

D

Lnew

Updating process
p,new
s tph,new w
Eph
4.44 f  N k
 

Rotor lamination geometry
r1
D  2g
Dsh
ry
w
wrt
wtrib
r2
d

Rotor slot dimensions
wrt
rb
d r0
h
br0
r1
2
r
ry
w
sh
D g
D

Calculation of width of rotor tooth
rt,max  Brt  wrt  Lki
Width of rotor tooth
Iron insulation factor

Maximum rotor tooth flux
 
rt,max
2
Nr
Nr
r
D
d L


B.ds  B  
   
B  B cos(
p

r p

rt,max
p
 r   r 
p
 2N   2N 
 
Bav DL
sin
 p 
 sin
 p 

Calculation of width of rotor yoke
2
p
i
 Bry  wry  Lk
Width of rotor yoke
Maximum flux in rotor yoke
ry
w

r
2
x
Rotor bar dimensions
y
2 2
rt
r
rt
r
 w

 
 d
 g  h sin 
 r0   2 
   

 d
 g  
   
 w  r 
2 1
 hr0 r1  sin 
r
 r1
 
 2   2  1 sin  
 2 
r1
w
d

Calculation of rotor bar current
mmf
 
Total Rotor Ampere Turns
1
Total Stator Ampere Turns
mmf
cpph tc c
Nr  Ib
 
3 N 2N  I
b
r
I
N


mmf 3 Ncpph 2Ntc  Ic

r
2
x
y
2 2
2
rt
r
rt
r
 w

 
 d
 g  h  d sin 
 r0 rb   2 
   

 d
 g    
  
 w
 r2 
 hr0 drb r2  sin 
r
 r2
 
 2   2  1sin  
 2 
2
r
w
d

2
180 180 2
r
r0 r0 rb 1 2
90 

r
90 

r
1
r  r   
aArb 
r2
 2 
r2
 2  h b  2 1 2
d  r  r cos 2 
 
rb
d r0
h
br0
r1
2
r
aArb 
Ib
Jb

Calculation of the depth of rotor bar

Calculation of the end ring current
r
 N 

I   2
 I  2p 
e,max  b,max 
   
Maximum end ring current
e
p
I 
Nr Ib
RMS value of maximum end ring current

End ring dimensions

Calculation of depth of end ring
e e
e
J
aAer  t d 
Ie
de
te

Efficiency
Calculation of the motor losses and efficiency

Total losses
Copper losses
Iron losses
Mechanical losses
bearing friction losses
windage losses of rotating rotor
ventilator losses
Additional losses
The difference between the total
losses and the sum of stator and rotor
resistive losses, stator and rotor iron
losses, and mechanical losses
IEC 60034-2-1
Magnet losses
Calculation of the motor efficiency

PCu  mR
RAC  kR  RDC
kR  kR ( f ,,...)
Number of phases
Copper losses: AC resistance factor
AC resistance
Phase current
AC resistance factor
• Frequency
• Load angle
• Rotor magnetic field
p (t)  R (i2
 i2
 i2
)
cu ph a b c
Pcu  pcu (t)
avg

tc T
cAsc
Rc,T  N  
Lmt
Mean turn length

T  
20 1 T
Calculation of the coil resistance
Coil resistance
Resistivity

End winding

Mean turn length
Lmt  2 Lstk  4 Lend  2.4 Lspan
span

D OSD
L
Lstk
Lstk
Lend
Lspan
D
OSD
Mean radius
Stator slot
pitch angle

ph c cpph
N2
R  R  N 
1 Number of parallel paths
Calculation of the phase resistance
p
Number of coils in each phase
p (t)  R (i2
i2
i2
)
cu ph a b c
Pcu  pcu (t)
avg

Cold phase resistance (Siemens)

Cold phase resistance (WEG)


T  
20 1 T
Ohmic loss of rotor bars
rb,T T
Lstk
R
aArb
  
cos
Skew 
length of the rotor bar
Rotor bar resistance
Resistivity
Cross-section area

Resistance of the end ring
er,T T
R   
D  2
Mean length
Cross-section area
End ring resistance
te
de

Ohmic loss of the rotor cage
P  N  R  I2
rb r b b
P  2 R  I2
er er e
Pcage  Prb  Per

Equivalent rotor resistance referred to the stator
b
Pcage
Rr 
3 I2
Total Ohmic losses of the cage
Rotor bar current
Equivalent rotor
resistance in rotor side

2
 m T K
Rrs  
s
 s
 ws
  Rr
 mr Tr Kwr 
Equivalent rotor
resistance referred
to the stator

Total losses
Hysteresis losses
Eddy current losses
Excess losses
2 2 2 1.5 1.5
Fe dc h c e
p B
 C k fB  k f B  k f
dc dc dc
C 1 k B2
kdc,default  0.65
Iron losses

Total losses
Hysteresis losses
Eddy current losses
Excess losses
2
pHyst  Cdckh fB
Iron losses: hysteresis losses
Hysteresis losses
increase by frequency

Total losses
Hysteresis losses
Eddy current losses
Excess losses
2 2
Eddy c
p  k f B
6
2

d2
kc 
conductivity Thickness of the lamination
Iron losses: eddy current losses

Total losses
Hysteresis losses
Eddy current losses
Excess losses
1.5 1.5
B
pExcess  ke f
Excess or anomalous loss is due to eddy
currents generated by the displacement
of the magnetic domain walls
Iron losses: excess losses

Iron losses in stator teeth
sy
w
wst1
bs0
b
hs0
hs1
D wst2
bs1 hs2
2
wst1  wst2 
Vst  hs
0
hs1  hs2  Lstk
W 
OSD
Iron loss density in stator tooth 
m3 

PFe,steeth  Ns  pFe,stooth Vst

Iron losses in stator yoke
wst1
bs0
hs0
hs1
D wst2
bs1 hs2
Fe,sy
p  C k f B2
 k f 2
B2
dc h s sy c s sy
 k f 1.5
B1.5
e s sy
Vsy OSD  wsy  wsy  Lstk
Iron loss density in stator yoke
W

PFe,sy  pFe,sy Vsy
sy
OSD
w
b

Iron losses in rotor teeth
Vrt  wrt  drb  Lstk
Iron loss density in rotor tooth
W 

m3 

PFe,rteeth  Nr  pFe,rtooth Vrt
r1
D  2g
Dsh
ry
w
w
wtrib
r2
d
fr  s  fs

Iron losses in rotor yoke
Fe,ry dc h r ry c r ry
p  C k f B2
 k f 2
B2  k f 1.5
B1.5
e r ry
wry  wry  Lstk
Vry Dsh
Iron loss density in rotor yoke
W

PFe,ry  pFe,ry Vry
r1
r2
D  2g
Dsh
w
wtrib
d
w
fr  s  fs

Mechanical losses
bearing friction losses
windage losses of rotating rotor
ventilator losses
prot
in out
Prot
P or P
 
%1prot  %4
Calculation of the mechanical losses

Sensitivity analysis
Sensitivity analysis of the design

Finite Element Analysis
FEA of the motor and calculation of its electrical parameters and its performance

Creation of the parametric model

Dynamic simulation
Dynamic simulation of the motor

Setup motion band

Rotor speed; Is the steady-state speed correct?

Phase currents; Is the phase current equal to the desired one?

Torque; Can the motor deliver the desired torque?

Stator winding loss

Rotor cage loss

Iron loss

Output power

Efficiency; Is calculated efficiency equal to desired one?

Start backward calculations!

Equivalent circuit
Calculation of equivalent circuit parameters

Per-phase equivalent circuit

Useful equations

Derivation of equivalent circuit from voltage equations
vas  Rsias
vbs  Rsibs
vcs  Rsics
var  Rriar
vbr  Rribr
vcr  Rricr
 das
dt
 dbs
dt
 dcs
dt
 dar
dt
 dbr
dt
 dcr
dt

Inductance matrix
L cos p
2
msr  3 
L cos p
2
msr  3 
s ms ms msr
L cosp msr
L cos p
2
ms s ms msr
L cos
ms ms S msr
L cos
L L L
L L L
L L L
 
as
 

bs 
 

 
 


ar 
 



cr 

L cos p
2
msr  3 
msr
L cos p msr
L cos
msr L








cs
  


br
 
  2
L cos  p
 
  3 

 


L

MATLAB Symbolic toolbox

Vector diagram
2
m msr
L 
3
L
Lls  Ls  Lms  Lm
Llr  Lr  Lmr  Lm

Equivalent circuit parameters
Calculation of the induction motor equivalent circuit parameters by FEA

Calculation of circuit parameters by FEA

No-load (open circuit) test
s  0
ph
Fe
P
3V 2
RFe  Rc 
Sin  3Vph  Iph
ph m
m m
in e
X
Q 
3V 2
X   L 
Pin  avg v i 
Q  S2
 P2
in in in

Locked-rotor (short circuit) test
s 1
ph
R  R'
s r

Pohmic
3 I2
ph
I
Z  Z'
ls lr

Vph
  
2 2
'
s r
X  X '
 Z  Z'
ls lr ls lr
 R  R
'
ls lr
e
X  X '
L  L  ls lr

Calculated equivalent circuit parameters

Segregation of leakage reactance

Magnetic loading
Calculation of the motor magnetic loading

Magnetic loading

Average absolute value

Fundamental component

DQ reference frames
Derivation of the induction motor DQ model


2
3
s
F  a
f (t)  a j
2
a  e 3
 
2
3
1
3






s
d
q
F  fa (t) 0.5 fb (t) 0.5 fc (t)
Fs
 fb (t)  fc (t)
a
Fs
D
Q
b
c
Amplitude invariant version
abc to stationary DQ reference frame
The induction motor per-phase equivalent circuit discussed so far is valid only for steady-state
operation. The dynamic model of the machine is important for transient analysis.

Clarke transformations
2
1
 2 

0

1

1 
2 
3 3
 2 2 
Tabc2dqs 
3
 
3
1
 
 1 0 



  
1




 
 3 



2 2 
ds ds
bs  dqs2abc
qs  qs 
cs
vas  
v v 
v  T
2 2  v v 

v  
 
 1 0 


3 
 
1
 2 2 





1 3 
2 2 
dqs2abc
T

DQ model in stationary reference frame
1
2 2
3
1
2 2
 
 1   1 0 

3
1  
2  
1 0
3
       0 1
 3  
 


0   
 2


2  
1 3 
2 2 
abc2dqs dqs2abc
T T


 

 

 

 
bs  
 cs 
br  r  br  br  
 cr 
v
dt  

vcs 

bs  s  bs 

ics 

var  iar 
v   R  i
dt  
vcr icr
 
as 
  R  i  
d   

 
ar  
 
d    


 

 

 
abc2dqs bs  abc2dqs abc2dqs bs  
 cs 
abc2dqs abc2dqs
 cr 
vas  ias  vas  ias 
T  v   T  R  i  T
dt  

vcs 

var 
s  bs 

ics 

iar 
T  v   T  R  i  T
dt  
vcr
br  abc2dqs r  br 

icr 

 
as  

d    

 
ar  


d    
br  

 
   
 

   
 

ds ds
s abc2dqs
qs   qs  qs  
dr dr
abc2dqs
qr   qr  qr  
v i
 R  T 
d 
T
v  i 
dt 
v i
 R  T 
d 
T
v  r i 
dt


ds  
dqs2abc    

   
  
dr     
  
ds ds
s abc2dqs dqs2abc
qs   qs  qs  
dr dr
abc2dqs dqs2abc
qr   qr  qr  
v i
 R   T T
v  i 
v i
 R   T T
dqs2abc    v  r i 

d  
ds  
dt    

d  
dr  
dt

   


s ms ms msr
ms s ms msr
as
ms S msr
L L L
L L L
Lms L L
L cosp
L cosp
L cos p
2
msr  3 
  
L cos p
2
msr  3  msr 
    
 
 bs  L cos p
2 L cos p
2
msr  3  msr  3 
     


ar 
 



cr 

3
msr r mr mr
msr mr r mr
L L L
L L L
Lmr Lmr Lr
L cosp
L cos p
2
msr  3 








cs
  
L cos p L cosp
2 L cosp
2
msr  3  msr  3 
   


br
 
L cosp L cosp
2
  2
L cos  p
msr  3  msr  3 
   

  2  2
L cos  p
3
L cos  p Lmsr cos p
msr   msr  
   

 as

L cos p
2
3  i 
 i 
  bs 
 i 
 
cs

 iar 
 i 
  br

 
icr 






0
0
2
3
2
2
3
2
0
0
3
2
3
2




 

3


2 
3 

2 
s ms msr msr
qs  
   qs 
dr
  
dr

msr msr r mr
qr qr
L  L
3
L
3
L
 ids 
Ls  Lms
 i 
L L L  L
 
i
Lr  Lmr
cosp cosp

ds 
Lmsr cosp Lmsr cosp i
 
 
cosp cosp

 

 Lmsr cosp Lmsr cosp

   
   
r s s
d d q
r s s
q d q
t
t
sin 
F  F cos t  F


F  F sin t  F cos 

Fr
 Fs
e j
t
Fs
 Fej
s
Fr
 Fej
r
 Fej(
s 
t )
     
 
 cos t  jsin 
t
r s s
d q
F  F  jF
Stationary to rotatory reference frame
dqs2dqr
d
r
Fs
cos
t
sin
t Fs

Fs
Fs

 T
F
Fr
  cos
t 

d
  
sin
t    
d

 d 

  d 

 
q   
dqr2dqs
T
sin 
cos
t sin
t

t cos
t 

 

Equations in rotor dq reference frame
 

ph
 qs  qs 
 r 
ids 
vs 
 R 
i
v
d 
ds 
  
dt   Tdqr2dqs
sin
t

cos
t
sin
t cos
t 
 
dr dr
dqr2dqs ph dqr2dqs dqr2dqs
v i d
T

   
  R T   T 

dr 
v  i 
dt   
 qr   qr  
 qr 
dr dr
dqr2dqs dqr2dqs dqr2dqs ph dqr2dqs dqr2dqs dqr2dqs
v i
T1 1 1
   
T   T  R T  T d 
T 

dr 
v  i 
dt   
 qr   qr  
 qr 
dr
dr dr
dqr2dqs
v i d
dt
1
  
     
 R   T 
d
T 

dr 
v  ph i  dqr2dqs  
dt  
 qr   qr   qr 
 qr 

Equations in rotor dq reference frame
Tdqr2dqs
sin
t

cos
t
sin
t cos
t 
 
d
1
vdr  idr  d 
dr 
v   Rph  i    

 qr 
dr dr dr qr
ph
v i d    
       
 R   
v  i    
dt  
 dr 
 qr   qr   qr  q
vd  Rphidr 
v 


d
q
Fs
rt
D
Q
      
 Fej(
s 
rt )
r
Fs
 Fej
s
Fr
 Fej
r
Fr
 Fs
e jt
r s s
d q
F  F  jF r r
 cos  t  jsin t
   
   
r s s
d d r q r
r s s
q d r q r
t
t
F  F cos  t  F sin 


F  F sin  t  F cos 

Stationary to rotatory reference frame

cos

A.B
A B
Calculation of the angle
between two vectors
Power factor

Calculation of the power factor
B
A
vs is
PF  cos

vdsids  vqsiqs

Calculation of the g_emf
emf
ph s
V V
 
Eph

Vm

Stator, rotor, and resultant field
Stator
Rotor Resultant

Calculation of the MMF ratio
mmf
cpph tc c
Nr  Ib
 
3 N 2N  I

Torque-speed curve
Calculation of torque-speed curve both analytically and by FEA and comparison

Analytic method

Torque-speed curve of induction machine

Operating speed

Breakdown torque

Variation of torque-speed curve by rotor resistance

Torque near synchronous speed
mV 2
 s
2
Te s
s r
m s
Te 

V 
R
 Rr 
Is the steady-state speed
correct?
Check Rr-error!

Magnetizing current
Calculation of magnetizing current analytically and by FEA

Magnetizing current for concentrated winding
m
t

AT
I
N

Magnetizing current for concentrated winding (Sinusoidal flux distribution)

Magnetizing current for concentrated winding (Non sinusoidal flux distribution)

The circle diagram
Calculation of the motor circle diagram

What is the circle diagram?

The induction motor circle diagram

Air gap sensitivity analysis

Variation of the air gap length
Air gap length   Power factor 
Air gap length   Leakage reactance   Over-load capacity 
Air gap length   Zigzag leakage flux   Pulsation loss  & Noise 
Air gap length   Better cooling Air gap length   Unbalanced magnetic pull 

Sensitivity analysis: full load

Sensitivity analysis: no-load

Double cage rotors
Rotor classes

Why double cage rotors?

Design types of induction motors

Ns-Nr combination
Selection of number of stator and rotor slots

Harmonic fields
The harmonic fields are produced because of:
i. Windings
ii.Slotting
iii.Saturation
iv.Gap length irregularity
v.Over hang leakage fields
vi.Axial leakage of the main flux
vii.Harmonics in the supply system
viii.Unbalance supply system

Position period, time period
r 1
B  B cos p
t 
 2 e 
 
f x,t cos
f x,t f x,t T  cosAx  Bt T   co
BT  2T 
2
in
,
wave speed 
X

Harmonic induction torques (asynchronous crawling)

Slot harmonics
1
s
f  f  2
 slots 
 poles 
 
poles
s 1 1  
 
 
1 
s sin2fstcos2f1t
f  f  f 
 2 slots
1


Safe choices

Some of references
I. J. Pyrhonen, T. Jokinen, and V. Hrabovcova, Design of rotating electrical machines. John Wiley & Sons, 2013.
II. T.A. Lipo, Introduction toAC machine design. John Wiley & Sons, 2017.
III. R.K.Agarwal, Principles Of Electrical Machine Design.
IV. A. K Sawhney, Acourse in electrical machine design.
V. P. Cochran, Polyphase induction motors, analysis: design, and application. CRC Press, 1989.

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