Electric Drive Systems
Electric Drive Systems
© 2014
2/00
Topics
•
•
•
•
•
•
•
Structure
Commutator & Brush
Torque Equation
EMF Equation
Steady State Model
Back EMF & Torque Constants
DC Machine Losses
DC Drive Systems- DC Machines
•
•
•
•
•
•
•
Efficiency
Speed-Torque Curve
Speed Control Methods
DC Machine Capability Curves
Field Weakening Region
Series DC Motor
Comparison of Small & Large
Motors
Electric Drive Systems
© 2014
3/00
DC Machine- Structure
Commutator
Field or
Stator Yoke
Armature
Winding
N turns
• Bli machine
Brush
• Stator - Field
I
S
I
+
V
-
• Rotor - Armature
N
• Commutator &
Brush
Field
Poles
Armature
Core
DC Drive Systems- DC Machines
Field
Winding
Electric Drive Systems
© 2014
4/00
DC Machine- Commutator & Brush
• Closed-loop circuit in armature winding
• Each segment of the commutator is connected to the
armature conductor.
• Commutator segments limit the motor voltage rating.
• Brush is placed at 90 apart from poles.
• The voltage between brushes maintains a constant (except
for a small commutator ripple).
• Brush is laminated along the rotating direction.
IR
Brush drop
1~2V
I
DC Drive Systems- DC Machines
Electric Drive Systems
© 2014
5/00
Derivation of Torque Equation
q
• From F=Bli,
f (q )  B(q )l  (i / a)
f avg  Bavg  l  (i / a )
r
N
S
2 / P
1
where Bavg 
B(q )dq

0
2 / P
  Apole  Bavg  (2 rl / P)  Bavg
T  r  ( Nf avg )  lrN  Bavg (i / a)
- Conductor length: l
- Number of conductor: N
- Armature current: i
- Number of parallel path: a
- radius of armature: r
- Number of poles: P
DC Drive Systems- DC Machines
NP
T 
i  K i  K t i
2 a
• Torque is proportional to the
field flux, armature current,
and pole number.
Electric Drive Systems
© 2014
6/00
Derivation of EMF Equation
• From e=Blv,
eavg = Bavglr
E
N
N P
eavg  

a
a 2
 E  K   Kv
• The EMF (Electromotive force)
is proportional to the field flux,
rotor speed, and pole number.
• A rectangular wave form of B(q)
is best for torque production.
 For ac machine, positive or
negative torque
DC Drive Systems- DC Machines
• Torque  Volume
i
T  rNBavg l  
a
 N i a  
Bavg 


2

r



A/ m
Wb/m 2
Current
Magnetic
loading
loading
 2 rl 
m3
Volume
• Current loading  thermal cond.
• Magnetic loading: saturation
• Motor Cost  Torque not power
ex) 10hp, 1800rpm & 10hp 900rpm
Electric Drive Systems
© 2014
7/00
DC Machine- Steady State Model
R
• Steady state voltage equation
La
Lf
+
I
V
E
+
Vf
T, 
-
V  IR  E
Rf
-
• Back EMF equation
E  K   Kv
• Torque equation
• R: resistance of armature winding
T  K I  Kt I
• La: armature inductance (0)
• Lf: field inductance
• Energy balance
VI  I 2 R  EI
Pmech  E  I  Kv I

Pout  T    Kt I
If
DC Drive Systems- DC Machines
 Kv  Kt in MKS unit
Electric Drive Systems
© 2014
8/00
Measuring Kv and Kt
• Measuring Kv
– e = Kv
– Rotate armature
– Measure open-circuit
voltage, no current flow
– Open-circuit test
DC Drive Systems- DC Machines
• Measuring Kt
– T = KtI
– Stall armature
– Measure stall torque using
the spring
– Measure current
– Short-circuit test
Electric Drive Systems
© 2014
9/00
Why Kt < Kv in data sheet?
• Rotational loss
– EI = KvI : Electrically converted mechanical power
– T = KtI : Mechanical shaft power
– Difference = (Kv - Kt ) I
: Mechanical loss (windage, friction) & armature iron loss (eddy
current & hysteresis)  5%
Note) No iron loss in field flux because of stationary flux.
• Flux loss caused by armature reaction such that
Kt = f(I): closed circuit, Kv  f(I): open circuit.
 Kt is measured smaller due to the saturation.
DC Drive Systems- DC Machines
Electric Drive Systems
© 2014
10/00
DC Machine Losses
 Armature resistive loss
 Iron core loss
- Pa,cu = i2R
- Pcore in armature core only
- DC field in stator core
 Brush loss
R
- Pbrush
La
+
IR
V
I
Rc
E
T, 
Brush drop
1~2V
I
 Friction & windage loss
- Pfw , Tfw = B
 Field winding resistive loss  Total loss
Ploss = Pa,cu + Pbrush + Pf,cu +
- Pf,cu = if2Rf
Pcore + Pfw
-  = = Lfif
DC Drive Systems- DC Machines
Electric Drive Systems
© 2014
11/00
DC Machine- Efficiency
• DC Motor
Pin  Pout  Ploss
 Pout

Efficiency m

  100
 Pout  Ploss 
EI
E
E



E  IR V
EI  I 2 R  Pf ,cu
Pout
 100 or
Pin

DC Drive Systems- DC Machines

Electric Drive Systems
© 2014
12/00
DC Machine- Speed-Torque Curve
• For a separately-excited
DC machine
E
E  K v    
Kv
V  IR
Kv
V
TR
T  K t I   

K v  K v Kt  2
E  V  IR   
Let Kv  = Kt  = K,
V
R
   2T
K K
DC Drive Systems- DC Machines
_
  noload
Speed Source
R
Slope=
TL
R
K2
Tstall
TR
 no _ load
T
V
V
 , Tstall  K
K
R
• For ideal speed source, R, K .
 Super-conducting machine 
Electric Drive Systems
© 2014
13/00
Speed Control Methods for DC Motors
Stable & Unstable Operating Points
V
R
   2T
K K

Stable
point
 Adjustable series armature
resistance R
 Adjustable armature voltage V
 Field weakening , K
Tload
Tmotor
T

Unstable
point
Tload
Tmotor
T
DC Drive Systems- DC Machines
Electric Drive Systems
© 2014
14/00
Speed Control by Series Armature Resistance
Rext
R
La
-
TL
V
K
+
V
Speed Source
 noload
_
Rtot 
E
T, 

Slope= 
R
K2
TR
• Economical
• Poor efficiency
DC Drive Systems- DC Machines
T
T
V
 ( R)   2 R 
K
K
Electric Drive Systems
© 2014
15/00
Speed Control by Armature Voltage
V1
K
V2
K
• Expensive
• Powerful
Speed Source
TL
R
Slope=  2
K

V3
K
VVV
>>
123
TR
1
RT
 (V )  V  2
K
K
DC Drive Systems- DC Machines
Variable DC
T
M
R
Constant
speed AC
motor
Variable

M
MS
Ward-Leonard Drives
Electric Drive Systems
© 2014
16/00
Speed Control by Flux Weakening
V
K1
V
K2

• For extending speed range
• Reduce Torque/Amp
Speed Source


KK<
12
R
T = Ki  K: Torq/Amp cap.
K12

R
K 22
3
R
2
Less speed source
As K decreases
R
T
V RT
 (K )   2
K K
• K = Kv or KtI
DC Drive Systems- DC Machines
2
TR
3
TR
T
Lower field flux  higher speed
 destructive mechanically
Electric Drive Systems
© 2014
17/00
DC Machine Capability Curves(1)
 Voltage source limit
- Vo  constrains speed
 Current limit
- Io  constrains torque
Operating Regions
• Constant Torque region
– Control armature voltage
– Constant rated field flux
 Field flux limit
- o  constrains speed
 Torque limit:
To = KtoIo = KoIo
Capability Representation
in Torque-Speed Curves
DC Drive Systems- DC Machines
• Constant Power region
– Field flux weakening
– Constant armature voltage
 Max. torque is limited by current
limit
Electric Drive Systems
© 2014
18/00
Torque- per unit
DC Machine Capability Curves(2)
Constant Torque Region Constant Power Region
Constant field flux
Field Weakening
Armature voltage control
Constant armature voltage
Corner T , 
point o c
Io, ec
1.0
(To)
KK<
1
Ko2

R
VVV
12<<
0
V1 V2
Ko Ko
DC Drive Systems- DC Machines
o
Ko2

R
Vo
 o 1
Ko
Speed- per unit
o
K12

R
Vo
K1
2.0
Electric Drive Systems
© 2014
19/00
DC Machine Capability Curves(3)
Vo
I=Io

 o  c

o
Pc

Definition of Corner point
c at To, Io , Vo , Ko , ec
c 
Vo
R
 2 To , To  K o I o
Ko Ko
V  RI o ec
 c  o

Ko
Ko
DC Drive Systems- DC Machines
o  Vo Ko
Pc  Toc  K o I o   ec K o   ec I o
If small R (large motor),  c   o
Electric Drive Systems
© 2014
20/00
Field Weakening Region
• Speed  > c
• Flux  <  c,  = f()?
e  Kv , ec  Kvoc
In the field weakening region, e=ec
 c 
   o  
 
Max. torque:
T  K t I o
 Kt 
• Torque/Ampere capability
is reduced.
• Speed regulation is worse
due to the slope of torquespeed curve.
• Maximum speed is limited
(  3 times rated speed) by
mechanical condition.
ec
P
Io  c
K v

DC Drive Systems- DC Machines
Electric Drive Systems
© 2014
21/00
Series DC Motor
R
L
Torque limit
+
Variable
DC
Lf
M

-
Assume linear iron (no saturation),
V  I ( R  R f )  KI 
T  K I  KI 2
Neglecting IR drop,
1 V2
T  KI   2
K 
2
DC Drive Systems- DC Machines
TL
Increase V
T
or
I
I
Speed
• High torque at low speed and
low torque at high speed
• At no load, run away !
Electric Drive Systems
© 2014
22/00
DC Motor driven by AC voltage?
• For shunt motor,
T  K I
 K  m cos  t  I m sin  t
Tavg  0
• For series motor,
T  K I
• Universal Motor
– AC or DC series motor
– Vacuum cleaner: high speed
25,000 ~ 30,000 rpm
– Drills
– Blenders
– Power tools
 K  m sin  t  I m sin  t
Tavg  0
 The series DC motor
operates at AC voltage.
 Universal motor
DC Drive Systems- DC Machines
Electric Drive Systems
© 2014
23/00
Comparison of Small & Large Machines(1)
•
•
•
•
•
P=10 hp, R =1750 rpm
Rcold = 0.57 
Rhot  1.2Rcold = 0.684 
Kv = 1.17 V/(rad/s)
Kt = 0.81 ft•lbs/A
ER = Kv•R = 1.17•1750(2/60) =
214.4 V
TR = P/R = 10•746/(1750 •2/60)
= 40.7 Nm or 30 ft•lbs
IR = TR/ Kt = 30/0.81 = 37 A
VR = IRRhot + ER = 37•0.684 +
214.4 = 239.7 V
Note) 1 Nm = 0.738 ft•lbs
DC Drive Systems- DC Machines
•
•
•
•
•
100 hp, 1750 rpm
Rcold = 0.0144 
Rhot  1.2Rcold = 0.0173 
Kv = 1.27 V/(rad/s)
Kt = 0.885 ft•lbs/A
ER = Kv•R = 1.27•1750(2/60) =
233 V
TR = P/R = 100•746/(1750 •2/60)
= 407 Nm or 300 ft•lbs
IR = TR/ Kt = 300/0.885 = 339 A
VR = IRRhot + ER = 339•0.0173 +
233 = 239 V
Note) 1 Nm = 0.738 ft•lbs
Electric Drive Systems
© 2014
24/00
Comparison of Small & Large Machines(2)
 = ER/VR = 214.4/239.7 = 0.89
 = ER/VR = 233/239 = 0.97
no_load = VR/ Kv = 239.7/1.17 •(60/ no_load = VR/ Kv = 239/1.27 •(60/
2) = 1956 rpm
Ishort_circuit = VR/Rcold =239.7/0.57 =
421 A  10 times rated
•
•
•
•
2) = 1797 rpm
Ishort_circuit = VR/Rcold =239/0.0144 =
16,600 A  40 times rated
Large machine is more efficient.
Large machine is more speed source.
Large machine has more starting or inrush current.
In the large machine machine, current and torque are more sensitive
to the input voltage variation due to low IR drop.
• For small machine, m >> e  mechanical system dominates.
• For large machine, e >> m  electrical system dominates.
DC Drive Systems- DC Machines
Electric Drive Systems
© 2014
25/00
DC Machine Dynamics
Assuming constant flux,
<Small machine>
• 2 energy storage mechanisms L  0,
d
– Mechanical energy  J  m
 V  K 
J
 Ki  TL  K  
  TL
dt
 R 
– Electrical energy  L  a
2
d

K
KV TL
• 2nd-order coupled system




dt RJ
RJ
J
• For small machine, m >> a
RJ
J
For large machine, a >> m
m  2  2
K
K /R
<Large machine>
di
J
L  Ri  V  K  const.

dt
Slope of T- curve
a  L / R

DC Machine Dynamics

Electric Drive Systems
© 2014
26/00
Block Diagram of Sep. Exc. DC Motor
di
V  L  Ri  K
dt
d
J
 Ki  TL  B
dt
V +
+
-
-
i  Ie pt ,   e pt
 Laplace Transform 
1
Lp
I
K
V  LpI  RI  K 
Jp  KI  TL
TL
T+ -
1
Jp

R
E
DC Machine Dynamics
K
Electric Drive Systems
© 2014
27/00
Transfer Function of DC Machine
1 R K2
 

1
K L JR


V JLp 2  JRp  K 2
R
R K2
2
p  p 
L
L JR
1
1

K  m a



V p2  1 p  1
a
 m a
L
JR
where  a  ,  m  2
R
K
• If L is negligible (small machine ), a  0
1 1

 K m

V p 1
m
DC Machine Dynamics
Electric Drive Systems
© 2014
28/00
Characteristic Poles- Small & Large Machines
• Characteristic poles: p1,2
Small Machine
• a / m << 1
p1,2

Large Machine
• a / m >> 1
 1 4 a 
1 

 2 m 
1
1
1
1
 ,  

1
1


2 a 2 a
m
a
m
p1,2  

m
4
1
1

 a
2 a 2 a
m
1
1
j
2 a
 a m

1  e t /  m
1  e t / 2 a
t
DC Machine Dynamics
4 a
1
1


1
2 a 2 a
m
t
Electric Drive Systems
© 2014
29/00
Root Locus
• Movement of eigenvalues as adjusting a / m
• a < m /4
Im
a

m

1
a
1

2 a
DC Machine Dynamics
2 real poles
Larger
machine
a 1

m 4
• a > m /4
2 complex poles
Re
Electric Drive Systems
© 2014
30/00
Standard Form for 2nd Order System
p 2  2 n p   n 2  0
p 2  1  a  p  1  a m  0
• Natural frequency
 n  1  a m
• Damping factor
1 m
 
2 a
Response
• Settling time(within 2%)

4
 n
 8 a
• % overshoot
 max   fin

 100[%]
 fin

1 2
e
 100[%]
• For 2 real poles,
 % overshoot=0
 Settling time = 4 a
DC Machine Dynamics
Electric Drive Systems
© 2014
31/00
Speed Control

+
-
V
GC
1 ( K a m )
1
1
p2  p 
a
 m a
Im

G  GC GM
 KP
Controller
Zero
Controller
Zero
DC Machine Dynamics
Im
Re
Re
Motor
Poles
1 ( K a m )
pa
 2
p
p  (1  a ) p  (1  m a )
Motor
Poles
Electric Drive Systems
© 2014
32/00
Current Control(1)
I* +
GI
V+
-
1
Lp  R
• Current Negative
Feedback
I

K
I
GI

I * Lp  R  GI
GI
I*
V'
+
GI
-
1
Lp  R
K
DC Machine Dynamics
I
1

V ' Lp  R  GI
I

• GI는 R을 변화시키는
효과
• For fast a, larger GI
• For unit dc gain, very
large GI
Electric Drive Systems
© 2014
33/00
Current Control(2)
V"
I* +
-
GI
Lp  R  GI
K/GI
I
• Feedback disturbance gain
K/GI 

• For PI controller,
GI  G1 
G2
p
 Effect:
Dynamic armature
resistance change
DC Machine Dynamics
Electric Drive Systems
© 2014
34/00
DC Machine Drives
DC Machine Drives
Electric Drive Systems
© 2014
35/00
Four Quadrants of Motor Drive Operation
Reverse Regenerating
Voltage <0
Current >0
Torque
R
Forward Motoring
L
+
I
V
Voltage >0
Current >0
-
M

Speed
Voltage <0
Current <0
Reverse Motoring
DC Machine Drives
Voltage >0
Current <0
Forward Regenerating
Electric Drive Systems
© 2014
36/00
DC Machine Drives
1. Thyristor DC Drives
• Use semi-controlled switches; SCR(Thyristor)
• Power converters (AC to DC)
 Single-phase full-wave controlled rectifier
 Three-phase full-wave controlled rectifier
2. DC Chopper Drives
• Use fully-controlled switches; BJT, MOSFET, IGBT
• Power converters(DC to DC)
 DC chopper
 Full bridge (H bridge) DC converter
DC Machine Drives
Electric Drive Systems
© 2014
37/00
Single-phase half-wave controlled rectifier
L
R
• Unipolar current
• DC current in AC source
+
Vs
I
V
-
DC Machine Drives
– Transformer
M

Electric Drive Systems
© 2014
38/00
Single-phase full-wave controlled rectifier(1)
L
R
+
T2
Vs
T1

I
V
T3
2
Inversion
 
 2
T4
2
 Vs ,m

• Average output voltage
 
Braking
Vdc 
 
2Vs sin  t  d ( t )

2 2
Vs cos  0.9Vs cos 

Motoring
M
-
1
Vs ,m
DC Machine Drives
2

Vs ,m
K

Motoring
Increase

2
Motoring
Braking

Vs ,m 
K
Electric Drive Systems
© 2014
39/00
Single-phase full-wave controlled rectifier(2)
vac
v
IRa  Ea v

vac
t
t
Ea  IRa

I dc
is
is
t
• RMS input current
Is 
1


0
I dc 2 dq  I dc
• Fundamental RMS input
I s1 
t
• Input power factor
PF 
Vs I s1  cos 2 2

cos
Vs I s

1 2 
2 2
I
sin
q
d
q

I dc
dc

0

2
DC Machine Drives
Electric Drive Systems
© 2014
40/00
Single-phase full-wave controlled rectifier(3)
• Output DC voltage
Vdc 
2 2

• Power factor varies as a
function of firing angle 
Vs cos 
• Output RMS voltage
Vo 

 
1
 

• Maximum PF  0.9
2
2Vs sin q dq  Vs • Poor PF
• Output DC & RMS
current: Idc
• Output power factor
PF 
Vdc I dc 2 2

cos
Vs I dc

DC Machine Drives
Electric Drive Systems
© 2014
41/00
Single-phase rectifier with freewheel diode(1)
L
R
+
T1
• Input fund. & rms voltage: Vs
• Input rms current
I
T2
M
Vs
V
T3
T4
vac
v

1
 
• Input fund. current
Is 
 

1 2 
I s1 
I dc sinq dq


2
IRa  Ea
t


2
is
PF 
t
I dc (1  cos  )

• Input power factor
I dc
DC Machine Drives
I dc 2 dq  I dc
2(1  cos )
 (   )
Electric Drive Systems
© 2014
42/00
Single-phase rectifier with freewheel diode(2)
• Output dc & rms current: Idc
• Output power factor
• Output rms voltage
Vo 

1


( 2Vs sin q ) 2 dq
• Output dc voltage
Vdc 

0.926
    (1/ 2)sin 2

PF1_input (  )
 Vs

1
 
2

DC Machine Drives
1
0.8
0.6
PF2_input (  )
PF2_output (  ) 0.4
2Vs sinq dq
Vs 1  cos  
2(1  cos )
 (    (1/ 2)sin 2 )
PF 
0.2
0
0
0
0
20
40
60

80
100
180

Electric Drive Systems
© 2014
90
43/00
Three-phase full-wave controlled rectifier
L
R
Vsa
+
c
Vs
T1
T2
I
T3
Vs
b
Va
T4
T5
M
T6
-
• Advantage of 3-phase vs 1-phase
– Smoother output:
– Higher ripple frequency: 360Hz  120Hz
– Lower harmonic distortion
DC Machine Drives
Electric Drive Systems
© 2014
44/00
Waveform of three-phase controlled rectifier
vsa
v
vsb
vsc
va
t

Va
t
I dc
isa
120
t
DC Machine Drives
Electric Drive Systems
© 2014
45/00
Three-phase controlled rectifier
• Output DC voltage
Vdc 

• Output RMS voltage
1

  3 3
3   3
3 2

2VLL sin q dq
VLL cos  1.35VLL cos 
 1
Vrms  

  3  
  3 3
 VLL 1 
3

2VLL sin q

2
1/ 2

dq 

3 3
cos 2
2
• Output DC & RMS current: Idc
• Output power factor
DC Machine Drives
Electric Drive Systems
© 2014
46/00
Three-phase controlled rectifier
• Input fund. & rms voltage: Vs
• Input fundamental RMS current
 1 2 5 6

I sa1  
I
sin
q
d
q

 dc
 2  6


• Input RMS current
• Input power factor
– Independent on firing angle
DC Machine Drives
I sa  I dc
6

I dc  0.78I dc
120
2

I dc  0.816 I dc
180
3
6  I

PF _ input 
 2 3I
dc
dc

3

 0.955
Electric Drive Systems
© 2014
47/00
Four Quadrant DC Drive
L
L
T2
Ia
Vs
M
T3
T1'
T2'
T3'
T4'
Va
T4
Vs
T1
+
-
DC Machine Drives
Electric Drive Systems
© 2014
48/00
DC Chopper Drive- 1 Quad
+
L
Va
-
DC Machine Drives
I
v
M
IRa  Ea
DT
T
t
Electric Drive Systems
© 2014
49/00
DC Chopper Drive- H-Bridge Converter
Va
L
-
M
+
I
DC Machine Drives
Electric Drive Systems
© 2014