ac motor drives are used in many industrial and domestic ... · application, such as in conveyer,...
TRANSCRIPT
AC DRIVES
The AC motor have a number of advantages :
• Lightweight (20% to 40% lighter than equivalent DC motor)
• Inexpensive
• Low maintenance
The Disadvantages AC motor :
* The power control relatively complex and more expensive
There are two type of AC motor Drives :
1. Induction Motor Drives
2. Synchronous Motor Drives
AC motor Drives are used in many industrial and domestic application, such as in conveyer, lift, mixer, escalator etc.
INDUCTION MOTOR DRIVES
Three-phase induction motor are commonly used in adjustable-speed
drives (ASD).
Basic part of three-phase induction motor :
• Stator
• Rotor
• Air gap Stator
Three-phase
windings
RotorAir gap
T
Rotor windings
Three-
phase
supply
ms
The stator winding are supplied with balanced three-phase AC voltage,
which produce induced voltage in the rotor windings. It is possible to
arrange the distribution of stator winding so that there is an effect of
multiple poles, producing several cycle of magnetomotive force (mmf) or
field around the air gap.
The speed of rotation of field is called the synchronous speed s , which
is defined by :
ps
2
ωs is syncronous speed [rad/sec] Ns is syncronous speed [rpm]
p is numbers of poles
ω is the supply frequency [rad/sec]
f is the supply frequency [Hz]
Nm is motor speed
Stator
Three-phase
windings
RotorAir gap
T
Rotor windings
Three-
phase
supply
ms
p
fNs
120
or
Stator
Three-phase
windings
RotorAir gap
T
Rotor windings
Three-
phase
supply
ms
The rotor speed or motor speed is : )1( Ssm
Where S is slip, as defined as : S
mSS
Or
S
mS
N
NNS
The motor speed
Equivalent Circuit Of Induction Motor
Stator
Three-phase
windings
RotorAir gap
T
Rotor windings
Three-
phase
supply
ms
Stator Air gap motor
Vs
Is
Im Ir’
Xs Xr’Rs
RmXm
Rr’/s
Where :
Rs is resistance per-phase of stator winding
Rr is resistance per-phase of rotor winding
Xs is leakage reactance per-phase of the
winding stator
Xs is leakage reactance per-phase of the
winding rotor
Xm is magnetizing reactance
Rm Resistane responsible for Core losses
Performance Characteristic of Induction Motor
Stator copper loss :
Stator Air gap motor
Vs
Is
Im Ir’
Xs Xr’Rs
RmXm
Rr’/s
sscus RIP2
3
'2')(3 rrcur RIP Rotor copper loss :
m
s
m
mc
R
V
R
VP
22
33 Core losses :
S
RIP r
rg
'
2')(3
)1()(3'
2'S
S
RIPPP r
rcurgd
)1( SPP gd
- Power developed on air gap (Power fropm stator to
rotor through air gap) :
Performance Characteristic of Induction Motor
- Power developed by motor :
or
- Torque of motor :
m
dd
PT
s
g
S
g P
S
SP
)1(
)1(or
m
dd
N
PT
2
60or
mssi IVP cos3
gcusc PPP
Input power of motor :
Performance Characteristic of Induction Motor
loadnodo PPP
gcusc
loadnod
i
o
PPP
PP
P
P
Output power of motor :
Efficiency :
)( cuscg PPP
loadnod PP
SP
SP
P
P
g
g
g
d
1)1(
If
and
so, the efficiency can calculated as :
Performance Characteristic of Induction Motor
)(222
ssm XRX
Generally, value of reactance magnetization Xm >> value Rm (core
losses) and also
So, the magnetizing voltage same with the input voltage : sm VV
Therefore, the equivalent circuit is ;
Stator Air gap motor
Vs
Is
Im Ir’
Xs Xr’Rs
RmXm
Rr’/s
Stator Air gap rotor
Vs
Ii
Im Ir’
Xs Xr’Rs
Rr’/s
PiPo
Is=Ir’
Xm
Performance Characteristic of Induction Motor
)(
)()(
''
''
rsmr
s
rsmrsm
i
XXXjS
RR
S
RRjXXXX
Z
Total Impedance of this circuit is :
Performance Characteristic of Induction Motor
Stator Air gap rotor
Vs
Ii
Im Ir’
Xs Xr’Rs
Rr’/s
PiPo
Is=Ir’
Xm
The rotor current is :
2
1
2'
2'
'
rsr
s
sr
XXS
RR
VI
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT
Stator Air gap rotor
Vs
Ii
Im Ir’
Xs Xr’Rs
Rr’/s
PiPo
Is=Ir’
Tmax
Smax
Tst
Td
S=0s
Ns
S=1
TL
S=Sm
m
NmNm =0
Tm=TL
Operating point
Torque – speed Characteristic
Tmax
Smax
Tst
S=0
s
Ns
S=1
S=Sm
Nm =0
ss =0s
-Tmax
-Smax
S=-1S=2
Forward
regenerationForward
motoring
Reverse
plugging
s m s m
s m
Torque
Three region operation :
1. Motoring :
2. Regenerating :
3. Plugging :
10 S
0S
21 S
Starting speed of motor is m = 0 or S = 1,
Performance Characteristic of Induction Motor
Starting torque of motor is :
2'
2'
2'3
rsr
ss
srst
XXS
RR
VRT
Slip for the maximum torque Smax can be found by setting : 0dS
Td d
So, the slip on maximum torque is :
21
2'2
'
max
rss
r
XXR
RS
2'2
2
max
2
3
rssss
s
XXRR
VT
Performance Characteristic of Induction Motor
Torque maximum is :
And the maximum regenerative torque can be found as :
2'2
2
max
2
3
rssss
s
XXRR
VT
Where the slip of motor s = - Sm
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT
Speed-Torque Characteristic :
2
'2'
S
RRXX r
srs
2'
2'3
rss
srd
XXS
VRT
2'
2'3
rss
srst
XX
VRT
For the high Slip S. (starting)
So, the torque of motor is :
And starting torque (slip S=1) is :
sr
rs RS
RXX
'2'
rs
sd
R
SVT
'
3 2
For low slip S region, the motor speed near unity or synchronous
speed, in this region the impedance motor is :
So, the motor torque is :
21
2'2
'
max
rss
r
XXR
RS
And the slip at maximum torque is :
The maximum motor torque is :
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT
Stator Voltage Control
Controlling Induction Motor Speed by
Adjusting The Stator Voltage
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT
Td
IM
AC
Variable
Voltage
Sources
Vs
Statorair
gaprotor
Ii
Im Ir’
Xs Xr’Rs
Rr’/s
PiPo
Is=Ir’
Vs
Tmax
S=0s
Ns
S=1
TL
Nm =0
Td
Vs1Vs Vs2> >
12
Tst
Tst1
Tst2
Frequency Voltage Control
Controlling Induction Motor Speed by
Adjusting the Frequency of Stator
Voltage Td
IM
AC
Variable
Voltage
Sources
Vs
f
StatorAir
gaprotor
Ii
Im Ir’
Xs Xr’Rs
Rr’/s
PiPo
Is=Ir’
Vsf
Tmax
S=0S=1
TL
m =0
Td
< <
1 2
Tst
Tst1
Tst2
s
fsS=0
fs1fs2
S=0
fs2 fsfs1
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT
CONTROLLING INDUCTION MOTOR SPEED USING
ROTOR RESISTANCE (Conventional Rotor Resistance Control)
Equation of Speed-Torque :
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT
rs
sd
R
SVT
'
3 2
In a wound rotor induction motor, an external
three-phase resistor may be connected to its
slip rings,
Three-phase
supply
Rotor
Stator
RX
RX
RX
Approximate Torque produced in three phase IM is
2 '' 2 2
' 2 2 2
2 2
d
KsE RT
R s X
2
2 2
2 2 2
2 2
d
KsE RT
R s X
External resistance is added in each phase of rotor through slip rings as shown in the fig. Corresponding torque,
The starting torque at s=1 for and can be written as and
2R '
2R
2
2 2
2 2
2 2
st
KE RT
R X
2 '' 2 2
' 2 2
2 2
st
KE RT
R X
The maximum torque condition i.e. We get
2 2/ Xs R
2
2max
22
KET
X
Maximum torque is independent of rotor resistance, whatever may be the rotor resistance.
These resistors Rx are used to control motor starting and stopping
anywhere from reduced voltage motors of low horsepower up to
large motor applications such as materials handling, mine hoists,
cranes etc.
The most common applications are:
AC Wound Rotor Induction Motors – where the resistor is wired into the
motor secondary slip rings and provides a soft start as resistance is
removed in steps.
AC Squirrel Cage Motors – where the resistor is used as a ballast for soft
starting also known as reduced voltage starting.
The developed torque may be varying the resistance Rx
The torque-speed characteristic for variations in rotor resistance
This method increase the starting torque while limiting the starting current.
The wound rotor induction motor are widely used in applications requiring
frequent starting and braking with large motor torque (crane, hoists, etc)
Advantages:
• Reduce the starting current
• Increase the starting torque
• Power factor of the line is improved
• There is no harmonics in the line current
• Speed control is smooth and of wide range
Disadvantages:
• Efficiency is reduced due to wastage of slip energy in the rotor
circuit
• If rotor resistances are not equal, unbalance in currents and
voltages
The three-phase resistor may be replaced by a three-phase diode rectifier
and a DC chopper. The inductor Ld acts as a current source Id and the DC
chopper varies the effective resistance:
)1( kRRe Where k is duty cycle of DC chopper
The speed can controlled by varying the duty cycle k, (slip power)
Three-phase
supply
Rotor
StatorD1
D2
D3
D6D4
D5
GTOR Vdc
Id
Ld
Vd
Static Rotor Resistance Control
Slip-Recovery Drives for Wound-Field Induction Motors
The power in the air gap portion which is not
converted into mechanical power is called
slip power.
In a wound-field induction motor the slip rings
allow easy recovery of the slip power which
can be electronically controlled to control the
speed of the motor.
Slip-Recovery Drives for Wound-Field Induction Motors (cont’d)
The oldest and simplest technique to invoke this slip-
power recovery induction motor speed control is to
mechanically vary the rotor resistance.
Slip-power recovery drives are used in the
following applications:
Large-capacity pumps and fan drives
Variable-speed wind energy systems
Shipboard VSCF (variable-speed/constant
frequency) systems
Variable speed hydro-pumps/generators
Utility system flywheel energy storage systems
The slip power in the rotor circuit may be returned to the supply by
replacing the DC converter and resistance R with a three-phase full
converter (inverter)
Three-phase
supply
Rotor
StatorD1
D2
D3
D6D4
D5
Id
Ld
Vd
T2
T5
T4
T3T1
T6
Vdc
Transformer Na:Nb
Diode rectifierControlled rectifier/
inverter
Slip Power
Example:
A three-phase induction motor, 460, 60Hz, six-pole, Y connected, wound rotor
that speed is controlled by slip power such as shown in Figure below. The
motor parameters are Rs=0.041 , Rr’=0.044 , Xs=0.29 , Xr’=0.44 and
Xm=6.1 . The turn ratio of the rotor to stator winding is nm=Nr/Ns=0.9. The
inductance Ld is very large and its current Id has negligible ripple.
The value of Rs, Rr’, Xs and Xr’ for equivalent circuit can be considered
negligible compared with the effective impedance of Ld. The no-load of motor is
negligible. The losses of rectifier and Dc chopper are also negligible.
The load torque, which is proportional to speed square is 750 Nm at 1175 rpm.
(a) If the motor has to operate with a minimum speed of 800 rpm, determine
the resistance R, if the desired speed is 1050 rpm,
(b) Calculate the inductor current Id.
(c) The duty cycle k of the DC chopper.
(d) The voltage Vd.
(e) The efficiency.
(f) The power factor of input line of the motor.
The dc voltage at the rectifier output is :
)1( kRIRIV dedd
ms
s
rsr nVS
N
NVSE
and
For a three-phase rectifier, relates Er and Vd as :
rrd EExV 3394.2265.1
Using : ms
s
rsr nVS
N
NVSE
msd nVSV 3394.2
If Pr is the slip power, air gap power is : S
PP r
g
Developed power is : S
SPS
S
PPPP rr
rgd
)1(3)(3)(3
Because the total slip power is 3Pr = Vd Id and mLd TP
So, )1(
)1(STT
S
IVSP mLmL
ddd
Substituting Vd from msd nVSV 3394.2 In equation Pd above, so
: Solving for Id gives :
ms
sLd
nV
TI
3394.2
Which indicates that the inductor current is independent of the speed.
From equation : )1( kRIRIV dedd and equation : msd nVSV 3394.2
So, msd nVSkRI 3394.2)1(
Which gives :
ms
d
nVS
kRIS
3394.2
)1(
The speed can be found from equation :
ms
d
nVS
kRIS
3394.2
)1( as :
ms
dssm
nV
kRIS
3394.2
)1(1)1(
2)3394.2(
)1(1
ms
sLsm
nV
kRT
Which shows that for a fixed duty cycle, the speed decrease with load
torque. By varying k from 0 to 1, the speed can be varied from minimum
value to s
sradm /77.8330/180
From torque equation : 2
mvL KT
Nmx 67.3471175
800750
2
From equation :
ms
sLd
nV
TI
3394.2
The corresponding inductor current is :
Axx
xId 13.78
9.058.2653394.2
66.12567.347
The speed is minimum when the duty-cycle k is zero and equation :
ms
dssm
nV
kRIS
3394.2
)1(1)1(
)9.058.2653394.2
13.781(66.12577.83
xx
R
And : 3856.2R
Speed Control by Rotor Rheostat
Recall that the torque-slip equation for an
induction motor is given by:
From this equation it is clear that the torque-slip
curves are dependent on the rotor resistance
Rr. The curves for different rotor resistances are
shown on the next slide for four different rotor
resistances (R1-R4) with R4>R3>R2>R1.
2
2 2 23 .
2 / ( )
sre
e s r e ls lr
VRPT
s R R s L L
Speed Control by Rotor Rheostat (cont’d)
An electronic chopper implementation is also
possible as shown below but is equally
inefficient.
Instead of wasting the slip power in the rotor
circuit resistance, a better approach is to convert
it to ac line power and return it back to the line.
Two types of converter provide this approach:
1) Static Kramer Drive - only allows
operation at sub-synchronous speed.
2) Static Scherbius Drive - allows
operation above and below
synchronous speed.
Static Kramer Drive (cont’d)
The machine air gap flux is created by the stator
supply and is essentially constant. The rotor current
is ideally a 6-step wave in phase with the rotor
voltage.
Static Kramer Drive (cont’d)
The motor fundamental phasor diagram referred to
the stator is as shown below:
Vs = stator phase voltage, Is=stator current, Irf’ = fundamental rotor current referred to the stator, g = air gap flux, Im=magnetizing current, and =PF angle.
Static Kramer Drive (cont’d)
The voltage Vd is proportional to slip, s and the
current Id is proportional to torque. At a
particular speed, the inverter’s firing angle can
be decreased to decrease the voltage VI. This
will increase Id and thus the torque. A
simplified torque-speed expression for this
implementation is developed next.
Expression for torque and speed
Voltage Vd (neglecting stator and rotor voltage
drops) is given by:
where s=per unit slip, VL= stator line voltage and
n1=stator-to-rotor turns ratio. The inverter dc
voltage VI is given by:
1
1.35 Ld
sVV
n
Expression for torque and speed
The inverter dc voltage VI is given by:
where n2=transformer turns ratio (line side to inverter
side) and =inverter firing angle.
2
1.35 cosL
I
VV
n
Expression for torque and speed(cont’d)
For inverter operation, /2<<. In steady state
Vd=VI (neglecting losses in inductor)
The rotor speed r is given by:
if n1=n2
1
2
cosn
sn
1
2
(1 ) (1 cos ) (1 cos )r e e e
ns
n
Expression for torque and speed(cont’d)
Thus rotor speed can be controlled by controlling
inverter firing angle, .
At =, r=0 and at =/2 , r=e.
Expression for torque and speed(cont’d)
Neglecting losses, the power equations can
be written as
Where =air gap power, =mechanical
output power, P= number of poles
2(1 s)P (1 s)
g I d
m g e m e e
sP V I
P T TP
gP mP
Expression for torque and speed (cont’d)
We know that the torque
The torque may be expressed as:
1
1.35
2L
e d
e
VPT I
n
2
g
e
e
PPT
Static Kramer Drive (cont’d)
At zero speed (s=1) the motor acts as a
transformer and all the real power is transferred
back to the line (neglecting losses). The motor
and inverter only consume reactive power.
At synchronous speed (s=0) the power factor is
the lowest and increases as slip increases. The
PF can be improved close to synchronous
speed by using a step-down transformer. The
inverter line current is reduced by the
transformer turns ratio -> reduced PF.
Static Kramer Drive (cont’d)
A further advantage of the step-down transformer
is that since it reduces the inverter voltage by the
turns ratio, the device power ratings for the
switching devices in the inverter may also be
reduced.
AC Equivalent Circuit of Static Kramer Drive(cont’d)
The per-phase equivalent circuit derived from
these equations (referred to the rotor) is shown
below:
Torque Expression
The average torque developed by the motor =
total fundamental air gap power
synchronous speed of motor
where Pgf’ = fundamental frequency per-phase
air gap power.
' 2
3 32 2
gf rf A
e
e
P I RP PT
s
Torque Expression (cont’d)
The torque equation in term of circuit
parameters
'2
22
' '
32
s Ae
Ae s ls lr
sV RPT
RsR sX sX
s
Static Scherbius Drive
The static Scherbius drive overcomes the
forward motoring only limitation of the static
Kramer drive.
Regenerative mode operation requires the slip
power in the rotor to flow in the reverse
direction. This can be achieved by replacing the
diode bridge rectifier with a thyristor bridge. This
is the basic topology change for the static
Scherbius drive from the static Kramer drive.
Modes of Operation
Four modes of operation of a Scherbius drive
Mode 1: Subsynchronous motoring
Mode 2: Supersynchronous motoring
Mode 3: Subsynchronous regeneration
Mode 4: Supersynchronous regeneration
Mode-1:Subsynchronous motoring
Identical to Static Kramer system
Stator I/P or air gap power(Pg)
is +ve
Slip power (sPg) is +ve and
Return back to line
Line supplies Pm=(1-s)Pg consumed
by the shaft
Slip frequency current creates RMF in the same
direction as in the stator
Mode 3: Subsynchronous regeneration
The shaft is driven by load
mechanical energy converted into electrical
energy and pumped out of stator
With –ve torque, mech. Power i/p Pm increases
with speed
Slip is +ve and Pg is –ve
-ve slip power is fed to the rotor
Mode 2:Supersynchronous motoring
Speed increases beyond synchronous speed
Slip is –ve
Slip power absorbed by the rotor
The phase sequence of slip frequency is reversed
so RMF is opposite to that of stator
Mode 4: Supersynchronous regeneration
Pg remains constant but additional mech power i/p is
reflected as slip power o/p
Cycloconverter phase sequence is now reversed so
that the rotor field rotates in opposite direction
Static Scherbius Drive (cont’d)
One of the limitations of the previous topology is
that line commutation of the machine-side
converter becomes difficult near synchronous
speed because of excessive commutation angle
overlap. A line commutated cycloconverter can
overcome this limitation but adds substantial
cost and complexity to the drive.