ECE 8830 - Electric Drives
Topic 11: Slip-Recovery Drives for
Wound-Field Induction Motors
Spring 2004
Introduction
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.
The oldest and simplest technique to
invoke this slip-power recovery induction
motor speed control is to mechanically vary
the rotor resistance.
Introduction (cont’d)
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
Speed Control by Rotor Rheostat
Recall that the torque-slip equation for an
induction motor is given by:
Vs2
 P  Rr
Te  3  
.
2
 2  s e  Rs  Rr / s    e2 ( Lls  Llr ) 2
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.
Speed Control by Rotor Rheostat
(cont’d)
Speed Control by Rotor Rheostat
(cont’d)
With R1=0, i.e. slip rings shorted, speed is
determined by rated load torque (pt. A). As
Rr increases, curve becomes flatter leading
to lower speed until speed becomes zero for
Rr >R4.
Although this approach is very simple, it is
also very inefficient because the slip energy
is wasted in the rotor resistance.
Speed Control by Rotor Rheostat
(cont’d)
An electronic chopper implementation is
also possible as shown below but is
equally inefficient.
Static Kramer Drive
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)
A schematic of the static Kramer drive is
shown below:
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.
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,
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.
Static Kramer Drive (cont’d)
Voltage Vd (neglecting stator and rotor
voltage drops) is given by:
1.35sVL
Vd 
n1
where s=per unit slip, VL= stator line voltage
and n1=stator-to-rotor turns ratio. The
inverter dc voltage VI is given by:
1.35VL cos 
VI 
n2
where n2=transformer turns ratio (line side
to inverter side) and =inverter firing angle.
Static Kramer Drive (cont’d)
For inverter operation, /2<<. In steady
state Vd=VI (neglecting ESR loss in inductor)
=>
n1
s
cos 
n2
The rotor speed r is given by:
n1
 r  (1  s ) e  (1  cos  ) e  (1  cos  ) e if n1=n2
n2
Thus rotor speed can be controlled by
controlling inverter firing angle, .
At =, r=0 and at =/2 , r=e.
Static Kramer Drive (cont’d)
It can be shown (see text) that the torque
may be expressed as:
 P  1.35VL
Te   
Id
 2  e n1
The below figure shows the torque-speed
curves at different inverter angles.
Static Kramer Drive (cont’d)
The fundamental component of the rotor
current lags the rotor phase voltage by r
because of a commutation overlap angle 
(see figure below). At near zero slip when
rotor voltage is small, this overlap angle
can exceed /3 resulting in shorting of the
upper and lower diodes.
Static Kramer Drive (cont’d)
The phasor diagram for a static Kramer
drive at rated voltage is shown below:
IL
Note: All phasors are referred to stator.
Static Kramer Drive (cont’d)
On the inverter side, reactive power is
drawn by the line -> reduction in power
factor (L> s). The inverter line current
phasor is IT. The figure shows IT at s=0.5
for n1=n2. The real component ITcos
opposes the real component of the stator
current but the reactive component ITsin
adds to the stator magnetizing current.
The total line current IL is the phasor sum
of IT and IS. With constant torque, the
magnitude of IT is constant but as slip
varies, the phasor IT rotates from =90
at s=0 to =160 at s=1.
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 stepdown 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.
A starting method for a static Kramer
drive is shown on the next slide.
Static Kramer Drive (cont’d)
The motor is started with switch 1 closed and
switches 2 and 3 open. As the motor builds up
speed, switches 2 and 3 are sequentially closed
until desired smax value is reached after which
switch 1 is opened and the drive controller takes
over.
AC Equivalent Circuit of Static
Kramer Drive
Use an ac equivalent circuit to analyze the
performance of the static Kramer drive. The
slip-power is partly lost in the dc link
resistance and partly transferred back to the
line. The two components are:
Pl=Id2Rd
1.35VL I d
cos 
and Pf 
n2
Thus the rotor power per phase is given by:

1.35VL I d
1 2
'
'
P '  Pl  Pf   I d Rd 
cos  
3
n2

AC Equivalent Circuit of Static
Kramer Drive (cont’d)
Therefore, the motor air gap power per phase
is given by:
P  I Rr  P ' P
'
g
2
r
'
m
where Ir=rms rotor current per phase,
Rr = rotor resistance, and
Pm’ = mech. output power per phase.
AC Equivalent Circuit of Static
Kramer Drive (cont’d)
Only the fundamental component of rotor
current, Irf needs to be considered. For a
6-step waveform,
I rf 
6

Id
Thus, the rotor copper loss per phase is
given by:
1 2
P  I Rr  I d Rd  I r2 ( Rr  0.5 Rd )
3
'
rl
2
r
AC Equivalent Circuit of Static
Kramer Drive(cont’d)
The mechanical output power per phase is
then given by:
Pm’ = (fund. slip power) (1-s)/s
 2
 (1  s)
 1.35VL
  I rf ( Rr  0.5Rd ) 
I rf cos  
3 6 n2

 s
AC Equivalent Circuit of Static
Kramer Drive(cont’d)
The resulting air gap power is given by:
RA
P  I RX  I
s
'
g
2
rf
2
rf
2 
where: RX    1 ( Rr  0.5Rd )
 9

 1.35VL
RA  ( Rr  0.5Rd ) 
cos 
and
3 6 n2 I d
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:
Static Kramer Drive Example
Example 6.3 Krishnan
Torque Expression
The average torque developed by the
motor = total fundamental air gap power
synchronous speed of motor

'
2

P
I
P
P
  gf
  rf RA 
Te  3  
 3  


 2  e
 2  s 
where Pgf’ = fundamental frequency perphase air gap power.
Torque Expression (cont’d)
A torque expression in terms of
inverter firing angle may be derived
(see text pg. 320) resulting in:
2
cos 
 P  V  cos   s

Te  3  
 
n2
 2  e Rr  sn2  n1
2
s
 s
cos   
  s 
 
sn2  
  n1

2
Torque Expression (cont’d)
The torque-speed curves at different firing
angles of the inverter are shown below:
Harmonics in a Static
Kramer Drive
The rectification of slip-power causes
harmonic currents in the rotor which are
reflected back into the stator. This results
in increased machine losses. The
harmonic torque is small compared to
average torque and can generally be
neglected in practice.
Speed Control of a Static
Kramer Drive
A speed control system for a static Kramer
drive is shown below:
Speed Control of a Static
Kramer Drive (cont’d)
The air gap flux is constant and the torque
is controlled by the dc link current Id
(controlled in the inner control loop). The
speed is controlled via the outer control
loop (see performance curves below).
Power Factor Improvement
As indicated earlier, the static Kramer
drive is characterized by poor line PF
because of phase controlled inverter.
One scheme to improve PF is the
commutator-less Kramer drive - see Bose
text pp. 322-324 for description.
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.
Static Scherbius Drive (cont’d)
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.
Static Scherbius Drive (cont’d)
Another approach is to use a double-sided
PWM voltage-fed converter system as
shown below:
Modified Scherbius Drive for
Shipboard VSCF Power Generation
Another approach that has been used for
stand-alone shipboard power generation
is shown below:
Modified Scherbius Drive for Shipboard VSCF Power Generation (cont’d)
In this approach an induction generator
provides real stator power Pm to a 3 60Hz
constant voltage bus which is equal to the
turbine shaft power and the slip power fed
to the rotor by a cycloconverter. The stator
reactive power QL is reflected to the rotor as
sQL which adds to the machine magnetizing
power requirement to give the total reactive
power QL’ of the cycloconverter. This power
is further increased to QL” at the
cycloconverter input by the shaft-mounted
synchronous exciter.
Modified Scherbius Drive for Shipboard VSCF Power Generation (cont’d)
The slip frequency and its phase sequence are
adjusted for varying shaft speed so that the
resultant air gap flux rotates at synchronous
speed.
At subsynchronous speeds the slip power
sPm is supplied to the rotor by the exciter
and so the remaining ouptut power (1-s)Pm
is supplied to the shaft. At supersynchronous
speeds, the rotor output power flows in the
opposite direction so that the total shaft
power increases to (1+s)Pm.
Modified Scherbius Drive for Shipboard VSCF Power Generation (cont’d)
Rotor voltage and frequency vary linearly
with deviation from synchronous speed.
For example, if the shaft speed varies in
the range of 800-1600 rpm with 1200 rpm
as the synchronous speed (s=0.33) the
range of slip frequency will be 0->20Hz
for a 60Hz supply frequency.