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ECE 8830 - Electric Drives
Topic 16: Control of SPM Synchronous
Motor Drives
Spring 2004
Introduction
Control techniques for synchronous
motor drives are similar to those for
induction motor drives. We will
consider both scalar and vector control
for surface PM motor (both sinusoidal
and trapezoidal PM motor) drives,
reluctance motor drives, and wound
field synchronous motor drives.
Sinusoidal SPM Motor Drives
The ideal synchronous motor torquespeed characteristic at a single
frequency excitation is as shown below:
Torque
Motoring
Mode
0
Generating
Mode
Speed
Sinusoidal SPM Motor Drives (cont’d)
Thus, the motor either runs at synchronous
speed or doesn’t run at all. Two control
approaches - open loop V/Hz control and
self-control mode.
In open-loop V/Hz control, the frequency
of the drive signal is used to control the
synchronous speed of the motor.
In self-control, feedback from a shaft
encoder is used to effect the control.
Sinusoidal SPM Motor Drives (cont’d)
Open-loop V/Hz control is the simplest
control approach and is useful when
several motors need to be driven together
in synchrony. Here the voltage is adjusted
in proportion to the frequency to ensure
constant stator flux, s. An implementation
of this control strategy is shown on the
next slide.
Sinusoidal SPM Motor Drives (cont’d)
Sinusoidal SPM Motor Drives (cont’d)
The control characteristics are shown in
the figure below:
Sinusoidal SPM Motor Drives (cont’d)
Neglecting the stator resistance, and using
the field flux f as the reference phasor, a
phasor diagram of the synchronous motor
is shown below:
Sinusoidal SPM Motor Drives (cont’d)
The torque developed by the motor is given by:
 P   s f
P
Te  3  
sin   3   s I s cos 
 2  Ls
2
where Iscos is the in-phase component of the
stator current and  is the torque angle.
If e* is changed too quickly, the system will
become unstable. The max. rate of
acceleration/deceleration is given by:
de*
1P
    Ter TL 
dt
J2
where Ter = rated torque and TL = load torque.
Sinusoidal SPM Motor Drives (cont’d)
A self-controlled scheme for an SPM motor is
shown below:
Here the frequency and phase of the inverter
output are controlled by the absolute position
encoder mounted on the motor shaft.
Sinusoidal SPM Motor Drives (cont’d)
The absolute position encoder required
for self-controlled drives for synchronous
motors are one of two types - an optical
encoder or a mechanical resolver with
decoder.
Sinusoidal SPM Motor Drives (cont’d)
An optical encoder has alternating opaque and
transparent segments. A LED is placed on one
side and a photo-transistor on the other side.
A binary coded disk is shown below:
With 14 rings (14-bit resolution) a resolution
of 0.04 electrical degrees can be achieved for
a four-pole motor with this type of encoder.
Sinusoidal SPM Motor Drives (cont’d)
Another type of optical encoder is the
slotted disk optical encoder. The below
encoder is specifically designed for a 4-pole
motor.
Sinusoidal SPM Motor Drives (cont’d)
There are many slots in the outer perimeter
and two slots 180 apart on the inner radius.
There are four optical sensors S1-S4. S4 is
located on the outer perimeter and the S1-S3
sensors are located 60° apart on the inner
radius. The sensor outputs are as shown below:
Sinusoidal SPM Motor Drives (cont’d)
The block diagram of a resolver with decoder
is shown below:
Sinusoidal SPM Motor Drives (cont’d)
The analog resolver is basically a 2
machine that is excited by a rotor-mounted
field winding. The primary winding of a
revolving transformer is excited by an
oscillator with voltage V=V0sint. The stator
windings of the resolver generate
amplitude-modulated output voltages:
V1  AV0 sin t sin 
and
V2  AV0 sin t cos
Sinusoidal SPM Motor Drives (cont’d)
The decoder converts the analog voltage
outputs to digital position information. The
high-precision sin/cos multiplier multiplies
V1 and V2 by cos  and sin  respectively. An
error amplifier takes the difference of these
two output signals to generate the signal
AV0 sin  t sin(   ). The phase sensitive
demodulator creates a dc output that is
proportional to sin(   ) . An integral
controller, VCO, and up-down counter
together generate an estimated  . Under
steady state conditions the tracking error
will be zero.
Sinusoidal SPM Motor Drives (cont’d)
Vector control of a sinusoidal SPM motor
is relatively simple. Because of the large
effective airgap in this type of motor, the
armature flux is very small so that s 
m  f . For maximum
torque sensitivity (and
therefore efficiency) we
set ids=0 and I s = iqs.
Sinusoidal SPM Motor Drives (cont’d)
The torque developed by the motor can be
expressed as:
3 P
Te    f iqs
2 2 
where  f is the space vector magnitude
( 2 f ) and  f   s cos    s cos  .
A block diagram of a vector control
implementation for a sinusoidal SPM motor
is shown in the next slide.
Sinusoidal SPM Motor Drives (cont’d)
Note: This vector control scheme is only
valid in the constant torque region.
Sinusoidal SPM Motor Drives (cont’d)
The upper limits of the available dc-link
voltage and current rating of the inverter
limit the maximum speed available at rated
torque to the base speed (b). However, it
is often desirable to operate at higher
speeds (e.g. in electric vehicles). Above
base speed, however, the induced emf will
exceed the input voltage and so current
cannot be fed into the motor. By reducing
the induced emf, by weakening the air gap
flux linkages, higher speeds can be
obtained.
Sinusoidal SPM Motor Drives (cont’d)
In order to achieve the field weakening, a
demagnetizing current -ids must be injected
on the stator side. However, this ids must
be large because of low armature reaction
flux, a. This small weakening of s results
in a small range of field-weakening speed
control.
Let us consider next how to extend the
vector control scheme to speeds beyond
base speed (b), i.e. into the field-weakening
region.
Sinusoidal SPM Motor Drives (cont’d)
A phasor diagram for field-weakening
control is shown below:
Sinusoidal SPM Motor Drives (cont’d)
The injected -ids which provides the flux
weakening results in a rotation of the I s
vector. At a’, I s  ids which corresponds to
zero torque and maximum speed, r1. At
this condition, =0, s=s’, Vf=Vf’ and
Vs=Vs’ (see phasor diagram).
The field weakening region can be
increased by increasing the stator
inductance (see torque-speed diagram on
next slide).
Sinusoidal SPM Motor Drives (cont’d)
Sinusoidal SPM Motor Drives (cont’d)
A block diagram of a vector control drive
for a sinusoidal SPM motor including the
field weakening region is shown below:
Sinusoidal SPM Motor Drives (cont’d)
In constant torque mode, ids*=0 but in
field-weakening mode, flux  s is
controlled inversely with speed with -ids*
control generated by the flux loop.
Within the torque loop, iqs is controlled to
be limited to the value,
*
qsm
i
2
s
 I  ids
2
where I s is the rated stator current.
Control of Brushless DC Motor
Drives
Trapezoidal synchronous permanent
magnet motors have performance
characteristics resembling those of dc
motors and are therefore often referred to
as brushless dc motors (BLDM).
Concentrated, full-pitch stator windings in
these motors are used to induce 3
trapezoidal voltage waves at the motor
terminals. Thus a 3 inverter is required
to drive these motors as shown in the
next slide.
Control of BLDM Drives (cont’d)
The inverter can operate in two modes:
1) 2/3 angle switch-on mode
2) Voltage and current control PWM mode
Control of BLDM Drives (cont’d)
The 2/3 angle switch-on mode is shown in
the below figure:
Control of BLDM Drives (cont’d)
The switches Q1-Q6 are switched on so that
the input dc current Id is symmetrically
located at the center of each phase voltage
wave. At any instant in time, one switch from
the upper group (Q1,Q3,Q5) and one switch
from the lower group (Q2,Q4,Q6) are on
together. The absolute position sensor is used
to ensure the correct timing of the
switching/commutation of the devices. At any
time, two phase CEMF’s (2Vc) of the motor
are connected in series across the inverter
input. The power into the motor is 2VCId.
Control of BLDM Drives (cont’d)
In addition to controlling commutation by
the timing of the switches in the PWM
inverter, it is also possible to control the
current and voltage output of the inverter
by operating the PWM in a chopper mode.
This is the voltage and current control
PWM mode of operation of the drive.
Control of BLDM Drives (cont’d)
The average output current and voltage are
set by the duty cycle of the switches in the
PWM inverter. Varying the duty cycle results
in variable average output current/voltage.
Two chopping modes can be used - feedback
mode and freewheeling mode.
In feedback mode, two switches are
switched on and off together (e.g. Q1 and
Q6) whereas in freewheeling mode, the
chopping is performed only on one switch at
a time.
Control of BLDM Drives (cont’d)
Control of BLDM Drives (cont’d)
Consider the feedback mode with Q1 and Q6
as the controlling switching devices. During
the time that these switches are on, the
phase a and b currents are increasing but
during the time that they are off, the
currents will decrease through feedback
through the diodes D3 and D4. The average
terminal voltage Vav will be determined by
the duty cycle of the switches.
Control of BLDM Drives (cont’d)
Now consider the freewheeling mode of
operation. When Q6 is on Vd is applied
across ab and the current increases. When
Q6 is turned off, freewheeling current flows
through Q1 and D3 (effectively shortcircuiting the motor terminals) and the
current decreases (due to the back emf).
Control of BLDM Drives (cont’d)
The steady state torque-speed characteristics
for a brushless dc motor can be easily
derived. Ignoring power losses, the input
power is given by:
Pin  eaia  ebib  ecic  2I dVc
The torque developed by the motor is simply,
Te 
Pin
e
Control of BLDM Drives (cont’d)
The back emf is proportional to rotor speed
and is given by:
Vc  K r
where K is the back emf constant and r is
the mechanical rotor speed (=P/2) e. The
steady state (dc) circuit equation for any
switch combination is:
Vd  2 Rs I d  2Vc
Control of BLDM Drives (cont’d)
The torque expression can be rewritten as:
Te  K .P.I d  K1I d
where P= # of motor poles. If we define the
base torque as:
Teb  K1 I d
I d  I sc
where Isc is the short-circuit current given by:
Vd
K1Vd
I sc 
=> Teb 
2 Rs
2 Rs
Control of BLDM Drives (cont’d)
The rotor base speed rb can be defined as:
 rb   r
Id 0
Vd

2K
The torque-speed relationship can be derived
by combining these equations, yielding:
r 

 Te 
  rb 1   => Te(pu)=1-r(pu)
 Teb 
where Te(pu)=Te/Teb and r(pu)= r/ rb
Control of BLDM Drives (cont’d)
This normalized torque-speed relation is plotted
below. Note the droop in the no-load speed
due to the stator resistance voltage drop.
Control of BLDM Drives (cont’d)
A closed loop speed control system for a
BLDM drive with a feedback mode operation
of the PWM inverter is shown below:
Control of BLDM Drives (cont’d)
Three Hall effect sensors are used to provide
the rotor pole position feedback. This gives
three 2/3-angle phase shifted square
waves (in phase with the phase voltage
waves). The six step current waveforms are
then generated by a decoder.
The speed control loop generates Id* from
the r* command speed. The actual
command phase currents are then generated
by the decoder. Hysteresis current control is
used to control the phase currents to track
the command phase currents.
Control of BLDM Drives (cont’d)
A freewheeling mode close loop current
drive for a BLDM is shown below:
Control of BLDM Drives (cont’d)
In this case the three upper devices (Q1,
Q3, and Q5) are turned on sequentially in
the middle of the positive half-cycles of
the phase voltages and the lower devices
(Q2,Q4 and Q6) are chopped sequentially
in the middle of the negative half-cycles
of the phase voltages to achieve the
desired current Id*. This is all timed
through the use of the Hall sensors and
the decoder logic circuitry. One dc
current sensor (R connected to ground) is
used to monitor all three phase currents.
Control of BLDM Drives (cont’d)
The controller section and power
converter switches outlined by the dotted
line can be integrated into a low-cost
power integrated circuit. An example of a
commercial BLDM controller IC is the
Apex Microtechnology BC20 (see separate
handout).
Control of BLDM Drives (cont’d)
Pulsating torque can be a problem with
BLDM motors (see figure below).
Control of BLDM Drives (cont’d)
The high frequency component is due to
ripple current from the inverter and is
filtered out by the motor. The rounding of
the torque is due to the rounding of the
phase voltages (caused by leakage flux
adjacent to the magnet poles) and this
generates significant 6th harmonic torque
pulsation. A higher number of poles in the
machine can help to alleviate this problem.
Control of BLDM Drives (cont’d)
The speed range of a BLDM motor can be
extended beyond the base speed range
(just as in the case of the sinusoidal SPM
motor). This can be achieved by advancing
the angle  which is used to locate the
position of the current waveforms with
respect to the phase voltage waveforms
(=0 locates the current waveforms in the
center of the voltage waveforms). Also, if
we change from a 2/3 conduction mode to
a  conduction mode.
Control of BLDM Drives (cont’d)
The normalized torque-speed curve for
extended range is shown below for different
 angles for 2/3 conduction mode (solid
lines) and  conduction mode (dotted lines).
Simulation of PM Synchronous
Motor Drives
Project 5 at the end of Ch. 10 Ong provides
a study of a self-controlled permanent
magnet synchronous motor. The motor
parameters for the 70 hp, 4-pole PM motor
are given in the table below:
Simulation of PM Synchronous
Motor Drives (cont’d)
The steady state equations used in the simulation are
given in the following table:
Simulation of PM Synchronous
Motor Drives (cont’d)
If we assume that the output torque
varies linearly with stator current Is, the
torque expression can be rewritten as:
 Vs
K 
x
 q
2

 Vs cos   Em 
 Vs cos   Em  EmVs
2
sin



(
x

x
)
sin 




d
q 
xd
xd
xq





2
This is a nonlinear equation with a single
unknown, . Once  is found, the current
and voltage components in the q and d
rotor reference frame and the power
factor angles and the stationary q, d
current components can be calculated.
Simulation of PM Synchronous
Motor Drives (cont’d)
The steady state curves are shown below:
Simulation of PM Synchronous
Motor Drives (cont’d)
Some observations from these curves:
 Output torque  Iqe and Iq (almost linear);
thus torque control can be accomplished
by controlling Iqe (or Iq) with Id controlled
as shown.
 The power factor angles
= 1/2 torque angle. This
results in the phasor
diagram shown (for the
motoring mode):
Simulation of PM Synchronous
Motor Drives (cont’d)
A Simulink simulation model for a selfcontrolled PM drive is shown below:
Simulation of PM Synchronous
Motor Drives (cont’d)
Some points regarding this simulation model:
 iq and id are used to control the output
torque.
 Torque command is implemented using a
repeating sequence source.
 A rate limiter is used to limit the reference
torque input to the torque controller.
 The inner id and iq control loops are closed
loops.
Simulation of PM Synchronous
Motor Drives (cont’d)


The feedback block uses the stator phase
currents and rotor position to generate id
and iq.
The coordinated reference values for id*
and Vs* are generated by separate
function generator blocks (Id-Iq and VsTem, respectively) implemented using a
curve fit to the steady state data shown
earlier.
Dynamic simulation results are shown on
the next slide.
Simulation of PM Synchronous
Motor Drives (cont’d)