PMSM Drives 2
Transcript of PMSM Drives 2
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Department of Electrical and Electronic Engineering
Advanced AC Drives
Permanent Magnet Machine Drives
Part VI
Control of PMSM Drives
Basic vector scheme and control design
Maximum Torque per Amp
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Operating PM synchronous machines
Normal BLAC or PMSM is not able to operate from a fixed voltage and
frequency supply.
If actually required, then a squirrel-cage can be incorporated in the rotor for
starting. When gets to synchronous speed the cage is ineffective.
Can we operate from an open-Loop V-f drive where V=kf? Theoretically yes.
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V-f or V/Hz open loop control
No speed or position sensor required. Increasing speed demand SLOWLY and smoothly. As f increases slowly zero to a speed
up to rated, the motor will run synchronously during the entire starting period. The voltageV f so that V matches the increasing back emf with speed.
The rate of change of frequency will depend on the inertia of the drive. If rate of change is
too high the machine will not start and large torque oscillations occur.
The open loop nature of this control scheme makes it VERY poor in transient performance.
The speed of the PMSM can however be precisely controlled by the excitation frequency
without slip compensation as for IM.
Can be easily supplied from a general purpose V/Hz IM drive.
Cage winding can be used to improve stability and start-up.
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Operating PM synchronous machines
Normal BLAC or PMSM is not able to operate from a fixed voltage and
frequency supply.
If actually required, then a squirrel-cage can be incorporated in the rotor for
starting. When gets to synchronous speed the cage is ineffective.
Can we operate from an open-Loop V-f drive where V=kf? Theoretically yes.
In practice, this is rarely used, especially as vector control comes with almost
no extra cost
Vector control follows the same structure as that with the IM.
We orientate on the rotor flux which is just the direction of the magnet ie. theflux angle is the same as the rotor position.
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IsV
*
V
r
iq*
PI
id* = 0
d/dt
iq
id
r
PI
rje
rje
PI
2/3
3/2
r*
r
Basic vector control of PM machine up to base speedi.e. No field weakening
The scheme is identical to the IM except that the flux angle is the rotor position since the
magnet field is fixed on the rotor
Both d and q currents MUST be controlled. For a non-salient machine, id* = 0
This provides for a simple way of controlling non-salient PMSM up to base speed:
This control strategy can also be used with salient PMSM. It works well, but does not operate atfull potential as reluctance torque component is not utilised.
P/2
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Current loop control of all PMSM machinesi.e. Non-salient and salient
qqrd
dsdd iLdt
diLRiv
mrddr
q
qqq iLdt
diLRiv
The dynamic equations are:
For the id loop design, the plant is just the 1st order linear terms since compensation termswill be used in the implementation:
sLR ds 1
PI
qqr iL
-
+
+
-
*di di
Similarly for the iq control loop design is the same. Note that Lq will be used for the plant
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qqr iLmrddr iL
IsV
*
V
Inverter (power amplifier) PM machine
r
iq*
PI
id* = 0
d/dt
iq
id
r
PI
rje
rje
2/3
3/2
r
The final scheme will have the rotational emf terms added as feed-forward (FF) terms inthe normal manner. All variables are available for the FF terms
As before, the FF terms are useful when speed is rapidly changing
Current loop control of all PMSM machinesi.e. Non-salient and salient
P/2
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Field weakening Control of non-salient machine
For SM PMSMs, can field weaken by imposing NEGATIVE id
In IM, id* began at rated value and was then reduced. In PMSM id*increases
But if we increase id* then the rated can be exceeded.
Therefore need a more sophisticated system see later
qqr iLmrddr iL
Is
V*
V
Inverter (power
amplifier)
PM machine
r
iq*
id*
d/dt
iq
id
r
rje
rje
2/3
3/2
r
PI
PI
22
max_ qda iiI
PI
r*
V
FW
P/2
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Salient Machines: Maximum Torque Per Amp strategy
For Salient PMSMs (buried or inset magnets), we can get increased torque byapplying a negative id* even when we are NOT above base speed
This was because there is also a reluctance torque when dq LL
)]([ qdqdqm LLiiikT
Applying ve id results in an advance angle
d
q
iq
id
i
iLLimm
T4
8sin
222
1max
ik m
)(2
2
qd LLi
k
max
The Torque in terms of is:
Which is maximum at:
)(2sin
2cos
2
qdm LLi
ikT
This is called the MTPAstrategy and should be used
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Salient Machines: Maximum Torque Per Amp strategy
The optimum advance angle is a function of the total current i Expected since reluctance torque is i2 whilst magnet torque is i
d
q
iq
id
i
For a given , can find max_T This gives anddi qi22
qd iii
di
A1i
A2i
A3iqi
iL
LimmT
4
8sin
222
1
max
)(2sin
2cos
2
qdm LLi
ikT
Put max_T into the torque expression:
6N1 AT
13N2 AT
20N3 AT
di qi Create look up table with T input and , output
Hence for a given T, there is an optimum , qidi
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Maximum Torque per Amp loci for various machines
1 shows MTPA locus for a non salient machine. Locus is on the q-axis as the d-axis
current component would not produce any torque.
2. If we had no magnets, (a synchronous reluctance machine), the angle from MTPA would
be such that -id=iq for any T
3. The MTPA locus produced by a salient PMSM is a hybrid of the above thus the locus will
be in between the two loci above
- at low currents, reluctance torque is small; high currents it is large because i2
Torque locus for a non salient PMSM MPTA locus for a synchronous reluctance
machine (salient PMSM without magnets)
field
-T
generating
+T
motoring
qi
di
0
0
loci of i for
maximum
torque per
amp1350
1max sin 0T 1
max
1sin
2T
Torque locus for a salient PMSM
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0
0 +Tmotoring
-Tmotoring
0
i
( )q qi f T
( )d di f T
di
qi
6N1 AT
13N2 AT
20N3 AT
Torque mapping functions
For any (required) torque, there will be a value of id and iq that willgive the maximum torque per amp.
These are shown for both motoring and generating torque
These are stored in a look up table and inserted in the speed loop
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The MTPA Scheme for Salient PMSM
And the control scheme becomes......
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Department of Electrical and Electronic Engineering
Advanced AC Drives
Permanent Magnet Machine Drives
Part VII
Control of PMSM Drives
Operation in constant power region
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Constant Power Applications 1 winding
T1, 1
F, vF, v
T2, 2
r1 r2
22 / rv 11 / rv
22 FrT 11 FrT
Winding applications: paper, fabrics, fibres, rolling mills (metal plate rolling)
Wind at constant force and speed ie: P =Fv = constant
As radius increases, reduces, T increases
Machine obviously rated at P
winding on to reel
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Constant Power Applications 2 - traction
Cars, buses, trams, trains primarily inertial loads, dominated by the moment of inertia J
For an inertial load driven by a motor of a given power rating, the best T- motorcharacteristic for maximising acceleration to any speed is the constant power characteristic
Or: for best acceleration to any speed, a prime mover with a constant power characteristic
will result in the minimum motor power rating
Lower the value ofbase the lower the motor power rating
Maximise the speed ratio max
/base
base max
T,P
Torque
Power
Best machine has the widest speed ratio
these are Salient PMSM designs
MachineTorque Density
Nm/m3Speed
rationoise Cost
AC Surface
Mount PM 28,000 2
AC IPM 25,000 3-10 Induction 15,000 3 Switched
Reluctance 12,000 6
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Constant Power Applications 3
Traction Applications
Note that internal combustion engines have a peak torque in the mid-speed range
This is not well matched
Matching done mechanically using a variable ratio gearbox
Electrical machines with constant power operation need no gearbox
T
Ideal characteristic
Internal combustion enginecharacteristic
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Field Weakening
For an IM and field weaken by reducing isd from isd_rated to zero
For PM machine ; field weaken by increasing negatively id from zero
Both have a voltage limiting condition
But for PMSM, there is a also a current limiting condition
mdod iL
domd iL
max
22Vvv qd
max
22Iii qd
Field weakening can be illustrated using the phasor
diagram (steady state operation)
E (and hence motor voltage V) increases with
speed since
the term acts to reduce the
magnitude ofVand hold it Vmax as speed increases
drddd LjIXjI mrE
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Field Weakening
For an IM and field weaken by reducing isd from isd_rated to zero
For PM machine ; field weaken by increasing negatively id from zero
Both have a voltage limiting condition
But for PMSM, there is a also a current limiting condition
mdord iL
domd iL
max
22Vvv qd
max
22Iii qd
sqrd
sdd Lidt
diLRiv
mrdr
q
qq Lidt
diLRiv
qrqrd Liv
drmrdrq Liv
222222 qrmrdrqd iLLivvv 2
22
qm
d
r
iL
iL
v
Both conditions must be considered together. This is done by studying the constraints in the
(id - iq) plane.
The condition is the equation of a circle in the (id - iq) plane, radius Imax
The voltage constraint can also be written in the (id - iq) plane
To make the working easier, assume a non-salient machine and neglect stator resistance
max
22Iii qd
ForL=Ld=Lq and R=0
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Voltage and Current Limit Circles for non-salient machine
2
22
q
m
dr
iLiL
v
The equation is a circle of radius
Its centre is offset at
L
v
r
Li md
drLV
maxradius
d
md
Li
1000rpm
di
qi
2000rpm
4000rpm
current limitcircle
voltage limit circles
Max speed is 4000rpm
(but zero Torque)
Max iq (and torque) at 2000rpm
occurs with id1, iq11qi
1di
1500rpm
Above 1500rpm, id1, iq1 mustbe inside hashed area
Current is called the
critical current.
If inside current circle, then
speed of machine not limited
by voltage
d
md
Li
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2
22
q
m
d
riLiL
v
The equation is a circle of radius
Its centre is offset at
L
v
r
Li md
Current is called the
critical current. If inside current
circle, then speed of machinenot limited by voltage
d
md
Li
Max speed is 4000rpm
(but zero Torque)
Max iq (and torque) at 2000rpm
occurs with id1, iq1
Above 1500rpm, id1, iq1 must beinside hashed areadrL
V
maxradius
d
md
Li
1000rpm
di
qi
2000rpm
4000rpm
voltage limit circles
1500rpm
Voltage and Current Limit Circles for non-salient machine
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Have:
Hence
The voltage circles can be re-calibrated to be constant flux circles
1maxradius k
L
V
dr
d
md
Li
0.4Wb
di
qi
0.2Wb
0.1Wb
voltage circles
0.3Wb
increasing T
Voltage and Current Limit Circles for non-salient machine
rV
sqr
d
sdd Lidt
di
LRiv
mrdr
q
qq Lidt
diLRiv
qrqrd
Liv
drmrdrq Liv
maxV
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sqqrd
dsdd iL
dt
diLRiv
mrddr
q
qqq iLdt
diLRiv
qqrd iLv For a Salient machine, we have
mrddrq iLv
Putting iq =0 gives the
maximum id coordinates of the
ellipse as:
Voltage and Current Limit ellipses for salient machine
d
m
d Li
qr
s
L
V
max
d
m
dr
s
LL
V
max
d
m
dr
s
LL
V
max
And the maximum iq
coordinates are:qr
s
L
V
max
22
2
2
maxqqd
d
md
r
s iLiL
LV
giving:
which is the equation of an ellipse:
The ellipses get smaller as speed increases
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The MTPA line is where the T lines
are tangential to the I circles
The Minimum Flux per T line is
where theT lines are tangential to
the V ellipses
MFPT means the id, iq for
maximum speed per Torque
Voltage and Current Limit ellipses for salient machine
d
m
d Li
qr
s
L
V
max
d
m
dr
s
LL
V
max
MTPA
MFPT
All points of a particular value of torque form a constant T line
Where the constant T lines are tangential to the current circles
gives the MTPA points(Blue line)
Can also calculate value of T for any value of and flux fromid, i
q
increasing T
)]([qdqdqm
LLiiikT
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Field Weakening Control 1 - Angle Advance method
d
qiq
id
i
Speed controller outputs T*
MTPA calculator yields or iand for MTPAid MTPA, iqMTPA
V
iq*
id*
d/dt
iq
idr
rje
rje
PI
PI
PI
r*
V
sin
cos)(Tfq
)(Tfd
iqMTPA*
idMTPA*
.
1tan
i
PI
.
+
-
+
+
T*
r
Is
V*
r
2/3
3/2
rP/2
Vlim
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r*
d
qiq
id
i
Voltage demands are measured and magnitude V* compared
with a value of voltage Vlim < Vmax (to allow for voltage to increasecurrent)
V*< Vlim (not FW) then will be zero and we are in MTPA mode
Function block has anti-wind up integrator (integrator off at limits)
Is
V*
r
iq*
id*
d/dt
iq
idr
rje
rje
2/3
3/2
r
PI
PI
PI
V*
P/2
V
sin
cos)(Tfq
)(Tfd
iqMTPA*
idMTPA
*
.
1tan
PI
.
Vlim
+
-
+
+
T*
i
Field Weakening Control 1 - Angle Advance method
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d
qiq
id
i
V> Vlim output of PI and function block will be +ve and an extra
will be added to to increase id negatively Field will weaken; Vwill decrease and be regulated to Vlim
In steady state, output of integrator will be finite with non-zero
Is
V*
r
iq*
id*
d/dt
iq
idr
rje
rje
2/3
3/2
r
PI
PI
PI
r*
V
P/2
V
sin
cos)(Tfq
)(Tfd
iqMTPA*
idMTPA*
.
1tan
PI
.
Vlim
+
-
+
+
T*
i
Field Weakening Control 1 - Angle Advance method
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.
Vlim
iq*
id* iq
id
PI
PI
id*
T*
*
iq* *
T*
PI
r* T* T*lim
Tlimit
Flux estimator
iq id
*
MTPAMFPT
Current generator determine id
* and iq
*
No field weakening, id* and iq* lies on OA
When >r_base, flux reduces; id* and iq* lies on
intersection of T* and * contours
Region bounded by OABC
rA
A
B
C
C
B
=0.4
=0.3
=0.2 O
T Limiter
Current generator
Flux contours whenV=Vmax
When V
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Summary of field weakening
Field weakening is very desirable for traction drives since it minimises the motor weightand volume for a given acceleration
For good FW characteristics, we require large Ld inductance so that demagnetising flux
per current is high; this favours the buried magnet PM machine
If is high enough, the speed ratio can be infinite
High saliency ratios also extend the speed ratio; aim to make Lq larger than Ld.
Saliency also allows an increase in torque per amp through exploiting reluctance torque
But, armature reaction effect of buried magnet machines is high, this can saturate the
stator iron paths, increasing the reluctance seen by the magnets; maximum torque per
volume is often higher in surface mount machines
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What you should know
Difference between BLDC and BLAC; basic principle of BLDC
Basic types of BLAC (PMAC) and concept of Saliency
Concept of reluctance torque in salient machines and concept of MTPA
Vector control structure for non-salient and salient types with MTPA
Field weakening, concept of current and voltage circles (or V ellipse)
MFPT and field weakening operating regions
Knowledge of basic dynamic equations; ability to manipulate equations to find flux and
inductances from parameters and operating conditions
Ability to calculate maximum torque given motor parameters
Ability to read current/voltage circles (ellipses) to estimate maximum speed and other
steady state operating conditions