pmsm drives 1
TRANSCRIPT
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Advanced AC Drives
Permanent Magnet (PM) Machines
Part I Introduction
Part II Brushless DC Drives
Part III Permanent Magnet (PM) AC Drive
Part IV PM AC Drive Equations
Part V Alternative Representations
Part VI Control of PMAC Drive MTPA
Part VII Control of PMAC Drive Field Weakening
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Advanced AC Drives
Permanent Magnet (PM) Machines
Part I
Introduction
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Characteristics of PM machines
6-pole permanentmagnet rotor
PM motors have the fastestgrowing market share
Magnetic field from PM affixed onrotor
No current in rotor- no rotor losses
- most efficient machine
No magnetising current- more torque per amp
- converters more efficient
High magnet flux densities- highest Torque/Power Density
of all machine types
Simple rotor, low inertia- very high dynamics
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Characteristics of PM machines
Relatively simple construction, no brushgear BRUSHLESS MACHINE
Design flexibility than induction- high pole number machines
- large radius
- axial flux machines
- transverse flux machines
- concentrated wound machines
Magnets are expensive- demand for machines pushing up price
- one country dominates market
More difficult to construct than IMs
Magnets lose magnetism at temperatures 150-250C- not suitable for use in high temperature environments
- higher the temperature, easier to demagnetise magnets
Cannot be operated without a power converter, cannot operate from mains
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Application Areas
High Performance servo drives
- high acceleration, positioning applications
High efficiency drives
Automotive applications- Hybrid and electric cars
- Starter generators
- Power steering
Aerospace Applications- Undercarriage actuators
- Cabin air compressors, air conditioning
- Future actuators for flight surfaces
Domestic Applications- Air conditioners
- Washing Machines
Aerospace actuation : tens of kW
Electric & Hybrid Vehicles
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Application Areas
Ship Propulsion : up to 18MW
Wind Generation : up to 5MW
High pole number, large radius drives
Low speed applications
Renewable energies- Directly connected wind generator
- tidal and sea current generators
Direct drive (no gear box) ship motors
http://www.ship-technology.com/contractors/propulsion/abb/ -
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Department of Electrical and Electronic Engineering
Advanced AC Drives
Permanent Magnet Machine Drives
Part II
The Brushless DC Drive
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BLAC - BrushLess AC PM Machine- also known as PM synchronous machine- sinusoidal back-EMF (open cct voltage)- sinusoidal current excitation
BLDC - BrushLess DC- also known as Trapezoidal motor- trapezoidal back-EMF
- square wave current excitation
BLAC BLDC
BLAC BLDC
Magnet flux density in air gap
BLAC: Sinusoidal back-emf achieved by
120 elec magnet span and windingsgiving sinusoidal mmf
BLDC: Trapezoidal back-emf achieved
by 180 elec magnet span and windings
square wave mmf
Types of PM machineTypes of PM machine
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The principle is simple
The flux lines constant over the 180; flux is maximum at 1, zero at 2 etc Voltage is rate of change of flux
At 1, current in A-phase as shown; stays like this until field reverses at 3
At 3 current commutates; a hall sensor gives a logic signal
Principle of BLDC machinePrinciple of BLDC machine
1 2 3 4
A
2 3 4
A
1
VI
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There are 3 phases, A, B, C
Each is switched when the change of
magnet polarity nears the phase
The switching of the current lasts for
120 and is provided by a 3-leggedinverter as shown. It is an electronic
commutator.
2 devices conduct at any time
Q1 Q3 Q5
Q2Q6Q4
The electronic commutatorThe electronic commutator
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The Torque developed is T = kBI
To vary the torque, we vary the current; the two conducting devices arepulse width modulated
The PWM converter voltage is shown below
IfI Vm, I rises etc; else off
Control of BLDC machine currentControl of BLDC machine current
1 2 3 4
A
2 3 4
A
1
VI
2 3 41
V
I
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I
Inverter (power amplifier)BLDC
I*
r
PI
r *
r
counter
commutatork
Hall effect devices mounted in the motor detect position. Crude - if greater resolution required a more expensive encoder can be used.
Position signal pulses can be used to give a speed signal. A speed loop
feeding a current loop is conventional; current loop is hysteresis control
Control of BLDC machineControl of BLDC machine
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BLDC machine torque rippleBLDC machine torque ripple
BLDC drive operation has lot of torque ripple.
Price paid for simple control and sensing
Torque ripple has a number of sources, some
machine related others due to the way the drive
is operated.
Sources of torque ripple are:
Back-EMF Harmonics (machine related).Causes hump in torque waveform
Switching Ripple (inverter related);proportional to the hf (>5kHz typical) PWMripple. Not a problem because the mechanical
load inertia filters out its effect on speed.Commutation Ripple (inverter related). Seriousdue to phase current commutations from off-going inverter phase to the next on-coming
phase at the end of each /3 interval.
Simulated torque waveform for a BLDC
drive with PWM-regulated six-step
current waveform.
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BLDC Drive RequirementsBLDC Drive Requirements
BLDC motor drives chosen for simple cheap applications.
Control strategy can easily be implemented using digital circuitry (no
P). But intelligent control processing becoming ever cheaper
BLDC output characteristics are however inferior to BLAC drives in
terms of torque and current smoothness. Torque density is high, potentially higher than BLAC due to better
utilisation of the magnetic circuit.
Machine needs to be star-connected since one phase needs to be
open-circuited at any one time.
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IM vs BLDC vs BLAC
In the rest of this course we will focus on brushless AC machines
Also called Permanent Magnet AC machines.
IM BLDC BLAC
Motor Efficiency + +++ +++
Torque Smoothness +++ + +++
Torque Density + +++ +++
Open Loop Control +++ - -
Closed Loop Simplicity + +++ +
Minimum Control Sensors + +++ +
Machine design flexibility + ++ +++
Extended Speed Range ++ + +++
Motor Robustness +++ + ++
Cost - motor
Cost converter, sensors&
control
(vector
drive)
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Department of Electrical and Electronic Engineering
Advanced AC Drives
Permanent Magnet Machine Drives
Part III
The Permanent Magnet AC Drive
Introduction
Magnetic propertiesSaliency
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d-q rotating reference frame for PMSM
f
d-
axis
q-axis
f
Flux plot of a 2-Pole PMSM with zero statorcurrent
Field orientation is in direction of magnet flux.
Unlike IM the magnet flux in PMSM rotates at the same
speed as the rotor
ie. sl = 0; called a synchronous machine since
Thus the direct or d-axis is aligned with the
Permanent Magnet flux vector
This means that the d-axis is fixed to the rotor
The q-axis bisects the section between
the permanent magnets.
er
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Idealised 3-phase, 2-pole Permanent Magnet Machine
M
Field will rotate at r = d/dt (electrical rad/s)
called the flux or rotor angle
With no id, the torque is: MqkiT
IfP knows all the time, then:Inject 3-ph currents which
transforms into id, iq
iqq
d
Currents iq setting up mmf in qdirection is called the torque
current
id is field current - Not required since
machine is magnetised by magnets
+ve id
will add to magnet flux
- but not much (iron will be near saturation)
- ve id will act against magnet flux (less flux in d-axis)
id
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IsV*
V
Inverter (power amplifier)PM machine
r
iq*
PI
id* = 0
d/dt
iq
id
r
PI
Ref [8,9]
rj
e
rje
PI
2/3
3/2
r *
r
Basic vector control of PM machinewithout id current
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Permanent Magnet Excitation
The permeability of a magnet is the
slope of the straight line which
intercepts the axis at the remenancepoint (Br). The permeability for
ferrite and rare earth magnets is
approximately that of free space
(r ~1.05 to 1.07)
Once off the linear part of the curve
(knee-point), the magnet is wholly orpartially demagnetised and must be
re-magnetised.
Permanent Magnets are Hardmagnetic materials: retain
magnetisation when the
external field is removed
Br remanent flux density
Hc coercive force
X103
06.1
10x720xx104/96.0
/
37
corr HB
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Permanent Magnet Materials
Example of temperature variation for a particulargrade of NeFeBr magnets
Metal magnets (Alnico)
- Oldest and rarely used
Ceramic magnets (Ferrites Ba, St)- Cheapest and widely used; Max B around
0.45T Rear Earth magnets (NdFeB and SmCo)
- Most modern and relatively expensive- Best performance max B around 1.25T
Magnetism lost at Curie Temperature- NdFeB is low: 120-180C
Easier to demagnetise as T goes up- Knee point travels up curve- Br and Hc also reduce as shown- Reversible up to Curie T, but still serious
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Permanent Magnet Properties
A current near the PM can also
demagnetise it armature reaction
important since best place to put load
current in a PM machine! see diagram
Can thus limit max transient torque
Option - bury PM inside iron; shields
magnet from torque current and gives
good field weakening capability- but field due to iq now much higher
since it is next to iron and not magnet- some loss of torque per amp
Load current iq near PM
d
q
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Concept of Saliency
PM machines can be salient - like traditional wound rotor salient synchronousmachines.
This means that magnetic (iron) path in one direction eg the d-axis, is not thesame as in the q-axis
In a traditional synchronous machine, the q-axis has a lot of air so that the q-axiscoil (red coil below) has low inductance; seen that Ld >Lq
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In a PM machine, the magnets, may be as shown
Permeability of the magnets is low compared to that of magnetic steel.(permeability of magnets ~ permeability of air)
In PMSM the inductance of the d-axis coil is smaller than the inductance of the qaxis coil Ie. LdLq
Concept of Saliency
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Different types of PM machine
Salient and non-salient
(a) Surface Mount PM machine; magnets fixed onto rotor; retaining sleeve forstrength
In a SM PM machine Ld = Lq since permeability of magnet and air are the same
(b) Inset PM machine (IPM); magnets set into surface; Lq>Ld - SALIENT
(c) Interior Magnet (or buried) PM machine: inside iron; Lq>Ld - SALIENT
c)
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Department of Electrical and Electronic Engineering
Advanced AC Drives
Permanent Magnet Machine Drives
Part IV
The Permanent Magnet AC Drive
Machine Equations
Maximum Torque per Amp
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The 3 stator coils A,B,C can be represented by
TWO stationary coils Each stationary coil has resistance and rate of
change of flux:
ssssdt
dRiv ssss
dt
dRiv
ssssdt
dRiv
There are no rotor coils
Dynamic Equation of PM BLAC machine
Mr
S
S
r
)cos( ssrmsss iLdtdRiv
)sin( ssrmsss iLdt
dRiv
)( iLedt
dRiv s
j
msssr
ssrms
ssrms
iL
iL
sin
cos
The flux in each stator coil is:
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s
q
r
e
xdxq
x
d
s
rj
ssdq evv
rj
ssdq eii
rj
ssdq e
rj
sdqs evv
rj
sdqs eii
rj
sdqs e
Now transform into rotating coordinates dq frame rotating at r
)( ssj
msss iLedt
dRiv r
mrsdqsr
sdq
sssdqsdq
j
mr
j
sdqsr
jsdqs
s
j
sdq
j
sdq
j
sdqs
j
ms
j
sdq
j
sdq
jiLjdt
diLRiv
ejeiLjedt
idLReiev
eiLedt
dReiev
rrrrr
rrrr
Dynamic Equation of PM BLAC machine
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r
r
M
sqsrd
sdd iLdt
diLRiv
mrdr
q
qq Lidt
diLRiv
Dynamic Equation of PM BLAC machine
qqrd
ddd iLdt
diLRiv
mrddr
q
dqq iLdt
diLRiv
For a salient machine, Ld Lq, then:
qqq iL
mddd iL The flux linking the d-axis coil is magnet+ flux due to any id:
The flux linking the q-axis coil is flux due to any i q:
Drop suffix s since only stator coils
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The back-emf of a PMAC machine
mrddr
q
dqq iLdt
diLRiv
Spin the rotor at a speed r with nocurrent applied to stator
- measure voltage at terminals AA
qqrd
ddd iLdt
diLRiv
0dv mrqv
mraqd Vvv ~22
mrI
a EV 0~
M
E
r
E is called the motor back-emf. It is easy tomeasure. Hence m is easy to determine
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Torque production in PMSM
Torque is: 32
Pk For the rms convention:
The d and q axis flux linkages are given by :
1st term is called the magnet alignment torque
2nd term is proportional to (Ld-Lq) is called the reluctance torque. Define angle called the advance angle from q-axis to the current vector.
For a negative id, is positive, for a positive id it is negative
Magnet alignment
componentReluctance
component
qqq
mddd
iL
iL
)()(
qdqdqm
dqqqmqdd
LLiiikT
iiLiiiLkT
d
q
iq
id
i
)(dqqd
iikT
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Express torque as a function of stator current
Determine the best operating point producing the torque with the minimum stator currentand hence with optimal efficiency.
Now, if we substitute for id and iq:
)](cossincos[2
qdm LLiikT
)]([qdqdqm
LLiiikT
aqd Iiii~22
cos
sin
ii
ii
q
d
Into the torque expression:
We get:
d
q
iq
id
i
The magnet flux and Ld, Lq are constant. Therefore, for a given ithere is a value of which will maximize T
In a SMPM machine, Ld = Lq. Therefore
and is maximum when
cosiT m0i.e.0 di
)(2sin
2cos
2
qdm LLi
ikT
Torque production in Salient PMSM
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For a given current, we plot
Maximum torque/amp occurs in a salient pole PMSM machine for >0
When =0 , i = Ia = iq and reluctance torque is zero.
If there is saliency, the required for max torque/amp, varies with current since thesaliency torque increases with i 2 while the magnet torque increases with Ia
The relative amplitudes of the magnet and reluctance torque terms are set during themachine design in order to vary the relative amplitudes ofLd and Lq.
)(2sin
2cos
2
qdm
LLi
ikT
ik m
)(2
2
qd LLi
k
as a function of
Torque production in Salient PMSM
d
q
iq
id
i
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The plot below shows torque varies as a function of , for various values ofIa.
The higher the current, the greater the angle of advance needs to be to operateat maximum efficiency.
To determine the maximum torque point we can differentiate the torque equationwith respect to and equate to zero.
Torque production in Salient PMSM
d
q
iq
id
i
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Maximum Torque per Ampere (MTPA)
Have
)(2sin2cos
2
qdm LL
i
ikT
0)(2cossin 2 qdm LLiikd
dT
02cossin2 Liim
0)sin21(sin 22 Liim
0sinsin2222 LiiiL m
where )( qd LLL
iL
LimmT
4
8sin
222
1
max
Which will be used in the vector control of all salient PM machines
The variation can be more complex since Ld, Lq and hence L vary aresubject to saturation as Ia increases. This can be experimentally obtained .
02 cbxaxof form
d
q
iq
id
i
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Department of Electrical and Electronic Engineering
Advanced AC Drives
Permanent Magnet Machine Drives
Part V
The Permanent Magnet AC Drive
Alternative representations
Phasor representation
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PMSM Dynamic model as equivalent circuit
D-axis equivalent circuit Q-axis equivalent circuit
qqrd
dsdd iLdt
diLRiv
mrddr
q
dsqq iLdt
diLRiv
qmqlqqqsq iLLiL )(
fmddmdld
mdmdldmddsd
iLiLL
iLLiL
)(
)()(
sqe
sde
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Phasor Representation of PMSM machines
We have introduced the PMSM equations in terms of space vectors
In nearly all text books and most papers, PMSM machines are alsorepresented in terms of phasors
i.e. steady state sinusoidal voltages and currents applied to Phase A(and B and C)
This is because PMSM has similarities to wound-rotor synchronousmachines which are the main generator in power systems
Machine designers also analyse their steady state characterisitcs interms of phasors
The relationship between the phasor tool (for steady state) andspace vector tool (for dynamic) representation is visually very close;
mathematically it is a little tricky
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If we say that A goes through zero at t=0
The rms magnitude becomes the magnitude of the complex number
The phase displacement (degrees or radians) becomes the angle of thecomplex number
10 B
80
A
4
B is: 804 tsin 802
4
tsin 10 02
10A is:
Revision of Phasors 1
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Ammeter 1
Ammeter 2
Ammeter 3
?1I
~
2I~
tsin)t(i 31
0
2
31 I~
tcos)t(i 42
902
42 I~
02
31 I~
902
42 I~ 3
4tan
2
5~~~ 1321
IIIi1(t) i2(t)
53
Revision of Phasors 2
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Difference between a vector and a phasor
A phasor relates only to steady state quantities
- phasor magnitude is the rms value of the SS sinusoid
- phasor direction is arbitrary, the angle between the phasors represents the phase
difference between sinusoids
A vector is in direction of mmf
direction of coil- This defines direction of voltage
across and current through coil
- Magnitude is size of voltage, current
etc
- For single coil, the vectors are in
same direction
C:\ac vector drives\vector ill
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Phasor equations from vector equations
For 3-phase coils in a machine, the 2-d space can be represented
as an argand diagram There is then a direct mapping between the steady state space
vectors and the phasor quantities in the 3-phase coils
A rotating vector in steady state has a dc value
Its value projected onto the A-coil axis (or alpha) axis is sinusoidal
Let rotating vector x (blue) trace/projects sinusoid as shown
X0
The vector y (red) traces/projects sine wave 90 aheadY90
The vector z (green) traces/projects sine wave lagging
Z-30
r = e
A
A
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r
r
M
Building Phasor equations of PM BLAC machine
qqrd
ddd iLdt
diLRiv
mrddr
q
dqq iLdt
di
LRiv
Let all be in steady state, with r = e
qqedd iLRiv
meddeqq iLRiv
Ridqqe iL
sdv
v
Riq
dde iL
Eme d
q
qv
EiLRiv ddeqq
Dynamic equations of Salient PM machine
- drop suffix s since no other coil
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sqqesdsd iLRiv
d
EiLRiv sddesqsq
phXx
2
1
As phasors, they are sinusoidal quantities, so we write x them as
The magnitude is the rms phase quantity
X~
RId~
qqIX~
sqRI~
ddIX~
q
qV~
aV~
dV~
We also use the impedances ded LX qeq LX
qqdd IXRIV ~~~
EIXRIV ddqq~~~~
dI~ is the Ia current which produces a field in
parallel with the magnet
is the Ia current which produces a field
perpendicular to the magnet
qI~
qda III~~~
22 ~~~
qda IIINote:
Eme~~
Building Phasor equations of PM BLAC machine
= +
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Phasors are always complex quantities:
It is conventionalto make the d-axis quantities purely real
And the q-axis quantities imaginary
Hence we multiply appropriate phasors by j to make their
directions consistent with the phasor Argand diagram
)/(tan~ 122 abbajbaX
0~ jII dd qq jII 0
~
a d d q qV E I R j I X j I X
EjXRIjXRIV qqdd~
)(~
)(~~
EIjXRIV ddqq~~~~
qqdd IjXRIV
~~~
qda III~~~
qd VVV~~~
)~~~
(notq
Vjd
VV
Building Phasor equations of PM BLAC machine
Ej de~~
RId~qqIjX
~
RIq~
ddIjX~
q
qV~
aV~
dV~
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Phasor diagram for Salient PM with positive Id
For Id>0, the stator produces MMF
distribution around the airgap that
augments the d-axis magnet flux
The stator current is said to bemagnetising.
The flux produced by the MMF
associated with Id induces a voltage jXdIdin the q-axis, which adds to Eas shownin the phasor diagram.
The d and q axis voltage magnitudes are:
sind q q d V V I X I R
cosq d d qV V E I X I R
EjXRIjXRIV qqdd~
)(~
)(~~
V: Supply Voltage phasor
E: Back EMF phasor
Load angle Current Angle Power Factor
angle
Phasor Diagram of salient PM machine +ve Id
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For Id
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Phasor Diagram of non-salient PM Machine
EjXRIV a~
)(~~
Phasor diagram for Non-Salient (surface mount)
PM with general Id
EjXRIjXRIV qd~
)(~
)(~~
qda III
~~~
Since:
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Phasor forms of Maximum Torque per Amp
)(2sin2cos
2
qdm LLi
ikT
)(2sin
2cos
2
qda
a
e
XXI
EIk
T
ded LX qeq LX meE
aIi~
a
a
TXI
XIEE
4
8sin
2221
maxAnd it's easy to show that:
EjXRIjXRIV qd~
)(~
)(~~
Note that T and max are independent ofe