PMSM Drives 1

7/29/2019 PMSM Drives 1

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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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Advanced AC 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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Advanced AC Drives


Part IV


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:


30/51

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



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r

r

M

sqsrd

sdd iLdt

diLRiv

mrdr

q

qq Lidt

diLRiv


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


d

q

iq

id

i


36/51

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.


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


38/51


Advanced AC Drives


Part V


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


40/51

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


42/51

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


43/51

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


44/51

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


45/51

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


46/51

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~~


= +


47/51

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


Ej de~~

RId~qqIjX

~

RIq~

ddIjX~

q

qV~

aV~

dV~


48/51

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


49/51

For Id


50/51

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:


51/51

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

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