PMSM Drives 2

7/29/2019 PMSM Drives 2

1/31

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


2/31

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.


3/31

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.


4/31

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.


5/31

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


6/31

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


7/31

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


8/31

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


9/31

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


10/31

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


11/31

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


12/31

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


13/31

The MTPA Scheme for Salient PMSM

And the control scheme becomes......


14/31

Department of Electrical and Electronic Engineering

Advanced AC Drives

Permanent Magnet Machine Drives

Part VII

Control of PMSM Drives

Operation in constant power region


15/31

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


16/31

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


17/31

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


18/31

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


19/31

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


20/31

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


21/31

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



22/31

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


rV

sqr

d

sdd Lidt

di

LRiv

mrdr

q

qq Lidt

diLRiv

qrqrd

Liv

drmrdrq Liv

maxV


23/31

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


24/31

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


25/31

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


26/31

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



27/31

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



28/31


29/31

.

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


30/31

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


31/31

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

Documents

PMSM Drives 2