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8/10/2019 Emmc Steps Daac Lesson5

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VECTOR CONTROL OF INDUCTION MACHINES

DYNAMIC ANALYSIS AND CONTROLOF AC MACHINES

ERASMUS MUNDUS MASTER COURSE on

SUSTAINABLE TRANSPORTATION AND

ELECTRIC POWER SYSTEMS


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Outline

Dynamic Analysis and Control of AC Machines - Lesson 5 Pagina 2

Principles of Vector Control for induction machines(steady state analysis)

Vector control problem and solutions:

Indirect VC and Direct VC Dynamic behaviour

Flux Observers


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Classical IM equivalent circuit (steady-state)

Dynamic Analysis and Control of AC Machines - Lesson 5

3

The circuit shows the two leakage inductances

The circuit gives explicit account for the air-gap flux

r r e

r r

e

I E P

I sr P

T

33 2

Pagina 3


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Generalized IM equivalent circuit (steady-state)


4

a is a generalized constant

a=N s /Nr yields the classical equivalent circuit

r E a~

Pagina 4


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Rotor flux IM equivalent circuit (steady-state)


5

r E a~

r

m

L L

a

Only one leakage inductance

The circuit gives explicit account for the rotor flux

Pagina 5


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Torque control (steady-state)


6

Stator current can be decomposed into two components.

The two components are in quadrature.

One component is proportional to (establishes) rotor flux. The other component, given the rotor flux, is proportional

to the torque.

s sT s I j I I ~~~

Pagina 6


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Rotor flux component of stator current


7

me

r

m

r

mr

m

r r

m

s L j E

jX E

X L

L

j

E L L

I

~~~

~

r er j E ~~

smr I L ~~

Pagina 7


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Torque component of stator current


8

sT r

mr I L

L I

~~

)()(33 sT r

m sme

er r

e

I L L

I L P

I E P

T

s sT r

m I I L

L P T 2

3

Pagina 8


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Slip frequency equation (steady state)


9

r r m

r

r

r

m

r r m

sT E r s

L L

sr

L

L

E L L

I ~

~~

2

2

s

sT

r

r e I

I Lr

s

smer I L j E ~~

ser

r sT I sr

L j I

~~ Fixing the current components

fixes also the slip frequency.

In fact, fixing the synchronousfrequency and the rotor fluxdefines the mechanicalcharacteristic. Therefore, fixingthe torque defines also the slip.

Pagina 9


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Phasor diagram (steady state)


10

Stator current can be viewed as the phasor sum of twocomponents in quadrature.

Is is proportional to rotor flux.

IsT is proportional to the torque (and is the stator image ofrotor current).

Pagina 10


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Phasor diagram (steady state)


11

+

Pagina 11


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Vector control for IM


12

To achieve vector control for IM means to determine thetwo components of the stator current I s and I sT which areproportional to the rotor flux and the torque.

As a consequence, also the amplitude Is and angle (andfrequency , of course) of the stator currents are determined.

Chosing the currents means also that the equivalent circuitcan be completely solved: it is possible to determine whichis the voltage that allow to achieve the required current.

Finally, also the slip frequency (and therefore themechanical speed) is determined by the currents.

Pagina 12


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From phasors to synch. reference frame


13

The synchronous reference frame is obtained from thearbitrary reference frame, when: )()( t t e

and the d-axis is aligned with the rotor flux: 0qr r dr

The phase relations that hold for phasors are still valid whenwe consider rotating vectors.

Pagina 13


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From phasors to synch. reference frame


14

It is possible to define the equivalent circuit in thesynchronous reference frame, valid in steady state:

Pagina 14


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Vector control problem for IM


15

Knowing the desired rotor flux and torque, it is possible todefine the desired stator current rotating vector.

By using the synchronous reference frame, aligned with therotor flux, the q- and d- axes components of the desiredcurrent are identifed.

PROBLEM

How do we know where the rotor flux is?In PM machines measuring rotor position was enough;

for IM slip must be considered!Pagina 15


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Indirect Vector Control (VSI inverter)


17

*

**

ds

qs

r

r e I

I

L

r s

Estimatedvalues!!!

Rotor flux position

Pagina 17


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Indirect Vector Control (CSI inverter)


18

*

*

*

ds

qs

r

r e I

I

Lr s

Estimatedvalues!!!

CR network =derivative operator

The derivation isneeded to add aterm whichcompensates forphase anglevariations

Pagina 18


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Indirect Vector Control (CSI inverter)


19

be detected. Therefore, the new reference will be I s * instead ofIqds2 *, with a phase error . If not compensated, this errorwill still go to zero eventually, but the dynamic perfomanceswill be deteriorated.

When there is a change inthe reference from I qs1 * toIqs2 *, the resolver blockwill identify the new

amplitude, while the slipcalculator block will helpdetermine the frequency.

The phase change will not

Pagina 19


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Direct Vector Control (VSI inverter)


20

Rotor flux position

Rotor flux position isidentified through the blockCFO (flux observer).

The same block estimatesalso the rotor fluxamplitude, which is usefulto estimate also the torque.

s sT r

m

I I L L

P T

2

3

qsr r

m I L L

P T 23

Pagina 20


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Direct Vector Control (CSI inverter)


21

Pagina 21


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Transient analysis of Vector Controlled IM


22

Machine equations in the synchronous reference frame

)(23

dsqr qsdr r

m ii L L

P T

dseqsqs sqs dt d

ir v

qsedsds sds dt d

ir v

dr r eqr qr r dt d

ir )(0

qr r edr dr r dt

d ir )(0

qr mqs sqs i Li L

dr mds sds i Li L

qr r qsmqr i Li L

dr r dsmdr i Li L

Pagina 22


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qr r edr dr r dt

d ir )(0

dr r eqr qr r dt d

ir )(0

23

Machine equations in the synchronous reference frame withthe d-axis aligned with rotor flux ( r= dr )

= 0

)(23

dsqr qsdr r

m ii L L

P T

dseqsqs sqs dt d

ir v

qsedsds sds dt d

ir v

qr mqs sqs i Li L

dr mds sds i Li L

qr r qsmqr i Li L

dr r dsmdr i Li L

Pagina 23


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24

Equations affected by the condition of rotor flux alignment:

qsdr r

m i L L

P T 23

dr r eqr r ir )(0

dr dr r

dt

d ir 0

0 qr r qsm i Li L

(1)

(2)

(3)

(4)

From (3) we have:

qs

r

mqr i

L

Li

extension of:

r m

r sT I L

L I

~~

and consistent with (2) insteady state:

0dr I Pagina 24


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25

Equations affected by the condition of rotor flux alignment:

qsdr r

m i L L

P T 23

dr r eqr r ir )(0

dr dr r

dt

d ir 0

0 qr r qsm i Li L

(1)

(2)

(3)

(4)

From (1) we have:

dr

qsm

r

r e

i L

Lr

s

extension of:

dr

qr r er e

ir s

or also:

s

sT

r

r e I

I Lr

s

Pagina 25


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Rotor current on d-axis


26

Combining (2) and (5) :

From (2) : 0dr I

during transients.

dr r dsmdr i Li L r

dsmdr dr L

i Li

(5)

dr dr r

dt

d ir 0 in steady state.

)()(

)( si sLr Lr

s dsr r

mr dr

From :

Deriving the rotor flux equation and substituting into (2) :

)()()( si s L si sLr dsmdr r r

Following a step change in i ds , the rotor fluxwill reach its steady state value L mids with afirst order transient defined by the rotor timeconstant r = L r /r r .

A transient current on rotor d-axis may existonly if there is a change in the stator d-axiscurrent. After a first order transient defined by

r = L r /r r , idr will go to zero. Pagina 26


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Indirect control implementation (i ds *,iqs *)


28

)()1(

)( si s

L s dsr

mdr

dr

qsm

r

r e

i L

Lr

s

*

**

11

1

dsr

qs

r

e

i s

i s

Pagina 28


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Indirect control implementation (i ds *,iqs *)


29

Assuming infinte BW of the current controller, a step change in i ds * will cause firstorder transient in the rotor flux dr , with a final value proportional to the current.

)()1(

)( si s

L s ds

r

mdr

*

**

11

1

dsr

qs

r e

i s

i s

Steady state Dynamic

Pagina 29


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Indirect control implementation ( dr *,iqs *)


30

Using dr * as the controlledvariable, instead of i ds *, means thatnow the controller has to calculateids * using (1) and therefore willincorporate a compensation forthe rotor transient behaviour.

)()

1(1

)( ** s s L

si dr r m

ds

*

**

11

dr m

qs

r e

L

i s

(1)

Pagina 30


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Flux Observers for Direct Vector Control


31

Inputs to Flux Observers aremeasurements at machineterminals (typically voltages andcurrents). Using the equations ofthe dynamic model for the IM it is

possible to estimate rotor flux inqd stationary reference frame.

Finally, from these components, itis possible to determine rotor fluxangle and magnitude.

Flux Observers can be open loopor closed loop

Pagina 31


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Flux Observers Voltage model


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Three parameters are needed: r s , Ls , L r /Lm

It is difficult to calculate the integral (1) at low frequencies (open loop observer) If the rotor has closed slots, then L s , even if it is a leakage inductance, will

depend on i r

In general, this observer gives good results at medium and high speeds.

dt r S qds sS qdsS qds iv

S

qdsr

m s

S qds

m

r S qdr

L

L L

L

Li

2

(1)

vqdsS

iqdsS

(r s)^

(Ls-Lm2/Lr )

^

(Lr /Lm )^

( qdsS )^

( qdsS )^

( qdr S )^

Pagina 33


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Flux Observers Current model


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Variables are expressed in the rotor qd reference frame (superscript R )

Rqdr

Rqdr r dt

d r i 0

Rqdr

r

r Rqdsm

Rqdr dt

d r

L L i

R

qdr r

R

qdsm

R

qdr L L ii

Rqdr

r

Rqdr dt

d r

i 1

Rqds

r

m Rqdr s

L i )

1(

Pagina 34


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Flux Observers Current model


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Two parameters are needed: r , Lm

Mechanical position is required in order to identify the rotor reference frame This observer is sensitive to saturation

This observer is suitable also for low speeds

Rqds

r

m Rqdr

s

Li

)

1(

q r

iqdsS

KR (Lm)^/(1+ ^

s)

( qdr R)^ ( qdr

S )^iqdsR

KR-1

Pagina 35


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Flux Observers Closed loop


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A closed loop form for the Flux Observer can be obtained by combining thevoltage model and the current model The gains of the PI regulator will determine a closed loop BW Below this BW, the output if the observer will follow the current model. Above the BW, the regulator will not have effect and therefore the output will

follow the voltage model

q r

iqdsS

KR (Lm)^/(1+ ^

s)

( qdr R)^

( qdr,IS)^

iqdsR

KR-1

vqdsS

iqdsS

(r s)^

(Ls -Lm2/Lr )

^

(Lr /Lm )^

( qdsS)^

( qdsS)^

( qdr,VS)^

PI

CURRENT MODEL VOLTAGE MODEL

Pagina 36

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