torque control of induction machines - lth 13/l12(inductionmotor).pdfdelta rect mod angle rec_to_pol...

Industrial Electrical Engineering and Automation

Lund University, Sweden

Torque Control of

Induction Machines ...

… as compared to PMSM

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© Namn Namn Föredragstitel

The Induction Motor

Three Phase Stator

No Magnets in the Rotor

Rotor as Short Circuited

”Cage”

The rotor current must be

induced

Three Phase Stator

Three phase power

electronics

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A look under the hood

Motoraxel

Kullager

Lagersköld

Uttagslåda

Fläkt

StatorplåtpaketRotor

Statorlindning

Kylfläns

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Advantages

• Self starting when connected to the power

grid

• Robust and reliable

• Cheap

• Low maintenance

• Standardized

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AM - dynamics

Start here … Move the stator current one

step – what happens in the

rotor?

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si

si

ri

Statorströmvektor- momentbildande komponent- magnetiserande komponent.

Rotorströmvektor

Consequencies

• The rotor current is

– Proportional to

The stator flux and

The speed difference (both tangentially and radially)

– Inversely proportional to the rotor resistance

– 90 degrees lag versus the flux

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Torque properties

r

srrs

RiT

2̂

T start T n

T m ax

n n n s

n

T

n k

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Connection

Motor 3~ 50 Hz IEC 34-1

No.

kW2.2 r/min2820

cos 0,89

V

A

380

4.7

V

A

220

8.15

IP 54 FCl.kg19.0

U1 V1 W1

W2 U2 V2

L1 L2 L3L1 L2 L3 L1 L2 L3

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Single phase operation

• Steinmetz connection

• Shaded pole motor

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Summering AM

• Rotationsproblemet – Med växelströmslindning i statorn

• Spänningen – Proportionell mot frekvensen

• Varvtalet – Proportionellt mot frekvensen, men med

eftersläpning proporttionell mot momentet

• Vridmomentet – Proportionellt mot strömmen (i y-led)

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Mechanical design of IM

• Stator same as PMSM

• Rotor:

Cast aluminum Wound copper /Slip ring

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Slip ring rotor

The rotor can be:

1 Short circuited

2 Given an external rotor

resistance

3 Fed by power electronics

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Mathematical model

• Stator

• Rotor

ri

si

r

r

s

s

su

su

dt

d s

ss iR dt

diRu

dt

diRu

rrsr

ssss

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How does it work?

1 A magnetizing stator

current is stationary vs.

the rotor.

2 The current is

instantly moved

and increased.

3 The rotor conserves

the (rotor-)flux and

thus the stator flux

Imagine the following sequence :

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Torque

Rotor flux orientation

Stator flux orientation

ssrs

mrs

s

mrrss ii

L

Li

L

LiiT

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Vector control of Induction motors

• Flux estimation (rotor- or stator- the most

difficult part)

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Rotor flux estimation 1

r y

s i

r q

s l q

a

b

x

y

s q

d q

drd

dt =

Lm

r isd - 1

r rd

dsl

dt =

Lm isq

r rd disddt

= usd - Rs isd - Lm

Lr

drd

dt + s Ls isq

1

Ls disq

dt = usq - Rs isq - s Ls isd +

Lm

Lr rd 1

Ls

• 2 vector equations -> 4 equations.

• Rewriting a lot gives:

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Rotor flux estimation 2

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Full Flux Observer 1

ψΩψ

dt

diRu

r

s

rr

s

r

s

r

ss

rrr

rr

ssss

jdt

d

i

i

R

Ru

jdt

diR

dt

diRu

0

00

0

0

0

0

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r

s

r

s

rm

ms

r

s

s

s

s

j

u

LL

LL

R

R

where

i

i

i

0

00;:),1(;

0

0

1;;;

0

0

ˆ

ˆ

ˆˆˆ

1 Ω

ψ

ψ

ψΩ

ψψΩψ

ψΩLψLi

iLψψΩ

ψ 1-1-

LCu

BLR

kRuBA

kRuCkR-LR

CkRuLRdt

d

uRiRudt

d

obs

1-

1-

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Voltage measurement

• Estimation by software

– Error prone at low speeds

• Analogue filtering and sampling

– slow

• Direct integration

– Needs galvanic isolation

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Split equation solving

ssormicroprocetheinentirelySolved

ikRAAdt

d

ssormicroprocetheoutsidepartlySolved

uikRAA

ikRuAAdt

d

ikR

ikRu

AA

AA

dt

ddt

d

srrobssobsr

sssrobssobs

sssrobssobss

sr

ss

s

r

s

obsobs

obsobs

r

s

222,21,

112,11,

112,11,

2

1

22,21,

12,11,

0ˆˆ

ˆˆ

ˆˆ

0

1

ˆ

ˆ

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Direct integration implemented

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Stator Flux Oriented Vector Control of

Torque and Flux

• 3 advantages:

– In a synchronously rotating reference frame,

there are no stationary errors since all

reference values are constant in stationarity

– The stator flux vector can in most cases be

observed with high accuracy and low

parameter sensitivity

– Direct flux control can be applied

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Equations, again ...

dsd

dt

L s

r

isd 1

r

sd L s disd

dt sl L s isq

usd R s isd

dsl

dt

L s isq Ls r disq

dt

r sd Ls r isd

usq R s isq

sd

r

• 2 vector equation, i.e. 4 scalar equations,

rewritten gives :

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Direct Flux Vector Control

s

sdsd

s

sds

sdssd

s

sdsdsdssd

sdsdssd

T

kk

L

kR

tystationariiniL

T

kkkkiRku

dt

tdtiRtu

)()()(

)()()1,()(

)()()(

*

**

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Control of the Torque producing

current component : 1

usq = Rs isq + r sd + Ls isq + Ls r

disq

dt

r sd - Ls r isd

sd

sdrsq

rssqrs

sdrsq

ssqrssq

dt

diLLiRR

dt

diLiRRu

)()(

)(

• The remaining two rewritten scalar equations:

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Control of the Torque producing

current component : 2

)(

)(ˆ)(

2

)(ˆ)(2

)(*

1

0

**

k

niniT

RR

LL

Tkiki

RR

T

LL

ku

sdr

kn

n

sqsq

s

rs

rs

ssqsq

rs

s

rs

sq

Use generic 1-phase load ...

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Vector Control System

ysqref

ysdref

Rough rotor speed replacement

• ws

1

us*

Demux

Ü>P isd &P isq_old

Ü> isq_ref

Demux

Ü> isd & isq

• delta

rect

mod

angle

rec_to_pol

old psis

old angle

v ect

angle

Out

alfa/beta Ü> d/q1

v ect

angle

Out

alfa/beta Ü> d/q

1

10e-3s+1

Transfer Fcn

ref

act

e

y

PIE

Torque control

ref

act

e

y

PIE

Stator flux control

Scope1

Scope

Saturation

Mux

Mux1

Ground

1/Ts

2/p

-1

v ect

angle

Out

d/q > alfa/beta

4

Tref

3

is

2

PsiR

1

Psiref

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DTC

• Compare to DCC.

• Replace with

• Replace with T sdi sd

sqi

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DTC system

increase/

decrease iq

rest

is5

vect

4 isdq

3

sc

2

sb

1

sa

f(u)

f(u)

vector

f(u)

f(u)

sector

rect

mod

angle

emf

rec_to_pol

In1 Out1

low speed?

increase/

decrease id

v ect

angle

Out

alfa/beta Ü> d/q

XY Graph

Scope3

Scope2Scope1

Memory

1

-1

2-D T[k]

Demux

[1 1 1]

[-1 -1 -1]

[1 -1 -1]

[1 1 -1]

[1 -1 1]

[-1 -1 1]

[-1 1 1]

7

8

[-1 1 -1]

|u|

Demux

-> isd & isq

4

Psis

3

T*

2

i

1

Psis*

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Simplified Stator Flux Model 1

si

r

sl

x

y

s

dq

s

us = R is + ds

dt = R is-is0 + R is0 +

ds

dt

ds

dt = - R is0 + us - R is-is0 =

no load running

is = is0 = s0

Ls

= - Rs0

Lsus = -

s0

sus

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Simplified Stator flux model 2

- +

- +Va

VbVc

Vb

VcRp

C

Rp

Rp

RpC

C

C

ss

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Simplified Stator Flux Model 3

dsd

dt

L s

r

isd 1

r

sd L s disd

dt sl L s isq

usd R s isd

dsl

dt

L s isq Ls r disq

dt

r sd Ls r isd

usq R s isq

sd

r

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Simplified estimation error

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Relation iq/id in stator flux frame

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ˆ (k 1) Fobs ˆ (k )Gobs u (k, k 1)K obs i s(k,k 1)

Fobs eAobsTs e(RL1RkC)Ts

eTs /2

e(RL

1RkC)Ts e

Ts / 2

0 0

0 ej r Ts / 2

Fobs, r0

0 0

0 ej rTs / 2

Fobs I Aobs Ts

2

1

I A obs Ts

2

I Aobs

Ts

2

2

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Gopinath Style Flux Observer


d𝛹𝑟𝑟

𝑑𝑡=𝑅𝑟𝐿𝑚 𝐼s

𝑟

𝐿𝑟−𝑅𝑟𝐿𝑟𝛹𝑟𝑟

𝑑𝛹𝑠𝑠

𝑑𝑡= 𝑉𝑠

𝑠 − 𝑅𝑠𝐼𝑠𝑠

𝑑𝛹𝑠𝑠

𝑑𝑡= 𝑉𝑠

𝑠 − 𝑅𝑠𝐼𝑠𝑠

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DB-DTFC


s

ss iL

rr iL

r

si

ri

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DB-DTFC


-14 -12 -10 -8 -6 -4 -2 0 2 4 6-8

-6

-4

-2

0

2

4

6

8

Voltage time vectors d (vs)

Voltage t

ime v

ecto

rs q

(vs)

Voltage time space

TsVdqs(k)

Stator flux (k+1)Change

in

torque

-14 -12 -10 -8 -6 -4 -2 0 2 4 6-8

-6

-4

-2

0

2

4

6

8

Voltage time vectors d (vs)

Voltage t

ime v

ecto

rs q

(vs)

Voltage time space

DC link

Limitation

Change

in

torque

Stator flux (k+1)

TsVdqs(k)

torque control of induction machines - lth 13/l12(inductionmotor).pdfdelta rect mod angle rec_to_pol...

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