field oriented control of ac machines - wiley.com controls are simple to implement and offergood...

4

Field Oriented Control of ACMachines

. The control of AC machines can be classified into ‘scalar’ and ‘vector’ controls.

. Scalar controls are simple to implement and offer good steady-state response; however, the

dynamics are very slow because transients are not controlled.. The vector control idea relies on the control of stator current space vectors in a similar, but

more complicated, way to a DC machine.. The principle of torque and flux control is called ‘field oriented control’ or ‘vector control’

for induction machines and later for synchronous machines.

Induction Machines Control

. It has been claimed that 90% of installed motors in the industry are Induction motors.

. Different control methods are popular in the industry

T Control of Induction Motor using V/f method

T Vector Control of Induction Motor

T Direct and Indirect Field Oriented Control

T Field Weakening Control

Control of Induction Motor using V/f method

. In this way of control, a constant ratio between the voltage magnitude and frequency is

maintained. This is to keep constant and optimal flux in the machine:

usx ¼ Rsisx þ dcsx

dt� vacsy

High Performance Control of AC Drives with MATLAB/Simulink Models, First Edition.Haitham Abu-Rub, Atif Iqbal, and Jaroslaw Guzinski.� 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.

usy ¼ Rsisy þdcsy

dtþ vacsx

The voltage vector magnitude is

jusj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðRsisxÞ2 þ ðRsisyÞ2 þ ðvacsxÞ2 þ 2 �Rsisy �vacsx

q

. Current and flux computation

jIsj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiI2sa þ I2sb

q

jcsj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic2sa þ c2

sb

q

time

speed

measurements

isx

isy

epsi rx

epsi ry

is

flux

Torque

m0

Torque Command

Step

pulse

constant

Speed Command

step

square

ramp

mixed

Scope

Double Click to Plot Data

IM

usx

usy

Tor

isx

isy

epsi rx

epsi ry

wr

INDUCTIONMOTOR

Control System

omegaR Command

omegaR

Usx

Usy

Clock

Figure 4.1 V/f control of induction motor

Usy2

Usx1

wr_demand

wrusy

usxomegaU

V/f Control

omegaU

Usx

Usy

Speed Controller

omegaR Command

omegaR

omegaU

omegaR2

omegaR Command1

Figure 4.2 V/f control system model

2 High Performance Control of AC Drives

The motor torque is given by

Me ¼ Lm

JLrðcraisb � crbisaÞ

. Control system

Torque3

flux2

is1

sqrt1

sqrt

sqrt

sqrt

+

+

+

+

+

−

current

flux

torque

Product 5

Product 4

Product 3

Product 2

Product 1

Product

Lm/Lr

Lm/Lr

epsi ry4

epsi rx3

isy2

isx1

is

flux

Torque

Figure 4.3 Current, flux, and motor torque calculations

omegaU1

omegaKp

omegaKp

omegaKi

omegaKi

SwitchSaturation 1

−1 to 1

Saturation−1 to 1

<=

Integrator

1s

Constant 1

0

Constant

0.4

Abs

|u|

omegaR2

omegaR Command1 +

−

+

+

Figure 4.4 Limited authority PI control systems model

Field Oriented Control of AC Machines 3

. Simulation results

Vector Control of Induction Motor

. Proper control of motor speed and produced electromagnetic torque is needed in high

performance adjustable speed drives. The torque production depends on the armature current

and machine flux.. The flux oriented control method allows representation of the mathematically complicated

induction machine in a similar manner as DC machines for obtaining control linearity,

decoupling, and high performance AC drives.. By using vector representation, it is possible to present the variables in an arbitrary co-

ordinate system.

0 200 400 600 8000

0.5

1

1.5

0 200 400 600 800-1

0

1

u s [p

u]u sx

[pu]

u sy [p

u]

0 200 400 600 8000

5

10

15

I s [p

u]

0 200 400 600 800-1

0

1

0 200 400 600 8000

0.5

1

0 200 400 600 800-1

0

1

ωr Demand

ωr Actual

Loadflux

ωr [

pu]

Figure 4.6 Simulation results

Usy2

Usx1

cos

sin

Product 1

ProductIntegrator

1s

Abs

|u|omegaU

1

AngleUs

Usx

Usy

Figure 4.5 V/f control


Relationships of motor model in frame d-q, rotating with rotor flux in the d axis (the q flux

component is zero ysq¼ 0), as

disd

dt¼ a1 � isd þ a2 � 0þ vcr � isq þ vr � a3:0þ a4 � usd

disq

dt¼ a1 � isd þ a2 � 0� vcr � isd � vr � a3 �Yr þ a4 � usq

dYr

dt¼ a5 �Yrd þ ðvcr � vrÞ � 0þ a6 � isd

0 ¼ a5 � 0� ðvcr � vrÞ �Yr þ a6 � isqdvr

dt¼ Lm

LrJðYrisq � 0 � isdÞ � 1

Jmo

. Basic control scheme

Com

puta

tion

Blo

ckPI

PI

PI

PI

+-

+-

+-

+-

SVPWM

Inverter

iA

isq*

isd*

γs

usα*

usβ*

dq

αβ

isα

isβ

dq

αβ

isq

isd

iB

Sensorless

usq*

usd*

UDC

3-φAC Machine

ωr*

ψr*

ωr

ψr

Figure 4.7 Basic scheme of FOC for the three-phase AC machine


. Matlab/Simulink model for induction motor vector control

. Control scheme

Uq2

Ud1

PSIr

PSIr_demand

Iq

Iq_demand

Id

Id_demand

wr_demand

wr

Outer Loop PSIr

100s+7s

Outer Loop Omega

100s+7s

Inner Loop Iq

100s+7s

Inner Loop Id

+

−

+

−

+

−

+

−

100s+7s

w dem6

w5

PSIr dem4

PSIr3

Id2

Iq1

Error PSIr Id demnad

Error Iq

Error Omega Iq demand

Error Id

Iq

Id

Figure 4.12 Two-loop control system for an induction motor

time

speed

m0

XY 2 Alpha-Beta

gama

Ud

Uq

Usx

Usy

Transformations

PSIry

PSIrx

isy

isx

PSIr

Id

Iq

gama

Double Click to Plot Data

Output

Motor Model

usx

usy

m0

isx

isy

epsi rx

epsi ry

wr

INDUCTIONMOTOR

Load

Step

pulseconstant

Controller

Iq

Id

PSIr

PSIr dem

w

w dem

Ud

Uq

1

Clock

Figure 4.8 Induction motor control



Direct and Indirect Field Oriented Control

. Motor state variables may be identified using direct or indirect measurement, using machine

models or observers.. In direct, as well as indirect, control methods, the stator current is measured directly.. In direct control schemes, the machine’s magnetic field is measured using special sensors

located in the machine air gap.. In indirect control schemes, the machine flux is computed using special methods.. Two basic advanced methods are used for flux computation and control purpose.. The first method is based on modeling the AC machine by its state space equations. A

sinusoidal magnetic field in the machine is assumed. The machine models are defined as

open-loop models.. The adaptive observers are receiving more attention than open loop models because of their

robustness against parameters variation and higher computation precision.

. Rotor and stator flux computation

The stator flux vector could be computed from the voltage models:

�cs ¼ðð�us � Rs

�isÞdt

�cs ¼ Ls�is þ Lm�ir

0 2 4 6 8 100

0.5

1

1.5

ωr [

pu]

ψr [

pu]

0 2 4 6 8 10

0

50

100

I d [p

u]

0 2 4 6 8 10−100

−50

0

50

100

I q [p

u]Lo

ad m

0 [p

u]

0 2 4 6 8 10−1

−0.5

0

0.5

1

0 1 2 3 4 5 6 70

0.5

1

time [sec] time [sec]

0 2 4 6 8 10−5000

0

5000

10000

volta

ge [p

u]

ωr Demand

ωr Actual

Iq Demand

Iq Actual

Id Demand

Id Actual

usx

usy

|us|

ψr Demand

ψr Actual



The rotor flux vector is

�cr ¼ Lr�ir þ Lm�is

The expressions of rotor flux vector components in the stationary coordinate system (ab):

cra ¼ Lr

Lmðcsa � dLsisaÞ crb ¼ Lr

Lmðcsb � dLsisbÞ

The rotor flux magnitude is computed as

jcrj ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffic2a þ c2

b

q

The angle of the rotor flux position is

gs ¼ tan�1crb

cra

� �

The disadvantage of this method is that it is operationally limited at lower frequencies (below

3%), because of problems with integrating small signals at low frequencies.

. Adaptive flux observers

The full-order observer used for estimating state variables (mostly stator current and rotor flux

components) is described as

d

dtx ¼ Axþ Bus þ Gðis � isÞ

In this, ^ means the estimated value, and G is the feedback observer gain.

One of the most used observers is Luenberger observer. This observer is mainly used for flux

and stator current computation.

The equations representing this type of observer are

disa

dt¼ a1 � isa þ a2 � Yra þ vr � a3 � Yrb þ a4 � usa þ kiðisa � isaÞ

disb

dt¼ a1 � isb þ a2 � Yrb � vr � a3 �Yra þ a4 � usb þ kiðisb � isbÞ

dYra

dt¼ a5 � Yra þ�vr � Yrb þ a6 � isa � kf1ðisa � isaÞ � kf2ðisb � isbÞ

dYrb

dt¼ a5 � Yrb þ a6 � isb þ vrYra þ kf2ðisa � isaÞ � kf1ðisb � isbÞ


Where:

a1 ¼ �RsL2r þ RrL

2m

Lrwa2 ¼ RrLm

Lrwa3 ¼ Lm

wa4 ¼ Lr

wa5 ¼ �Rr

Lra6 ¼ Rr

Lm

Lr

w ¼ sLrLs ¼ LrLs � L2m s ¼ 1� L2mLsLr

Stator Flux Orientation

. The operation at the absolute voltage limit of the inverter for maximum torque production

eliminates the voltage margin required by the current controllers to adjust the respective

current components id and iq.

1s

Integrator7

1s

Integrator6

1s

Integrator5

1s

Integrator1

fry0Goto3

frx0Goto2

isy0Goto1

isx0Goto

frx0From9

fry0From8

frx0From7

isy

From6

usy

From5

usx

From4 isxFrom3

isy

From25

wr

From24

fry0From23

frx0

From22

isy0From21

isx0From20

isy

From2

isx

From19

wr

From18

wr

From17

wr

From16

fry0From15

frx0

From14

isy0From13

isx0From12

isx

From11

fry0

From10

isy0

From1

isx0From

a6*u(4)+a5*u(6)+u(5)*u(7)+kf2*(u(1)-u(2))-kf1*(u(3)-u(4))

Fcn3

a6*u(2)+a5*u(5)-u(6)*u(7)-kf1*(u(1)-u(2))-kf2*(u(3)-u(4))

Fcn2

a1*u(3)+a2*u(5)-a3*u(4)*u(6)+a4*u(1)+ki*(u(2)-u(3))

Fcn1

a1*u(3)+a2*u(4)+a3*u(5)*u(6)+a4*u(1)+ki*(u(2)-u(3))

Fcn

Figure 4.14 Simulink diagram of Luenberger observer for stator currents and rotor fluxes estimator


Field Weakening Control

. When the machine operates at speeds higher than the rated one, then it is running in the field

weakening region, such as spindle and traction drives.. To increase the produced torque to a maximum level in the field weakening region, it is

essential to properly adjust the machine’s magnetic field by maintaining the maximum

voltage and maximum current.. The machine flux should be weakened to such a level that it will guarantee a maximum

possible torque at the whole speed range called field weakening control.. Field weakening control can be categorized into three methods:

1. adjustment of the machine flux in inverse proportion to speed (1/v),2. forward control of the flux based on simplified machine equations, and

3. closed loop control of the stator voltages to keep a maximum level.. The voltage control field weakening method ensures maximum torque production in the

whole field weakening region when in a steady-state. The method provides maximum

required torque during a steady state, and is not dependent to motor parameters and DC

link voltage.

Open loop model

PI

PI

PI

Tra

nsfo

rmat

ion

of v

aria

bles

+-

+-

+-InverterPWMVSI

is*

M

ωr*

ωr^

ψs*

ψs^

is

u*

is

^φ

u*

Figure 4.15 Stator flux oriented vector control


Vector Control of Double Fed Induction Generator (DFIG)

. The DFIG is a rotor-wound three-phase induction machine; the stator windings of the

machine are connected to the utility grid without using power converters, and the rotor

windings are fed by an active front-end converter.

Com

puta

tion

Blo

ck

PI

PI

PI

PI

+-

+-

+-

+-

SVPWM

Inverter

iA

isq*

γs

usβ*

usα*

dq

αβ

isα

isβ

dq

αβ

isq

isd

iB

Sensorless

usq*

usd*

ωr*

ωr

ψr*

ψr

UDC

3-φAC Machine

+- PIusmax

*

us usqmax*

+

-is

2max

isd*

x2

(usα*2 + usα*2)

Figure 4.16 A field weakening system

DFIG

Grid

Supply

Wind Turbine

Grid-side

Converter

Machine-side

Converter

Figure 4.17 General view of DFIG connected to wind system and utility grid


The active and reactive powers of stator and rotor circuits are needed in the control of DFIG

and may be described in per unit as

Ps ¼ ðvdsids þ vqsiqsÞ

Qs ¼ ðvqsids � vdsiqsÞ

Pr ¼ ðvdridr þ vqriqrÞ

Qr ¼ ðvqridr � vdriqrÞ

In practice, vector control of DFIG is similar to the vector control of the squirrel cage

induction motor with a difference in controlled variables. The control depends on vector

transformation from three-phase to rotating frame.

DFIG

Computation Block

PI

PI

PI

PI

+-

+-

+-

+-

PWM Inverter

Stator

Rotor

Us

Is

IR

γ fri

( fri)

γksi(ksi)

γksi

P

Q

P*

Q*

P

Q

irα* irαR* UαR

UβR

irαR

irαR

irβR

irβR

irβR*irβ*

(irx*)

(iry*)

Figure 4.18. Block diagram of the DFIG control system


. Matlab/Simulink model for DFIG vector control


x

y

r

x

y

r

xy -> polar

x

y

r

us

1

Double Click to initialise.

Double Click to plot

omegaS

1

Scope

Power Regulator

P

Q

Pdem

Qdem

irxR

iryR

ksi

urx

ury

irxRF dem

iryRF dem

Demand Signals

P dem

Q dem

OmegaR

DFIG Model

urx

ury

irxRF dem

iryRF dem

OmegaR

us

OmegaS

P

Q

fsx

fsy

isx

isy

irx

iry

irxR

iryR

ksi

ir

is

fs

Figure 4.19 DFIG power regulation model

0 100 200 300 400 500−0.5

0

0.5

1

Act

ive

Pow

er, P

[pu]

0 100 200 300 400 500−0.5

0

0.5

1

Rea

ctiv

e P

ower

, Q [p

u]

0 100 200 300 400 500−1

−0.5

0

0.5

1

I rxR

[pu]

time [sec]

0 100 200 300 400 500−1

−0.5

0

0.5

1

I ryR

[pu]

time [sec]

demand

actual

Figure 4.25 Simulation results – tracking


Permanent Magnet Synchronous Machine (PMSM)

Advantages

. Higher torque for the same dimension. For the same power, the dimension is lower by almost

25%. Lower weight for the same power, around 25%. Lower rotor losses, which results in higher efficiency of up to 3%

Disadvantages

. In the case of inverter faults, it is not possible to reduce the magnetic field by reducing the

torque surge, which forces a use of switch between the motor and the inverter. It is possible to connect only one motor to the inverter; therefore, group motor work is not

possible. The use of permanent magnet forces using enclosed motor housing complicates the cooling

process

Vector Control of PMSM in dq Axis

The produced torque of the machine could be presented as

Te ¼ 3p

2Yf iq þ id iqðLd � LqÞ� �

0 50 100 150 200 250 300 350 400 450 500−2

0

2

Sta

tor

Flu

x [p

u]

|fs|

fsx

fsy

0 50 100 150 200 250 300 350 400 450 500−2

0

2

Sta

tor

Cur

rent

[pu]

|is|

isx

isy

0 50 100 150 200 250 300 350 400 450 500−1

0

1

Rot

or C

urre

nt [p

u]

time [sec]

|ir|

irx

iry

Figure 4.26 Other machine variables


And in per unit as

Te ¼ cf iq þ ðLd � LqÞid iq

Hence the torque could be expressed as

Te ¼ cf issin b

The torque gets maximum value for b (torque angle) equal to 90 degrees for a given value of

stator current. This gives maximum torque per ampere and hence a higher efficiency

PI

PI

+-

+-

VoltageInverter

d-q

PI+-

PMSM

isd*

isq*

usd*

usq*

d-q

usα*

usβ*

isα’ isβ

isd

isq

(usx*)

(usy*)

(isx’ isy)

UDC

ωr*

ωr

1–s

α−β

α−β

θ

θ

Figure 4.27 Vector control scheme of permanent magnet synchronous machine


. Matlab/Simulink model for vector control of PMSM


0 20 40 60 80 100−0.1

0.1

0

I sd

[pu]

I sq

[pu]

Usx

’ Usy

[pu]

0 20 40 60 80 100

0

0.5

1

0 20 40 60 80 100−1

0

1

2

3

0 20 40 60 80 1000

20

40

60

80

0 20 40 60 80 100−4

−2

0

2

4

Usx

Usy

0 20 40 60 80 100−0.5

0

0.5

1

ωr [

pu]

θ [p

u]m

0’ [p

u]


Figure 4.28 Vector control of PMSM


Vector Control of PMSM in a-b axis using PI controller


0 200 400 600 800 1000−0.4

−0.3

−0.2

−0.1

0

0.1

0 200 400 600 800 1000−4

−2

0

2

4

0 200 400 600 800 1000−0.5

0

0.5

1

1.5

ωr [p

u]I s

d [p

u]

m0

[pu]

I sq

[pu]

time [sec]0 200 400 600 800 1000

−0.4

−0.2

0

0.2

0.4

time [sec]

Figure 4.38 Simulation results – tracking

Figure 4.31 Vector control of PMSM


Scalar Control of PMSM

The voltage to frequency ratio should be constant (V/f ¼ const) to maintain constant flux in

the machine. Otherwise the machine may reach under- or over-excitation conditions, which

are not recommended from stability and economical points of view

V/f = const.VsVn

fsfn

Vs*fs*

Vα

Vβ VSI

UDC

PMSMsin /cos

fs*

Figure 4.40 Block diagram of constant volt by frequency control of PMSM

0 200 400 600 800 1000−4

−2

0

2

4

I sx

[pu]

f sy

[pu]

θ [r

ad]

I sy

[pu]

u sx

[pu]

u sd

[rad

]

f sx

[pu]

u sy

[pu]

u sq

[rad

]

0 200 400 600 800 1000−4

−2

0

2

4

0 200 400 600 800 1000−2

−1

0

1

2

0 200 400 600 800 1000−2

−1

0

1

2

0 200 400 600 800 1000−4

−2

0

2

4

0 200 400 600 800 1000−4

−2

0

2

4

0 200 400 600 800 1000

0

pi

2*pi

time [sec]

0 200 400 600 800 1000−4

−2

0

2

4

time [sec]

0 200 400 600 800 1000−2

−1

0

1

2

time [sec]

Figure 4.39 Other machine variables


field oriented control of ac machines - wiley.com controls are simple to implement and offergood...

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