Lab 5 PMSM Permanent magnetised synchronous machine 11/Lecture_20_20110401_Lab_5_PMSM.pdf · a permanent magnet synchronous machine (PMSM) torque control will be studied. • The

Lab 5 PMSMPermanent magnetisedsynchronous machine

Mathematical Model

mψ

x

y

α

β

ai

bi

ci

si

( )αβαβαβαβ

αβαβ ψψ

ssmsss

sss iLdt

diR

dt

diRu

rrrr

rr⋅++⋅=+⋅=

( ) ( )

( )xyss

xymr

xys

sxy

ss

xyss

xymr

xyss

xym

xyss

xys

iLjdt

idLiR

iLjiLdt

diRu

rrr

r

rrrrrr

⋅+⋅+⋅+⋅=

⋅+⋅+⋅++⋅=

ψω

ψωψ

Torque Control

( )sysxsysxsym

sxsysysysxsxm

sxsysysxss

iiLLi

iiLiiL

iiiT

⋅⋅−+⋅=

=⋅⋅−⋅⋅+=

=⋅−⋅=×=

)(ψ

ψ

ψψψrr

Better – max Torque/Ampére control• Orient the current vector for maximum Torque.

)sin()cos()()cos(

)(

2 δδδψ

ψ

⋅⋅⋅−+⋅⋅=

=⋅⋅−+⋅=

ssysxsm

sysxsysxsym

iLLi

iiLLiT

-20 -10 0 10 20-20

-10

0

10

20ISO-torque (blue) and max(T/I) (red)

Lsy=5mH /Lsx=2mH

-20 -10 0 10 20-20

-10

0

10

20ISO-torque (blue) and max(T/I) (red)

-20 -10 0 10 20-20

-10

0

10

20ISO-torque (blue) and max(T/I) (red)

[isy]

[isx]

[isy]

[isx]

[isy]

[isx]

Lsy=5mH /Lsx=5mH Lsy=2mH /Lsx=5mH

Voltage limitation( ) ( )( )22

sxsxmrsyssysyrsxss iLiRiLiRu ⋅+⋅+⋅+⋅⋅−⋅= ψωωr

• What current combinations satisfy a limited voltage vector?

-20 -10 0 10 20-20

-15

-10

-5

0

5

10

15

20ISO-torque (blue), max(T/I) (red) and Constant Voltage (green)

Follow (T/I)max toVoltage limit, then T=const. [isy]

[isx]

”Iso”-torque curves at magnetic saturation

-400 -300 -200 -100 0 100 200 300 400-500

-400

-300

-200

-100

0

100

200

300

400Increasing torqe

mψ x

y

si

[isy]

[isx]

Diagram explanation

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

T=constant us=constant

increasingspeed

increasingtorque

optimalstator current

maximumlstator current

[isy]

[isx]

Torque control

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

[isy]

[isx]

Example 1

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

[isy]

[isx]

Example 2

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

[isy]

[isx]

Example 3

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

[isy]

[isx]

Example 4

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

[isy]

[isx]

[isy]

[isx]

-200 -150 -100 -50 0 50 100 150 200-600

-400

-200

0

200

400

600

Torque refernce [Nm]

isx*

(blu

e) a

nd is

y* (r

ed)

Look up tables for minimal stator currents references

The PMSM motor

ψa

ua

ia

A+

A-

B-

B+ C+

C-

ψb

ψc

uc

ic

ψα

uα

iα

ψβ

iβ

uβ

a

b

Im

c

Re

ib ub

ix

ux

iy uy

ψx

ψy

ω

x

y

θ

The scope of the laboratory• In this lab a sampled vector current controller for

a permanent magnet synchronous machine (PMSM) torque control will be studied.

• The control system is a Simulink block diagram-based model that is run in the dSpace real-time hardware.

• The scope of the laboratory work covers a comparison of some PWM modulating references that can be used for three phase PWM modulators and a vector control for PMSM including a field-weakening controller.

Laboratory Set-Up

Laboratory Set-Up, simulink model

The Laboratory Exercises• Measuring the induced voltage of the PMSM and

calculating the corresponding flux linkage

• Studying the converter output and a current ripple at the different 3-φ modulating references

• Adjusting the sampled vector current controller for the PMSM

• Investigating a voltage and a current limit for the PMSM and the 3-phase converter

• Implementing the field-weakening control;

Measuring the induced voltage

sxsyu ψω ⋅=

Torque control

Torque control, mathematical background

( ) loadsysxsysxsypmsxsysysxss

sysysy

pmsxsxsx

sxsy

syssy

sysx

sxssx

Tdtd

pJiiLLiiiiT

iL

iL

dtd

iRu

dtdiRu

+⋅=⋅⋅−+⋅=⋅−⋅=×=

⎪⎩

⎪⎨⎧

⋅=

+⋅=

⎪⎪⎩

⎪⎪⎨

⎧

⋅++⋅=

⋅−+⋅=

ωψψψψ

ψ

ψψ

ψωψ

ψωψ

rr

Field Weakening

Field Weakening

sLuuu

i

sLudtu

Li

dtdiLu

qd22

max9.0*

1

+−⋅=

=⋅=⇒⋅= ∫

Field weakening control

Field weakening control

System Data

• The data of the PMSM necessary for the torque control

• For design of the PIE current controller which can be applied for the fieldweakening controller.

Measure Symbol ValueUnit

Nominal flux linkage of the PMSM Ψpm 0.16

Vs

Stator inductance of the PMSM Lsx= Lsy 3

mH

Stator resistance of the PMSM Rs 0.5

Ω

The nominal current of the PMSM In 12

A

The nominal voltage of the PMSM ULn 400

V

Sample time Ts 2e-4s

System Input/OutputInput dSpace

Interface symbol source/measurement

dc-link voltage ADC1 Udc C&V measurement card

Armature current ADC2 ia C&V measurement card

Mechanical speed ADC3 w Flux linkage estimator

Stator current phase a ADC5 ipha C&V measurement card

Stator current phase b ADC6 iphb C&V measurement card

Resolver position (cos) ADC7 cos Resolver & Sin/Cos card

Resolver position (sin) ADC8 sin Resolver & Sin/Cos card

Output dSpace Interface symbol source/measurement

2φ PWM PWM1 PWM2 va vb DS1104SL_DSP_PWM

3φ PWM PWM1 PWM2PWM3

va vb vc DS1104SL_DSP_PWM3

Reference current on direct/quadrature axis* DAC1 ixy* RT Simulink model

Feedback current on direct/quadrature axis DAC2 ixy RT Simulink model

Predicted current on direct/quadrature axis DAC3 ixy^ RT Simulink model

Reference voltage on direct/quadrature axis DAC4 uxy* RT Simulink model

Filtered speed# DAC5 w RT Simulink model

End of PMSM story