lab 5 pmsm permanent magnetised synchronous machine 11/lecture_20_20110401_lab_5_pmsm.pdf · a...
TRANSCRIPT
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