electricas maquinas

Transcription

electricas maquinas

UPC
PMSM Control (FOC & DTC) for
WECS & Drives
Dr. Antoni Arias.
Universitat Politècnica de Catalunya. Catalonia. (Spain)
1/94
Guidelines
UPC
• Introduction
& motivation
• Permanent Magnet
Synchronous Machine
(PMSM)
– Dynamic equations
– Modeling
• Vector Control Strategies
– Field Oriented Control (FOC)
• Current & Speed Loops
• PI & IP controllers: root locus,
specifications, tuning and DSP
C code
–Direct Torque Control (DTC)
• VSI review
• Flux & Torque Loops
• Hysteresis Comparators
• Space Vector Modulation
(SVM)
• Case study: Wind Turbine
• Experimental approach:
– Platforms
– Implementing issues
2/94
Introduction & Motivation
UPC
• An electric drive is an industrial system which performs the
conversion of electrical energy to mechanical energy (in
monitoring) or vice versa (in generator braking)
– Production plants, transportation, home appliances, pumps, air
compressors, computer disk drives, robots, etc…
Electric
Power
Source
Voltage
Sensors
Power
Electronic
Converter
ELECTRIC
MOTOR
Current
Sensors
Power Electronic Converter Control
Torque Control
Speed / Position Control
Regenerative
braking
Power Source Performance Commands
Motion Commands
Load
Speed / Position
Sensors
or
Observers
DRIVE CONTROL
User Interface
3/94
UPC
• Electric drives involves many applications ranging from
below 1kW up to several dozens of MW.
High performance means:
(i) wide speed range,
(ii) fast and precise response
in speed or position.
Field Orientated Control (FOC) & Direct Torque Control (DTC)
deserve special attention since both are high performance vector controllers.
4/94
UPC
• Electric machines drives absorb a large amount of the
electrical energy produced.
– 50% of the electrical energy is used in electric drives today (1).
– In the industrial countries, EM take around 65% of the entire electrical
energy available (2).
I. Boldea, S. A. Nasar. “Electric Drives”. CRC Press. Second Edition. 2006
(2) Kazmierkowski, M. P; Tunia, H. “Automatic Control of Converter-Fed Drives".
Elsevier. Studies in Electrical and Electronic Engineering 46. 1994.
(1)
• Electric Drives market by 2017: US$ 62.3 billion by 2017 (3).
(3)
Global Industry Analysts, Inc.
• Sensorless and High Performance Controls are still hot
research topics (4).
(4)
IEEE Xplore & Elsevier
5/94
UPC
• AC versus DC: (i) brushless (ii) higher torque density (iii)
lower initial and maintenance costs, (iv) power electronics
for AC and DC have comparable prices.
DC
25%
DC
40%
AC
60%
1990
DC
30%
AC
70%
1995
AC
75%
2000
DC
20%
AC
80%
2005
AC versus DC electric drives market evolution (1)
(1)
I. Boldea, S. A. Nasar. “Electric Drives”. CRC Press. Second Edition. 2006
6/94
UPC
classification
• DC
• AC
SRMs possess potential market.
Second machine most used in China !
http://green.autoblog.com/2011/06/28/need-rare-earthmetals-switched-reluctance-motors-dont/
– Induction
– Switched Reluctance. Stepper. Hybrid.
– Permanent Magnet
• PMDC – Brushless
• PMSM: SMPMSM, IPMSM
• Linear
• Nano
• etc...
PMSMs are gaining market
becoming a key point for the
sustainable development
of the present century.
7/94
Permanent Magnet Machines
UPC
• Magnetic material to establish the rotor flux.
– Neodymium-iron-boron (Nd2Fe14B) magnet is the strongest type of
rare-earth permanent magnet, which was developed in 1982 by GM.
• Advantages:
– No rotor currents => no rotor losses => higher efficiency => energy
saving capability. Attractive for Wind applications.
– Smaller rotor diameters, higher power density and lower rotor inertia.
– Higher torque per ampere constant.
– Less weight and volume for the same power. Attractive for aerospace
applications such as aircraft actuators.
– Other applications: machine tools, position servomotors (replacing the
DC motors).
• Inconvenience:
– Synchronous machines => need of rotor position. Sensorless control.
– Price.
– Permanent magnet is becoming a scarce raw material.
8/94
UPC
Unimotor. Emerson. Control Techniques.
0,72-73,2 (Nm) 2000-6000 (rpm) 230/400(V)
General purpose
Mavilor. Might be used
in Electrical Vehicles
1,3 - 31,8 (Nm)
6000 - 9000 (rpm)
9/94
UPC
4Q Motor Drive System
4kW DC – PMSM 1 kW
General purpose laboratory rig
PMSG 11kW
Multi-pole. External rotor
Wind turbine laboratory rig
(in collaboration with
Robotiker - Tecnalia)
10/94
UPC
• Considering the shape of the back EMF
• PMDC – brushless DC (BLDC) - trapezoidal
• PMAC – sinusoidal
Surface Mount Permanent Magnet
Synchronous Machine (SMPMSM)
Interior Mount Permanent Magnet
Synchronous Machine (IMPMSM)
11/94
PMSM Dynamic Equations
UPC
• Space vector transformation
• Combines the individual phase
quantities into a single vector in
the complex plane
2
4

j
j

i  c   ia (t )  ib (t )e 3  ic (t )e 3

 2 3 non power invariant
c 2
 3 power invariant



• Same transformation is applied to
all other magnitudes such as
voltages, fluxes, etc…
12/94
UPC
• Basic equation for phase windings voltages
va 
ia 
 a 
v   R i   d  
s b
b
 b
dt  
 vc 
ic 
 c 
ib
b
+
vb
-
• Total flux linkage
ψ a   La
ψ    M
 b   ba
ψc   M ca
M ab
Lb
M cb
M ac  ia 
 cos( r ) 
M bc   ib   ψ m cos( r  23 )
cos( r  43 )
Lc  ic 
flux produced by the rotor magnet ψ m
Leakage inductance Ll
m
b
r
a 
a
ia
vc
-
-
va
+
c
+
ic
c
Magnetising inductance Lm
Self inductance
La  Lb  Lc  Ll  Lm
Mutual inductance M ab  M bc  M ca   Lm 2 ; M ab = M ba ; M bc = M cb ; M ca = M ac
13/94
UPC
• Voltage vector equation in the stationary - frame
v 
i  
3  d i 
d  cos( r ) 
v   Rs i    Ll  Lm  i   ψm cos(   )
2  dt   
dt 
r
2 
 
  
ib
b
+
vb

m
b
r
v
Clarke
a 
a
vc
-
c
+
ic
c
va
-
m
transformation
ia
-
i
+
-
r
+

x  c   xa  xb cos 60º  xc cos 60º 
x  c   xb cos 30º  xc cos 30º 

c

2
3
2
3
-
v
i
+
non power invariant
power invariant
14/94
UPC
1

1


 x 
2

c


x 
3
 
0
2

ib
b
1  x 
a

2  x  ; c  

3   b 


 xc 
2 

2
3
2
3
non power invariant
power invariant
+
-
Clarke Transformation
m
b

i
+
vb
v
r
a 
a
-
m
ia
vc
-
-
c
+
ic
c
•
va
+

 1

 xa 
 x   c   1
 2
 b
 1
 xc 

 2
Clarke-1 Transformation

0 

 1 non power invariant
3   x 

;
c

 2
 
2   x 

3


2 
Non power invariant versus power invariant. See the comparison.
r

-
v
i
+
15/94
UPC
• Saliency: Variation of the stator phase inductance as function of the
rotor position.

La  Ll  L m  Lm cos(2 r )
M ab   L m
2
 Lm cos(2 r  23 )
Lb  Ll  L m  Lm cos(2 r  43 )
M bc   L m
2
 Lm cos(2 r )
La  Ll  L m  Lm cos(2 r  23 )
M ca   L m
2
 Lm cos(2 r  43 )

q

d
q
m
d

m
d
m
r

q
r

La = Ll + L m - ΔLm cos( 2θr ) = La = Ll + L m - ΔLm cos( 2θr ) = La = Ll + L m - ΔLm cos( 2θr ) =
= Ll + L m
= Ll + L m + ΔLm
= Ll + L m - ΔLm
16/94
UPC
• voltage vector equation in the stationary - frame
considering saliency
Ls sin(2 r )  i 
v 
i  d  Ls  Ls cos(2 r )
 
v   Rs i    L sin(2 )

Ls  Ls cos(2 r ) i 
s
r
 
   dt 
d  cos( r ) 
 ψm 
dt cos( r  2 )
• Where
3
3
Ls  Ll  Lm ; Ls  Lm
2
2
• If Lm  0 there is no saliency and it is obtained the previous
equation.
17/94
UPC
• Voltage vector equation in the synchronous reference d/q
frame fixed to the rotor
• Angle chosen equal to the PM position
• Direct axis ( Ld = LS-ΔLS ) and quadrature ( Lq = LS+ΔLS ) axis
inductances
vd 
id   Ld d dt
 v   Rs i    L 
 q
 q  d r

i
d
+

 Lqr  id 
0
    ψmr  

Lq d dt  iq 
1 
q
v
-
Park
m
r
transformation

-
v
i
iq
+
+
vq
m
-
-
vd
r
+

18/94
id
UPC
 xd   cos 
x   
 q   sin 
Park Transformation
i

d
+

sin    x 
 

cos    x 
q
v
iq
-
m
r
+
+
vq

-
v
i
+
m
-
-
vd
r
Park-1 Transformation
 x  cos 
x   
    sin 

 sin    xd 
 

cos    xq 
19/94
id
UPC
• Non power invariant
• Different constant values. (c=2/3) for Clark & (c=1) for Clarke-1.
• Same amplitudes for (a,b,c) & (α,β) & (d,q).
0.25
0.2
0.15
0.1
[A]
0.05
0
i alpha
-0.05
i
-0.1
i
b
ic
-0.15
iq
-0.2
-0.25
beta
i
0
0.05
0.1
0.15
0.2
Time [ s ]
0.25
0.3
d
0.35
20/94
UPC
• Power invariant
• Same constant value. ( c=sqrt(2/3) ) for Clark & Clarke-1.
• Different amplitudes for (a,b,c) versus (α,β) & (d,q)
0.3
0.2
0.1
[A]
0
i alpha
-0.1
i beta
i
-0.2
i
c
iq
-0.3
i
i
-0.4
b
0
0.05
0.1
0.15
0.2
Time [ s ]
0.25
0.3
d
a
0.35
21/94
UPC
• Direct (Clarke & Park) transformation
 xd   cos 
x   
 q   sin 
cos   2 
3
 sin   2 
3
 cos 
 xd 
x   c  
 sin 
 q

; where c  

2
1  x 
a

2  x 
3   b 

x 
2   c

x 
2




cos  
3   x 
 sin   2   
3   x 
a
b
c
non power invariant
3
2
1

1


sin  
2

c


3
cos  
0
2

3
power invariant
22/94
UPC
• Direct (Clarke & Park) Inverse transformation

 1
 xa 
 x   c   1

 b
 2
 xc 
 1
 2

0 
3   cos 
2   sin 

 3 
2 
 sin    xd 
 

cos    xq 


cos 
 sin 
 xa 
  xd 
 x   c  cos   2
 sin   2    
b
3
3
 
xq 



2
2
 xc 
cos   3  sin   3 
 1 non power invariant
; where c   2








23/94
UPC
• Instantaneous torque expression:


Te  c  P    i  c  P   d  iq   q  id 
 c  P   m  Ld  id   iq  Lq  iq   id 
 c  P    m  iq  id  iq Ld  Lq 

 3 2 non power invariant
; where c  
, P is the pair poles' number
and  m - psi is the permanent magnet flux
• First term, usually called as magnet torque, is directly
proportional to iq and independent of id .
• Second term, or reluctance torque, is only present in
salient machines where ( Ld - Lq ) ≠ 0 and is proportional to
the current product ( id ·iq).
24/94
UPC
• Motion equation
• Drive Inertia ( J )
• Damping constant due to Friction ( D or F )
• Load Torque ( TL )
 dwm
J
 D  wm  Te  TL ; diferentia l equation

 dt

 wm  Te  TL ; transfer function

Js  D

25/94
PMSM Modeling
UPC
Exercise: Sketch a complete PMSM scheme model
• Use the d/q model equations
• Find out all the required equations involved
• Determine where the Clarke (a,b,c) to (α,β) & Park (α,β) to (d,q)
transformations should be applied to get a more realistic model
26/94
PMSM Modeling
UPC
27/94
PMSM Modeling
UPC
•The adopted parameters for the model are as follows:
Lq=0.009165; Ld=0.006774; R=1.85; psi=0.1461; P=3.
(specific motor data is on the next page)
•For the motion equation of the whole drive it can be used:
J=0.77e-3; F=1e-3.
28/94
PMSM Modeling
UPC
How to obtain the parameters
from a commercial catalogue?
•
unimotor fm
Emerson Control Techniques
Model: 115E2A300BACAA115190
Number of poles:
6
Lq  Ld
Rated speed:
3000 (rpm)
2
2
Lq  Ls  Ls ; Ld  Ls  Ls
Rated torque:
3.0 (Nm)
Rated power
0.94 (kW)
KT:
0.93 (Nm/Arms)
KE:
57.0 (Vrms/krpm)
Inertia:
4.4 (kgcm²)
R (ph-ph):
3.7 (Ohms)
L (ph-ph):
15.94 (mH)
Continuous stall:
3.5 (Nm)
Peak:
10.5 (Nm)
Ld and Lq values?
Ls 
Lq  Ld
; Ls 
• ΔLs can be obtained measuring the
inductance for different rotor positions.
• The first order system, composed by
an L and R, can be identified by
supplying a step voltage in the d and q
components.
29/94
PMSM Modeling
UPC
• How to obtain the J and F values?
• The first order system, composed by a F and F, can be identified by
supplying a step torque.
• Usually, the machine manufacturer provides the J value. In a laboratory
rig composed by two machines, the total J value can be then worked
out from the manufacturer data.
• Why KT and KE are not equal?
• The units must be in the International System.
VF
T
3  VF  I F  T  m ; 3 

m I F
3  K E  KT ;
56.22
3
1000
 
Vrms
rpm
star

connected
VL
T
3

3  m I F
60 s
1
  min  
1
2 
rev
 rad
  0.929 ANm 
rms
• Experimental (taken in the laboratory) KE value is 56.22 instead of 57.
30/94
PMSM Modeling
UPC
•How to obtain the
 m value?
From the torque expression, Te  c  P  m  iq and the KT (Nm/Arms)
parameter, it can be deduced the following expression:
Te
KT
 KT  c  P  m 
 m 
iq
cP
Finally, the numerical value will be:
KT
0.93  1 2
m 

 0.1461 Wb
c P 3 3
2
And the factor
1
2
is used to convert the rms to the maximum value.
31/94
Types of Controllers
UPC
32/94
Field Oriented Control (FOC) for PMSM
UPC
• Instantaneous torque for the PM synchronous machine
3
3
Te   P   ψmiq  id iq ( Ld  Lq ) 
 P  ψm  iq
id = 0 2
2
• If id = 0, for not demagnetizing the PMSM, the reluctance torque is 0.
• Therefore, the electromagnetic torque will be regulated with iq .

d
q
Iq>0

Te > 0
m
Te < 0
d
q
r
m
r

Iq<0

• Duality with the DC Machine control.
33/94
FOC in PMSM
UPC
Te

m
d
q
m
d
q
r
iq>0


q
m
m
d
q
r
Four quadrant
m

d
m
r
iq>0

iq<0
m

m
m
r

iq<0

Motor (Q1 & Q3) Generator (Q2 & Q4)
34/94
FOC Scheme
UPC
• 3 PI control loops:
• 2 inner (and faster) current loops.
• 1 outer (and slower) speed loop.
UsA
LC filter
Current
Speed
m*
id* +
V
PI
dq
+
PI
Kt
PI
-1
-
iq* +
-

e
dq

Grid
UsB
UsC
2
V
UA
SVM
PWM
4 step
UB
UC
Matrix
Converter
ia
ib
ic
PMSM
P
m
3
d/dt
discretization time /
switching frequency
Closed loop time response /
band width
Current
100 µs / 10kHz
5ms / 200Hz
Speed
5ms / 200Hz
0.5s / 2Hz (inertia dependent)
Typical dynamic values
(for a PMSM 0.5 / 10 kW)
Limited by the
semiconductors
switching frequency
Separation principle will be applied
35/94
Current Controller
UPC
• The current loop, for controlling design purposes, can be modeled as
a first order system.
• The coupling terms are eliminated, since they are considered as a
perturbation.
i
1 Rs
0
vd 
id   Ld s  Lqe  id 
 

;

R



ψ

v L Rs s  1
s 
m e 
 

  
iq   Ld e
 vq 
vd
+
Lq s  iq 
1 Rs
id
Ld R s  s 1
1 
  L Rs
vd
1 Rs
id
Ld R s  s 1
Lq·we·iq
vq
-
1 Rs
iq
Lq R s  s 1
vq
1 Rs
iq
Lq R s  s 1
( Ld·id +PM )·we
36/94
Current Controller
UPC
• The current loop can be modeled as a first order system, whose
transfer function in Laplace domain is:
I ( s)
1 Rs

V ( s) ( L R s ) s  1
• Its open loop step time
response is:
i (t )  1 Rs (1  e
t

)v (t )
t   ; i (t )  1 Rs 0.632  v (t )
t  3 ; i (t )  1 Rs 0.95  v (t )
t  4 ; i (t )  1 Rs 0.98  v (t )
t  5 ; i (t )  1 Rs 0.99  v (t )

4
37/94
Current Controller
UPC
• Considering the motor
parameters given before:
Step Response
0.7
I ( s)
1 1.85

V ( s ) 7.97·103 1.85 s  1
System: g
Time (seconds): 0.0172
Amplitude: 0.531
0.6
System: g
Time (seconds): 0.0298
Amplitude: 0.54
0.5
7.97·103

 4.31(ms)
1.85
• Time response at 98%
4  17.23(ms)
• Final value:
1
 0.54
1.85
Amplitude
• Time constant:
0.4
0.3
0.2
0.1
0
0
0.005
0.01
0.015
0.02
Time (seconds)
0.025
38/94
0.03
Current Controller
UPC
• P controller always
introduces the
Position Error E0
E0 = Rs / (Rs+KP)
Open loop
s = -Rs/L = -232
 = L/Rs = 4.3(ms)
500
i* +
i
1 Rs
L R s  s 1
KP
-
KP=1
s = -(KP+Rs)/L = -358
 = L/(KP+Rs) = 2.8(ms)
Final value: KP/(RS+KP) = 0.35
KP=10
s = -(KP+Rs)/L = -1486
 = L/(KP+Rs) = 0.6(ms)
Final value: KP/(RS+KP) = 0.84
0.8
Root locus
0.6
0
0.4
-Rs / L
-500
-1000
-500
0.2
0
• Solution: add a PI controller
0
0
Step response
0.01
0.02
0.03
39/94
Current Controller
UPC
i* +
-
KP  s  K I
s
i
1 Rs
L R s  s 1
• Specifications:
Settling time at 2% = 4ms
Overshoot  4.23%  Damping =0.707
1000
KP = 14.09 KI = 15945
Closed loop poles  -1000+1000j
Root locus
0
-KI / KP
0
-Rs / L
-1000
-3000
-2000
-1000
0
40/ 94
Current Controller
UPC
• The integrator makes the Error E0 = 0
• The specifications are not fulfilled:
The overshoot (17%) is too large !
The settling time is not fulfilled !
1
Step
response
0.5
0
0
1
2
3
Time (seconds)
4
5
x 10
-3
• What is the problem ?
41/94
Current Controller
UPC
• What is the closed loop transfer function?
 KP


s  1
i
 KI


 Rs K P  K I
*
2
s

s



i
L
L

 L
KI
L
• Is it a pure 2nd
order term?
A pre filter is used
to cancel the zero
i
i
*

1
 KP


s  1
K
 I

n2
s 2  2 n  s  n2
i*
KP  s  K I
s
i*PF +
1
KP K I s1
-
 KP


s  1
 KI

K  K
R
s 2  s s  P   I
L  L
 L
KI
L
NO! There is an
unwanted zero !
i
i
*

i
1 Rs
L R s  s 1
KI
L
K  K
R
s 2  s s  P   I
L  L
 L
42/94
Current Controller
UPC
i* +
-
KP  s  K I
s
i
1 Rs
L R s  s 1
i*
i*PF
1
KP K I s1 + -
KP  s  K I
s
i
1 Rs
L R s  s 1
1
PI
PF+PI
0.5
0
0
zero
1
2
3
4
Time (s)
5
6
7
-3
x 10
 KP

KI
KI

s  1
KI
i
K


L
L

 Ps

K  K
K  K
K  K
KI
R
R
R
*
s 2  s s  P   I
s 2  s s  P   I s 2  s s  P   I
i
L  L
L  L
L  L
 L
 L
 L
KI
L
43/94
Current Controller
UPC
i* +
-
KI
s
i
1 Rs
L R s  s 1
+
-
i* +
KI
s
-
KP
1
i
R s  KP
L
s 1
R s  KP
KP = 14.09 KI = 15945
Closed loop poles 
-1000+1000j
Settling time at 2% = 4ms
Overshoot  4.23%  Damping =0.707
2000
Root locus
1000
0
-1000
-2000
-2500
0
-(Rs +KP )/ L
-2000
-1500
-1000
-500
0
44/94
Current Controller
UPC
Current loop TF with PI or IP
KI
i
L

 Rs K P  K I
*
2
s

s



i
L
L

 L
2nd order TF
n2
s 2  2 n  s  n2
R  KP
2 n  s
L
Identifying coefficients
K P  2    n  L  Rs
Ts2%
KP 
8 L
 Rs
Ts2%
n2 
KI
L
K I  L  n2
4

  n
KI 
16  L
 2  Ts22%
Fixing the settling time at 2% (Ts2%) and the damping factor (ζ)
the KP and KI can be calculated
4.22 instead of 4 when ζ = 0.707
45/94
Current Controller
UPC
P
PI
KP  s  K I
s
i* +
-
++
i
1 Rs
L R s  s 1
i* +
P
IP
-
KI
s
i
1 Rs
L R s  s 1
++
+
-
KP
P
i
1 Rs
L R s  s 1
+
-
KP  s  K I
s
P
+
Step Response
+
0.04
KP
KI
s
0.03
Amplitude
i
1 Rs
L R s  s 1
+
0.02
0.01
0
0
2
4
6
Time (seconds)
8
-3
1
s
i
L

K  K
P
R
s 2  s s  P   I
L  L
 L
x 10
In terms of Perturbation, both solutions (PI & IP) have the same performance
46/94
Current Controller
UPC
• Current loop with PI + PF (d axis) and IP (q axis)
• Decoupling terms have to be added:
Control
id*
1
KP K I s1
id*PF
PI
+-
v d*
+
-
+
Lq·we·iq
Lq·we·iq
Control
iq*+
-
IP
+
PMSM
id
1 Rs
Ld R s  s 1
PMSM
vq*
+
Ld·we·id +PM·we
-
1 Rs
iq
Lq R s  s 1
( Ld·id +PM )·we
47/94
Current Controller
UPC
• Implementing PI in a DSP
– From S to Z domain
s+K
PI ( s ) = K P
s
– Ts=100us
s + 800
s
PI ( s ) = 5 ,5
I
KP
z - ( 1 - K K Ts )
→ PI ( z ) = K P
z -1
I
P
→ PI( z ) = 5 ,5
z - 0 ,92
z -1
Root Locus Editor (C)
1
Step Response
0.8
1.4
0.6
1.2
0.4
Imag Axis
0.2
0.2
0.15
Root Locus Editor (C)
1
0
-0.2
0.8
Amplitude
-0.4
0.1
-0.6
Imag Axis
0.05
0.6
-0.8
0
-1
-1
-0.05
-0.8
-0.6
-0.4
-0.2
0
Real Axis
0.2
0.4
0.6
0.8
1
0.4
-0.1
0.2
-0.15
0
-0.2
0.84
0.86
0.88
0.9
0.92
Real Axis
0.94
0.96
0.98
1
0
1
2
3
4
5
6
7
Time (sec)
8
-3
x 10
48/ 94
Current Controller
UPC
• Implementing a PI Controller in a DSP
vq _ ref ( z )
z - ( 1 - K K Ts )
= KP
– From Z to discrete time domain PI( z ) =
iq _ error ( z )
z -1
I
P
vq _ ref ( z )( z - 1 ) = iq _ error ( z )[ K P ( z - ( 1 - K
I
KP
Ts ))]
vq _ ref ( z )( 1 - z -1 ) = iq _ error ( z )[ K P ( 1 - z -1 ( c _ Ki _ K p ))]
vq _ ref = vq _ ref _ last + K P ( iq _ error - iq _ error _ last ( c _ Ki _ K p ))
– C code for the TI DSP 6711
// start iq PI controller
iq_error = iq_ref-iq;
vq_ref = vq_ref_last+c_Kp*(iq_error-c_Ki_Kp*iq_error_last);
iq_error_last = iq_error;
if (vq_ref > VPI_MAX) vq_ref = VPI_MAX;
if (vq_ref < -VPI_MAX) vq_ref = -VPI_MAX;
vq_ref_last = vq_ref;
// end iq PI controller
49/94
Speed Controller
UPC
• The plant can be simplified as follows
• First order with one pole s = - D J
• Mechanical time constant might be 50 times slower than the
electrical one. Current loop can be neglected.
• Typical sampling time 5ms.
TL
 e*
+
-
PI
+
Te*
+
1
J s+D
50/94
Speed and Current Controller
UPC
• Windup phenomenon
– Limits of the real plant (currents and voltages)
– Might end up with instability
• Anti Windup PI
+e_sat
In
e_ref
Kp
e_out
e_pro
+
Kt
+
-e_sat
Adapt TàI
0
Ki
0
1
1
s
Out
eo
Saturation
e_int
<>
e_dif
51/94
Exercise
UPC
• Sketch a complete FOC scheme for a PMSM. It has to
include:





Speed and currents control loops
(PI + pre filter) or IP
Saturations (software protections)
Anti Windup
Feed forward (decoupling) terms
• Draw the magnitudes (speed reference, speed response, iq
reference and iq response) waveforms for the cases: (i)
electrical car & (ii) lift. Indicate, in the drawn waveforms,
the motoring or generating operating modes.
• Propose a programming code (any generic language) to
implement a PI.
52/94
UPC
• SISO tool. Matlab
• Matlab/Simulink PMSM FOC. Waveforms.
• FOC in a DSP
53/94
Direct Torque Control
UPC
• Direct Torque Control (DTC) was firstly introduced by Takahashi in 1986
[Ref 1]. It was an important new method becoming very popular.
• Depenbrock in 1988 [Ref 2] introduced a similar idea under the name
Direct Self Control.
• However, just ABB company has got a popular commercial drive based
on DTC, the ASC600.
– Great number of applications such as: pumps, conveyors, lifts…from 2.2kW
until 630kW.
– Thanks to its 40MHz Toshiba processor plus ASIC, ASC600/800 closes the
entire control loop every 25us.
Takahashi, I and Nogushi, T. “A New Quick-Response and High-Efficiency Control Strategy of
an Induction Motor”, IEEE Trans. Industry Appl., Vol. 1A-22, pages 820-827, October 1986.
Depenbrock, M. "Direct Self Control of Inverter-Fed Induction Machines". IEEE Trans. on Power
Electronics. vol: PE-3, no:4 October 1988. pp: 420-429.
54/94
Classical DTC schematic
UPC
Flux ref
+
-
Torque
ref
+
Table
-
VSI
induction
motor
wm
flux sector
stator flux
torque
estimators
Advantages
Features
– Direct torque and stator flux control
– Indirect control of stator currents and
voltages
– Sinusoidal stator fluxes and currents
DT
–
–
–
–
–
Fastest torque response.
Absence of co-ordinate transform.
Absence of voltage modulator block
Absence of PI controllers for flux and torque.
Robustness against parameters variation.
55/94
VSI Review (i)
UPC
• Voltage Source Inverter (VSI) General Scheme:
Sap
Sbp
Scp
ia
a
N
ib
b
c
San
Sbn
ic
Scn
56/94
VSI Review (ii)
UPC
• Vector representation using the space vector transformation:
E2
a
b
c
2
+Vb
+Vb
-Vc
E1
-Vb
Questions:
a
+Va
+Vc
4
j
j
2
3
v   va (t )  vb (t )e  vc (t )e 3
3
b
c
(i) How many vectors?
(ii) Deduce the other
vectors.
57/94



VSI Review (iii)
UPC
• Hexagonal 8 (6 active + 2 zero) voltage vectors representation:
E3
E0
E7
a
a
b
E2
c
a
b
b
c
a
c
2
a
b
c
+Vb
3
E4
b
1
+Vb
E1
-Vb
-Vc
c
a
b
c
Van = 90º
+Va
+Vc
6
4
5
E5
a
b
c
E6
a
b
c
Van = 0º
58/94
DTC Principles
UPC
'
Lm
3
te  P
 r   s  sin s  r 
2
2 Ls L r  L m
 s  u s t
3
v3(010)
v2(110)
2
tg


S1
TI
V2
T=
V0
TD
V6
TI
V3
T=
V7
TD
V5
v2 (FI,T I)
v3(FD,T I)
v5(FD,T D)
v4(011)
n
v6(FI,T D)
FI
v1(100)
4
1
5
v5(001)
v6(101)
Tangential component - torque
6
FD
Normal component - modulus flux
59/94
Classical Look up Table
UPC

FI
FD

S1
S2
S3
S4
S5
S6
TI
V2
V3
V4
V5
V6
V1
T=
V0
V7
V0
V7
V0
V7
TD
V6
V1
V2
V3
V4
V5
TI
V3
V4
V5
V6
V1
V2
T=
V7
V0
V7
V0
V7
V0
TD
V5
V6
V1
V2
V3
V4
Questions:
(i) How could it be improved?
(ii) Deduce the look up table if the sectors are shifted 30º.
60/94
Classical DTC disadvantages
UPC
•
Inherent torque and flux ripples. Non of the VSI states is able to generate the exact
voltage value required for make zero both the torque error and the stator flux error.
Tz
Tz
Te*
3_states
modulation
•
•
V2
classic DTC
2_states
modulation
V2
V7
V1
V2
V0
V1
V0 V1
V2
V2
V7
THESIS
V7
V2
V1 V0
SVM
The discrete or digital implementation of the hysteresis is possible only for huge
sampling frequency.
Variable switching frequency.
S/H
1/Tz
Te* + hst
Te*
Te*
Te* - hst
t1
t2
t3
Tz
Tz
Tz
61/94
Space Vector Modulation
UPC
N
PMSG
la
n
V
ia Va
lb
ib
lc
ic
Sa Sb Sc
Vb
SVM
V
Vc

3
Angle Estimation
Algorithm
Vα
Vβ
SVM
Sa
Sb
Sc
Dead
Time
Sap
San
Sbp
Sbn
Scp
Scn
I d*
PI
dq
-
PI

2
+
I q*
-+
m*
PI
+
-
dq
^
e
d/dt
Sap
Sbp
Scp
a
N
b
c
San
Sbn
Scn
Va
Vb
Vc
62/94
UPC
Vα
Vβ
SVM
Sa
Sb
Sc

Vref  V  jV
β
V3
a
b
V2
c
3
a
b
c
Vβ
V4
a
b
α
Vref
c
V1
Vα
6
4
5
V5
a
b
c
a
b
c
V6
a
b
c
63/94
UPC



Vref  d1 V1  d 2 V2
V2
a
b
c
d1 
Vref
V1
θ
d2·V2
a
b
d1·V1


V1  d1 sin 60º  Vref sin  60º 


V2  d 2 sin 60º  Vref sin 
T1
TPWM
c
T1  TPWM
T2  TPWM
; d2 
T2
TPWM

Vref sin  60º 
2 V
sin 60º
3 dc

Vref sin 
2 V
3 dc sin 60º
T7  T0  TPWM  T1  T2
T7  T0
64/94
UPC
Sa
Sb
Sc
Dead
Time
Sap
San
Sbp
Sbn
Scp
Scn
• Ton < Toff  The DC bus can be short circuited.
Sap
N
1
Sa
0
on
Sap
a
off
San
on
San
1
Sa
• Turn on transitions
have to be delayed.
off
0
on
Sap
dead time
• Dead time appears.
off
on
San
off
65/94
UPC
van  23 vaN  13 vbN  13 vcN

1
2
1
vbn   3 vaN  3 vbN  3 vcN
v   1 v  1 v  2 v
3 aN
3 bN
3 cN
 cn
• Voltage equations for
star connected loads
vin  viN  v Nn ; i  a, b, c 

v v v
v Nn   aN bN cN 

3

ia
LA
Sap
Sbp
Scp
a
N
eA(t)
ib
b
c
San
+
ia
Sbn
ic
n
Scn
ib
ic
66/94
UPC
• Voltage waveforms for star connected load and using
double sided pattern:
V0
V1
V2
V7
V2
V1
V0
T0 /2
T1 /2
T2 /2
T7
T2 /2
T1 /2
T0 /2
• All sequence and V0 and V7 are placed in order to
minimize the commutations.
van  23 vaN  13 vbN  13 vcN

1
2
1
vbn   3 vaN  3 vbN  3 vcN
v   1 v  1 v  2 v
3 aN
3 bN
3 cN
 cn
67/94
V1
V0
UPC
a
b
c
a
b
V2
c
a
b
V7
c
a
b
V2
c
a
b
V1
c
a
b
V0
c
a
b
c
TPWM
Vdc/2
VaN
-Vdc/2
Vdc/2
VbN
-Vdc/2
Vdc/2
VcN
-Vdc/2
Vdc/2
Vdc/6
-Vdc/6
VNn
-Vdc/2
2/3Vdc
Vdc/3
Van
Vdc/3
Vbn
-Vdc/3
Vcn
-Vdc/3
-2/3Vdc
68/94
UPC
vab  vaN  vbN

 vbc  vbN  vcN
v  v  v
cN
aN
 ca
• Voltage equations & waveforms
(double sided SVM) for delta
connected loads
ia
Sap
Sbp
c
Sbn
+
ib
b
San
Lu
ia
a
N
iu
Scp
eU(t)
iw
-
ic
Scn
ib
iv
ic
69/94
V0
UPC
a
b
V1
c
a
b
V2
c
a
b
V7
c
a
b
V2
c
a
b
V1
c
a
b
V0
c
a
b
c
TPWM
Vdc/2
VaN
-Vdc/2
Vdc/2
VbN
-Vdc/2
Vdc/2
VcN
-Vdc/2
Vdc
Vab
Vdc
Vbc
Vca
-Vdc
70/94
Case study: Wind Turbine Classification
UPC
Fixed-speed WT
Advantages:
• Robust.
• Low Maintenance.
• Low Price
Drawbacks:
•Uncontrollable reactive power
consumption
•More mechanical strees.
•Gear box
Variable-speed WT
Advantages:
• More energy production.
• Less mechanical stress.
• Reduce power fluctuation.
• Capacity of noise reduction.
• Greater grid currents control.
Drawbacks:
• Need of power electronic
converters.
• More expensive.
In collaboration with Dr. Josep Pou
71/94
Case study: Wind Turbine fixed speed
UPC
Induction generator operating at fixed speed
Advantages:
- Robust design.
- No need for maintenance.
- Well enclosed.
- Produced in large series.
- Low price.
- Can withstand overloads.
Disadvantages:
- Uncontrollable reactive power consumption.
- Fixed speed means more mechanical stress.
72/94
UPC
Capacitor Banks
- Capacitors banks compensate for reactive power from the induction
generator.
- Maxim use of the electrical grid is done operating at unity power
Voltage
factor.
Current
C
C
C
73/94
UPC
Gearbox
Why a gearbox is needed?
-The gearbox is used to increase the
speed of the electrical generator.
- Without a gearbox, for a wind
turbine rotational speed of 30 rpm, a
generator of 100 pair of poles (!!!!)
would be needed (assuming 50-Hz
grid frequency).
- Furthermore, the mass of the rotor
has to be roughly proportional to the
torque.
T=P/; if  then T for a constant P.
T: Torque, P: Power, : Rotational speed
74/94
Case study: Wind Turbine variable speed
UPC
The frequency of the generator voltages can be different from the
electrical grid (50-60 Hz) and therefore the turbine speed can change.
Advantages:
- More energy production.
- Less mechanical stress.
- Reduce power fluctuation.
- Capacity of noise reduction.
- May have more control on the grid currents.
Drawbacks:
- The system requires power electronic converters.
- More expensive.
75/94
UPC
Doubly-Fed Induction Generator (DFIG)
ALSTOM-ECOTECNIA
- The slip of the rotor can change within a wide range (and therefore the
wind-turbine speed as well).
- It is the most common topology produced by large manufacturers
nowadays.
76/94
UPC
Multipole Synchronous Generators (MPSG)
?
ENERCON E-126 (7 MW)
-Multipole synchronous generators may not need a gearbox (these
generators have a large diameter).
- The rotational speed can change within a wide range.
- This is expected to be the most common wind turbine configuration in
the future.
77/94
UPC
Matrix Converter (from AC to AC)
UA
UsA
Bi-directional
switch
iA
i sA
UsB
N i
sB
UB
SAa
SAb
S Ac
UC
SBa
SBb
S Bc
SAc
iB
UsC
i sC
iC
Input RL filter
D1
T2
T1
SCa
SCb
SCc
ib
ia
Ua
Ub
D2
ic
Uc
LOAD
n
78/94
UPC
 Back-to-back-connected (three-level) converter
Wind-Turbine NPC Converter
Grid-Connected NPC Converter
Multipole
Synchronous
Wind Turbine
vC2
Electrical
Grid
C
vr
a
Vd
b
c
c
ig
iwt
s
t
(NP)
vC1
r
3*Lg
vs
vt
C
79/94
Case study: Wind Turbine Control
UPC
Wind
Models
80/94
UPC
• 2 Power Converters & 4 control loops.
– PMSM. Inner current control & outer speed control
– Electrical Grid. Inner current control & outer voltage control
Permanent Magnet
Synchronous Generator
Electrical Grid
DC
AC
DC
DTC (Direct Torque Control)
FOC (Field Oriented Control)
AC
DPC (Direct Power Control)
VOC (Voltage Oriented Control)
Dual Solution
81/94
UPC
N
FOC
UsC
PMSG
la
sB
LC filter
U UA
V
ia Va
lb
ib
lc
PWM Pattern
Vb
ic
Vc
d/dt
*
Vdc
MAF(Tg )
Voltage
Controller
Grid
Voltages
vr vs vt
Id*
id
v dc
ir is it
Angle
Pos. Sequ.
Dip
Detector
 d
Transf.
rst-dq
iq
I q*
Yes
B
SVM
V
test pulses
n
UC
Grid
U UsA
Angle Estimation
Algorithm
Current
Controller
v d

3
-
PI
2

+
Iq*
-+
 m*
PI
+
-
dq
^
d/dt
v d'
Grid
Voltages
vr vs vt
Transf.
dq-rst
 Lg
v q
Id*
PI
e
 Lg
Current
Controller
dq
Converter
Voltages
vrc vsc vtc
v q'
Modification
of Id* and I q*
VOC
82/94
Experimental Platforms. dSPACE
UPC
r
Wind Turbine
Emulator
vwind
r
Tm
Control
dc
Motor
PMSG
Strategy
dc  Link
Maximum Power Tracking
Power Suply
• Fast implementation
• Research platform
• dSPACE 1103 (Power
PC & DSP TI240)
dSPACE 1103 Digital Controller
opt  f (wind )
r
FOC
PWM
r*  opt
In collaboration with Dr. Jordi Zaragoza
EUROTHERM
Model ER  340 XRi
Generator
Converter
Dissipating
Resistor
83/94
Experimental Platforms. dSPACE
UPC
• Easy to monitor and debug with the Control Desk
In collaboration with Dr. Jordi Zaragoza
84/94
Experimental Platforms. DSP/FPGA
UPC
• Research platform
N
PMSG
la
n
ia Va
lb
ib
lc
ic
Vb
V
Sa Sb Sc
SVM
V
Vc
dq

3
Angle Estimation
Algorithm
FPGA
On/off switching signals
Dead time
ADC
Hardware protections &
trips
I d*
PI
-
PI
2

+
I q*
-+
m*
PI
+
-
dq
^
e
d/dt
DSP
PC
All controllers
Estimations
SVM
Software protections
Host
Programing
Debug & Monitor
85/94
UPC
In collaboration with Dr. Lee Empringham & Dr. Liliana de Lillo. University of Nottingham. UK. 86/94
Experimental Platforms. DSPIC
UPC
• Industrial platform
With the permission of MICROCHIP
http://www.microchip.com/pagehandler/en
-us/technology/motorcontrol/home.html
87/94
Experimental implementing issues
UPC
• Synchronisation: in order to minimise the commutation noise, the
currents’ sampling instant must be either at the middle or at the end of
the PWM period (i.e. during the applications of zero states V0 or V7).
V0
a
c
a
b
V2
c
a
b
V7
c
a
b
V2
c
a
b
V1
c
a
b
V0
c
a
b
c
2/3Vdc
1/3Vdc
Van
Vbn
b
V1
1/3Vdc
-1/3Vdc
Vcn
-1/3Vdc
-2/3Vdc
• Current and speed controllers must be also synchronised with the PWM.
88/94
UPC
• Priorities: computing resources can be optimised if current loop task
has the highest priority. After the speed loop task and finally any software
for monitoring or debugging.
Current loop task
Speed loop task
Same priority
Tint
Tint
Tint
Different priorities
Tint
Tint
Tint
Tint
Tint
89/94
UPC
• Incremental encoder: Number of pulses per interruption?
• It is assumed a sampling time of 100 (µs) and 5 (ms) for the current and
speed, respectively.
1  min 
 rev   pulses 


 N

6 
 min   rev  60 10  s 

N
1 4  pulses 

10 
60
 100s 
N
1
 pulses 
102 

60·2
 5ms 
N
3000 (rev/min)
30 (rev/min)
16384 (pulses/rev)
819,2 (pulses)
40960 (pulses)
8,192 (pulses)
409,6 (pulses)
4096 (pulses/rev)
204,8 (pulses)
10240 (pulses)
2,048 (pulses)
102,4 (pulses)
• Two speeds must be calculated for the speed (higher
accuracy) and current (lower accuracy) loops separately.
90/94
Sensorless Control: still a research topic
UPC
• Dynamic control of electrical machines
without need for position encoder
• No encoder => less electronics
– Volume and cost reduction
– Increases reliability (fault tolerant,
redundancy)
dynamic
model
based
steady state
model based
Open loop
estimators
MRAS
machine saliency
Injection
methods
Observers
transient
Modified
PWM
test
pulses
continuos
hf
rotating

pulsating
dq
91/94
Summary
UPC
• Permanent Magnet Synchronous Machines
– Advantages:
• No rotor currents => no rotor losses.
• Higher efficiency => energy saving capability.
• Smaller rotor diameters, higher power density and lower rotor
inertia.
• Attractive for Wind applications, Aerospace applications such
as aircraft actuators, Machine tools, position servomotors
(replacing the DC motors).
– Inconveniences:
• Synchronous machines => need for rotor position.
• Price.
• Permanent magnet is becoming a scarce raw material.
92/94
Summary
UPC
• PMSM dynamic equations and modelling
• FOC for PMSM has been introduced
– Principles & Scheme.
– PI & IP Controllers: root locus, specifications, design and
implementation.
• Classical DTC
– VSI Review.
– Principles, features & scheme.
– Hysteresis controllers.
• Space Vector Modulation
– Voltage equations & voltage waveforms.
– Dead time.
93/94
UPC
Summary
• Case study: Wind Turbine
– Constant versus variable speed.
– Dual solution for the Grid Connected Power Converter.
• Experimental approach
– Hardware platforms.
– (Some typical) implementing issues.
• Research: Sensorless Control of PMSM
94/94

electricas maquinas

Transcription

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