Transcript PPT

Last Comments on Control
J. McCalley
Modeling of Variable Speed Wind Turbine
•
•
•
•
•
Aerodynamic model, evaluates the
turbine torque Tt as a function of
wind speed Vv and turbine
angular speed t .
Pitch system, evaluates the pitch
angle dynamics as a function of
pitch reference  ref .
Mechanical system, evaluates the
generator and turbine angular
speed as a function of turbine
torque and generator torque Tem .
Electrical machine and power
converters transform the generator
torque into a grid current as a
function of voltage grid.
Control system, evaluates the
generator torque, pitch angle and
reactive power references as a
function of wind speed and grid
voltage.
Block Scheme of a variable speed wind turbine
model
Wind turbine control levels
Rotor-side converter (RSC) is
controlled so that it provides
independent control of Tem
and Qs.
Level I: Regulates power flow
between grid and generator.
Level II: Controls the amount
of energy extracted from the
wind by wind turbine rotor.
Level III: Responds to windfarm or grid-central control
commands for MW dispatch,
voltage, or frequency control.
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Basic topology and View of Level 1 Control
Below is the basic topology of the basic back-to-back two-level voltage source
converter (VSC).
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Level 1 control
We achieve
RSC control
objectives by
controlling rotorside voltage.
This (openloop) control
not heavily
used for DFIGs
DC bus voltage is
controlled by grid-side
converter (GSC) to a predetermined value for
proper operation of both
GSC and RSC. Qg also
controlled via GSC.
We control rotor
voltage to achieve a
specified torque and
stator reactive power.
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Overview of Level 1 Control
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Grid-side converter
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Dwell time and switching sequence
(4.59)      (k  1)
(4.61) ma 
3vref
VDC
Ta 
3vref TS
Tb 
3vref TS
(4.60)
VDC
VDC

for 0    
3

3
Modulation index




sin      maTS sin    
3

3

TS sin   maTS sin 
T0  TS  Ta  Tb
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See the next slide,
for Table 4-4
A larger view
Sector
9
Switching Sequence



V2
V0
V2
I

V0

V1

V1

V0
II
000

V0
100

V3
110

V2
111

V0
110

V2
100

V3
000

V0
III
000

V0
010

V3
110

V4
111

V0
110

V4
010

V3
000

V0
IV
000

V0
010

V5
011

V4
111

V0
011

V4
010

V5
000

V0
V
000

V0
001

V5
011

V6
111

V0
011

V6
001

V5
000

V0
000

V0
001

V1
101

V6
111

V0
101

V6
001

V1
000

V0
VI
000
100
101
111
101
100
000
PI Controllers
Observe the currents idr*
and iqr* being supplied as
control signals for the target
values of torque Te* and
stator reactive power Qs*.
These target currents are
compared to the actual
currents, and the difference
drives a PI controller which
generates the control signals
vdr* and vqr*.
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There are similar
controllers for the
GSC as well (not
shown in this
diagram).
Comments on PI Controllers
• PI stands for “proportional plus integral”
• PI control (also known as lag compensation) provides zero steadystate error to a step input. Since the input is the difference between
the target value and the actual value, the PI control forces the
target value to equal the actual value in the steady state.
• The transfer function of the PI controller is given by
K 

s  KI / KP 
PI  K P  I   K P 

s 
s


• Block diagram representations can be viewed as follows:
idr
KP
idr* +
Σ
v'dr
KI/s
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
s  KI / KP  *
v'dr ( s )  K P 
idr ( s )  idr ( s )

s



Comments on PI Controllers
idr
idr*
+

KP
-
Σ
v'dr
KI/s
s  KI / KP  *
v'dr ( s )  K P 
idr ( s )  idr ( s )

s


The corresponding time-domain
expression is given by:
v'dr (t ) 

*
K P idr
(t )  idr (t )



t *
 K I idr (t )  idr (t )
0
dt
One reference [1] provides a slightly different control law:
v'dr (t ) 

*
K P bidr
(t )  idr (t )


t *
 K I idr (t )  idr (t )
0
dt
From [1], “For this particular case, both PI controllers in (13) have been tuned applying
the pole assignment method, in an attempt to reach a critically damped inner loop
response with a 40-ms settling time. Furthermore, inclusion of parameter b allows
placing independently not only the inner loop poles, but also the unique zero inherent to
the PI controller. Particularly, if b is made equal to zero, the PI controller zero is placed
at s= -∞, and, as a result, its influence on the closed-loop time response is cancelled out.
• The point is that the PI controller must be tuned to obtain the
desired response. This tuning can be done in time-domain. A
12 procedure for doing it in the z-domain is illustrated in [2].
Comments on PI Controllers
• A compensation term is added in all of the references, like this:
idr
KP
idr*
+
Σ
v'dr
+
KI/s
Σ
vdr
+
Compensation
term
It appears the term is added to diminish coupling between the d-axis quantities and
the q-axis quantities. I have not been able to identify a satisfying explanation for it.
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Some References That Address PI Control Design
[1] Arantxa Tapia, Gerardo Tapia, J. Xabier Ostolaza, and José Ramón Sáenz,
“Modeling and control of a wind turbine driven doubly fed induction generator,” IEEE
Transactions on Energy Conversion, Vol. 18, No. 2, June 2003.
[2] P. Pena, J. Clare, and G. Asher, “Doubly fed induction generator using back-to-back
PWM converters and its application to variable speed wind energy generation,” IEEE
Proc. Electr. Power Applications, Vol 143, No. 3, May 1996.
[3] O. Anaya-Lara, N. Jenkins, J. Ekanayake, P. Cartwright, and M. Hughes, “Wind
Energy Generation: Modelling and Control,” Wiley 2009, pp. 84-89.
[4] G. Abad, J. Lopex, M. Rodriguez, L. Marroyo, and G. Iwanski, “Double fed induction
machine: modeling and control for wind energy generation,” Wiley, 2011, pp. 304-311.
[5]www.mathworks.com/help/physmod/sps/powersys/ref/windturbinedoublyfedinduction
generatorphasortype.html
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