Applications of the
Doubly Fed Induction Machine (DFIM)
Authors:
1University
of Mondragon, Spain
2Ingeteam Transmission & Distribution S.A., Spain.
3Warsaw University of Technology, Poland.
Gonzalo Abad1
Miguel Ángel Rodríguez2
Grzegorz Iwanski3
Outline
1. Variable Speed Wind Energy Generator Systems.
„
Basic Modeling of the Wind Turbine.
„
Wind Turbine Control System.
„
Different Configurations According to the Electrical Generator.
2. Doubly Fed Induction Machine based Wind Energy Generator System.
„
Control System.
„
Basic Numbers of an 1,75 MW Wind Turbine.
3. Industrial solutions. DFIM Wind Turbine Manufacturers.
„
Different Industrial Solutions.
4. Applications with Prime Movers Different from Wind - Review.
„
Different Applications.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
2
Outline
1. Variable Speed Wind Energy Generator Systems.
„
Basic Modeling of the Wind Turbine.
„
Wind Turbine Control System.
„
Different Configurations According to the Electrical Generator.
2. Doubly Fed Induction Machine based Wind Energy Generator System.
„
Control System.
„
Basic Numbers of an 1,75 MW Wind Turbine.
3. Industrial solutions. DFIM Wind Turbine Manufacturers.
„
Different Industrial Solutions.
4. Applications with Prime Movers Different from Wind - Review.
„
Different Applications.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
3
Variable Speed Wind Energy Generator Systems
„ Basic Modeling of the Wind Turbine.
H. Camblong, M. Rodríguez Vidal, J. R. Puiggali. “Principles of a Simulation Model for a Variable-Spedd PitchRegulated Wind Turbine”. Wind Engineering, Vol 28, Pg 157-175. March 2004.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
4
Variable Speed Wind Energy Generator Systems
„ Basic Modeling of the Wind Turbine.
Tt =
1
⋅ ρ ⋅ π ⋅ R 3 ⋅ Vv2 ⋅ Ct
2
λ=
R ⋅ ωt
Vp
C =λ C
p
t
k
⎛ k2
⎞⎛⎜ λ7i ⎞⎟
k5
C p = k1 ⎜⎜ − k3 β − k4 β − k6 ⎟⎟ e
⎝ λi
⎠⎜⎝ ⎟⎠
1
Pt = ⋅ ρ ⋅ π ⋅ R 3 ⋅ Vv2 ⋅ C p
2
Power coefficient Cp
Cp_max
0.5
ßopt =-2°
0.4
1
λ + k8
Torque coefficient Ct
0.06
ß=2
0.3
λi =
ß=-2°
ß=2°
ß=5
0.04
ß=5
0.2
ß=40
0.02
0.1 ß=40
λopt
0
0
4
0
8
12
16
20
0
4
8
λ
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
λ
12
16
20
5
Variable Speed Wind Energy Generator Systems
„ Wind Turbine Control System.
λ Estimator
Vv
λest
β*
Ωm_nom
+
Ωm _min
Regulator
Tem *
-
Ωm
Tem
β
Vv
β*=βopt
Vv
Max power
tracking
Ωm*
+
T em*
Regulator
-
Ωm
Vv
Vv
Ω m_Nom
+ -
Regulator
Tem
β *=β op t
β*
kopt
T em *=Tem_ nom
T em *
+
Ωm
Ωm
D t_m
Ω m2
^2
H. Camblong, I. Martinez Alegría, M. Rodríguez, G. Abad. “Experimental evaluation of wind turbines maximum power point tracking
controllers”. Energy Conversion and Management Vol 47, Issues 18-19, November 2006, Pg 2846-2858.
H. Camblong, G. Tapia, M. Rodríguez. “Robust digital control of a wind turbine for rated-speed and variable-power operation regime”.
IEE Proceedings Control Theory & Applications Vol 153, Issue 1, Pg 81-91. January 2006.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
6
β
Variable Speed Wind Energy Generator Systems
„ Different Configurations According to the Electrical Generator.
Wind
GEARBOX
Doubly Fed
Induction Machine
Network
Transformer
Rotor side VSC
rotor
filter
Grid side VSC
grid
filter
Characteristics (DFIM):
•
Limited operating speed range (-30% to +30%).
•
Small scale power electronic converter.
•
Complete control of active power and reactive power exchanged with the grid.
•
Need for slip-rings and gear box.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
7
Variable Speed Wind Energy Generator Systems
„ Different Configurations According to the Electrical Generator.
PM-Synchronous Machine Multi-Pole
and
Multipole wound rotor synchronous generator
Machine side VSC
Wind
Grid side VSC
Network
stator
filter
grid
filter
Transformer
Characteristics (MPMG and WRSG):
•
Full operating speed range.
•
Full scale power electronic converter.
•
Complete control of active power and reactive power exchanged with the grid.
•
Elimination of the gear box.
•
No brushes on the generator in PMSM.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
8
Variable Speed Wind Energy Generator Systems
„ Different Configurations According to the Electrical Generator.
Wind
Induction Machine
Machine side VSC
GEARBOX
Grid side VSC
Network
stator
filter
Transformer
grid
filter
Characteristics (SCIM):
•
Full operating speed range.
•
Full scale power electronic converter.
•
Complete control of active power and reactive power exchanged with the grid.
•
No brushes on the generator but Need for gear box.
•
Manufacturer: Ecotecnia 47 Variable Speed 750 kW (some prototypes)
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
9
Variable Speed Wind Energy Generator Systems
„ Different Configurations According to the Electrical Generator.
Wind
GEARBOX
PM-Synchronous Machine
Multi-Pole
Machine side VSC
Grid side VSC
Network
stator
filter
Transformer
grid
filter
Characteristics (PMSM):
•
Full operating speed range.
•
Full scale power electronic converter.
•
Complete control of active power and reactive power exchanged with the
grid.
•
Multipole generator, permanent magnets needed in large quantities.
•
No brushes on the generator.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
10
Outline
1. Variable Speed Wind Energy Generator Systems.
„
Basic Modeling of the Wind Turbine.
„
Wind Turbine Control System.
„
Different Configurations According to the Electrical Generator.
2. Doubly Fed Induction Machine based Wind Energy Generator System.
„
Control System.
„
Basic Numbers of an 1,75 MW Wind Turbine.
3. Industrial solutions. DFIM Wind Turbine Manufacturers.
„
Different Industrial Solutions.
4. Applications with Prime Movers Different from Wind - Review.
„
Different Applications.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
11
Doubly Fed Induction Machine based
Wind Energy Generator System
„ Control System.
WIND TURBINE CONTROL:
07-09-2009
-
Divided in different control levels.
-
Only first control level is studied in
this tutorial.
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
12
Doubly Fed Induction Machine based
Wind Energy Generator System
„ Basic Numbers of an 1,75 MW Wind Turbine.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
07-09-2009
Velocidad
(rpm)
975
1100
1450
1615
1760
1800
1800
1800
1800
1800
1800
1800
1800
1950
1950
Potencia salida
(KW)
100
167
400
600
800
1000
1200
1400
1700
1700
1700
1700
1700
1842
2125
Factor de
potencia
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.9 inductivo
0.95 capacitivo
0.95 capacitivo
0.9 inductivo
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
Tensión línea
(VRMS)
690
690
690
690
690
690
690
690
690
621
759
690
690
690
690
13
Doubly Fed Induction Machine based
Wind Energy Generator System
„ Basic Numbers of an 1,75 MW Wind Turbine.
Vsnom
Motor 1.5 MW
690 V
PU
Motor 1.4 MW
690 V
Isnom
1395 A
1400 A
u=Ns/Nr
0.36
0.39
Vrnom
1916 V
1769 V
PU
Rs
Rr
Lh
0.0015 Ω
0.0015 Ω
3.34 mΗ
0.0052
0.0052
3.68
0.0018 Ω
0.0019 Ω
2.78 m Η
0.0065
0.0068
3.07
Lfs
95.49 μΗ
0.105
86.58 μΗ
0.096
Lfr
Rfer
τr
τs
σ
66.85 μΗ
26.2 Ω
2.27 s
2.29 s
0.047
0.074
91.74
−3
7.23 e
7.29 e − 3
0.047
108.23 μΗ
66.28 Ω
1.50 s
1.56 s
0.067
0.119
232.93
−3
4.76 e
4.96 e −3
0.067
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
14
Outline
1. Variable Speed Wind Energy Generator Systems.
„
Basic Modeling of the Wind Turbine.
„
Wind Turbine Control System.
„
Different Configurations According to the Electrical Generator.
2. Doubly Fed Induction Machine based Wind Energy Generator System.
„
Control System.
„
Basic Numbers of an 1,75 MW Wind Turbine.
3. Industrial solutions. DFIM Wind Turbine Manufacturers.
„
Different Industrial Solutions.
4. Applications with Prime Movers Different from Wind - Review.
„
Different Applications.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
19
Industrial solutions.
DFIM Wind Turbine Manufacturers
•
Gamesa
G52 - 58 850k, 80 – 87 & 90 2MW
http://www.gamesacorp.com/es/productos/aerogeneradores/c
atalogo-de-aerogeneradores
•
Acciona
AW-70 77 & 82 1500 kW
AW-100 109 & 116 3000 kW
http://www.acciona-energia.com/default.asp?x=0002020601&lang=Es
•
Ecotecnia (Alstom)
Eco 74 1670kW, 80 2MW
Eco 100 3MW
http://www.power.alstom.com/home/new_plants/wind/wind_t
urbines/38796.EN.php?languageId=EN&dir=/home/new_pl
ants/wind/wind_turbines/
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
20
Industrial solutions.
DFIM Wind Turbine Manufacturers
•
Vestas (NEG MICON):
V90 (only USA market)
http://www.vestas.com/es/soluciones-e%C3%B3licas/aerogeneradores.aspx
•
General Electric:
1.5, 2.5 & 3.6 MW (off-shore)
http://www.gepower.com/prod_serv/products/wind_turbines/en/index.htm
•
Sulzon:
S 82 – 88, 1500 & 2100kW
http://www.suzlon.com/
•
RePower:
2.05, 3.3 & 5MW
http://www.repower.de/index.php?id=12&L=1
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
21
Industrial solutions.
DFIM Wind Turbine Manufacturers
•
Siemens (Bonus):
SWT-3.6-107, SWT-2.3-101
http://www.powergeneration.siemens.com/products-solutionsservices/products-packages/wind-turbines/products/Products.htm
•
Fuhrlaender:
FL2500
http://www.fuhrlaender.de/index_en.php
•
Nordex
N100 2.5MW
http://www.nordex-online.com/en/produkte-service/wind-turbines.html
•
Mitshubishi
MWT 95, 2.4 MW
http://www.mhi.co.jp/en/products/category/wind_turbine_generator
s.html
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
22
Industrial solutions.
DFIM Wind Turbine Manufacturers
•
DeWind
D6, D8 & D8.2, 1 & 2 MW
http://www.compositetechcorp.com/OurCompanies/DeWindInc/tabid/145/Defau
lt.aspx
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
23
Outline
1. Variable Speed Wind Energy Generator Systems.
„
Basic Modeling of the Wind Turbine.
„
Wind Turbine Control System.
„
Different Configurations According to the Electrical Generator.
2. Doubly Fed Induction Machine based Wind Energy Generator System.
„
Control System.
„
Basic Numbers of an 1,75 MW Wind Turbine.
3. Industrial solutions. DFIM Wind Turbine Manufacturers.
„
Different Industrial Solutions.
4. Applications with Prime Movers Different from Wind - Review.
„
Different Applications.
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
24
Applications with Prime Movers
Different from Wind - Review
22MW adjustable speed generation unit with DFIG and
cycloconverter for Narude Power Station (Japan) – 1987 [1]
80MW adjustable speed pumped storage unit with DFIG and
cycloconverter at Yagisawa Power Plant (Japan) – 1990 [2]
2x400MW adjustable speed pumped storage units with DFIG and
cycloconverter for Ohkawachi Power Station (Japan) – 1993 [1]
2x350MVA adjustable speed pumped storage units with DFIG and
cycloconverter for Goldisthal Power Station (Germany) – 2003 [3]
[1] T. Kuwabara, A. Shibuya, H. Furuta, E. Kita, K. Mitsuhashi, “Design and Dynamic Response Characteristics of 400MW Adjustable Speed
Pumped Storage Unit for Ohkawachi Power Station”, IEEE Transaction on Energy Conversion, Vol. 11, Issue 2, June 1996, pp. 376 – 384.
[2] S. Furuya, T. Taguchi, K. Kusunoki, T. Yanagisawa, T. Kageyama, T. Kanai, “Successful Achievement in a Variable Speed Pumped Storage
Power System at Yagisawa Power Plant”, Power Conversion Conference – PCC’93, Yokohama, 19-21 April 1993, pp. 603 – 608
[3] K. Grotenburg, F. Koch, I. Erlich U. Bachmann, “Modeling And Dynamic Simulation Of Variable Speed Pump Storage Units Incorporated
Into The German Electric Power System”, 9th European Conference on Power Electronics and Applications – EPE’09, Graz, Austria, pp.10
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
25
Applications with Prime Movers
Different from Wind - Review
2500kVA range series diesel engine based rotary uninterruptible
power supply system with slip ring induction machine by
Starshine™ [1]
Flywheel based energy storage systems with DFIG described in
several papers [2][3][4][5]
Variable speed power system with UPS function [6].
[1] http://www.onsitepowerinc.com/documents/supplierDocs/Rotary%20UPS%20Brochure.pdf
[2] Yoon-Ho Kim; Kyoung-Hun Lee; Young-Hyun Cho; Young-Keun Hong, „Comparison of harmonic compensation based on wound/squirrelcage rotor type induction motors with flywheel”, IPEMC 2000, Volume 2, 15-18 Aug. 2000 Page(s):531 – 536
[3] H. Akagi, H. Sato, „Control and performance of a doubly-fed induction machine intended for a flywheel energy storage system”, IEEE Trans.
on Power Electronics, Volume 17, Issue 1, Jan. 2002, Page(s):109 - 116
[4] Gang Li; Jing Zhang; Shijie Cheng; Jinyu Wen; Yuan Pan, „State Space Formulation and Stability Analysis of a Doubly-fed Induction
Machine with a Flywheel Energy Storage System” Int. Conf. on Power System Technology, 2006. PowerCon 2006. 22-26 Oct. 2006 Page(s):1 - 6
[5] C. Batlle, A. Doria-Cerezo, R. Ortega, „Power flow control of a doubly-fed induction machine coupled to a flywheel”, Int. Conf. on Control
Applications, 2004. Vol. 2, 2-4 Sept. 2004 Page(s):1645 - 1650
[6] G. Iwanski, W. Koczara: “DFIG based Power Generation System with UPS Function for Variable Speed Applications” IEEE Trans. on
Industrial Electronics. Vol. 55, Issue 8, pp. 3047 – 3054, Aug. 2008
07-09-2009
Applications of the Doubly Fed Induction Machine,
by G. Abad, M.A. Rodríguez and G. Iwanski
26
Mathematical Model of the
Doubly Fed Induction Machine.
Authors:
1University
of Mondragon, Spain
2Ingeteam Transmission & Distribution S.A., Spain.
3Warsaw University of Technology, Poland.
Gonzalo Abad1
Miguel Ángel Rodríguez2
Grzegorz Iwanski3
Outline
1. Dynamic Model of the DFIM.
„
Simplified Model of the DFIM.
„
Space Vector Representation.
„
αβ Model of the DFIM.
„
dq Model of the DFIM.
„
State Space Representation of the αβ Model.
„
State Space Representation of the dq Model.
2. Dynamic Model of the DFIM Considering the Iron Losses.
„
αβ Model of the DFIM Considering the Iron Losses.
„
dq Model of the DFIM Considering the Iron Losses.
„
State Space Representation of the αβ Model.
3. Dynamic Modeling of the DFIM based on Symmetrical Components Analysis.
„
Basic Definitions.
„
DFIM in Balanced Operation.
„
DFIM in Unbalanced Operation.
4. Steady-State Analysis of the DFIM.
„
Basic Operation Modes Attending to the Speed and Powers.
„
Performance Analysis. Amplitude, Frequency and Phase Shift Variation.
„
Performance Analysis. Torque and Reactive Power Control.
5. Estimator and Observer Structures for the DFIM.
„
Directly Measurable and Estimated Magnitudes.
„
Stator Active and Reactive Power Estimation.
„
Stator and Rotor Fluxes Estimator.
„
Stator Flux Estimator from Stator Voltage.
„
Stator Flux Synchronization from the Stator Voltage.
„
Stator and Rotor Flux Observer.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
2
Outline
1. Dynamic Model of the DFIM.
„
Simplified Model of the DFIM.
„
Space Vector Representation.
„
αβ Model of the DFIM.
„
dq Model of the DFIM.
„
State Space Representation of the αβ Model.
„
State Space Representation of the dq Model.
2. Dynamic Model of the DFIM Considering the Iron Losses.
„
αβ Model of the DFIM Considering the Iron Losses.
„
dq Model of the DFIM Considering the Iron Losses.
„
State Space Representation of the αβ Model.
3. Dynamic Modeling of the DFIM based on Symmetrical Components Analysis.
„
Basic Definitions.
„
DFIM in Balanced Operation.
„
DFIM in Unbalanced Operation.
4. Steady-State Analysis of the DFIM.
„
Basic Operation Modes Attending to the Speed and Powers.
„
Performance Analysis. Amplitude, Frequency and Phase Shift Variation.
„
Performance Analysis. Torque and Reactive Power Control.
5. Estimator and Observer Structures for the DFIM.
„
Directly Measurable and Estimated Magnitudes.
„
Stator Active and Reactive Power Estimation.
„
Stator and Rotor Fluxes Estimator.
„
Stator Flux Estimator from Stator Voltage.
„
Stator Flux Synchronization from the Stator Voltage.
„
Stator and Rotor Flux Observer.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
3
Dynamic Model of the DFIM
„ Doubly Fed Induction Machine (DFIM).
Machine under study:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
4
Dynamic Model of the DFIM
„ Simplified Model of the DFIM. Objectives.
-
First dynamic modelling approach of the machine.
-
Oriented to design control strategies and validate performances of the machine.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
5
Dynamic Model of the DFIM
„ Simplified Model of the DFIM
-
3 windings in the stator (ABC) and 3 windings
in the rotor (abc).
-
The windings are considered as ideal [1]-[2].
-
Oriented to design control strategies and
validate performances of the machine.
[1] W. Leonhard, “Control of electrical drives”. Springer-Verlag, 2001.
[2] M.P. Kazmierkowski, R. Krishnan, F. Blaabjerg, “Control in Power Electronics Selected Problems,” Academic Press, 2002.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
6
Dynamic Model of the DFIM
„ Electric Equivalent Circuit of the DFIM
3 phase equations for the stator (Pulsation ωs )
3 phase equations for the rotor (Pulsation ωr )
[1] W. Leonhard, “Control of electrical drives”. Springer-Verlag, 2001.
[3] J.L. Rodriguez Amenedo, "Analisis dinamico y disefno del sistema de control de aeroturbinas de velocidad variable con
aerogenerador asincrono de doble alimentacion", Ph. Thesis, Universidad Carlos III, 2000.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
7
Dynamic Model of the DFIM
„ Space Vector Representation. Reference frames.
1.- The stator reference frame (α-β): Aligned with the stator, the rotating speed of the frame is
zero, and the space vector referenced to it, rotates at the synchronous speed ωs.
2.- The rotor reference frame (D-Q): Aligned with the rotor, the rotating speed of the frame is the
angular speed of the rotor ωm, and the space vector referred to it rotates at the angular speed ωr.
3.- The synchronous reference frame (d-q): The rotating speed of the frame is the synchronous
speed ωs, and the space vector referenced to it does not rotate, i.e. it presents constant real
and imaginary parts.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
8
Dynamic Model of the DFIM
„ Space Vector Representation. Reference frames.
One space vector can be represented in
3 different reference frames.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
9
Dynamic Model of the DFIM
„ αβ Model of the DFIM.
Equivalent electric circuit:
Voltage and Flux
Space Vector equations:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
10
Dynamic Model of the DFIM
„ αβ Model of the DFIM.
Torque equation (there are several versions):
Stator and rotor, active and reactive power equations:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
11
Dynamic Model of the DFIM
„ dq Model of the DFIM.
Equivalent electric circuit:
Voltage and Flux
Space Vector equations:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
12
Dynamic Model of the DFIM
„ dq Model of the DFIM.
Torque equation (there are several versions as well):
Stator and rotor, active and reactive power equations:
Equivalent equations to
the αβ model !!
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
13
Dynamic Model of the DFIM
„ State Space Representation of the αβ Model.
Compact version:
-
Fluxes as state-space magnitudes.
-
Useful for simulation purposes.
Expanded version:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
14
Dynamic Model of the DFIM
„ State Space Representation of the αβ Model.
-
Currents as state-space magnitudes.
Expanded version:
Compact version:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
15
Dynamic Model of the DFIM
„ State Space Representation of the dq Model.
Compact version:
-
Fluxes as state-space magnitudes.
-
Useful for evaluation purposes.
Expanded version:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
16
Dynamic Model of the DFIM
„ State Space Representation of the dq Model.
-
Currents as state-space magnitudes.
Compact version:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
17
Dynamic Model of the DFIM
„ State Space Representation of the dq Model.
-
Currents as state-space magnitudes.
Expanded version:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
18
Outline
1. Dynamic Model of the DFIM.
„
Simplified Model of the DFIM.
„
Space Vector Representation.
„
αβ Model of the DFIM.
„
dq Model of the DFIM.
„
State Space Representation of the αβ Model.
„
State Space Representation of the dq Model.
2. Dynamic Model of the DFIM Considering the Iron Losses.
„
αβ Model of the DFIM Considering the Iron Losses.
„
dq Model of the DFIM Considering the Iron Losses.
„
State Space Representation of the αβ Model.
3. Dynamic Modeling of the DFIM based on Symmetrical Components Analysis.
„
Basic Definitions.
„
DFIM in Balanced Operation.
„
DFIM in Unbalanced Operation.
4. Steady-State Analysis of the DFIM.
„
Basic Operation Modes Attending to the Speed and Powers.
„
Performance Analysis. Amplitude, Frequency and Phase Shift Variation.
„
Performance Analysis. Torque and Reactive Power Control.
5. Estimator and Observer Structures for the DFIM.
„
Directly Measurable and Estimated Magnitudes.
„
Stator Active and Reactive Power Estimation.
„
Stator and Rotor Fluxes Estimator.
„
Stator Flux Estimator from Stator Voltage.
„
Stator Flux Synchronization from the Stator Voltage.
„
Stator and Rotor Flux Observer.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
19
Dynamic Model of the DFIM Considering the Iron Losses
„ αβ Model of the DFIM Considering the Iron Losses.
- The iron losses can be approximated to:
Ploss=k*f*B2
- The iron losses are modelled as a resistance (Rfe)
in parallel to the mutual inductance (Lh) of each phase.
- Rfe is approximately proportional to the frequency.
- Current ife does not create flux.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
20
Dynamic Model of the DFIM Considering the Iron Losses
„ αβ Model of the DFIM Considering the Iron Losses.
Equivalent electric circuit:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
21
Dynamic Model of the DFIM Considering the Iron Losses
„ αβ Model of the DFIM Considering the Iron Losses.
Space vector equations:
- Voltage equations (same as previous model)
- Flux equations (different from previous model)
- New node equations (voltage and current)
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
22
Dynamic Model of the DFIM Considering the Iron Losses
„ αβ Model of the DFIM Considering the Iron Losses.
Torque equation (only equivalence with the previous model):
only this expression is
equivalent with
the previous model !!!
Stator and rotor, active and reactive power equations:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
23
Dynamic Model of the DFIM Considering the Iron Losses
„ dq Model of the DFIM Considering the Iron Losses.
Equivalent electric circuit:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
24
Dynamic Model of the DFIM Considering the Iron Losses
„ dq Model of the DFIM Considering the Iron Losses.
Voltage, flux and node space vector equations
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
25
Dynamic Model of the DFIM Considering the Iron Losses
„ dq Model of the DFIM Considering the Iron Losses.
Torque equation:
Stator and rotor, active and reactive power equations:
Equivalent equations to
the αβ model !!
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
26
Dynamic Model of the DFIM Considering the Iron Losses
„ State Space Representation of the αβ Model.
-
Currents as state-space magnitudes.
Compact version:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
27
Dynamic Model of the DFIM Considering the Iron Losses
„ State Space Representation of the αβ Model.
-
Currents as state-space magnitudes.
Expanded version:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
28
Outline
1. Dynamic Model of the DFIM.
„
Simplified Model of the DFIM.
„
Space Vector Representation.
„
αβ Model of the DFIM.
„
dq Model of the DFIM.
„
State Space Representation of the αβ Model.
„
State Space Representation of the dq Model.
2. Dynamic Model of the DFIM Considering the Iron Losses.
„
αβ Model of the DFIM Considering the Iron Losses.
„
dq Model of the DFIM Considering the Iron Losses.
„
State Space Representation of the αβ Model.
3. Dynamic Modeling of the DFIM based on Symmetrical Components Analysis.
„
Basic Definitions.
„
DFIM in Balanced Operation.
„
DFIM in Unbalanced Operation.
4. Steady-State Analysis of the DFIM.
„
Basic Operation Modes Attending to the Speed and Powers.
„
Performance Analysis. Amplitude, Frequency and Phase Shift Variation.
„
Performance Analysis. Torque and Reactive Power Control.
5. Estimator and Observer Structures for the DFIM.
„
Directly Measurable and Estimated Magnitudes.
„
Stator Active and Reactive Power Estimation.
„
Stator and Rotor Fluxes Estimator.
„
Stator Flux Estimator from Stator Voltage.
„
Stator Flux Synchronization from the Stator Voltage.
„
Stator and Rotor Flux Observer.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
29
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ Basic Definitions.
Phasor – complexor:
steady state representation or sinusoidal variables (x can be a voltage,
current or flux)
x (t ) = X cos( ω t + δ ) = Real (X e j( ωt +δ ) ) = Real ( x e jωt )
x = X e j(δ )
Three phase system
x a (t ) = k 1Uˆ cos (ω t + ϕ + θ 1 )
2Π ⎞
⎛
x b (t ) = k 2Uˆ cos ⎜ ω t + ϕ + θ 2 −
⎟
3 ⎠
⎝
4Π ⎞
⎛
x c (t ) = k 3Uˆ cos ⎜ ω t + ϕ + θ 3 −
⎟
3 ⎠
⎝
07-09-2009
X
X
X
a
b
c
= k 1Uˆ e (ϕ + θ 1 )
= k 2 Uˆ e
= k 3Uˆ e
2Π ⎞
⎛
⎜ ϕ +θ 2 −
⎟
3 ⎠
⎝
4Π ⎞
⎛
⎜ ϕ +θ 3 −
⎟
3 ⎠
⎝
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
30
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ Basic Definitions.
Fortesquieu:
Representation of unbalanced system by means of three balanced systems
⎡ xo ⎤
⎡1 1
⎢ +⎥ 1 ⎢
⎢ x ⎥ = 3 ⎢1 a
⎢x− ⎥
⎢⎣1 a 2
⎣ ⎦
1 ⎤ ⎡xa ⎤
a 2 ⎥⎥ ⋅ ⎢⎢ x b ⎥⎥
a ⎥⎦ ⎢⎣ x c ⎥⎦
a=e
j
2π
3
x , x and x
a b
c
unbalanced system
xc
the three phase
system phasors,
xa
unbalanced
xb
ax
+
xo the zero sequence component
ax −
2π /3
x−
xo
2π /3
2π /3
2π /3
2π /3
x
2π /3
a2 x+
xo
xo
+
positive sequence
07-09-2009
a2 x−
negative sequence
zero sequence
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
x+
the
component
positive
sequence
x- the negative
component
sequence
31
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ Basic Definitions.
Space vector :
Represents three phase systems in steady or transient state
(
r
2
x (t ) = xα (t ) + j ⋅ x β (t ) = xa (t ) + a ⋅ xb (t ) + a 2 ⋅ xc (t )
3
B
Im
a
3/2 u
a2 uc(t)
u
a ub(t)
ua(t)
1
A, Re
a2
C
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
32
)
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ Basic Definitions.
Relationship: Space vector and Phasor
r
x = x e jωt = x e j (ωt +θ )
+
−
r
r
r
r
r
+
−
0
0
x (t ) = x + + x − + x = x e jωt + x e − jωt + x =| x + | ⋅e j (ωt +θ ) + | x − | ⋅e − j (ωt +θ ) + x
Three wire connection system, i.e. not neutral point connection
i a ( t ) + ib ( t ) + i c ( t ) = 0
va (t ) + vb (t ) + vc (t ) = 0
r
r+
r−
r+
r+
r−
r−
x (t ) = x (t ) + x (t ) = ( xα (t ) + jx β (t )) + xα (t ) + jx β (t ))
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
33
0
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ DFIM in Balanced Operation.
Stator flux, rotor flux and open rotor voltage
Vs
Steady state
r
r dΨs
r
vs = Rs is +
dt
r
r
dΨs
vs ≅
dt
r
r
vs
Ψs ≅
jω s
ψs
r
Lh r
Ψr =
Ψs
Ls
07-09-2009
r
r
Lh dΨs
vr = (
− jω m Ψs )
Ls dt
Lh vs
vr =
( s)
Ls j
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
s=
34
ωr
ωs
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ DFIM in Balanced Operation.
Stator flux, rotor flux and open rotor voltage
Transient state
r
r dΨs
r
vs = Rs is +
dt
r
r
r
ψ s (t ) = ψ sf + k ψ so e
( − t + t0 )
τ
τ = L /R
s s
Vector k is calculated in such a way the flux keep continuous
For example for a three phase dip from v to v in t=t
1
2
0
r
r
r
ψ s (t > t 0 ) = ψ sf + k ψ so e
07-09-2009
( − t + t0 )
τ
=
vs 2
jω s
e jω s t +
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
v s 2 − v s1
jω s
e jω s t 0 e
35
− ( t − t0 )
τ
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ DFIM in Balanced Operation.
Stator flux, rotor flux and open rotor voltage
Transient state
r
Lh r
Ψr =
Ψs
Ls
r
r
Lh dΨs
vr = (
− jωm Ψs )
Ls dt
p = v s 2 − v s1 = p v s
v
L
v ro = h vs ( s(1 − p)e jωst − (1 − s) pe jωst0 e
Ls
DQ
ro
=
Lh
vs ( s(1 − p)e jωst − (1 − s) pe jωst0 e
Ls
−( t − t0 )
τ
−( t −t0 )
τ
) e − jωmt
Rotor voltage is much higher than slip of
the stator voltage ¡¡
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
36
)
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ DFIM in Unbalanced Operation.
Stator flux, rotor flux and open rotor voltage
Steady state
r+
r+
r+
v s = Rs i s + jωs Ψs
r−
r−
r−
v s = Rs i s − jωs Ψs
r + vrs+
Ψs ≅
jω s
β
r
r−
vs−
Ψs ≅
− jω s
r+
r−
+ jωs t
− − jω s t
r
v
e
v
vs
vs
se
s
Ψs ≅
−
=
−
jω s − jω s
jω s
jω s
07-09-2009
r
vs+
r
r
v s+ −Rs i s+
ωs
r
−Rs is+
α
r
vs−
r
r
v s− −Rs is−
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
r
Ψs+
r
−Rs is−
r
Ψs−
37
ωs
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ DFIM in Unbalanced Operation.
Stator flux, rotor flux and open rotor voltage
Transient state
r
r
r
ψ s (t ) = ψ sf + k ψ so e
− ( t −t0 )
vr = k e
τ
+
− ( t −t0 )
τ
r
r
Lh dΨs
vr =
− jω m Ψs )
(
Ls dt
Lh
((2 − s )vs− e jωst + s vs+ e − jωst )
Ls
(2 − s ) = (ω s + ωm ) / ω s
Rotor voltage is increased in term (2-s) for
negative sequence ¡¡
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
38
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ DFIM in Unbalanced Operation.
Active and reactive power
r
3 rr
S ( t )= P ( t )+ jQ ( t )= v ⋅i *
2
{
}
rr 3
3
P ( t )= Re v ⋅i * = ( v α i α +v β i β )
2
2
{
r r
r
i = (i + + i − ) = iα + jiβ = (iα+ + iα− ) + j (iβ+ + iβ− )
}
r r
r
v = (v + + v − ) = vα + jv β = (vα+ + vα− ) + j (v β+ + v β− )
{
r
3r r * r r * r r * r r *
S ( t )=P ( t )+ jQ ( t )= v + ⋅i + +v − ⋅i − +v + ⋅i − +v − ⋅i +
2
AP =
r r *
3
3
Re{v + ⋅ i + } = (vα+ iα+ + v β+ iβ+ )
2
2
BP =
r r *
3
3
Re{v − ⋅ i − } = (vα− iα− + vβ− iβ− )
2
2
DP =
r r *
3
3
Re{v − ⋅ i + } = (vα− iα+ + vβ− iβ+ )
2
2
AQ =
r r *
3
3
Im{v + ⋅ i + } = (vβ+ iα+ − vα+ iβ+ )
2
2
07-09-2009
{ }
rr 3
3
Q ( t )= Im v⋅i * = ( v β iα −v α i β )
2
2
Constant terms
}
Q= AQ + B Q +C Q + D Q
P = AP + B P + C P + D P
r r *
3
3
Re{v + ⋅ i − } = (vα+ iα− + vβ+ iβ− )
2
2
r r *
3
3
BQ = Im{v − ⋅ i − } = (vβ− iα− − vα− iβ− )
2
2
CP =
CQ =
Oscillating 2ωs
terms
r r *
3
3
Im{v + ⋅ i − } = (vβ+ iα− − vα+ iβ− )
2
2
r r
3
3
D Q = Im{v − ⋅i +* }= ( v β− i α+ −v α− i β+ )
2
2
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
39
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ DFIM in Unbalanced Operation.
Torque
Tem =
Tem
{
r *r
r *r
r *r
r *r
3
p Im Ψs+ is+ + Ψs+ is− + Ψs− is+ + Ψs− is −
2
}
{
}
r+ 2
r− 2
r + r +* r − r −* r − r +* r + r −*
3 1
= p Re v s is − v s is − v s is + v s is − Rs (| is | − | is | )
2 ωs
Es _ T
Tem =
07-09-2009
r+ 2
r− 2
= Rs (| is | − | is | )
p
ωs
( As _ P − Bs _ P + C s _ P − Ds _ P − E s _ T )
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
40
Dynamic Modeling of the DFIM based
on Symmetrical Components Analysis
„ DFIM in Unbalanced Operation.
Torque and reactive power
Ps = As _ P + B s _ P + C s _ P + D s _ P
Ps =
07-09-2009
Tem ⋅ ω s
+ 2 ⋅ Bs _ P + 2 ⋅ Ds _ P + E s _ T
p
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
41
Outline
1. Dynamic Model of the DFIM.
„
Simplified Model of the DFIM.
„
Space Vector Representation.
„
αβ Model of the DFIM.
„
dq Model of the DFIM.
„
State Space Representation of the αβ Model.
„
State Space Representation of the dq Model.
2. Dynamic Model of the DFIM Considering the Iron Losses.
„
αβ Model of the DFIM Considering the Iron Losses.
„
dq Model of the DFIM Considering the Iron Losses.
„
State Space Representation of the αβ Model.
3. Dynamic Modeling of the DFIM based on Symmetrical Components Analysis.
„
Basic Definitions.
„
DFIM in Balanced Operation.
„
DFIM in Unbalanced Operation.
4. Steady-State Analysis of the DFIM.
„
Basic Operation Modes Attending to the Speed and Powers.
„
Performance Analysis. Amplitude, Frequency and Phase Shift Variation.
„
Performance Analysis. Torque and Reactive Power Control.
5. Estimator and Observer Structures for the DFIM.
„
Directly Measurable and Estimated Magnitudes.
„
Stator Active and Reactive Power Estimation.
„
Stator and Rotor Fluxes Estimator.
„
Stator Flux Estimator from Stator Voltage.
„
Stator Flux Synchronization from the Stator Voltage.
„
Stator and Rotor Flux Observer.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
42
Steady-State Analysis of the DFIM
„ Basic Operation Modes Attending to the Speed and Powers.
Power curves at constant torque:
Basic Steady-State equations:
Four Operating Modes:
Basic relations:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
43
Steady-State Analysis of the DFIM
„ Basic Operation Modes Attending to the Speed and Powers.
One simple approach to derive the space vector locations:
-
The speed of the machine defines clockwise or anticlockwise rotation of the space
vectors.
-
The electromagnetic torque defines the relative position between the rotor flux and
the stator flux, i.e. motoring or generating mode of operation on equation.
-
The stator voltage space vector is always approximately 90º shifted with the rotor
flux vector.
-
The rotor voltage space vector is always approximately 90º shifted with the rotor
flux vector.
-
The reactive power of the stator defines the relative position between the space
vectors of the stator current and stator voltage.
-
The rotor current can be calculated from the flux-current equations.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
44
Steady-State Analysis of the DFIM
„ Basic Operation Modes Attending to the Speed and Powers.
Mode 1. Motoring at
Hypersynchronous Speed
Qs < 0
Qs > 0
Mode 2. Generating at
Hypersynchronous Speed
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
45
Steady-State Analysis of the DFIM
„ Basic Operation Modes Attending to the Speed and Powers.
Mode 3. Generating at
Subsynchronous Speed
Qs > 0
Qs < 0
Mode 4. Motoring at
Subsynchronous Speed
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
46
Steady-State Analysis of the DFIM
„ Performance Analysis. Amplitude, Frequency and Phase Shift Variation.
The torque and the speed can be
established by a giver rotor voltage:
- Variation of the rotor voltage.
- No torque control.
- Stability problems.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
47
Steady-State Analysis of the DFIM
„ Performance Analysis. Amplitude, Frequency and Phase Shift Variation.
Electromagnetic torque performance at different rotor voltage operation (2MW, 690V, Ns/Nr=1/3 DFIM)
- Maximum Torque available at different voltages.
- Depending on the speed the angle and amplitude must be changed to reach positive or negative torque.
- Limited performance.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
48
Steady-State Analysis of the DFIM
„ Performance Analysis. Torque and Reactive Power Control.
- The control imposes the rotor voltage,
from Tem and Qs references .
- Good performance.
Formula:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
49
Steady-State Analysis of the DFIM
„ Performance Analysis. Torque and Reactive Power Control.
- Modification of Tem and Qs references not simultaneously.
- Most relevant magnitudes of the machine as function of time.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
50
Steady-State Analysis of the DFIM
„ Performance Analysis. Torque and Reactive Power Control.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
51
Steady-State Analysis of the DFIM
„ Performance Analysis. Torque and Reactive Power Control.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
52
Outline
1. Dynamic Model of the DFIM.
„
Simplified Model of the DFIM.
„
Space Vector Representation.
„
αβ Model of the DFIM.
„
dq Model of the DFIM.
„
State Space Representation of the αβ Model.
„
State Space Representation of the dq Model.
2. Dynamic Model of the DFIM Considering the Iron Losses.
„
αβ Model of the DFIM Considering the Iron Losses.
„
dq Model of the DFIM Considering the Iron Losses.
„
State Space Representation of the αβ Model.
3. Dynamic Modeling of the DFIM based on Symmetrical Components Analysis.
„
Basic Definitions.
„
DFIM in Balanced Operation.
„
DFIM in Unbalanced Operation.
4. Steady-State Analysis of the DFIM.
„
Basic Operation Modes Attending to the Speed and Powers.
„
Performance Analysis. Amplitude, Frequency and Phase Shift Variation.
„
Performance Analysis. Torque and Reactive Power Control.
5. Estimator and Observer Structures for the DFIM.
„
Directly Measurable and Estimated Magnitudes.
„
Stator Active and Reactive Power Estimation.
„
Stator and Rotor Fluxes Estimator.
„
Stator Flux Estimator from Stator Voltage.
„
Stator Flux Synchronization from the Stator Voltage.
„
Stator and Rotor Flux Observer.
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
53
Estimator and Observer Structures for the DFIM
„ Directly Measurable and Estimated Magnitudes.
Available magnitudes in general:
-
Stator voltage (αβ frame).
-
Stator current (αβ frame).
-
Rotor current (DQ frame).
-
Speed of the machine (also position).
Depending on the used control strategy, it will be
necessary to estimate:
-
Rotor Flux (DTC, DPC).
-
Stator Flux (Vector Control).
-
Torque (DTC, Vector Control)
-
Stator active and reactive powers (DPC, Vector
control).
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
54
Estimator and Observer Structures for the DFIM
„ Stator Active and Reactive Power Estimation.
From stator voltage and current measurements
(simplest solution):
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
55
Estimator and Observer Structures for the DFIM
„ Stator and Rotor Fluxes Estimator from Currents Measurements.
It is possible to simply estimate the stator and
rotor fluxes in αβ reference frame:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
56
Estimator and Observer Structures for the DFIM
„ Stator Flux Estimator from Stator Voltage.
The model of the machine, defines a
simple expression to derive the flux
from measured variables:
For the Vector Control: Only the angle is required
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
57
Estimator and Observer Structures for the DFIM
„ Stator Flux Estimator from Stator Voltage.
Integrator: Problems with the offsets => low pass filter
Discretize:
Compensation of mod and angle:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
58
Estimator and Observer Structures for the DFIM
„ Stator Flux Synchronization from the Stator Voltage.
Neglecting the stator resistance voltage drop:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
59
Estimator and Observer Structures for the DFIM
„ Stator and Rotor Flux Observer.
Flux observer with stator current feedback:
07-09-2009
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
60
Estimator and Observer Structures for the DFIM
„ Stator and Rotor Flux Observer.
Closed loop observation of the fluxes.
07-09-2009
Useful also for torque estimation:
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
61
Estimator and Observer Structures for the DFIM
„ Stator and Rotor Flux Observer.
Choice of G matrix:
Observer dynamic:
07-09-2009
k times faster than the machine’s dynamic:
Mathematical Model of the DFIM,
by G. Abad, M.A. Rodríguez and G. Iwanski
62
Control Strategies for Grid Connected
DFIM based Wind Turbines
Authors:
1University
of Mondragon, Spain
2Ingeteam Transmission & Distribution S.A., Spain.
3Warsaw University of Technology, Poland.
Gonzalo Abad1
Miguel Ángel Rodríguez2
Grzegorz Iwanski3
Outline
1. Introduction.
2. Scalar based Control. Voltage – Frequency Control.
„
Block Diagram.
„
Experimental Rig.
„
Experimental Results.
3. Field Oriented Control (Vector Control).
„
Block Diagram. Vector Control Oriented to the Stator Flux.
„
Dynamic Differential Equations.
„
Control loops.
„
Flux Estimator.
„
Reference Frames.
„
PI Controllers – Tuning Procedure.
„
Experimental Results.
4. ‘Classic’ Direct Torque Control (DTC) and Direct Power Control (DPC).
„
‘Classis DTC’.
„
‘Classic’ DPC.
„
Conceptual Analysis of DPC.
5. Predictive Direct Torque Control (PDTC) and Direct Power Control (PDPC).
„
DPC Block Diagram. Classic Control Blocks.
„
DPC Block Diagram. PDPC Control Blocks.
„
Experimental Results.
„
Performance Comparison.
„
Predictive DTC (PDTC).
6. Predictive DTC and Predictive DPC for Multilevel NPC Converters.
„
Predictive DPC Block Diagram.
„
Experimental Results.
7. Start-up of the Wind Turbine.
„
Encoder Calibration.
„
Grid Synchronization.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
2
Outline
1. Introduction.
2. Scalar based Control. Voltage – Frequency Control.
„
Block Diagram.
„
Experimental Rig.
„
Experimental Results.
3. Field Oriented Control (Vector Control).
„
Block Diagram. Vector Control Oriented to the Stator Flux.
„
Dynamic Differential Equations.
„
Control loops.
„
Flux Estimator.
„
Reference Frames.
„
PI Controllers – Tuning Procedure.
„
Experimental Results.
4. ‘Classic’ Direct Torque Control (DTC) and Direct Power Control (DPC).
„
‘Classis DTC’.
„
‘Classic’ DPC.
„
Conceptual Analysis of DPC.
5. Predictive Direct Torque Control (PDTC) and Direct Power Control (PDPC).
„
DPC Block Diagram. Classic Control Blocks.
„
DPC Block Diagram. PDPC Control Blocks.
„
Experimental Results.
„
Performance Comparison.
„
Predictive DTC (PDTC).
6. Predictive DTC and Predictive DPC for Multilevel NPC Converters.
„
Predictive DPC Block Diagram.
„
Experimental Results.
7. Start-up of the Wind Turbine.
„
Encoder Calibration.
„
Grid Synchronization.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
3
Introduction
„ Doubly Fed Induction Machine (DFIM) based Wind Energy Generation
Machine under study:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
4
Introduction
„ Simplified Model of the DFIM. Objectives.
-
First dynamic modelling approach of the machine.
-
Oriented to design control strategies and validate performances of the machine.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
5
Introduction
„ Wind Turbine Control Requirements.
GENERAL CONTROL REQUERIMENTS
„ Quick Flux-Torque or Active-Reactive Power Control (Dynamic Response).
„ Capacity to Operate at Variable Speed.
„ Reduced Flux-Torque or Active-Reactive Power Ripples (Power Quality).
„ Reduced THD of Currents (In Some Cases Rotor side Filter Requirement).
„ On Line Implementation Simplicity.
„ Robustness Against Model Uncertainties.
„ Reduced Tuning and Adjusting Efforts of the Controllers.
„ Good Perturbation Rejection.
„ Reduced Stress of the Semiconductors (‘Low’, Constant Switching
Frequencies, etc…)
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
6
Introduction
„ Doubly Fed Induction Machine Control, State of the Art.
General classification of AC Induction machines Control Techniques [3]
Variable Frequency
Control
Scalar Based
Controllers
V/F=Constant
Volt/Hertz
Vector Based
Controllers
is=f(wr)
Stator Current
Field Oriented
Rotor Flux
Oriented
Direct
(Blaschke)
Stator Flux
Oriented
Indirect
(Hasse)
Feedback
Linearization
Direct Torque-Power
Control
Direct Torque Space
Vector Modulation
Open Loop NFO
(Jonsson)
Circle Flux Trajectory
(Takahashi)
Constant Switching
Variable Hysteresis (Idris)
Passivity Based
Control
Hexagon Flux Trajectory
(Depenbrock)
Constant Switching
Predictive DTC-DPC
[1] M.P. Kazmierkowski, R. Krishnan, F. Blaabjerg, “Control in Power Electronics Selected Problems,” Academic Press, 2002.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
7
Introduction
„ Doubly Fed Induction Machine Control, State of the Art.
Benefits of Predictive Direct Control
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
8
Introduction
„ Doubly Fed Induction Machine (DFIM) based Wind Energy
Generation System.
Supplying topology under study:
Torque and Flux control
Power flow control (Ps & Qs)
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
9
Outline
1. Introduction.
2. Scalar based Control. Voltage – Frequency Control.
„
Block Diagram.
„
Experimental Rig.
„
Experimental Results.
3. Field Oriented Control (Vector Control).
„
Block Diagram. Vector Control Oriented to the Stator Flux.
„
Dynamic Differential Equations.
„
Control loops.
„
Flux Estimator.
„
Reference Frames.
„
PI Controllers – Tuning Procedure.
„
Experimental Results.
4. ‘Classic’ Direct Torque Control (DTC) and Direct Power Control (DPC).
„
‘Classis DTC’.
„
‘Classic’ DPC.
„
Conceptual Analysis of DPC.
5. Predictive Direct Torque Control (PDTC) and Direct Power Control (PDPC).
„
DPC Block Diagram. Classic Control Blocks.
„
DPC Block Diagram. PDPC Control Blocks.
„
Experimental Results.
„
Performance Comparison.
„
Predictive DTC (PDTC).
6. Predictive DTC and Predictive DPC for Multilevel NPC Converters.
„
Predictive DPC Block Diagram.
„
Experimental Results.
7. Start-up of the Wind Turbine.
„
Encoder Calibration.
„
Grid Synchronization.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
10
Scalar based Control. Voltage – Frequency Control
„ Block Diagram.
Simplest solution
CHARACTERISTICS:
07-09-2009
-
Implementation simplicity.
-
Good power quality.
-
No good dynamic response.
-
No torque control.
-
Constant switching frequency modulator
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
11
Scalar based Control. Voltage – Frequency Control
„ Experimental Rig.
Laboratory set-up
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
12
Scalar based Control. Voltage – Frequency Control
„ Experimental Results.
Ps
is
ir
Rotor
is - spectrum
ωm
T em
Tem - spectrum
Stator
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
13
Outline
1. Introduction.
2. Scalar based Control. Voltage – Frequency Control.
„
Block Diagram.
„
Experimental Rig.
„
Experimental Results.
3. Field Oriented Control (Vector Control).
„
Block Diagram. Vector Control Oriented to the Stator Flux.
„
Dynamic Differential Equations.
„
Control loops.
„
Flux Estimator.
„
Reference Frames.
„
PI Controllers – Tuning Procedure.
„
Experimental Results.
4. ‘Classic’ Direct Torque Control (DTC) and Direct Power Control (DPC).
„
‘Classis DTC’.
„
‘Classic’ DPC.
„
Conceptual Analysis of DPC.
5. Predictive Direct Torque Control (PDTC) and Direct Power Control (PDPC).
„
DPC Block Diagram. Classic Control Blocks.
„
DPC Block Diagram. PDPC Control Blocks.
„
Experimental Results.
„
Performance Comparison.
„
Predictive DTC (PDTC).
6. Predictive DTC and Predictive DPC for Multilevel NPC Converters.
„
Predictive DPC Block Diagram.
„
Experimental Results.
7. Start-up of the Wind Turbine.
„
Encoder Calibration.
„
Grid Synchronization.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
14
Field Oriented Control (Vector Control)
„ General Control Block Diagram.
CHARACTERISTICS:
-
Tuning of regulators is required
-
Torque control in full speed range.
-
Good power quality.
-
Constant switching frequency modulator
-
Good dynamic response.
[2] R. Pena, J.C. Clare and G.M. Asher, “Doubly fed induction generator using back-to-back PWM converters and its application to variable-speed
wind-energy generation,” Proc. IEE. Elec. Power Appl., vol. 143, no. 3, pp. 231–241. May 1996.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
15
Field Oriented Control (Vector Control)
„ Vector Control Oriented to the Stator Flux.
-
One speed loop.
-
One reactive power loop.
07-09-2009
-
Two current loops.
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
16
Field Oriented Control (Vector Control)
„ Dynamic Differential Equations.
Vector Control Oriented to the Stator Flux
From the original model equations:
Synchronously rotating dq reference
frame aligned with the stator flux vector
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
17
Field Oriented Control (Vector Control)
„ Dynamic Differential Equations.
The stator flux and iqr determines the torque:
Stator flux:
The stator voltage determines the stator flux:
The stator flux and idr determines the reactive power:
Relation between the rotor voltages and currents:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
18
Field Oriented Control (Vector Control)
„ Control Loops.
Coupling terms:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
19
Field Oriented Control (Vector Control)
„ Flux Estimator.
The model of the machine, defines a
simple expression to derive the flux
from measured variables:
For the Vector Control: Only the angle is required
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
20
Field Oriented Control (Vector Control)
„ Flux Estimator.
Integrator: Problems with the offsets => low pass filter
Discretize:
Compensation of mod and angle:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
21
Field Oriented Control (Vector Control)
„ Reference Frames.
Coordinates transformation:
Angle calculation:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
22
Field Oriented Control (Vector Control)
„ PI Controllers – Tuning Procedure.
Simplified dq current loops dynamics:
With Ti = τi
Current PI Controller:
Closed loop dynamics:
07-09-2009
Gains:
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
23
Field Oriented Control (Vector Control)
„ Vector Control. PI Controllers – Tuning Procedure.
Simplified speed loop dynamic:
Closed loop dynamics:
07-09-2009
Gains:
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
24
Field Oriented Control (Vector Control)
„ Vector Control. PI Controllers – Tuning Procedure.
Simplified reactive power loop dynamic:
Closed loop dynamics:
07-09-2009
Gains:
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
25
Field Oriented Control (Vector Control)
„ Experimental Results.
Experimental transient (15kW step) & steady-state performance at 1kHz switching frequency
Rotor
ωm
T em
Stator
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
26
Field Oriented Control (Vector Control)
„ Experimental Results.
Experimental transient (15kW step) & steady-state performance at 1kHz switching frequency
Ps
is
ir
Rotor
is - spectrum
ωm
T em
Tem - spectrum
Stator
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
27
Outline
1. Introduction.
2. Scalar based Control. Voltage – Frequency Control.
„
Block Diagram.
„
Experimental Rig.
„
Experimental Results.
3. Field Oriented Control (Vector Control).
„
Block Diagram. Vector Control Oriented to the Stator Flux.
„
Dynamic Differential Equations.
„
Control loops.
„
Flux Estimator.
„
Reference Frames.
„
PI Controllers – Tuning Procedure.
„
Experimental Results.
4. ‘Classic’ Direct Torque Control (DTC) and Direct Power Control (DPC).
„
‘Classis DTC’.
„
‘Classic’ DPC.
„
Conceptual Analysis of DPC.
5. Predictive Direct Torque Control (PDTC) and Direct Power Control (PDPC).
„
DPC Block Diagram. Classic Control Blocks.
„
DPC Block Diagram. PDPC Control Blocks.
„
Experimental Results.
„
Performance Comparison.
„
Predictive DTC (PDTC).
6. Predictive DTC and Predictive DPC for Multilevel NPC Converters.
„
Predictive DPC Block Diagram.
„
Experimental Results.
7. Start-up of the Wind Turbine.
„
Encoder Calibration.
„
Grid Synchronization.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
28
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DTC.
DTC (Direct Torque Control) Block Diagram
CHARACTERISTICS:
[3]
-
Implementation simplicity.
-
Very Fast dynamic response
-
No tuning of controllers
-
Torque control in full speed
range.
-
Non-constant switching
frequency behaviour
Gomez, S.A., Amenedo, J.L.R., “Grid synchronisation of doubly fed induction generators using direct torque control ”, IECON 02,vol. 4, Nov. 2002.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
29
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DTC.
DTC Space vector diagram for two level converter
- Torque expression:
- The stator flux is imposed
by the stator voltage:
r
r
rs
dΨss
s
v s = R s is +
dt
- Keep the rotor flux controlled
by using rotor voltage vectors
(Tem control is also achieved).
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
30
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DTC.
Rotor Flux Vector Variation in Motor Mode:
- Relation between rotor
voltage and flux:
- If one rotor vector is injected,
the new rotor flux:
- So the rotor flux variation yields:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
31
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DTC.
Rotor Flux Vector Variation in Motor Mode:
- Relation between rotor
voltage and flux:
- If one rotor vector is injected,
the new rotor flux:
- So the rotor flux variation yields:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
32
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DTC.
DTC rotor voltage vector selection (Look-up table)
-
07-09-2009
The rotor voltage vector is chosen according to:
-
The sector where the rotor flux vector is located.
-
To correct the torque and flux errors.
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
33
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DTC.
DTC Torque and Flux waveforms
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
-
Torque and flux control.
-
Non-constant switching
frequency behaviour.
34
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DTC.
On-Off Controllers
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
35
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DTC.
Torque, Flux and Sector Estimation
07-09-2009
-
There are several possibilities.
-
This is a very simple version.
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
36
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DPC.
DPC (Direct Power Control) Block Diagram
-
Same principles as DTC
-
Very Similar characteristics to DTC
[4] Datta, R. and V.T. Ranganathan, , “Direct power control of grid-connected wound rotor induction machine without rotor position sensors,” IEEE Trans. Power
Electron., vol. 16, no. 3, pp. 390-399, May 2001.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
37
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DPC.
Conceptual Analysis of DPC
-
The stator active and reactive power depends on the rotor and stator fluxes
and the phase shift between them (δ)
-
The stator reactive power can be controlled by:
-
The stator active power can be controlled by:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
38
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DPC.
Conceptual Analysis of DPC
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
39
‘Classic’ Direct Torque Control (DTC) and
Direct Power Control (DPC)
„ ‘Classic’ DPC.
DPC rotor voltage vector selection (Look-up table)
The rotor voltage vector is chosen according to:
-
The sector where the rotor flux vector is
located.
-
To correct the stator active and reactive
power errors.
Look-up table
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
40
Outline
1. Introduction.
2. Scalar based Control. Voltage – Frequency Control.
„
Block Diagram.
„
Experimental Rig.
„
Experimental Results.
3. Field Oriented Control (Vector Control).
„
Block Diagram. Vector Control Oriented to the Stator Flux.
„
Dynamic Differential Equations.
„
Control loops.
„
Flux Estimator.
„
Reference Frames.
„
PI Controllers – Tuning Procedure.
„
Experimental Results.
4. ‘Classic’ Direct Torque Control (DTC) and Direct Power Control (DPC).
„
‘Classis DTC’.
„
‘Classic’ DPC.
„
Conceptual Analysis of DPC.
5. Predictive Direct Torque Control (PDTC) and Direct Power Control (PDPC).
„
DPC Block Diagram. Classic Control Blocks.
„
DPC Block Diagram. PDPC Control Blocks.
„
Experimental Results.
„
Performance Comparison.
„
Predictive DTC (PDTC).
6. Predictive DTC and Predictive DPC for Multilevel NPC Converters.
„
Predictive DPC Block Diagram.
„
Experimental Results.
7. Start-up of the Wind Turbine.
„
Encoder Calibration.
„
Grid Synchronization.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
41
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram.
Predictive DPC
2 level Converter
CHARACTERISTICS:
7 Tasks (Blocks):
-
Implementation simplicity.
„
Blocks 1-4: Basic Direct Power Control Principles.
-
Fast dynamic response.
„
Blocks 5-7: Predictive Direct Power Control Principles.
-
No tuning of controllers.
-
Constant switching frequency
behaviour.
[5]
E. Flach, R. Hoffmann, P. Mutschler, “Direct mean torque control of an induction motor,” in Proc. EPE’97 Conf., 1997.
[6]
J. K. Kang and S.K. Sul, “New direct torque control of induction motor for minimum torque ripple and constant switching
frequency,” IEEE Trans. Ind. Applicat., vol. 35, no.5, pp. 1076-1086, Sept.-Oct. 1999.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
42
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. Classic Blocks.
Predictive DPC
2 level Converter
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
43
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. Classic Blocks.
Predictive DPC
2 level Converter
1
ePs
-1
ON-OFF Controllers
without hysteresis band
1
-1
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
44
eQs
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. Classic Blocks.
Predictive DPC
2 level Converter
Only one active vector per
constant switching period (h),
selected from a Look-up table
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
45
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. Classic Blocks.
Predictive DPC
2 level Converter
Two active vectors per constant
switching period (h), selected from
two Look-up tables.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
46
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ DPC Space vector Diagram for 2 Level Converter.
DPC first active vector selection
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
47
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ 3 Vectors per Switching Period.
AC machines demand sinusoidal waveforms.
Efficient generation of AC voltage, with VSC.
3 vectors at constant switching period (SV,PWM…)
Nearest 3 vectors principle:
- 2 consecutive active vectors
- 1 zero vector
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
48
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. Classic Blocks.
Predictive DPC
2 level Converter
First active vector selection
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
Second active vector
49
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. PDPC Control Principles.
Predictive DPC
2 level Converter
Necessary for duty
cycles calculation
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
50
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. PDPC Control Principles.
Ps =
(
3
vαs iαs + v βs i βs
2
)
⎛ dv
dv
di βs
⎜ αs i + diαs v + βs i + v
αs
αs
βs
βs
⎜
dt
dt
dt
⎝ dt
r 2
⎛ Rs
⎞
dPs
R
3
|
v
r
s|
⎟ −ω Q + ω
= − Ps ⎜
+
+
r
s
r
⎜ σLs σLr ⎟
dt
2
σ
L
ω
s
s
⎝
⎠
dPs
3
=
dt
2
+
r
π
Vbus | vs | sin( ω r t + δ − ( n − 1 ))
3
σLs Lr
Lh
07-09-2009
Qs =
Derivative Expressions.
⎞
⎟
⎟
⎠
(
3
v βs iαs − vαs i βs
2
)
⎛ dv βs
di βs
di
dv
⎜
iαs + αs v βs − αs i βs − vαs
⎜ dt
dt
dt
dt
dt
⎝
r
⎛ Rs
dQs
Rr ⎞⎟
3 Rr | vs |2
⎜
= −Qs
+
+ ω r Ps +
−
⎜ σLs σLr ⎟
dt
2
L
σ
L
ω
r
s
s
⎝
⎠
dQ s
=
−
3
2
r
π
Vbus | vs | cos( ω r t + δ − ( n − 1 ))
3
σLs Lr
Lh
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
51
⎞
⎟
⎟
⎠
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. PDPC Control Principles.
Ps(k+1)
Ps(k)
slope s1
slope s3
Ps_ref
slope s2
- Predictive horizon: One switching period (h).
slope s11
Qs(k)
Qs(k+1)
- At the beginning of the switching period:
- The vector sequence is selected (AV1, AV2, ZV).
Qs_ref
slope s33
slope s22
hc1
- The duty cycles are calculated (hc1 and hc2).
- The cost function is minimized.
hc2
h
Active Active
Zero
Vector 1 Vector 2 Vector
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
52
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. PDPC Control Principles.
Minimization Criteria.
Ps(k+1)
Ps(k)
slope s1
Power Ripples (Cost Functions):
slope s3
Ps_ref
slope s2
slope s11
Qs(k)
Qs(k+1)
Qs_ref
slope s33
slope s22
hc1
hc1 and hc2 are calculated in order to
minimize the cost functions (power ripples):
hc2
h
Active Active
Zero
Vector 1 Vector 2 Vector
Active and Reactive Power Ripples Root Mean Square Minimization
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
53
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Predictive DPC Block Diagram. PDPC Control Principles.
Ps(k+1)
Ps(k)
slope s1
slope s12
- Unique analytic solution (non-recursive).
slope s3
Ps_ref
- Implementation simplicity.
slope s2
slope s11
Qs(k)
Qs(k+1)
Qs_ref
slope s33
slope s22
hc1
hc2
h
Active Active
Zero
Vector 1 Vector 2 Vector
Active and Reactive Power Ripples Root Mean Square Minimization
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
54
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ PDPC Experimental Results.
Experimental transient & steady-state performance at constant speed and 1kHz switching frequency
Rotor
ωm
T em
Stator
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
55
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ PDPC Experimental Results.
Experimental transient & steady-state performance at constant speed and 1kHz switching frequency
Ps
is
ir
Rotor
is - spectrum
ωm
T em
Tem - spectrum
Stator
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
56
Predictive Direct Torque Control (PDTC) and
Direct Power Control (PDPC)
„ Performance Comparison.
Performance comparison
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
57
Outline
1. Introduction.
2. Scalar based Control. Voltage – Frequency Control.
„
Block Diagram.
„
Experimental Rig.
„
Experimental Results.
3. Field Oriented Control (Vector Control).
„
Block Diagram. Vector Control Oriented to the Stator Flux.
„
Dynamic Differential Equations.
„
Control loops.
„
Flux Estimator.
„
Reference Frames.
„
PI Controllers – Tuning Procedure.
„
Experimental Results.
4. ‘Classic’ Direct Torque Control (DTC) and Direct Power Control (DPC).
„
‘Classis DTC’.
„
‘Classic’ DPC.
„
Conceptual Analysis of DPC.
5. Predictive Direct Torque Control (PDTC) and Direct Power Control (PDPC).
„
DPC Block Diagram. Classic Control Blocks.
„
DPC Block Diagram. PDPC Control Blocks.
„
Experimental Results.
„
Performance Comparison.
„
Predictive DTC (PDTC).
6. Predictive DTC and Predictive DPC for Multilevel NPC Converters.
„
Predictive DPC Block Diagram.
„
Experimental Results.
7. Start-up of the Wind Turbine.
„
Encoder Calibration.
„
Grid Synchronization.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
58
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Predictive DPC Block Diagram.
Predictive DPC for Multilevel NPC VSC
3 level NPC Converter
7 Tasks (Blocks):
07-09-2009
„
Blocks 1-4: Basic Direct Power Control Principles.
„
Blocks 5-8: Predictive Direct Power Control Principles.
„
Block 7: Capacitor Voltage Balancing
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
59
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Predictive DPC Block Diagram.
3 Level NPC Voltage Source Converter
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
60
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Space Vector Diagram.
Case study: Three level NPC VSC
07-09-2009
Implementation simplicity: Sector and region calculation
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
61
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Space Vector Diagram.
Case study: Three level NPC VSC
07-09-2009
Implementation simplicity: Sector and region calculation
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
62
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Space Vector Diagram.
Case study: Three level NPC VSC
07-09-2009
Implementation simplicity: Sector and region calculation
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
63
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Space Vector Diagram.
Case study: Three level NPC VSC
07-09-2009
Implementation simplicity: Sector and region calculation
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
64
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Vector selection Procedure.
First vector selection
Second and third vector selection
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
65
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Power variation Waveforms.
Steady-state stator active and reactive power variations waveforms:
Stator active (Ps) and reactive (Qs) power reduction criteria:
Duty cycles:
With:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
66
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Derivative Expressions.
Slopes calculation
Constants and vectors
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
67
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Predictive DPC Block Diagram.
Table selection procedure
3 level NPC Converter
Angle of equivalent voltage vector
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
Region calculation
68
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Predictive DPC Block Diagram.
Table selection procedure
3 level NPC Converter
First vector selection
Second and third vector selection
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
69
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Predictive DPC Block Diagram.
Table selection procedure
3 level NPC Converter
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
70
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Predictive DPC Block Diagram.
Table selection procedure
3 level NPC Converter
Medium vectors
07-09-2009
Equivalence of currents
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
71
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Predictive DPC Block Diagram.
Table selection procedure
3 level NPC Converter
Real vector definition
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
72
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Experimental Results.
Steady-state waveforms at nominal power (15kW) at 2 different speeds and 0.5kHz switching frequency
CH1: Vinv composed
CH2: Vinv simple
CH3: is Ch4: ir
1250 rev/min
07-09-2009
750 rev/min
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
73
Predictive-DTC and Predictive-DPC for Multilevel
NPC Converters.
„ Experimental Results.
Experimental tracking behaviour performance at constant speed and 0.5kHz switching frequency
Ps vs QS
wm
Ps and QS
Rotor
is - spectrum
ωm
T em
Stator
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
74
Outline
1. Introduction.
2. Scalar based Control. Voltage – Frequency Control.
„
Block Diagram.
„
Experimental Rig.
„
Experimental Results.
3. Field Oriented Control (Vector Control).
„
Block Diagram. Vector Control Oriented to the Stator Flux.
„
Dynamic Differential Equations.
„
Control loops.
„
Flux Estimator.
„
Reference Frames.
„
PI Controllers – Tuning Procedure.
„
Experimental Results.
4. ‘Classic’ Direct Torque Control (DTC) and Direct Power Control (DPC).
„
‘Classis DTC’.
„
‘Classic’ DPC.
„
Conceptual Analysis of DPC.
5. Predictive Direct Torque Control (PDTC) and Direct Power Control (PDPC).
„
DPC Block Diagram. Classic Control Blocks.
„
DPC Block Diagram. PDPC Control Blocks.
„
Experimental Results.
„
Performance Comparison.
„
Predictive DTC (PDTC).
6. Predictive DTC and Predictive DPC for Multilevel NPC Converters.
„
Predictive DPC Block Diagram.
„
Experimental Results.
7. Start-up of the Wind Turbine.
„
Encoder Calibration.
„
Grid Synchronization.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
75
Start-up of the Wind Turbine
„ Overall Control Structure (Idea taken from ABB).
The Wind Turbine covers the following states:
-
Encoder Calibration.
-
The current control is maintained.
-
Grid Synchronization.
-
The current references are modified.
-
Normal Operation Conditions.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
76
Start-up of the Wind Turbine
„ Encoder calibration. Initial (Zero) Position of the Encoder.
DQ reference frame:
-
rotates at ωm speed.
-
must be aligned with the three phase
windings of the rotor.
The encoder in general:
-
It is mechanically coupled to the rotor’s
axis.
-
Its zero position (index signal) is not
aligned with the zero position of the
machine.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
77
Start-up of the Wind Turbine
„ Encoder Calibration. Initial (Zero) Position of the Encoder.
This phase shift
must be corrected !!
DQ reference frame:
-
rotates at ωm speed.
-
must be aligned with the three phase
windings of the rotor.
The encoder in general:
-
It is mechanically coupled to the rotor’s
axis.
-
Its zero position (index signal) is not
aligned with the zero position of the
machine.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
78
Start-up of the Wind Turbine
„ Encoder Calibration. Initial (Zero) Position Correction.
The Wind Turbine is driven as follows:
-
The grid side converter operates at normal conditions.
-
The pitch control establishes a constant speed (ωm).
-
The rotor side converter controls the rotor currents (ir). Normally iqr=0.
-
The stator breaker is opened, so there is not current in the stator side (is=0).
-
Due to the rotor currents, there is a stator voltage induced (vs).
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
79
Start-up of the Wind Turbine
„ Encoder Calibration. Initial (Zero) Position Correction.
The current is only flowing through the rotor:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
80
Start-up of the Wind Turbine
„ Encoder Calibration. Initial (Zero) Position Correction.
Stator Flux estimation from the induced stator voltage and using θm:
They must have
Rotor Flux estimation from the rotor currents:
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
equal phase !!!
81
Start-up of the Wind Turbine
„ Encoder Calibration. Initial (Zero) Position Correction.
Angle correction until the fluxes present the same phase:
When both fluxes are aligned,
the cross product is zero.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
82
Start-up of the Wind Turbine
„ Initial (Zero) Position Correction. Block Diagram.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
83
Start-up of the Wind Turbine
„ Grid Synchronization. Wind Turbine Operation.
The Wind Turbine is driven as follows:
-
The grid side converter operates at normal conditions.
To close the stator breaker:
-
The pitch control establishes a constant speed (ωm).
-
vs must be synchronized with vl.
-
The encoder calibration has already finished.
-
The transient is minimized.
-
The rotor side converter controls the rotor currents (ir).
-
The stator breaker is opened, so there is not current in the stator side (is=0).
-
Due to the rotor currents, there is a stator voltage induced (vs).
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
84
Start-up of the Wind Turbine
„ Grid Synchronization. Control Loops.
By the rotor side of the machine:
-
The amplitude of the stator voltage induced, must be
equal to the grid voltage.
-
The phase of the stator voltage induced, must be
equal to the grid voltage.
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
85
Start-up of the Wind Turbine
„ Grid Synchronization. Amplitude Control Loop.
d components of current and voltages
modify the amplitude of the induced
stator voltage
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
86
Start-up of the Wind Turbine
„ Grid Synchronization. Phase Control Loop.
q components of current and voltages
modify the phase angle of the induced
stator voltage
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
87
Start-up of the Wind Turbine
„ Switch to Normal Operation.
Once the stator voltage is synchronized:
-
The stator breaker is switched.
-
The current references are switched.
-
The incoming PI regulators must be
initialized to the actual current
references.
In that case: The transient is minimized !!
07-09-2009
Control Strategies for Grid Connected DFIM based Wind Turbines,
by G. Abad, M.A. Rodríguez and G. Iwanski
88