Copyright by Mithunprakash G Vyas 2010
156
Copyright by Mithunprakash G Vyas 2010
Transcript of Copyright by Mithunprakash G Vyas 2010
Copyright
by
Mithunprakash G Vyas
2010
The Thesis committee for Mithunprakash G Vyas
Certifies that this is the approved version of the following thesis :
Simulation and Modeling of Wind Power Plants : A Pedagogical
Approach
APPROVED BY
SUPERVISING COMMITTEE:
Surya Santoso, Supervisor
W.Mack Grady
Simulation and Modeling of Wind Power Plants : A Pedagogical
Approach
by
Mithunprakash G Vyas, BSEE
THESIS
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science in Engineering
THE UNIVERSITY OF TEXAS AT AUSTIN
May 2010
Dedication
This work is dedicated to my loving parents and my brother
Without their continuous support, care and understanding
the completion of this work wouldn’t have been possible.
Acknowledgments
I wish to thank and express my sincere gratitude to my advisorand mentor,
Surya Santoso for the continuous support and encouragementsince I joined grad-
uate school in fall 2008. In addition I sincerely acknowledge the work of Dave
Burnham on dynamic rotor resistance control of a WTG, the work of Mohit Singh
and Keith Faria on the doubly-fed induction generator.
I wish to extend my sincere thanks and gratitude to Mohit Singh for his help
and continuous support in learning Latex. Lastly, I wish to thank my family and my
friends without their guidance and support this work would not have been possible.
I would also to like to extend unrestricted access to all my models imple-
mented in PSCAD/MATLAB to Dr. Santoso and his research group for future re-
search.
v
Simulation and Modeling of Wind Power Plants : A Pedagogical
Approach
Mithunprakash G Vyas, MSE
The University of Texas at Austin, 2010
Supervisor: Surya Santoso
This thesis report describes the modeling procedure for available the wind
turbine generator (WTG) technologies. The models are generic in nature and man-
ufacturer independent. These models are implemented on commercially available
dynamic simulation software platforms like PSCAD/EMTDC andMATLAB/SIMULINK.
A brief introduction to the available WTG types is provided tounderstand the tech-
nological differences and their key features. The related theoretical concepts to the
working of a WTG are explained, which acts as an aid for model development and
implementation. Using the theoretical concepts as basis, aWTG model is divided
into four parts :
• Aerodynamic model
• Mechanical drive train model
• Electrical machine model
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• Controller model
Once the different parts of a WTG are introduced, a groundworkfor model
implementation on the software platforms is laid. A step-by-step process of imple-
menting a PSCAD or MATLAB model of a WTG is introduced in this thesis. Start-
ing with the most fundamental WTG technology such as fixed-speed also known as
direct-connect wind turbine. The model implementation is adanvced to other supe-
rior technology like the dynamic rotor resistance control (DRR) and the doubly-fed
induction generator (DFIG). To better understand the working of a DFIG, a current-
source regulated model (without electrical machine) emulating the DFIG is built on
both PSCAD and MATLAB. A full blown converter model of the DFIG with back-
to-back converter is then built in PSCAD/EMTDC.
An approach to determine the reactive power capability (Q limits) of a DFIG
is described. Rotor current limitation and stator current limitation of the DFIG are
considered in determining the minimum and maximum reactivepower delievered
by the DFIG. Variation in theQ limits of a DFIG for change in wind speed is
analysed with two different wind speed scenarios.
• Wind speed from cut-in to rated i.e. 6 m/s - 14 m/s.
• Wind speed above rated to cut-out i.e. 14 m/s - 20 m/s.
Such an analysis, is useful in determining the operating mode of the DFIG.
At low wind speeds (below rated), the DFIG can be operated as aSTATCOM for
exporting and importing reactive power (similar to synchronous machines). While
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above rated wind speeds, the DFIG can be set to produce maximum active power.
Using the DFIG current-source model implemented in MATLAB/SIMULINK, lab-
oratory experiments to plot the power profile of the DFIG is explained. Another
experiment to perform independent P-Q control of the DFIG isalso included in this
report.
viii
Table of Contents
Acknowledgments v
Abstract vi
List of Tables xii
List of Figures xiii
Chapter 1. Introduction 11.1 Background and Motivation . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Prior Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Objective and Approach . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 Technical Contributions . . . . . . . . . . . . . . . . . . . . . . . . 5
1.5 Organisation of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.6 Statement of Originality . . . . . . . . . . . . . . . . . . . . . . . . 7
Chapter 2. Wind Turbine Technologies 82.1 Fixed-speed wind turbine generator . . . . . . . . . . . . . . . . .. 8
2.2 Dynamic rotor resistance control wind turbine generator . . . . . . . 10
2.3 Doubly-fed induction generator . . . . . . . . . . . . . . . . . . . .11
2.4 Full-converter based wind turbine generator . . . . . . . . .. . . . 12
Chapter 3. Wind Turbine Modeling 143.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2 Modeling Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Modeling the Prime Mover of a WTGS . . . . . . . . . . . . . . . . 18
3.3.1 Power available in wind stream and its extraction . . . .. . . 18
3.3.2 Relation of power coefficient with pitch angle and tip speedratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
ix
3.3.3 Blade pitching . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.4 Modeling the Drive Train of a WTGS . . . . . . . . . . . . . . . . . 26
3.5 Modeling the Electric Generator of a WTGS . . . . . . . . . . . . . 28
3.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.5.2 Reference frame theory and the Clarke and Park transforms . 30
Chapter 4. Model Development and Implementation 394.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 Fixed speed wind turbine . . . . . . . . . . . . . . . . . . . . . . . 42
4.2.1 Fixed-Speed Wind Turbine Model in PSCAD/EMTDC . . . . 43
4.2.2 Fixed-speed Wind Turbine Model in MATLAB/SIMULINK . 49
4.3 Variable speed wind turbine . . . . . . . . . . . . . . . . . . . . . . 55
4.3.1 Pitch control . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.2 Dynamic rotor resistance control . . . . . . . . . . . . . . . 58
4.3.3 Hybrid control . . . . . . . . . . . . . . . . . . . . . . . . . 79
Chapter 5. Doubly-fed Induction Generator Modeling 815.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
5.2 PSCAD/EMTDC Regulated Current-Source Model . . . . . . . . . 85
5.3 MATLAB/SIMULINK Regulated Current-Source Model . . . . . . 90
5.4 PSCAD/EMTDC complete DFIG Model . . . . . . . . . . . . . . . 96
5.4.1 Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.4.2 Inverter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5.4.3 Grid model . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5.5 Reactive power capability of the DFIG . . . . . . . . . . . . . . . . 106
5.5.1 Analysis of Rotor Current Limits . . . . . . . . . . . . . . . 107
5.5.2 Analysis of Stator Current Limits . . . . . . . . . . . . . . . 112
5.5.3 Verification ofQ limits for the PSCAD DFIG model . . . . . 114
5.6 Simulation : Regulated Current-Source DFIG model . . . . . . .. . 119
5.6.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.6.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.6.3 To plot the power profile of a DFIG . . . . . . . . . . . . . . 125
x
5.6.4 To demonstrate decoupled control of active (P) and reactivepower (Q) . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
Chapter 6. Summary and Future Work 1306.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Appendices 133
Appendix A. Machine specifications 134
Appendix B. Drive-train model Specifications 135
Bibliography 136
Vita 140
xi
List of Tables
4.1 Look-up table for PI controller tuning . . . . . . . . . . . . . . .. 61
4.2 Active power recorded for increasing slip . . . . . . . . . . . .. . 65
4.3 Torque slip data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.1 Power tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
5.2 GE 1.5 MW DFIG turbine field data [1] . . . . . . . . . . . . . . . 102
5.3 Maximum reactive produced at 14 m/s and 9 m/s with step changeof 0.1 MW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
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List of Figures
2.1 Fixed speed WTG . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Dynamic rotor resistance WTG . . . . . . . . . . . . . . . . . . . . 10
2.3 Doubly-fed induction generator WTG . . . . . . . . . . . . . . . . 12
2.4 Full-converter WTG . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.1 Model types and their applications [2] . . . . . . . . . . . . . . .. 15
3.2 Functional block diagram for a generic wind turbine generator sys-tem [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.3 Block diagram for a fixed-speed stall-regulated wind turbine . . . . 17
3.4 Wind flow conditions before and after the converter . . . . .. . . . 21
3.5 Blade geometry of a horizontal axis wind turbine [4] . . . . .. . . 23
3.6 Power coefficient Cp as a function of tip speed ratioλr . . . . . . . 24
3.7 Two-mass model for the drive train . . . . . . . . . . . . . . . . . . 27
3.8 Two-mass model for the drive train with opposing torque action . . 28
3.9 Schematic winding diagram [3] . . . . . . . . . . . . . . . . . . . 30
3.10 Equivalent Circuit (2-pole, 3-phase, wye-connected IM[3]) . . . . 31
3.11 Block diagram for abc-αβ -qd0 transform used for DFIG . . . . . . 32
3.12 Transformation fromabc- rotating qd0 frame . . . . . . . . . . . . 35
3.13 Aligning equivalent stator fluxλtotal alongq− axis . . . . . . . . . 36
4.1 Generic model for fixed speed wind turbine . . . . . . . . . . . . .42
4.2 PSCAD simulation model for a WT . . . . . . . . . . . . . . . . . 43
4.3 Aerodynamic torque computation . . . . . . . . . . . . . . . . . . 43
4.4 Power profile for fixed speed wind turbine model . . . . . . . . .. 47
4.5 Rotor and generator speed variation with wind speed . . . . .. . . 48
4.6 Torque slip characteristics . . . . . . . . . . . . . . . . . . . . . . 49
4.7 Aerodynamic model in SIMULINK . . . . . . . . . . . . . . . . . 51
4.8 Fixed speed wind turbine model in SIMULINK . . . . . . . . . . . 52
xiii
4.9 Active and reactive power profile for fixed speed wind turbine modelin SIMULINK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.10 Generator torque and speed profile in SIMULINK . . . . . . . .. . 54
4.11 Torque slip characteristics of induction machine in SIMULINK . . . 55
4.12 Blade geometry of horizontal axis wind turbine [4] . . . . .. . . . 58
4.13 Rext estimation module in PSCAD using PI controller . . . . . . . . 60
4.14 Wind power profile for a variable speed wind turbine using rotorresistance control . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.15 Power excursion: constant power strategy using PI control from14.2m/s - 15.2 m/s - 16.2m/s . . . . . . . . . . . . . . . . . . . . . 63
4.16 Power excursion: constant power strategy using PI control from17m/s - 18m/s - 19 m/s - 20m/s . . . . . . . . . . . . . . . . . . . . 64
4.17 Torque Slip characteristics with varyingRext at 8 m/s, 16 m/s and20 m/s wind speed . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.18 Complete Torque Slip characteristics withRext = 0, 0.039Ω,0.22Ωat 8m/s, 16m/s, 20m/s wind speed respectively . . . . . . . . . . . .68
4.19 Rext estimation module in PSCAD using self built PID controller . .68
4.20 Power excursion: constant power strategy using PID control from14.2m/s - 15.2 m/s - 16.2m/s . . . . . . . . . . . . . . . . . . . . . 69
4.21 Power excursion: constant power strategy using PID control from17m/s - 18m/s - 19 m/s - 20m/s . . . . . . . . . . . . . . . . . . . . 70
4.22 Rext estimation module in PSCAD using built-in PI controller . . . .71
4.23 Power excursion: constant current strategy using PI control from14.2m/s - 15.2 m/s - 16.2m/s . . . . . . . . . . . . . . . . . . . . . 73
4.24 Power excursion: constant current strategy using PI control from17m/s - 18m/s - 19 m/s - 20m/s . . . . . . . . . . . . . . . . . . . . 75
4.25 Rext estimation module in PSCAD using PID controller . . . . . . . 76
4.26 Power excursion: constant current strategy using PID control 14.2m/s- 15.2 m/s - 16.2m/s . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.27 Power excursion: constant current strategy using PID control from17m/s - 18m/s - 19 m/s - 20m/s . . . . . . . . . . . . . . . . . . . . 79
5.1 DFIG Wind Turbine Schematic [3] . . . . . . . . . . . . . . . . . 83
5.2 DFIG Model Structure [3] . . . . . . . . . . . . . . . . . . . . . . 84
5.3 DFIG model in PSCAD . . . . . . . . . . . . . . . . . . . . . . . . 86
5.4 |λd| = |λs| = 0.075 and|λq| = 0 . . . . . . . . . . . . . . . . . . . . 87
xiv
5.5 Voltage alongd-q axis . . . . . . . . . . . . . . . . . . . . . . . . 88
5.6 Computing reference currentsId andIq . . . . . . . . . . . . . . . . 88
5.7 Pgenre f = Pgen = 50-400 MW in steps of 50 MW,Qgenre f = Qgen = 0MVAr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
5.8 Qgenre f = Qgen = 50-400 MW in steps of 50 MW,Pgenre f = Pgen =50 MW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.9 Block diagram of DFIG model in SIMULINK . . . . . . . . . . . . 91
5.10 Block diagram forabc−αβ −qd0 tranformation . . . . . . . . . . 92
5.11 Active power excursion . . . . . . . . . . . . . . . . . . . . . . . . 93
5.12 Wind active power profile for the DFIG . . . . . . . . . . . . . . . 95
5.13 Rectifier control [5] . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5.14 Rectifier model in PSCAD . . . . . . . . . . . . . . . . . . . . . . 98
5.15 PSCAD block diagram for rectifier control circuit . . . . . .. . . . 98
5.16 Inverter control [5] . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.17 PSCAD block diagram for inverter control circuit . . . . . .. . . . 100
5.18 Block diagram for DFIG using back-to-back converters inPSCAD . 101
5.19 Expected active power and speed profile for the DFIG model simu-lation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.20 DecoupledP-Q control with variable wind speed, Q = 0 Mvar . . . 104
5.21 DecoupledP-Q control with step change of 0.2 Mvar inQ . . . . . 105
5.22 DC link capacitor voltage and the actual rotor current .. . . . . . . 106
5.23 Steady state per phase equivalent circuit of inductionmachine . . . 109
5.24 Q limit band for maximum rotor current . . . . . . . . . . . . . . . 111
5.25 Q limit band for maximum stator current . . . . . . . . . . . . . . . 113
5.26 Q limit band for maximum rotor and stator currents . . . . . . . . . 114
5.27 Q limit comparison between calculated, at 9 m/s and at 14 m/s windspeed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.28 Q limit comparison between calculated and at 14 m/s wind speed. . 118
5.29 Q limit comparison between calculated and at 9 m/s wind speed .. 119
5.30 Q limit comparison between 14 m/s and at 9 m/s wind speed . . . . 120
5.31 DFIG Wind Turbine Schematic [3] . . . . . . . . . . . . . . . . . 121
5.32 Schematic diagram of regulated current-source representation ofthe DFIG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.33 Block diagram for obtaining the reference currents . . . .. . . . . 124
xv
5.34 SIMULINK block diagram of the DFIG . . . . . . . . . . . . . . . 126
xvi
Chapter 1
Introduction
1.1 Background and Motivation
In the United States, wind power is expected to make up a significant por-
tion of future generation portfolios. A scenario in which wind power will supply
20% of U.S. peak demand by 2030 has been examined and found feasible [6]. A
challenge facing power system planners and operators, in the near future, is the grid
integration of large amounts of wind power. To determine theimpacts of large wind
power plants on system stability, reliable computer modelsare necessary. Computer
models are also required as teaching tools to develop a senseof understanding of
different wind turbine generator (WTG) technologies among undergraduate stu-
dents.
However, wind turbine models are not readily available in most dynamic
simulation software. The diversity and manufacturer-specific nature of technolo-
gies used in commercial wind turbines exacerbates the modeling problem [7]. A
solution to this problem is to develop a generic, manufacturer-independent mod-
eling framework that can be implemented in any software capable of simulating
power system dynamics. Such a framework can also be used as a teaching tool,
describing the modeling process. This thesis report describes the development of
1
generic models for:
1. A fixed-speed (FS) wind turbine,
2. A wind turbine employing the principle of rotor resistance control, also known
as dynamic rotor resistance control (DRR),
3. A turbine with a doubly-fed induction machine employing flux-vector control
(DFIG).
The focus of this report is on the wind turbines which use induction generators,
since they comprise the largest installed base of wind turbines and also have more
significant effects on the bulk power system than other machines. A detailed de-
scription of the wind turbine models is provided along with details of their im-
plementation on two different software platforms, widely used in industry and
academia namely PSCAD/EMTDC and MATLAB/SIMULINK. While the central
purpose of these models is to study the interaction between the wind turbine and the
power system, they may also be used to examine the interaction of aerodynamic,
mechanical, and electrical functions within the wind turbine.
1.2 Prior Art
Models of the fixed-speed WTG and the variable speed WTG available in
the literature are implemented in PSCAD/EMTDC [7, 8]. Current-source regulated
model of the DFIG (without actual machine model) is also implemeted in PSCAD.
2
Using the available models in PSCAD, parallel models for the fixed-speed WTG
and the DFIG are implemented in MATLAB/SIMULINK. Using the current-source
regulated model of the DFIG as base work, a full-blown converter model is im-
plemented in PSCAD/EMTDC. For determining the reactive powercapability of
the DFIG, stator current and rotor current equations are obtained from the machine
model ind−q reference frame.
For the given machine specification, reactive power limit that can be de-
livered for a given value of active power is determined. Oncethe limit of reac-
tive power (maximum) is determined, a controller is implemented to set the reac-
tive power command below the specified limit. The report further discusses two
laboratory experiments using the current source reglated model of the DFIG in
SIMULINK to plot the active power excursion and decoupled active-reactive power
control profiles of the DFIG.
1.3 Objective and Approach
Work presented in this thesis report outlines and explains in detail the gen-
eral framework to be followed for modeling different WTG’s oncommercially
available software platforms like PSCAD/ EMTDC and MATLAB/SIMULINK.
Most of the available models for the WTGs are manufacturer specific. Most others
greatly simplify the models mathematically. The need for detailed generic mod-
els, which are manufacturer independent is often felt. Again implementation of the
models on commercially available software platforms is notthe only objective. A
detailed explanation of the modeling problem and approach towards modeling is
3
required. This work can be used in academia as a teaching toolfor undergradu-
ate students interested in wind power plant modeling. The objetive of this work is
to establish the need for modeling the WTGs and explain the step-step modeling
procedure, focussing on the DFIG and its reactive power capability.
To meet the aforementioned objectives, the approach followed is mentioned
below:
• Introduction to different wind turbine technologies available - fixed speed
(FS), dynamic rotor resistance control (DRR), doubly-fed induction generator
(DFIG), full-converter (FC)
• Introduction to wind turbine modeling - explain the basic concepts and in-
troduce the different blocks of a wind turbine model (aerodynamic model,
mechanical drive train model, machine model, grid model, converter control
blocks).
• Once, the concepts related to modeling are explained, we canjump directly to
modeling the mentioned WTGs on PSCAD/EMTDC and MATLAB/SIMULINK.
• Results showing the working of different WTGs are presented and compari-
son is drawn between PSCAD and MATLAB models.
• A special issue concerning reactive power capability of theDFIG is addressed
analyzing the rotor and stator current limits. Thus, determining the reactive
power delivering capacity of the DFIG at different wind speeds.
4
• Lastly, a laboratory experiment on MATLAB/SIMULINK is described to
draw the active power profile and decoupled control of activeand reactive
power profile of the DFIG
1.4 Technical Contributions
Parallel models of the fixed-speed WTG, and the current-source regulated
model of the DFIG is implemented in MATLAB/SIMULINK. Results obtained
from both the models compare very well with the already validated models of the
same WTG type respectively in PSCAD/EMTDC. Reactive power limits for a DFIG
are determined by creating bands for stator current limitation and rotor current lim-
itation. Utilizing the machine specifications such as stator terminal voltage (Vs),
magnetizing inductance (Lm) and stator inductance (Ls). For a maximum allow-
able rotor current of 1.2 p.u.Q limit band is determined. SimilarQ limit band for
maximum allowable stator current of 1.5 p.u. is also determined.
By superimposing the two bands for Q limits, maximum reactivepower
value at a particular wind speed for a particular value of active power can be de-
termined. The PSCAD/EMTDC model of the DFIG is used to implement the Q
limits above and below the rated wind speed. Using the upper limit for the maxi-
mum value of reactive power available from the DFIG, reference value for reactive
power demand can be set. The reactive power capability of theDFIG can be used
to determine its operating mode at varying wind speeds. At low wind speeds, when
enough active power cannot be generated, the DFIG can be operated as a STAT-
COM. Thus, exporting or importing reactive power according to the requirement.
5
Laboratory experiments utilizing the MATLAB/SIMULINK model of the DFIG is
developed for drawing the active power excursion profile andto show decoupled
control of the active and the reactive power.
1.5 Organisation of Thesis
Organization of rest of the thesis report is as follows:
• Chapter 2 introduces the different WTG technologies available. It draws a
picture of each WTG and briefly explains its working. It also briefly describes
the characteristic of a given WTG type.
• Chapter 3 explains the physics behind the working of a generalWTG. It di-
vides the modeling problem in four different blocks - aerodynamic model,
mechanical drive train model, electrical generator model,and grid model.
Depending on the type of the WTG modeling of the controller will be de-
scribed in the succeeding chapters. This chapter also presents an introduc-
tion to the referenc frame theory and Clarke-Park transforms. Introduction
to these modeling concepts is crucial to the understanding of DFIG and full-
converter WTG.
• Chapter 4 describes the implementation of the wind turbine models for each
of the mentioned technologies, using the general framework. The imple-
mentation is carried out using PSCAD/EMTDC and MATLAB/SIMULINK
platforms. The practical modeling issues, such as tuning ofcontrollers for
6
proportional and integral gain, the tuning algorithm used for the various sub-
systems, are also discussed in this section.
• Chapter 5 exclusively deals with the modeling of the DFIG in PSCAD/EMTDC
and MATLAB/SIMULINK. It also discusses the approach to determine the
reactive power delivering capability of the DFIG. Furthermore, two labora-
tory experiments with the DFIG SIMULINK models are also discussed in
this chapter.
• Chapter 6 discusses the summary of this thesis work and identifies the future
work that can be done with this thesis work as the basis.
1.6 Statement of Originality
I hereby certify that this thesis submission is the result ofmy own work
and efforts and my thesis does not infringe upon anyone’s copyright nor violate any
proprietary rights. I hereby attest that, any work of other authors is fully acknowl-
edged in accordance with the standard referencing practices. I also certify that I
have completed the online ethics training modules of The University of Texas At
Austin - Graduate School. I fully understand the Universitypolicies and regulations
related to academic integrity. I declare that this is a true copy of my thesis report,
including any final revisions, as approved by my thesis committee and the Office of
Graduate Studies, and that this thesis has not been submitted for a higher degree to
any other University or Institution.
7
Chapter 2
Wind Turbine Technologies
2.1 Fixed-speed wind turbine generator
Fixed-speed wind turbines are so named because they operatewith less than
2% variation in turbine rotor speed. They employ squirrel-cage induction machines
directly connected to the power grid. The rotor blades are attached to the hub at
a fixed pitch, and are designed in such a manner that the air flowover the blades
changes from streamline flow to turbulent flow at high wind speeds. This limits
the kinetic power extracted from the wind at high wind speedsin order to protect
the induction machine and drive train from overheating and overspeeding. Turbines
using this design are known as stall-regulated. A side-effect of stall regulation is
that energy capture from the wind is optimal for one wind speed only, and sub-
optimal for other wind speeds.
Fixed-speed wind turbines are low-cost, robust, reliable,simple to maintain,
and proven in the field [9]. A large number of fixed-speed wind turbines have been
installed over the past decade-and-a-half, and more continue to be installed. While
variable-speed wind turbines form the bulk of te new installed capacity, a niche for
fixed-speed wind turbines still exists. Therefore, it can beexpected that fixed-speed
wind turbines will continue to play a role in the power systems of the future. While
8
Drive TrainSquirrel cage IM
To grid
Turbine blades
Connection transformer
Excitation capacitor
Figure 2.1: Fixed speed WTG
there are many wind turbine dynamic models available in the literature, the focus is
largely on modeling variable-speed wind turbines [10, 11, 12, 13, 14, 15]. These
models often oversimplify the mechanical drive train and aerodynamics, since the
aim is to evaluate power and rotor speed control mechanisms.
In the model developed here as shown in Figure 2.1, a modular approach
is used to represent each of the turbine’s functions. One block represents the aero-
dynamics, another the mechanical drive train, and a third represents the electrical
generator. A control block may also be included. The blocks are integrated to form
the complete wind turbine model, which is implemented in PSCAD/EMTDC and
MATLAB/SIMULINK. This model is a platform on which more advanced variable-
speed wind turbine models can be developed.
9
2.2 Dynamic rotor resistance control wind turbine generator
Variable-speed turbines use wound-rotor induction machines as generators
(WRIG), and control over the output power is achieved through control of the rotor
resistance, or through the use of power electronic converters in the rotor circuit in
the DFIG turbines. In contrast with fixed-speed WTG, variable-speed wind turbines
are designed to operate at a wide range of rotor speeds. The rotor speed may vary
with the wind speed, or with other system variables, depending on the design em-
ployed. Typically in variable-speed turbines, the blades are not rigidly fixed to the
hub, and can be rotated a few degrees to turn them out of or intothe wind. Addi-
tional speed and power controls allow these turbines to extract more energy from a
wind regime than would be possible with fixed-speed turbines.
Drive TrainWound rotor IM
To grid
Turbine blades
Connection transformer
Controls
Excitation capacitor
Pitch control
Dynamic rotor resistance control
Figure 2.2: Dynamic rotor resistance WTG
Wind turbines employing dynamic rotor resistance control,modify the torque-
slip characteristic of the machine. Thus, the maximum electromagnetic torque
10
(corresponding to rated active power) is obtained at all wind speeds above rated.
Since, the rotor resistance is changed during wind turbine operation, hence the
namedynamic rotor resistance control. Figure 2.2 shows the block diagram for a
dynamic rotor resistance control WTG. The succeeding chapter on WTG model de-
velopment explains the principle behind dynamic rotor-resistance control in detail,
and discusses different control strategies for achieving optimal power extraction.
2.3 Doubly-fed induction generator
In order to achieve high efficiency, modern WTGs adopt a variable-speed
operation by the use of power converters. Either direct AC-ACfrequency con-
verter, such as cyclo converter [16, 17] is used or a voltage source converters (AC-
DC-AC). One such WTGS which has become very popular these days isa system
incorporating the doubly-fed induction generator.
The DFIG shown in Figure 2.3 consists of a WRIG with the stator winding
connected directly to grid and the rotor windings interfaced through a back-to-back
bidirectional voltage souce converter. The back-to-back converter converts power
at varying frequencies (rotor frequency) to DC and then backto fixed frequency
(grid frequency) [18, 19]. In a DFIG wind turbine, the decoupling of active and re-
active power is achieved through the use of power electronicconverters using field
oriented control (FOC).
11
Drive TrainWound rotor IM
To grid
Turbine blades
Connection transformer
Controls
Converter transformer
Pitch control
Power converter
Figure 2.3: Doubly-fed induction generator WTG
2.4 Full-converter based wind turbine generator
Drive Train IM/SM
To grid
Turbine blades
Connection transformer
Controls
Pitch control
Power converter
Figure 2.4: Full-converter WTG
12
For a full-converter based wind turbine generator, stator of the machine is
connected to the grid through a back-to-back converter. Figure 2.4 shows a full-
converter representation. As the stator is directly connected to the converter pair,
there is no need to incorporate slip ring connections to the rotor. Such connections
have high maintenance cost. The advantage of full-converter WTG is, synchronous
as well induction machines can be used. While, induction machines offer advan-
tages like low maintenance cost and ruggedness, synchronous machines can have
high number of pole pairs. High pole pair number correspondsto low rotor speeds,
thus eliminating the need of a gear-box. Gear-box maintenance accounts one of the
highest maintenance cost in a wind turbine.
13
Chapter 3
Wind Turbine Modeling
3.1 Introduction
Models of wind turbine generator systems (WTGS) can be broadly classi-
fied into:
1. Steady-state models
2. Dynamic models
Static models of WTGS can be used for steady state analysis or quasi-steady state
analysis such as load flow studies, short circuit calculations whereas a dynamic
model of WTGS is needed for various types of system dynamic analysis e.g. sta-
bility study, control system analysis, optimization techniques to mention just a few.
Considering the steady-state models of a WTGS, they are characterized by a simple
voltage source (V), a voltage and real power source (P, V) or areal and reactive
power source (P, Q). The choice of model used depends on specific application and
the type of WTGS [2]. The tree diagram of Figure 3.1 shows the model types and
their applications. In this chapter the focus is on functional models designed for
studying transient stability.
14
Machine model types
Steady state models
(V),(P,V),(P,Q)
• Analysis of voltage variation• Analysis of load flow• Analysis of short circuits
• Analysis of transient stability• Analysis of small signal stability• Analysis of transient response• Analysis of steady state waveforms• Synthesis control• Optimization
• Analysis of start up transient• Analysis of load transient effects• Analysis of fault operation• Analysis of harmonics
Transient state models
(dynamic models)
Functional models
Mathematical physical models
Figure 3.1: Model types and their applications [2]
In general, a WTGS can be equipped with either a synchronous orinduction
generator, it can be directly connected to the grid or connected through a power
electronic converter. It may use aerodynamic torque control (blade pitching, stall
control) and/or generator torque control (varying the rotor resistance, flux-vector
control) for output power optimization. The possibilitiesstated give rise to a very
general model framework, whose block diagram in shown in Figure 3.2. This gen-
eral framework is used to represent each wind turbine technology that is modeled in
this chapter, with suitable modifications for each technology. This general frame-
work is software-independent. In this chapter, each block of the framework is dis-
cussed. The physical theory behind each block is presented,and implementation of
each block is also described. The development of the complete models is achieved
by combining these blocks.
15
Turbine rotor
Gear train
Generator
Grid side converterRotor side converter
Grid
Asynchronous/synchronous
3-Ф voltage source
Controls rotor geometry (blade pitch angle)
Converter controlTurbine control
Low speed shaft
High speed shaft
Optional Gear Train
Optional Controls and Converters
Incident Wind
Figure 3.2: Functional block diagram for a generic wind turbine generator system[3]
3.2 Modeling Concepts
Wind turbines are designed to capture the kinetic energy present in wind
and convert it to electrical energy. An analogy can be drawn between wind tur-
bines and conventional generating units which harness the kinetic energy of steam.
From a modeling standpoint, a fixed-speed wind turbine consists of the following
components:
1. Turbine rotor and blade assembly (prime mover)
2. Shaft and gearbox unit (drive-train and speed changer)
16
3. Induction generator
4. Control system
The interaction between each of the components listed abovedetermines how much
kinetic energy is extracted from the wind. Figure 3.3 illustrates the interaction be-
tween the wind turbine components in a basic fixed speed wind turbine. Modeling
of the electrical subsystems is fairly straightforward, aspower system modeling
software usually includes a built-in induction machine model. However, modelling
of the aerodynamics and mechanical drive-train is more challenging. These com-
ponents are modeled based on the differential and algebraicequations that describe
their operation. The following subsections describe the modelling of the four com-
ponents listed above.
Tip Speed Ratio
Calculation
Rotor Power Coefficient Calculation
Cp
Aerodynamic Torque
Calculation
Two-mass Shaft Model
including Gearbox
Induction Generator
`
Pitch Angle
Vwind
rotor
rotor
rotor
Cp
rotor
gen Grid
electrical
Aerodynamic Block Mechanical Block
Electrical Block
Control Block
Figure 3.3: Block diagram for a fixed-speed stall-regulated wind turbine
17
3.3 Modeling the Prime Mover of a WTGS
The aerodynamic block consists of three subsystems: tip-speed ratio calcu-
lation, rotor power coefficient (Cp) calculation, and aerodynamic torque calculation.
Wind speed and pitch angle are user-defined inputs. Since themodel is intended to
study the dynamic response of wind turbines to grid events, the assumption is usu-
ally made that the wind speed stays constant during the grid event. However, the
models allow the wind speed input signal to be set to any valueat the start of the
simulation run-time and also to be modified during the run. Itis also possible to use
a time-series of actual wind speed data.
3.3.1 Power available in wind stream and its extraction
The kinetic energy (KE) in any object of massm moving with a velocityv
is given by
KE =12
mv2 (3.1)
A wind turbine is an electromechanical energy conversion device, that cap-
tures kinetic energy available from wind. This kinetic energy is turned into me-
chanical energy of the rotor and eventually into electricalenergy from the generator.
Power available in moving air is given as follows
Pwind =d(KE)
dt=
12
m′v2 (3.2)
wherem′ is the mass flow rate. For a wind turbine rotor sweeping an areaA of
radiusR, power available in that area is given by Eq.(3.3)
18
Pwind =12
ρAv3 (3.3)
whereρ is the air density,A = πR2 andv is the velocity of the moving air particles
or in general wind. To determine the power extracted by a windturbine rotor, Betz
model (1926) is widely used. Betz model is not only used to find the power from
an ideal turbine rotor, but also to find the thrust of the wind on the ideal rotor
and the effect of the rotor operation on the local wind field. This simple model is
based on linear momentum theory. The analysis assumes a control volume whose
boundaries are the surface of a stream tube and its two cross sections. The turbine
in the analysis is represented by a uniformactuator diskor converterwhich creates
a discontinuity of pressure in the stream tube of air flowing through it. Betz analysis
further assumes that [4]
• Air is homogeneous, incompressible and has achieved steadystate fluid flow,
• There is no frictional drag,
• Number of blades on the rotor are infinite,
• Uniform thrust occurs over the disk or rotor area,
• A non-rotating wake, and
• The static pressure far upstream and far downstream of the rotor are equal to
the undisturbed ambient static pressure.
19
Figure 3.4 shows the wind flow conditions for an energy converter. The
power extracted from wind using such a converter, is given bythe difference in
moving air particle power before and after the converter. The power extracted by
the energy converter is given by Eq.(3.4)
Pextracted= Pwind1−Pwind2 =12
ρ(A1v31−A2v3
2) (3.4)
Figure 3.4 below describes the change in wind velocity before and after the
converter. To achieve ideal efficiency in energy conversionit is required that the
air velocity after the converter (v2) becomes zero. This is physically impossible,
because that would render a need for the wind velocity beforethe converter to be
zero and the air to be still. A more practical energy converter, will have air pressure
increase just before the converter, which would simultaneously result in air velocity
decrease, thus exerting a force given by Eq.(3.5)
F = m′(v1−v2) (3.5)
Thus, the power extracted from wind is given by Eq.(3.6)
Pextracted= Fv′= m
′(v1−v2)v
′(3.6)
By comparing the two equations obtained forPextracted(Eq.(3.4) - Eq.(3.6)),
and assuming that the mass flow rate through the converter is constant, the air ve-
locity through the converter is the average wind velocityv′= 1
2(v1 +v2). Then the
power extracted from the converter can be computed as
20
P
1 V1
Pwind1
Pwind2
A
A
V
A
21
2
A1V’
extracted
V
Figure 3.4: Wind flow conditions before and after the converter
Pextracted=14
ρA(v21−v2
2)(v1 +v2) (3.7)
The term rotor power coefficient can now be defined (since,Pextracted< Pwind) as
follows
Cp =Pextracted
Pwind(3.8)
It is the ratio of power extracted from the rotor to the power available from wind,
also known as rotor performance coefficient and sometimes referred as Betz factor.
As described earlier, Betz created a (1D) model based on linear momentum theory,
along with some assumptions for the analysis. The power coefficient can achieve a
maximum value of 0.593, whenv2v1
= 13 . This is the maximum theoretically possible
value ofCp. Due to aerodynamic losses, actual value of power coefficient never
achieves 0.593. In practice three effects are accounted fordecrease in maximum
achievable value ofCp :
1. Rotation of wake behind the rotor
21
2. Finite number of possible rotor blades and their associated tip losses, and
3. Non-zero aerodynamic drag [4]
In the next section, the relation betweenCp and tip speed ratio (λr ) at a particular
value of blade pitch angle (β ) will be presented. This relation can be used to develop
Cp - λr curves. These are used to determine the rotor power for any combination
of wind speed and rotor speed. These curves provide immediate information on the
maximum value ofCp and optimum tip speed ratio. The data for such a relationship
is found from turbine tests and modeling [4].
3.3.2 Relation of power coefficient with pitch angle and tip speed ratio
An empirical relation betweenCp (rotor power coefficient), tip speed ratio
(λr ) and blade pitch angle (β ) is used for developing a look-up table that provides
a value ofCp for a given value of wind speed and tip speed ratio. Blade pitchangle
(Figure??bladepitch)) can be defined as the angle between the plane of rotation and
blade chord line. Tip speed ratio is defined as the ratio of theblade-tip linear speed
to the wind speed [4]
λr =ωrotR
v1(3.9)
whereR is the rotor radius andωrot is the angular velocity of the rotor.
Shown below is one such empirical relation betweenCp, λr andβ . Equation
(3.10) is used to generate a look-up table forCp. When provided with the values of
22
α
chord line
Plane of blade rototion
Angle of attackβp
ФθT
βp,0
α ---
βp--- Section pitch angle
βp,0--- Blade pitch angle
--- Angle of relative wind
θT --- Section twist angle
Ф
Figure 3.5: Blade geometry of a horizontal axis wind turbine [4]
λr andβ , the corresponding value ofCp can be found. The Cp(λr) curve obtained
from the equation works only for positive values of pitch angle β .
Cp(λ ,β ) = c1(c21Λ−c3β −c4β x−c5)e
−c61Λ (3.10)
1Λ
=1
λ +0.08β− 0.035
1+β 3 (3.11)
while the coefficientsc1− c6 are proposed as equal to :c1 = 0.5,c2 = 116,c3 =
0.4,c4 = 0,c5 = 5,c6 = 21 [2]. Once,Cp is determined, aerodynamic torque of the
rotor can be computed using Eq.(3.3), (3.8) and (3.12). A mechanical model for the
drive train developed in next Section 1.2.3 is used to determine the angular speed of
the generator,ωgen and angular speed of the turbine rotor,ωrot . For all the models
developedωgen is provided as an input to the induction machine.
Pextracted= τrotωrot (3.12)
23
Figure 3.6 shows theCp vs λr characteristics obtained from Eq.(3.10), note
that only positive values of blade pitch angle can be used with these curves.
0 5 10 150
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Tip speed ratio
Pow
er c
oeffi
cien
t
β = 0 °β = 2 °β = 4 °β = 6 °β = 8 °β = 10 °β = 12 °β = 14 °β = 16 °β = 18 °β = 20 °β = 22 °β= 24 °
Figure 3.6: Power coefficient Cp as a function of tip speed ratioλr
3.3.3 Blade pitching
Blade pitch angle control is used to directly vary the power coefficient of a
wind turbine. As it determines the operating power coefficient, it can be effectively
used to control the mechanical output power of the rotor. A reduction in mechanical
power of the rotor can be achieved by reducing or minimizing the angle of attack
above its critical value. By limiting the power coefficient, power extracted from the
wind is limited. This kind of power control is also known aspitch control. Pitch
24
control can be used to serve different purposes such as
• Optimizing the power output of the wind turbine, by maximizing the mechan-
ical power output for a given wind speed, this is generally applied for low and
moderate wind speeds below rated wind speed.
• Preventing excess mechanical power output in strong winds above rated wind
speeds. This keeps a check on the mechanical power and keeps it below the
rated value in strong winds.
• To prevent disconnected wind turbines from turning [5].
There are two common ways in which pitch angle control can be used for regulating
the power output of wind turbines
• Active pitch control : For variable-speed pitch-regulatedwind turbines, wind
turbine operation and power output can be affected either byspeed changes or
blade pitch angle changes [4]. Below rated power, such machines operate at
variable speed to optimize the tip speed ratio at fixed pitch.After rated power
output is achieved generator torque control is used to maintain output power,
while pitch control is used to maintain rotor speed. At high wind speeds,
power output of the generator can be maintained constant, with an increase
in rotor speed. This increased energy available from the wind is stored as
kinetic energy in the rotor. This results in reduced aerodynamic torque and
thus deceleration of the rotor. If the wind speed continues to remain high,
25
aerodynamic efficiency of the rotor can be reduced by changing the pitch,
resulting in reduced rotor speed.
• Passive pitch control : In case of passive control wind speedis used to provide
the actuator power, which adjusts the blade pitch angle to shape the power
curve of the wind turbine [4]. In such wind turbine designs, the effects of
change in rotor speed or wind speed are related to change in blade pitch angle.
3.4 Modeling the Drive Train of a WTGS
The drive train of a wind turbine generally consists of turbine rotor, low
speed rotor shaft, gearbox with transmission ratioa, high speed shaft of the gen-
erator and the generator itself (either synchronous or induction). In case of wind
turbines using synchronous generators, usually the designcalls for a generator with
a high pole count, thus reducing the mechanical speed of the generator shaft. The
gearbox can then be omitted from the drive train. More than 90% of the drive train
moment of inertia is accounted for by the rotor (blades and hub) [2]. The generator
accounts for 6-8%, while the remaining parts account for 2-4% of the total moment
of inertia. Since the generator’s torsional stiffness is very high, approximately two
orders of magnitude higher than that of the rotor shaft, and about fifty times higher
than the hub with blades, the torsional vibration on the drive train elements cannot
be ignored. Their characteristics (frequency and amplitude) can affect wind turbine
performance. Hence, it is impossible to model the drive train as a lumped single
mass. Typically the masses of the rotor and the generator aremuch larger than the
mass of the gearbox. If we neglect the mass of the gearbox, theproperties (stiff-
26
ness constant and torsional constant) of the two shafts can be combined into one
equivalent shaft resulting in a two-mass model as shown in Figure3.7. Moreover,
the equivalent shaft of the two-mass model is not infinitely stiff, and thus the model
cannot be generally reduced to a one-mass model. Hence, atwo−massmodel is
preferred.
Aerodynamic torque
Jrotor
Jgen
N1
N2
Krotor, Brotor
Kgen, Bgen
Electromagnetic torque
Rotor inertia referred to the generator side
KT, BT
Kgen, Bgen
JT
Jgen
Figure 3.7: Two-mass model for the drive train
Note from Figure 3.8 that the aerodynamic torque from the rotor is counter-
acted by the electromagnetic torque from the generator. Also note from Figure 3.7
that rotor speedωrot , torqueτrot and moment of inertiaJrot are all referred to the
generator side using the gear transmission ratioa.
By balancing the torque for each mass, differential equations formed can be
solved to determine the rotor, generator speedsωrot andωgen respectively. For each
rotating mass, the product of moment of inertiaJ and angular accelerationθ ′′ must
equal the sum of the torques acting on the mass.
27
rot, gen
T
gen
Figure 3.8: Two-mass model for the drive train with opposingtorque action
For the turbine rotor torque, equation can be written as
JTθ ′′T = τT −Beqv(ωT −ωG)−Keqv(θT −θG) (3.13)
For the generator torque, equation can be written as
JGθ ′′G = −τG +Beqv(ωT −ωG)+Keqv(θT −θG) (3.14)
Subscript T used in Eq.(3.13) and Eq.(3.14) denotes the rotor parameters referred
to the generator side of the gearbox and subscript G denotes generator parameters.
3.5 Modeling the Electric Generator of a WTGS
The induction machine has typically been favored for use in wind turbines
due to the fact that induction generators do not need to be synchronized with the
grid. Since wind turbines operate under varying wind speed conditions, resulting
in varying shaft speeds, conventional synchronous generators cannot be easily used
for this application. In a conventional synchronous machine connected to a steam
28
turbine, it is possible to control real and reactive power output independently of
each other by varying the steam flow rate and the excitation respectively. This
decoupling effect cannot be achieved in fixed-speed and rotor-resistance control
based technologies. In a DFIG turbine, the decoupling of real and reactive power
is achieved through the use of power electronics and flux-vector control. In this
subsection the considerations for modeling an induction machine and the concept
of flux-vector control are introduced.
3.5.1 Introduction
The winding arrangement of a conventional 2-pole, 3-phase,wye-connected
symmetrical induction machine is shown in Figure 3.9. The stator windings are
identical with equivalent turnsNs and resistancers. The rotor windings can be
approximated as identical windings with equivalent turnsNr and resistancerr . The
model assumes the air-gap is uniform and the windings are sinusoidally distributed.
In Figure 3.9, the winding of each phase is represented by an elementary
coil. One side of the coil is represented by a⊗ indicating that the assumed positive
direction of current is down the length of the stator (into the plane of the paper). The
other side of the same coil is represented by a⊙ which indicates that the assumed
positive direction of current is out of the plane of the paper. The axesas, bsandcs
represent the positive directions of the magnetic fields produced due to the currents
flowing in the stator windings of phasea, b andc respectively. These directions are
obtained using the right hand rule on the phase windings. Similarly axesar, br and
cr with respect to the rotor windings are shown. These rotor axes are fixed to the
29
as'
as
bs'
bs
cs'
cs
cr'
br
ar'
cr
br'
ar
as axis
ar axis
bs axis
cs axis
cr axis
br axis
r
r
Figure 3.9: Schematic winding diagram [3]
rotor and rotate with it at an angular velocity ofωr . The angular displacement of
the rotor with respect to the positiveas axis isθr . In the stationaryabc reference
frame, the relationships between voltages, currents and flux linkages of each phase
for this machine can be written from Figure 3.10.
3.5.2 Reference frame theory and the Clarke and Park transforms
It is known that for rotating machine inductances are functions of the rotor
speed, due to which the coefficients of the differential equations (voltage equations)
describing machine operation vary with time, except when the rotor is stationary. It
is difficult to develop machine models that can be used for dynamic studies, using
these complex equations. These time-varying equations canbe written in a time-
30
ias
Ns
Vbs
Vcs
Var
Vbr
Vcr
ibs
ics
iar
icr
Vas
NrNs
Ns
Nr
Nr
rs
rs
rs
rr
rr
rr ibr
Figure 3.10: Equivalent Circuit (2-pole, 3-phase, wye-connected IM [3])
invariant form by choosing a frame of reference that is rotating at the appropriate
speed. Referring machine variables to a rotating frame can, not only reduce the
complexity of modeling the machine but also serve as a tool for better understand-
ing of machine operation. Two such transformations to be used for developing a
doubly-fed induction generator based wind turbine model are the Clarke and Park
transforms. These are two different transformations used to achieve independent
active and reactive power control for induction generators. When used in conjunc-
tion, these transforms convert statorabcquantities toα −β quantities (stationary
two axis frame also known as (α −β )frame - Clarke transform) and eventually to
the rotatingqd0frame (Park Transform) as shown in Figure 3.11.
Transformation from abc frame to qd0 frame
In the stationaryabc reference frame, the relationships between the voltages, cur-
rents and flux linkages of each phase for an induction machinecan be written as
31
Stator quantities
abc - frame
Clarke Transform
frameVabc, abc,Iabc V , ,I
V qd0, qd0,I qd0
Power controller
Inverse Clarke
Transform
( ) frame abc frame
Inverse
Park Transform
qd0 frame ( ) frameId , Iq
I , I
r
Iar,Ibr,Icr
r
s
s - r
Vas,Vbs,Vcs
Statorside
Rotor sideGenerator
Park Transform
qd0 frame
-+
Figure 3.11: Block diagram for abc-αβ -qd0 transform used for DFIG
follows:
~Vabcs= ~rs ~iabcs+d( ~λabcs)
dt(3.15)
~V ′abcs= ~rs
~i′abcs+d( ~λ ′
abcs)
dt(3.16)
where,λ is the flux linkage, subscripts s and r stand for variables andparameters
associated with the stator and rotor side respectively, Eq.(3.16) represents machine
parameters when referred to the rotor side. The flux linkagesin the Eq.(3.15)-(3.16)
can be written as
~λabcs= ~Lsr ~iabcs+ ~L′sr
~i′abcr (3.17)
32
~λ ′abcr =
~L′Tsr
~i′abcs+~L′
r~i′abcr (3.18)
The resultant voltage equations from Eq.(3.15)-(3.16)-(3.17)-(3.18) are as
follows
~Vabcs= (~rs+d ~Lsr
dt) ~iabcs+
d ~L′sr
dt~i′abcr (3.19)
~V ′abcr =
d ~L′Tsr
dt~i′abcs+(~r ′r +
d~L′r
dt) ~i′abcr (3.20)
As can be seen in Eqs. (3.19) and (3.20) voltages, inductances and currents
are in the stationaryabc reference frame. They are thus time-variant. Analysis
and modeling of time-variant equations is cumbersome. Using the Clarke and Park
transforms these time-variant quantities can be convertedinto time-invariant quanti-
ties. Applying Park transform, theabc frame quantities are converted inqd0 frame
quantities.qd0 frame is rotating at the synchronous frequency.
~Vqd0s = ~rs ~iqd0s+ωqds~λdqs+
d ~λqd0s
dt(3.21)
~V ′qd0r = ~r ′r ~i′qd0r +(ωs−ωr) ~λ ′
dqr +d ~λ ′
qd0r
dt(3.22)
33
whereωs andωr are the rotational speed of the synchronously rotatingqd0 frame
and rotor frame respectively
A wound rotor induction machine can be represented in a synchronously
rotatingqd0 reference frame as described above. Assuming that the stator currents
are balanced, a resultant stator magnetic field (Htotal) with a constant magnitude and
rotating at synchronous speed (ωs) is produced [20]. Using Clarke’s transform,θs
can be obtained andqd0 frame rotated at synchronous speedωs. Now, since the
angular speeds of the stator magnetic field and theqd0 rotating frame are identical,
stator magnetic field vector~λtotal is fixed with respect to theq− andd− axes of the
qd0 rotating frame. If theq- axis of the rotatingqd0 frame is oriented in such a
manner, so that it aligns perfectly with the~λtotal, field along theq− axis would be
of zero magnitude. Figure 3.13 shows MATLAB plots for the stator magnetic field
in stationaryabc, αβ and rotatingqd0 frames.
Since,λtotal is aligned along theq− axis,
λqs = λtotal (3.23)
and
λds = 0 (3.24)
substituting Eq.(3.23)-(3.24) in Eq.(3.21)-(3.22),Vds andVqs are obtained
34
−2 −1 0 1 2−2
−1.5
−1
−0.5
0
0.5
1
1.5
2Stationary abc frame
−2 0 2−2
−1
0
1
2Stationary α β 0 frame
−2 0 2−2
−1
0
1
2Rotating dq0 frame
λcs
λtotal
λas
λbs
λβ
λtotal
λα
λd
λβ λtotal
λq
λα
Figure 3.12: Transformation fromabc- rotating qd0 frame
Vds = −ωsλqs = ωsλtotal = constant (3.25)
and
Vqs = 0 (3.26)
From Eq. (3.25) speed of the stator fieldωs is constant, henceVds is time
invariant andVqs is almost negligible, withλds = 0, the statorq− axis current can
be obtained as
35
-120o
q
λas+λbs
λq = λtotal = λas+λbs + λcs
a
b
c
- c
λas
λbs
λcs
λd = 0 d
Figure 3.13: Aligning equivalent stator fluxλtotal alongq− axis
iqs =λqs−Lmi′qr
Lls +Lm(3.27)
Similarly, the statord− axis current can be obtained as
ids =−Lmi′dr
Lls +Lm(3.28)
From these results it can be seen that the stator currents arelinearly depen-
dent on the rotor currents. Inductance and flux quantities inEq.(3.27) and (3.28) are
time-invariant, thus the statorqd0 axis currents can be controlled by adjusting the
rotor q− axis andd−axis currents appropriately. The next step is to show that the
real and reactive power output of the machine can be decoupled, and control over
36
real and reactive power can be achieved through controllingrotor q− andd−axis
currents respectively. The real and reactive power in the stator windings can be
derived as follows:
S= VsI∗s (3.29)
Vs = Vqs+ jVds (3.30)
Is = Ids+ jIqs (3.31)
Thus, apparent powerS is given by
S= Ps+ jQs = (VqsIds+VdsIqs)+ j(VdsIds−VqsIqs) (3.32)
Ps =32(Vqsids+Vdsiqs) (3.33)
Qs =32(Vdsids−Vqsiqs) (3.34)
Since,Vqs = 0, Eq.(3.33) and Eq.(3.34) can be written as
Ps =32Vdsiqs (3.35)
Qs =32Vdsids (3.36)
37
From Eq.(3.35),(3.36,(3.27) and (3.28) active and reactive power equations can be
simplified as follows
Ps =−32
ωsλqs(λqs−Lmi′qr
Lls +LM) (3.37)
Qs =32
ωsλqs(Lmi′dr
Lls +LM) (3.38)
From Eq.(3.37)-(3.38) it can be noted that, quantities likeλqs, ωs, Lls, LM,
Lm are all time invariant quantities, thus Eq.(3.37)-(3.38) can be further simplified
as
Ps = (kps1−kps2)i′qr (3.39)
Qs = kqsi′dr (3.40)
wherekps1, kps2, kqs are the respective constants of active and reactive power equa-
tions. It can be clearly seen from Eq.(3.39)-(3.40) that stator active powerPs can
be independently controlled byq−axis rotor current, while stator reactive powerQs
can be independently controlled byd−axis rotor current in an induction machine.
38
Chapter 4
Model Development and Implementation
4.1 Introduction
This section decribes wind turbine models developed in PSCAD/EMTDC
and MATLAB/SIMULINK platforms. The first model developed wasa fixed speed
wind turbine model, it produces rated active power at rated wind speed (one wind
speed only). As the wind turbine operates at a constant angular speed (rpm), maxi-
mum power is obtained at one wind speed only. It should be noted that blade pitch
angle is kept constant for the model. Hence, the efficiency ofsuch a wind turbine at
varying wind speeds is less. The blade pitch angle for such wind turbines is a preset
value, determined by wind speed in the area of installation.The blade pitch angle
at which maximum power is obtained varies for differentCp vs λr characteristics.
For simulation purposes, the rated wind speed was set at 14 m/s, with cut-
in speed of 6 m/s and cut-out speed of 20 m/s. The blade pitch angle was set to
-6.1667. With the basic model at hand, the fixed speed model is furtherdeveloped
into a variable speed wind turbine model. The advantage of a variable speed wind
turbine is that, the torque speed characteristics of the machine can be manipulated,
to obtain maximum/rated power at varying wind speed. To put it very precisely
a variable speed wind turbine has larger generator speed variations than the fixed
39
speed wind turbine. It is capable of producing maximum torque, thus maximum
power at different generator speeds.
To achieve rated power output above rated wind speed, different control
strategies are implemented. Now, rated power above rated wind speed can be pro-
duced in two ways
• Pitch control
• Rotor resistance based control
In case of the first method, the operating, blade pitch angle is varied to obtain rated
power at any wind speed above rated. This method does not manipulate the torque
speed characteristics of the machine. It can be visualized as fixed speed wind tur-
bine, which operates at variable pitch angles, achieved by calculating the optimum
pitch angle for a given wind speed and output power. This is done by physically
changing the rotor blade pitch angle, while the turbine is inoperation. The second
method entails, more control over the torque speed characteristics of the machine.
As the rotor resistance is varied, generator speed changes,and the machine operates
with new torque speed curve depending on the output torque and thus the power re-
quirement.
As discussed earlier, in case of utilizing an induction machine for wind tur-
bines, it can be directly connected to the grid, or through a power electronic con-
verter. When the rotor and stator side of the machine are switched using converters
40
(rectifier and inverter), such a system is called the doubly-fed induction generator
system (DFIG). Using a DFIG provides independent active (P)and reactive (Q)
power control of the machine. When using a variable-speed rotor resistance control
or variable-speed pitch control strategy, desired active power can be obtained, but
their is no control over the reactive power absorbed or generated by the machine. In
Section 4.2 - 4.3, a detailed model development procedure for fixed speed, variable
speed and DFIG based wind turbine system has been discussed.Given below is a
list of wind turbine models. All models employ induction machine, which is rated
at Vll = 690 V, S = 1.8 MVA. A detailed machine specification including stator and
rotor resistances and inductances can be found in the appendix section. The rated
power output of the turbine was set to 1.5 MW.
The different configurations of wind turbine models, that were implemented
are listed below
• Fixed speed wind turbine model
• Variable speed wind turbine model
– Rotor resistance control
∗ Constant power strategy
∗ Constant current strategy
41
4.2 Fixed speed wind turbine
For a fixed speed wind turbine, over the entire wind sweep fromcut-in speed
of 6 m/s to cut-out speed of 20 m/s, generator speed does not vary much, hence the
namefixed speed wind turbine. The aerodynamic model developed for a fixed speed
wind turbine, is used for all the other wind turbine models. The only function of
the aerodynamic model is to provide the speed input to the generator. As the gen-
erator speed input varies with wind speed, the power output of the generator varies
accordingly. In case of the fixed speed wind turbine, the output power profile builds
up with increase in wind speed from cut-in wind speed of 6 m/s,peaks at 14 m/s
(rated wind speed) and then drops later due to passive stalling of the rotor blades.
Figure 4.1 shows the specific block diagram representation of the fixed speed wind
turbine which is modeled, based on the more general diagram given in Figure 3.3 .
Tip speed ratio
calculation
Power coefficient
lookup
Aerodynamic torque
calculation
Two-mass model
Induction machine
Step-up transformer
Power grid
Vwind β
λr τaeroCp
τgen
ωrot
ωgen
Aerodynamic modelMechanical drive train
modelMachine + Grid model
Figure 4.1: Generic model for fixed speed wind turbine
42
4.2.1 Fixed-Speed Wind Turbine Model in PSCAD/EMTDC
As can be seen from the block diagram in Figure 4.1, wind speedvariable
Vwind and rotor speedωrot are used to compute the tip speed ratio (λr ) given by the
relation in Eq.(3.9), whereR= 36 m. Usingλr and the a blade pitch angle as inputs
to a lookup table, corresponding value of power coefficient (Cp) is computed. The
relation between Cp, λr and blade pitch angle (β ) used for all models are given in
Eq.(3.10) and Eq.(3.11). TheCp vs λr characteristics obtained are shown in Figure
3.6. Once,Cp is obtained, it is then used by the aerodynamic torque calculation
block to calculate the instantaneous aerodynamic torque ofthe rotor. Shown in Fig-
ure 4.2.1 is the internal block diagram of the aerodynamic torque calculation block.
Vwind
Lambda
Compute
wRot
Vwind
lambdawRot
VwindLook-up table
xy
x
y
zPitch
CpAero
dynamic
torque
wRot
Radius
Cp
Vwind
AeroT
Vwind36.0Radius
Radius
Radius
wRot
AeroT
Reffered
AeroT
Tem
wRot
wGenpu
AeroT wRot
wGenpu
TemCompute tip speed ratio
Aerodynamic torque Shaft model
Variable wind speed
Figure 4.2: PSCAD simulation model for a WT
wRot
Radius
Cp
Vwind
* * * **
rho pie Radius Radius Vwind
* *
Vwind Vwind
Constant
0.5Constant
1.225rho
pie3.1416pie
Constant
rho
wRot
Radius
Cp
Vwind
*N
D
N/D
wRot
Aerodynamic torque
AeroT
Pwind
Cp
A
B
Ctrl
Ctrl = 1
1
0.0
TIME
Figure 4.3: Aerodynamic torque computation
43
Since, the rotor shaft is a low speed shaft rotating between 15 and 20 rpm.
A gear train has to be included, which is then connected to thehigh speed shaft of
the induction generator rotating at a base frequency of 125.667 rad/sec. For a 6 pole
machine it converts to 1200 rpm. To model the gear train, incorporating the rotor
slow speed shaft, gear train and generator high speed shaft as a two-mass model.
The two-mass model is governed by three differential equations, Eq.(4.1), (4.2) and
(4.8) and a gear ratio ofa = 70 was assumed. A detailed list of constants used for
modeling the gear train and the rotor,generator shafts is provided in the Appendix
B section. Given below is the set of differential equations used to model the gear
train and rotor generator shafts as a two-mass.
X′1 = ωrotr −ωgen (4.1)
ω ′rotr =
τaeror−Beqv(ωrotr −ωgen)−KeqvX1
Jrotr(4.2)
ω ′gen=
−τgen−Beqv(ωrotr −ωgen)+KeqvX1
Jgen(4.3)
Jrotr =Jrot
a2 (4.4)
Beqv=Brot
a2 +Bgen (4.5)
44
Keqv=Krota2 Kgen
Krota2 +Kgen
(4.6)
Equarions (4.1), (4.2) and (4.8) can be solved with initial conditions of the
integrator set forωrot = ωgen = 125.66 rad/sec from Eq.(4.7), (4.8).τaeror is the
aerodynamic torque referred to the generator shaft, obtained by dividing it by the
gear ratio.Jrotr is the moment of inertia of the rotor referred to the generator shaft.
Electromagnetic torque output of the induction machineτgen is converted from its
per unit equivalent by multiplying it by the rated generatortorque = 15914.67 Nm
(refer Eq.(3.12)). A negative value ofτgen is applied to the two-mass model, as it
operates against the rotor torque. Before feedingωgento the machine, it is converted
to its per unit equivalent by dividing it by the rated speed of125.667 rad/sec.
N =120f
P(4.7)
ωgen=2πN60
(4.8)
whereN is the generator speed in rpm,P is the number of poles andf is the syn-
chronous frequency.
The PSCAD machine model is directly connected to the grid. A step up
transformer connected indelta−wye is used to connect the stator terminals to a
three-φ voltage source (representing the grid). Once the model is ready, the blade
pitch angle has to be set to obtain rated power of 1.5 MW. It wasobserved that, a
maximum power of 1.5 MW was obtained atβ = −6.166. β is then kept fixed and
45
rated wind speed is set at which machine outputs 1.5 MW. The model is then run at
wind speed ranging from 6 m/s to 20 m/s. The power profile for the model is then
obtained as shown in Figure 4.4
A look at the power profile of the wind turbine shows that ratedpower of 1.5
MW is obtained at a fixed wind speed of 14 m/s and, fixed pitch of−6.166. As the
wind speed varies power produced varies roughly as the cube of the wind speed. At
rated wind speed the electrical power generated becomes equal to the rating of the
turbine, and then stalling takes place above the rated wind speed. This is achieved
by making use of post-stall reduction in lift coefficient andassociated increase in
drag coefficient. It places a ceiling on the output power as wind speed increases. As
can be seen from Figure 4.4 power output of the generator falls below 1.5 MW at
any wind speed above 14 m/s. It can be also noted that, the output of the generator
drops significantly almost 0.079 MW at a wind speed of 6 m/s. This stalling of the
wind turbine is attributed to the increase in angle of attackas wind speed increases,
and increasingly large part of the blade enters the stall region. The stalling effect
reduces the rotor efficiency and puts a cap on the output power. Stall regulated
machines generally suffer from the disadvantage of uncertainties in aerodynamic
behavior post-stall, which can result in inaccurate power levels and blade loading
at the rated wind speed and above.
For a fixed speed wind turbine, rotor speed and thus the generator speed
variation as wind speed varies are very less. As can be seen from Figs.4.5(a) and
46
6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Wind speed in m/s
Pow
er o
utpu
t in
MW
Figure 4.4: Power profile for fixed speed wind turbine model
4.5(b), the generator speed reaches a maximum of 126.281 rad/sec at 14 m/s and
then decreases due to passive stalling. The overall slip variation is a maximum of
-0.49% . Results obtained from the PSCAD model are later compared with those
from a similarly developed MATLAB/SIMULINK model to demonstrate that the
model can be implemented in different platforms.
A torque slip plot for the model shows that, the torque rise isvery steep.
As the wind speed increases, the generator speed does not increase, as shown in
Figure 4.5(a) it attains a maximum value at 14 m/s. The generator torque achieves
maximum value at 14 m/s and then drops above rated speed. Figure 4.6 shows the
47
6 8 10 12 14 16 18 20110
115
120
125
130
135
140Generator speed vs Wind speed
Wind speed in m/s
Gen
spee
d in
rad/
s
(a) Generator speed variation with wind speed
6 8 10 12 14 16 18 201.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4Rotor speed vs Wind speed
Wind speed in m/s
Roto
r spe
ed in
rad/
s
(b) Rotor speed variation with wind speed
Figure 4.5: Rotor and generator speed variation with wind speed
torque slip characteristics of the machine during the entire wind speed sweep from
6 m/s - 20 m/s.
48
−3−2.5−2−1.5−1−0.50−15000
−10000
−5000
0Torque vs Slip
Slip in %
Torq
ue in
Nm
Figure 4.6: Torque slip characteristics
4.2.2 Fixed-speed Wind Turbine Model in MATLAB/SIMULINK
For the purpose of demonstrating the generality of the modelin Figure 4.1,
the results obtained from the PSCAD/EMTDC model of fixed speedwind turbine
are compared with those from a parallel MATLAB/SIMULINK model. A similar
approach for modeling the wind turbine was used. Initially an aerodynamic model
simulating the rotor blades, rotor shaft, gear train and generator shaft was modeled
in SIMULINK. Generator speed outputωgen was then fed to a induction machine
model, working in the squirrel cage mode (rotor circuit shorted). The built-in ma-
chine model in SIMULINK provides a number of options for machine specifica-
tions. The machine can be customized very well according to the model demand. It
provides a greater depth in terms of setting the reference frame with options of sta-
tionary, synchronous and rotor frames. The machine stator is connected to a three
phase RLC voltage source through adelta−wyeconnected 0.69 kV/34.5 kV step
49
up transformer. X/R ratio for the voltage source is set at 10.Figure 4.7 shows the
internal block diagram for the aerodynamic model developedin SIMULINK. The
results from both the models were seen to match closely.
The aerodynamic model in Figure 4.8 is provided a ramp input for wind
speed, the simulation time is set for 100 seconds with a ramp rate of 0.14 m/s2,
with an initial wind speed of 6 m/s, which means that at 100 seconds, the wind
speed reaches a peak of 20 m/s. The rotor blade pitch angle is set to−5.8 and an
empirical lookup table is used to determineCp using tip speed ratio (λ ) and pitch
angle(β ) as inputs. Once,Cp is determined a subsystem block calculating the power
available from the wind usesCp to determine the power extracted from the wind and
thus, the aerodynamic torque of the rotor blades.
This input is then used in the two-mass model of the rotor shaft, gear train
and generator shaft to solve the differential equations forgenerator speed (ωgen)
and rotor speed (ωrot). The generator speed (ωgen) thus obtained is then fed to the
built in asynchronous machine model in SIMULINK, with rotorcircuit shorted and
neutral grounded (squirrel cage mode). The electromagnetic torque (Tem) obtained
from the machine model is then fed back to the two-mass model.Figure 4.8 shows
the entire SIMULINK model of a fixed speed wind turbine, a multimeter measuring
the stator voltage and currents is used, whose outputs areVabc andIabc. The voltage
and currents measured are used to determine the active and reactive power flowing
out of the stator circuit of the machine.
50
pitch
lambda
Rotor speed and Generator speed
wgen
1
rpm 1
-K-
powergui
Continuous
pitch controlslider
-5.8
pitch
1
lambda calculation
wrot
wind speed
lambda
lambda
aerodynamic torque calculation
Vwind
Cp
wrot
AeroTaerodynamic
Vwind
Vwind
Switch 1
[wrot ]
[Cp]
[wrot ]
[wrot ]
[Cp]
Drive train model
AeroT
Tgen
wrot
wgen
Cp limiter
Cp Lookup Table
Clock1
0
CPvalues
AeroT initial
0
AeroT
Tgen
2
Wind speed
1
Figure 4.7: Aerodynamic model in SIMULINK
51
speed
speed
slip compute
speed slip
slip
slip
rpm
-K-
Vabc
Vabc
Torque and speed
Three -PhaseV-I Measurement
A
B
C
a
b
c
Real power
Pout
Reactive power
Qout
Ramp
P and Q
Mean Value 1
In Mean
MW/MVAR
-K-
Iabc
Iabc
High R in parallel
A B C
A B C
[Tgen ]
[Tgen ]
Aerodynamic model
Wind speed
Tgen
wgen
34 .5/0.69 kV 10 MVA
A
B
C
a
b
c
34 .5 kV 2000 MVA
A
B
C
2 MW 0.69 kV Induction Machine
w
m
A
B
C
Active & Reactive Power
Vabc
IabcPQ
Active power
Reactive power
<Rotor speed (wm)>
<Electromagnetic torque Te (N*m)>
Figure 4.8: Fixed speed wind turbine model in SIMULINK
52
6 8 10 12 14 16 18 200
0.5
1
1.5
2
Wind speed in m/s
Act
ive
pow
e in
MW
6 8 10 12 14 16 18 20−0.65
−0.6
−0.55
−0.5
−0.45
Wind speed in m/s
Rea
ctiv
e po
wer
in M
Var
Figure 4.9: Active and reactive power profile for fixed speed wind turbine model inSIMULINK
The active and reactive power profile obtained from the SIMULINK model
of the turbine are shown in Figure 4.9. It can be seen that the active power peaks
at 14 m/s, while there is no control over the reactive power generated. It remains
negative, indicating that the machine constantly absorbs some reactive power from
the grid. A typical fixed speed wind turbine power profile is obtained from the
model, which is comparable to the PSCAD model described earlier in the previous
section. After the wind speed crosses its rated value, the active power output of the
machine drops to almost 1.2 MW.
A drop similar to the active power output of the machine can beseen in the
53
6 8 10 12 14 16 18 20−15000
−10000
−5000
0
Wind speed in m/s
Gen
erat
or to
rque
in N
m
6 8 10 12 14 16 18 201200
1202
1204
1206
Wind speed in m/
Gen
erat
or s
peed
in r
pm
Figure 4.10: Generator torque and speed profile in SIMULINK
torque profile too, at 14 m/sTem reaches a peak value of approx -12 kNm, as the
wind speed increases beyond 14 m/sTem drops. A look at the speed profile of the
machine, shows that it does not vary much during the entire wind speed sweep from
6 m/s to 20 m/s it holds almost a constant value above 1200 rpm and reaches a high
of approx 1205 rpm, when the wind speed reaches its rated value of 14 m/s. Over-
all, ωgen variation with wind speed is very less. It can be observed from the torque
slip characteristics of Figure 4.11, that slip reaches a maximum value of -0.49% at a
maximum torque of approx -12000 Nm. Thus, a peak torque (producing peak active
power) occurs at only one slip or speed value of the inductionmachine. The work-
ing and functional characteristics of a fixed speed wind turbine have been shown
54
−0.015−0.01−0.0050−14000
−12000
−10000
−8000
−6000
−4000
−2000
0
Slip
Tor
que
in N
m
Figure 4.11: Torque slip characteristics of induction machine in SIMULINK
through models built on two different platforms. The results obtained are similar in
many respects. The power profile, torque, speed and torque-slip characteristics ob-
tained clearly show the stalling effect after rated wind speed. With the two models
at hand, working of a fixed speed wind turbine and further gridintegration of such
a turbine can be studied in detail.
4.3 Variable speed wind turbine
As described in the Section 4.2, for a fixed-speed wind turbine, there is no
active control over the power output of the machine, once therotor blade pitch angle
is set. In variable-speed machines however, it is possible to control the output power
55
using torque control. Various possible torque control methods exist to achieve con-
stant power output above rated wind speed in variable-speedwind turbines. Two of
these torque control methods are implemented in this chapter. These are:
• Aerodynamic torque control
• Generator torque control
Aerodynamic torque output from the rotor is determined by tip speed ratio andCp,
rotor geometry (blade pitch and aileron settings), wind speed, yaw error and ro-
tor drag. Since, there is no control over the wind speed, other parameters have be
used to control the aerodynamic torque. Any change in the tipspeed ratio changes
the rotor efficiency thus changing the rotor torque. A changein rotor geometry
i.e. varying the rotor pitch angle results in a change in liftand drag forces thereby
changing the torque output. Pitching the blade can regulatethe torque output either
by reducing the angle of attack or increasing it, as in case ofstalling. Rotor blades
for pitch-regulated wind turbines are designed to operate at maximum efficiency
(maximum power production) for relatively high angles of attack. At these high
angles of attack, change in rotor blade position (typicallymoving the turbine into
the stall region) is accomplished with more exact control, is faster and results in a
quieter overall operation. The downside is that inducing stalling from the very start
results in unsteady loads, less accuracy in control, and greater thrust on the turbine
due to unsteady nature of the stalled flow [5].
56
In case of generator torque control, torque of the generatorcan be either
changed through the design characteristics or by the use of power converters. As
demonstrated in the fixed speed wind turbine model, grid connected generators op-
erate over a very small or no speed range and provide the required torque at or
near synchronous speed, which depends on the type of machine(induction or syn-
chronous). For a grid connected induction generator changein ωgen is a small
percentage of the synchronous speed, this results in low torque spikes and softer re-
sponse. In contrast, for a synchronous generator any forcedtorque change results in
an instantaneous compensating torque, which can result in higher torque and power
oscillations.
An induction generator can very rapidly achieve any desiredvalue of tar-
get torque by the use of a power converter.The converter determines the frequency,
phase angle and value of the currents to be injected into the machine windings, this
allows the machine to be set to any desired value of torque, thus controlling the
power output of the generator.
4.3.1 Pitch control
As explained above, aerodynamic torque control can be achieved by chang-
ing the rotor blade geometry (blade pitch angleβ ) for varying wind speeds. Pitch
control is somewhat analogous to steam governor action in a synchronous machine,
as both mechanisms control the mechanical input power to thegenerator. It can be
57
visualized as fixed speed operation with an optimum pitch angle to produce maxi-
mum power at any wind speed above rated.
V rotational
V relative
Vwind
Drag
Thrust
Lift
TorqueAngle of attack
Figure 4.12: Blade geometry of horizontal axis wind turbine [4]
4.3.2 Dynamic rotor resistance control
This section describes the simulation results of a variablespeed wind turbine
using PSCAD/EMTDC. PSCAD has been used to model and simulate theturbine.
A built in machine model of a wound rotor induction machine isused to imple-
ment constant power and constant current strategy. The rotor pitch angle is set to
−6.483 (rated pitch) to obtain a maximum power output of 1.5 MW at 14.2 m/s
(rated wind speed). The wind turbine uses a 6-pole, 690V, 1.8MVA wound rotor
induction machine as a generator.
58
Constant power strategy to maintain constant power above rated wind speed
Constant power strategy aims to maintain a constant power output of the WTGS
above rated wind speed in the stall region. It was observed for the fixed speed
WTGS, that output power falls as wind speed exceeds the rated value. With the use
of PI controllers, rotor resistance of induction machine can be varied in such a man-
ner, that active power output remains constant. To maintainconstant active power
output, reference value of active power is compared with actual power generated.
The error signal is then fed to a PI controller. The output of the PI controller is the
new value of single phase rotor resistance. Rotor resistancevalue thus calculated
is equal for all three-phases. To obtain a rated slip of 2.25%an internal rotor re-
sistance of 0.048Ω is included in the rotor circuit. Figure 4.13 shows the PSCAD
block diagram for the PI control implemented [8].
A rated slip of 2.25% is obtained at 14.2 m/s and 1.5 MW output power.
As the wind speed increases above the rated wind speed outputpower of the gen-
erator tends to fall. To maintain the output power constant calculated value ofRext
is included in the rotor circuit, to increase the torque and thus the output power.
To calculate the exact value ofRext, actual generated power is compared with rated
power (1.5 MW) and the corresponding error is converted into per unit (base as
rated power) and error signal is fed to the PI controller. Once the output of the PI
controller converges,Rext is obtained.
59
Pgen
A
B
Ctrl
Ctrl = 1
Vwind
0.0
Rext
Re
xt
D -
F
+G
1 + sTN
D
N/D
I
P
slip
*1.0
Control loop to determine externalrotor resistance Kp = 0.01, Ti = 45
Figure 4.13:Rext estimation module in PSCAD using PI controller
Ziegler Nichols tuning algorithm was used to tune the PI controller. Tuning
of the PI controller was done as follows:
1. Critical gainKc was found by setting a very high value of integral time con-
stantTi = 106 sec. At critical gainKc = 0.026 the output of the PI loop starts
to oscillate sustainably, belowKc the output just manages to converge and
achieve a constant value. Further integral gainKi can be calculated using the
formula shown.Ki = 1.2∗KcPc
= 0.0226 whereKp = 0.45∗Kc = 0.011 andPc =
0.6 sec is the oscillation period of the PI controller output. Ti = 1Ki
= 45 secs.
2. Ziegler Nichols method is an iterative process. Using thevalues obtained
above as initial values, further fine tuning of the controller was achieved fol-
lowing the Table 4.1. The table shows the effect of increasing or decreasing
the proportional and integral gainKp andKi and was effectively used as guide
60
Table 4.1: Look-up table for PI controller tuning
Parameter Rise time Settling time Overshoot Steady-state error
Kp Decrease Small change Increase DecreaseKi Increase Increase Increase EliminateKd Indefinite Decrease Decrease None
in fine tuning the PI controller.
It is clear from the above Figure 4.14 that power remains constant above rated speed
of 14.2 m/s. The real power excursions with step changes in wind speed from 14.2
m/s (rated) - 15.2 m/s - 16.2 m/s are obtained using PSCAD model. Graph in Figure
4.15 shows the real power excursions while the wind speed is changed in steps of
1m/s, starting from 14.2 m/s - 16.2 m/s . It can be seen that an undershoot for a wind
speed change from 14.2 m/s(rated) - 15.2 m/s is quite large (1.5 MW - 1.2 MW).
It can be attributed to the proportional gain and integral gain of the integrator. The
PI controller when tuned for low undershoot and overshoot increases the settling
time. It is also evident from the graph that the undershoot isvery less (1.5MW -
1.41MW) for a step change from 15.2 m/s - 16.2 m/s.
Power excursion for change in wind speed from 18 m/s - 19m/s ismore than
that for 15.2 m/s - 16.2 m/s, with a variation from 1.5 MW - 1.38MW. It can also be
seen that the undershoot increases over further step changes from 18 m/s - 19 m/s
(1.5 MW - 1.33 MW) and 19 m/s - 20 m/s (1.5 MW - 1.26 MW) simultaneously the
settling time goes down. Better results with reduced undershoots are demonstrated
61
6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Wind speed in m/s
Pow
er in
MW
Pgen
Figure 4.14: Wind power profile for a variable speed wind turbine using rotor resis-tance control
PID controller, at the cost of increased settling time, which seems like a reasonable
trade-off.
Table.4.2 for wind speed, slip,Rext, rotor currentIrrms, rotor current fre-
quencyfr and rotor thermal losses over a range of wind speed from 6m/s -20 m/s.
From the Table.4.2, it is quite evident that thermal losses increase to almost
175 kW with largestRext = 0.229737Ω at 20 m/s.
It is observed that the power output of the generator is maintained constant
at 1.5 MW above rated wind speed. As the slip increases, the frequency of rotor
62
0 10 20 30 40 50 60 70 80 90 1001.1
1.2
1.3
1.4
1.5
1.6
Time in seconds
Pow
er in
MW
0 10 20 30 40 50 60 70 80 90 10014
14.5
15
15.5
16
16.5
Time in seconds
Win
d sp
eed
in m
/s
PgenPref
Vwind
Figure 4.15: Power excursion: constant power strategy using PI control from14.2m/s - 15.2 m/s - 16.2m/s
currentIrrms increases.
Torque slip characteristics in operating region
The torque slip characteristics plotted in Figure 4.17 shows a large variation of slip
from 6 m/s to 14.2 m/s. This increased slip variation is attributed to the internal
rotor resistanceRint = 0.048Ω and can be changed to vary the rated slip from 2
% to 2.5 %. As the slip variation is large over a range of increasing electromag-
netic torque (negatively), the wind turbine can be controlled using PI controller to
63
30 40 50 60 70 80 90 1001.1
1.2
1.3
1.4
1.5
1.6
Time in seconds
Pow
er in
MW
30 40 50 60 70 80 90 10016
17
18
19
20
Time in seconds
Win
d sp
eed
in m
/s
PgenPref
Vwind
Figure 4.16: Power excursion: constant power strategy using PI control from 17m/s- 18m/s - 19 m/s - 20m/s
achieve a constant power output of 1.5 MW. Table.4.3 shows the Torque and slip
values measured for wind speeds ranging from 6 m/s - 20 m/s, with different values
of Rext (at 8 m/s,14m/s,16m/s,20m/s).
Another way of plotting the torque speed characteristics isby the use of
electromagnetic torque formula as follows,
τe =3
ωs.
V2s
(Rs+ Rrss )2 +(Xls +Xlrs)
.Rrs
s(4.9)
64
Table 4.2: Active power recorded for increasing slipVwind Power Slip Rext Irrms fr Thermal lossm/s MW % Ω kA kA 3I2Rext (kW)
6 0.0626898 0.101731 0 0.0219736 0.061 07 0.234182 0.358456 0 0.0776121 0.2151 08 0.470513 0.711219 0 0.154201 0.42677 09 0.733481 1.10329 0 0.23903 0.661974 010 0.990709 1.48686 0 0.322002 0.892113 011 1.20692 1.80992 0 0.391725 1.08595 012 1.36852 2.05207 0 0.443857 1.23124 013 1.46404 2.19557 0 0.474688 1.31734 014.2 1.5 2.24971 0 0.486307 1.34983 015 1.5 2.693 0.0092183 0.487657 1.61576 6.57616 1.5 4.14581 0.0397002 0.489889 2.48749 28.58317 1.5 6.3168 0.084751 0.493219 3.79009 61.85018 1.5 8.37859 0.127001 0.496372 5.02716 93.87319 1.5 10.7532 0.175041 0.499985 6.45198 131.27220 1.5 13.496 0.229737 0.504125 8.09766 175.157
whereτe - Electromagnetic torque of the machine
Vs - Generator terminal voltage
ωs - synchronous speed
Rs - stator resistance
Rrs - Rotor resistance referred to the stator side
Xls - Stator leakage reactance
Xlrs - Stator leakage reactance referred to the stator side
To improve the transient response of the machine, for step changes in wind
65
Table 4.3: Torque slip dataTorque Slip % Torque Slip % Torque Slip %(Nm) (Rext = 0) (Nm) (Rext = 0.039) (Nm) (Rext = 0.22)
541.439 0.101731 536.919 0.185216 515.651 0.5799311913 0.358456 1889.69 0.650712 1783.52 2.003813799.03 0.711219 3744.37 1.28856 3501.86 3.931825892.02 1.10329 5825.94 2.00513 5492.332 6.165147933.57 1.48686 7871.16 2.71126 7593.96 8.52669645.12 1.80992 9671.18 3.33559 9639.19 10.83171092.71 2.05207 11053.1 3.81739 11508.4 12.947611675.1 2.19557 11956.3 4.13367 13126.7 14.788811953.9 2.24971 12432.6 4.30097 14696.4 16.58511829.8 2.22509 12384.7 4.28413 15467.3 17.471611293.8 2.12289 11952.6 4.13238 15897.5 17.967610541.3 1.97981 11140.6 3.84797 15811.2 17.8689547.83 1.79151 10210.6 3.52337 15085.1 17.03168360.5 1.56729 8771.25 3.02305 13693.5 15.4367515.3 1.40813 7955.67 2.74051 11925 13.4206
speed, a PID controller can also be used. Figure.4.19 shows the internal PSCAD
block diagram for the PID controller. PID controllers are tuned in a similar fashion
as demonstrated for the PI controller.
A differentiator is included in the PI control loop to reducethe overshoot
and settling time, with a flip side of increased system instability. Results obtained
for the PID controller show improvements not only on reducedundershoot and no
overshoot, but also highly accurate steady state value. As can be seen from the
power excursion shown in Figure 4.15 the undershoot goes as low as 1.2 MW and
an overshoot of 1.52 MW. Opposed to this, the power excursionof the PID con-
troller has imporved undershoot of 1.38 MW and overshoot totally eliminated. This
66
−18−16−14−12−10−8−6−4−20−16000
−14000
−12000
−10000
−8000
−6000
−4000
−2000
0
Slip in %
Ele
ctro
mag
netic
torq
ue o
f the
gen
erat
or in
Nm
Figure 4.17: Torque Slip characteristics with varyingRext at 8 m/s, 16 m/s and 20m/s wind speed
improvement can be attributed to the inclusion of the differentiator and reduced val-
ues of integrator time constant.
As visible from the Figure 4.20, overshoot is almost eliminated and under-
shoot reduced with the use of PID controller. For a step change in wind speed from
14.2 m/s - 15.2 m/s, the output falls till 1.38 MW and then tracks the rated value.
Similarly, the undershoot for a change in wind speed from 15.2 m/s- 16.2 m/s has
been reduced to 1.41 MW.
A similar power excursion profile can be seen in Figure 4.21 for step change
67
−1−0.8−0.6−0.4−0.200.20.40.60.81−3
−2
−1
0
1
2
3x 10
4
slip in %
Tor
que
in N
m
Figure 4.18: Complete Torque Slip characteristics withRext = 0, 0.039Ω,0.22Ω at8m/s, 16m/s, 20m/s wind speed respectively
D -
F
+G
1 + sTPgenN
D
N/D
slip1
sT
*1.0
A
B
Ctrl
Ctrl = 1
0.0
Rext
Re
xt
D +
F
+G
+
Vwind
*0.0156Rraw
sT
Self Built PID controllerTuned for Kp = 0.0156 , Ti = 1 sec, Td = 0.05 sec
Figure 4.19:Rext estimation module in PSCAD using self built PID controller
from 17 m/s - 18 m/s -19m/s - 20 m/s. The profile obtained is similar to that ob-
tained with PI controller. Thus, a PID controller proves to be better in reducing the
overshoots than the PI controller.
68
0 5 10 15 20 25 30 35 40 45 50 55
1.2
1.4
1.6
Time in seconds
Pow
er in
MW
0 5 10 15 20 25 30 35 40 45 50 5514
14.5
15
15.5
16
16.5
Time in seconds
Win
d sp
eed
in m
/s
Vwind
PgenPref
Figure 4.20: Power excursion: constant power strategy using PID control from14.2m/s - 15.2 m/s - 16.2m/s
Constant current strategy to maintain constant power aboverated wind speed
Another method to implement variable speed wind turbine model is constant cur-
rent technique. In this method rotor current is not allowed to fluctuate beyond a
bandwidth. Initially, constant current was implemented using an error signal ob-
tained from theIrre f - Iract . Where,Irre f is the rms value of rotor current at rated
wind speed (with rated pitch) andIract is the rms value of rotor current at any wind
speed above rated. As we try to maintain the current in the rotor same as the rated
value of rotor current, it was observed that the power outputfalls, above rated wind
69
40 50 60 70 80 90 100
1.2
1.4
1.6
Time in seconds
Pow
er in
MW
40 50 60 70 80 90 10017
18
19
20
Time in seconds
Win
d sp
eed
in m
/s
Vwind
PrefPgen
Figure 4.21: Power excursion: constant power strategy using PID control from17m/s - 18m/s - 19 m/s - 20m/s
speed. The total variation in output power was 1.5 MW - 1.45 MW, for a range
of wind speed from 14.2 m/s - 20 m/s . Though the rotor current was maintained
constant at rated value, the error current method did not provide a constant output
power as desired for a variable speed wind turbine. This is due to the phase angle
of the rotor current, which was not accounted, while maintaining constant current
(only magnitude was considered).
To maintain output power constant, another error loop ofPre f - Pact was
added to the overall control loop calculatingRext, wherePre f = 1.5 MW andPact is
70
the actual power generated at any wind speed above rated. Error signal is then given
to the PI controller. Output of the PI controller when added to theIrated = Ire f . This
Ire f is then compared withIact and output fed to the PI controller. Output of the PI
controller forms theRext estimated. This method works, and is found to converge to
constant power output eventually. Wind power profile remains the same as shown
in Figure 4.14), since the output power converges to 1.5 MW for all wind speeds
above rated.
Initially a PI controller is used to implement constant current strategy. Tun-
ing of the cascaded PI controllers in done using the same tuning algorithm as de-
mostrated for constant power strategy.
A
B
Ctrl
Ctrl = 1
Vwind
0.0
RextI
P
Re
xt
ItrG
1 + sT D -
F
+N
D
N/D
D -
F
+I
PN
D
N/DPgen
slipM
D +
F
+
0.486307
PI controller 1 Kp = 0.037575,Ti = 36.97 sec,Td = 0.05sec
PI controller 2 Kp = 0.0252,Ti = 49.49 sec,Td = 0.05 sec
Figure 4.22:Rext estimation module in PSCAD using built-in PI controller
Tuning of the PI controller 1 using Ziegler Nichols tuning algorithm :
1. Integrator time constant was set to a high value ofTi = 106 sec
71
2. Starting with a critical gain ofKc = 0.05, it was increased until sustained
oscillations in the output of the PI loop were obtained
3. Eventually, atKc = 0.0835, the output of the PI loop starts to oscillate.Kp =
0.45· Kc = 0.037575 was obtained
4. Similarly,Ki = 1.2KpPc
= 0.0156, andKd = Kp · Pc8 , wherePc = 1.667 sec
5. Integral time constantTi = 1Ki
= 36.97 sec
Value of the integral time constant set for PI loop 1 (Figure 4.22) is not used
as the final value. This is chiefly because, the final value ofTi (integral time con-
stant) also depends on proper tuning of PI loop 2 (Figure 4.22).
Tuning of the PI controller 2 using Ziegler Nichols tuning algorithm :
1. With PI loop 1 tuned to the values shown above,Kc = 0.02 was set for PI
loop 2 and increased until the output of the loop (Rext) started oscillating
sustainably at ,Kc = 0.056.
2. Kp = 0.45· Kc = 0.0252 was obtained.
3. With Pc = 1.49 sec,Ki = 1.2KpPc
= 0.0202.
4. Integral time constantTi = 1Ki
= 49 sec was set .
5. As Ziegler Nichols is an iterative process, it does not provide the final value
of proportional gain and integral gain in one iteration.
72
6. By setting the initial values as calculated above, the model was run andTi
(for both the loops) reduced until the overshoots and oscillations in the output
reduced considerably
7. Still the final output could be improved by introducing a differentiator in the
control loop.
Power excursions for step change in wind speed from 14.2m/s -15.2m/s -
16.2m/s has been shown in Figure 4.23. The settling time increases, with increased
oscillations before the output settles.
0 5 10 15 20 25 30 35 4014
14.5
15
15.5
16
16.5
Time in seconds
Win
d sp
eed
in m
/s
0 5 10 15 20 25 30 35 400.8
1
1.2
1.4
1.6
Time in seconds
Pow
er in
MW
PgenPref
Vwind
Figure 4.23: Power excursion: constant current strategy using PI control from14.2m/s - 15.2 m/s - 16.2m/s
The undershoot in this case is quite high 0.5 MW, while you canalso see
73
an overshoot till 1.9MW. This is mainly because, there are two PI controllers, min-
imizing error in power output and then rotor current to obtain Rext so as to achieve
constant power output of 1.5 MW. The power excursion for stepchange in wind
speed from 15.2 m/s - 16.2 m/s is far better, as the undershootand overshoot is very
less 1.4 MW and 1.55 MW respectively.
Though the power output converges after oscillating for some time, still the
power excursions obtained using constant current strategyare worse as compared to
constant power strategy. While obtaining a reference current for each wind speed,
the rotor current oscillates a lot more as compared to the rotor current oscillations
in constant power strategy.
Power excursion shown Figure 4.24 is for step change in wind speed from
17m/s - 18m/s - 19m/s - 20m/s. With a step change in wind speed from 17m/s -
18m/s, the output power oscillates from 1.38MW - 1.57MW, similarly larger oscil-
lations can be seen for step wind speed change from 18m/s - 19 m/s and from 19m/s
- 20 m/s. Even with increased oscillations, the power outputconverges and settles
down to a constant value of 1.5 MW after some time.
Comparing the two methods used to achieve constant power, constant power
strategy is clearly better than constant current. It is mainly due to reduced oscilla-
tions during power excursion for step changes in wind speed.Even the rotor current
oscillations are less for constant power strategy. The phase angle of the rotor current
has not been accounted for, while keeping the current magnitude constant. As we
74
55 60 65 70 75 80 85 90 95 10017
18
19
20
Time in seconds
Win
d sp
eed
in m
/s
55 60 65 70 75 80 85 90 95 1000.8
1
1.2
1.4
1.6
Time in seconds
Pow
er in
MW
PgenPref
Vwind
Figure 4.24: Power excursion: constant current strategy using PI control from17m/s - 18m/s - 19 m/s - 20m/s
are considering only the current magnitude, results obtained using constant current
strategy are not as accurate, as obtained using constant power strategy. To improve
the accuracy of rotor resistance estimation, PID controllers are employed, it can be
seen from the results obtained, that overshoots and undershoots have been reduced.
Tuning of the PID controller is difficult as compared to the PIcontroller. Mostly
because, inaccurate gainKd (differential gain) can make the system unstable.
Tuning of the PID controller 1 using Ziegler Nichols tuning algorithm :
1. Integrator time constant was set to a high value ofTi = 106 sec
75
D -
F
+N
D
N/DPgen
slipM
1sT
*1.0 D +
F
+G
+*
0.0276
sT
PID controller 1 Kp = 0.0276, Ti = 1s, Td = 0.05s
A
B
Ctrl
Ctrl = 1
Vwind
0.0
Rext
Re
xt
ItrG
1 + sT D -
F
+N
D
N/D
D +
F
+
0.486307
1sT
*1.0 D +
F
+G
+
sT
*0.0336
Iref
PID controller 2 Kp = 0.0336, Ti = 1.46s, Td = 0.05s
Figure 4.25:Rext estimation module in PSCAD using PID controller
2. Starting with a critical gain ofKc = 0.03, it was increased until sustained
oscillations in the output of the PID loop were obtained.
3. Eventually, atKc = 0.046, the output of the PID loop starts oscillate.Kp = 0.6
· Kc = 0.0276 was obtained.
4. Similarly,Ki = 2KpPc
= 0.0189, andKd = Kp · Pc8 , wherePc = 2.92 sec
5. Integral time constantTi = KpKi
= 1.46 sec .
6. Time constant for differentiatorTd = 0.365 sec
Value of the integral time constant set for PID loop 1 was not used as the
final value. This is chiefly because, the final value ofTi also depends on proper
tuning of PID loop 2.
Tuning of the PI controller 2 using Ziegler Nichols tuning algorithm :
76
1. With PI loop 1 tuned to the values shown above,Kc = 0.02 was set for PID
loop 2 and increased until the output of the loop (Rext) started oscillating
sustainably at,Kc = 0.056
2. Kp = 0.6 · Kc = 0.0336 was obtained
3. With Pc = 1.49 sec,Ki = 2KpPc
= 0.0202
4. Integral time constantTi = KpKi
= 1 was set
5. Time constant for differentiatorTd = 0.18625 sec
6. As Ziegler Nichols is an iterative process, it does not provide the final value
of proportional gain and integral gain in one iteration
7. It was observed that the above set values forTi work perfectly well.
8. The value ofTd had to be reduced to 0.05 sec for both the controllers, as the
system became unstable at such high values ofTd
Power excursions obtained for the PID controller are betterthan the PI con-
troller, the undershoot has reduced and the output falls till 1.23 MW for step change
in wind speed from 14.2 m/s - 15.2 m/s . Similarly, the oscillation period and the
settling time of the power output has also been reduced for the change in wind
speeds shown in Figure 4.26.
It is fair to conclude that the performance of self built PID controller is bet-
ter than built in PI controller, even during wind speed change from 17m/s - 18m/s -
77
0 5 10 15 20 25 301
1.2
1.4
1.6
Time in seconds
Pow
er in
MW
0 5 10 15 20 25 3014
14.5
15
15.5
16
16.5
Time in seconds
Win
d sp
eed
in m
/s
PgenPref
Vwind
Figure 4.26: Power excursion: constant current strategy using PID control 14.2m/s- 15.2 m/s - 16.2m/s
19m/s - 20m/s there are less oscillations. Figure 4.23 can becompared with Figure
4.26, while Figure 4.24 can be compared with Figure 4.27 to observe the differ-
ence, still the output fluctuates far more as compared to the constant power strategy
implemented previously.
Constant power strategy and constant current strategy were successfully im-
plemented with PI as well as PID controller for a variable speed wind turbine. The
output power was maintained at 1.5 MW for any wind speed aboverated wind speed
of 14.2 m/s. If we compare the performance of PID controllerswith PI controllers,
78
50 55 60 65 70 75 80 85 90 95 1001
1.2
1.4
1.6
Time in seconds
Pow
er in
MW
50 55 60 65 70 75 80 85 90 95 10017
18
19
20
Time in seconds
Win
d sp
eed
in m
/s
PgenPref
Vwind
Figure 4.27: Power excursion: constant current strategy using PID control from17m/s - 18m/s - 19 m/s - 20m/s
it was observed that PID controllers, helped in reducing theundershoots, overshoots
and oscillations in output power response. It was also observed that constant power
strategy is more favorable for faster response with almost no oscillations as com-
pared to constant current strategy.
4.3.3 Hybrid control
In the case of fixed speed wind turbine, the pitch angle (β ) is set such that
power output reduces with increase in wind speed beyond the rated speed. This is
due to passive stalling above rated wind speed. The power extracted from the wind
can be obtained from Eq.(3.8)-(3.3). In case of rotor resistance control, external
79
resistances are added to the rotor circuit to vary the slip orgenerator speed at which
maximum generator torque is obtained. Since external resistance is implemented
electronically, it responds fast to rises in wind speed [8].However, due to the
inclusion of the extra resistance, rotor thermal losses canbe several hundreds of
kW. A solution to this problem is adjusting the value of the blade pitch angle for
the purpose of power control sinceCp is dependent on pitch angle as well. Since
pitching rate is slow due to the high inertia of the rotor blades, rotor resistance can
be included in the circuit only until the time the pitch is re-adjusted.
Figure 3.6 shows theCp vs λ curves for different pitch angles. In low to
medium wind speeds the pitch angle is controlled to allow thewind turbine to oper-
ate at its optimum condition (maximumCp condition). In high wind speed region,
the pitch angle is increased to shed some of the available wind power. Figure 4.12
shows the blade geometry of a horizontal axis wind turbine. With increase in the
pitch angle, the angle of attack decreases, decreasing the lift force resulting in re-
duced power output. Similarly, a reduction in the pitch angle increases the power
output. Therefore, at low wind speeds the pitch angle is set low whereas at high
speeds the angle is increased to relatively higher values.
The succeeding chapter deals exclusively with the DFIG model implemen-
tation in PSCAD/EMTDC and MATLAB/SIMULINK. An approach to determine
the reactive power capability of the DFIG based on stator androtor current limita-
tions is also discussed.
80
Chapter 5
Doubly-fed Induction Generator Modeling
5.1 Introduction
It has been already shown in the case of rotor resistance control that, the
variable wind speed turbines provides better optimizationof output power produced
by the rotor. In the case of rotor resistance control, changing the rotor resistance
changes the slip and thus required the torque is produced at varying wind speeds
above the rated wind speed. When induction machine operationis controlled by
the use of power converters to achieve variable speed operation, it is observed that
independent active and reactive power control can be achieved.
The DFIG is a wound rotor induction generator in which the rotor wind-
ings are connected to the grid through power converters. TwoVSIs are used for
such a connection, linked using a DC-link capacitor. With theuse of a DFIG, it is
possible to transfer power in both the directions across theinverter-converter pair.
This enables the generator to operate above and below the synchronous speed [5].
Operating the machine over synchronous speed initiates a power flow from the ro-
tor circuit to the grid, while operating the machine below synchronous speed (sub
synchronous speed) initiates a power flow from the grid connected stator circuit to
the rotor circuit [5].
81
The amount of active and reactive power transferred to the grid and the ma-
chine slip are controlled by the rotor current injection into the rotor circuit. For
this purpose, reference frame theory is used to obtain theqd0− axis rotor currents,
which can independently control the active and reactive power output of the ma-
chine.
On comparison with the traditional induction generator, DFIG configuration
has many advantages:
• Provides the ability to achieve independent active and reactive power control.
• Supports grid voltage by controlling the reactive power produced or absorbed,which
helps maintain a stable grid voltage.
A schematic representation of a DFIG wind turbine system is shown in Fig-
ure 5.1. In the DFIG turbines, the induction generator is a wound-rotor induction
machine. Because only part of the real power output flows through the rotor cir-
cuit, the power rating of the converter need only be about 20%to 30% of the rated
turbine output. A control system is employed to regulate currents in the rotor to
extract the maximum possible power from the wind.
Figure 5.2 shows the connection of these subsystems and the signals they
exchange.
A point to be noted is that the electrical dynamic performance of the DFIGs
at fundamental frequency is dominated by the converter. Thecombined electrical
82
Control
System
DFIG
Generator
Grid
Gear Box
Stator
connection
Rotor
connection
AC AC
DC DC
Power Electronic Converters
Figure 5.1: DFIG Wind Turbine Schematic [3]
behavior of the generator and the converter in the DFIG is largely like that of a
current-regulated voltage source inverter, which may be simplified for modeling
purposes as being equivalent to a regulated current source [3]. Therefore, the gen-
erator and the converter can be combined and modeled as a single current source.
This current source is controlled using flux-vector controlto obtain the desired real
and reactive power flows.
Flux-vector control allows the decoupled control of real and reactive power.
For decoupled control over real and reactive power output a controller based on
flux-vector control is modeled. As mentioned before, wound rotor induction ma-
chines are used in DFIG wind turbines. In the stationaryabc reference frame, the
relationships between the voltages, currents and flux linkages of each phase for a
machine of this type are time variant. Analysis in this reference frame is cumber-
some, so time variant quantities are made time invariant by transforming them into
an appropriate rotating reference frame, i.e. the rotatingqd0 reference frame.
83
Reactive Power
Control Model
Real Power
Control Model
Generator
Converter
Model
Wind Turbine
Model
Pitch Control
Model
Id (Q) command
Iq (P) command
Shaft speed (&)
Blade Pitch ()
Reference
speed (&ref)
Converter
Control Model
Reference
power (Pset)
Pmeasured,Qmeasured
Pmeasured,
Qmeasured
To grid
Pmeasured
Figure 5.2: DFIG Model Structure [3]
The currents flowing in the stator are assumed to be balanced.These cur-
rents produce a resultant stator magnetic field which has a constant magnitude and
is rotating at the synchronous speed. Since the angular speeds of the stator magnetic
field and theqd0 rotating frame are identical, the vector of the stator magnetic field
is fixed with respect to theq- andd- axes of theqd0 rotating frame. Theq−axis
of the reference frame is oriented in such a way that it alignswith the vector of the
stator magnetic field. The real and reactive power can be controlled by adjusting the
statorq− andd−axis current. The statorq- andd- axis currents can be controlled
by adjusting the rotorq- andd-axis currents. The stator real and reactive power can
thus be written as [3]:
Ps = kps· i′qr (5.1)
Qs = −kqs1 +kqs2 · i′dr (5.2)
84
wherekps, kqs1, andkqs2 are the respective constants for the stator real and reactive
power. Equations 5.1 and 5.2 clearly show that the stator real and reactive power
can be controlled by the rotorq- andd- axis currents independently. In both the
positive-sequence model and the three-phase model, the referenceq- andd- axis
currents are generated by the converter control block, as shown in Figure 5.2. In the
three-phase model, theseq- andd- axis currents are converted back to three-phase
currents using the inverse Park transform [20] prior to injection into the collector
system. The other subsystems, namely, the converter control model, wind turbine
mechanical model, and pitch control model have been modeledin the same manner
as in [21].
5.2 PSCAD/EMTDC Regulated Current-Source Model
This section describes the simulation results for a regulated current-source
representation of the doubly fed induction generator (DFIG) using PSCAD/EMTDC.
The real and reactive power of a wind turbine generator can beindependently con-
trolled using a doubly-fed induction generator. A regulated current-source repre-
sentation of the DFIG is modeled and the principle of flux vector control applied
to show independentP andQ control. Steps involved in developing the model and
implementing vector control, along with results obtained have been shown below.
1. Perform Clarke Transform (abc-αβ ): Stator voltageVsa, Vsb, Vsc are con-
verted from three-axis (abc) quantities to two-axis quantities (αβ ) Vα and
85
PI
COUPLED
SECTION
RR
L
Vsa Vsb Vsc
Iraref
Irbref
Ircref
P = 50Q = 20
V = 1.002
VA
Current regulated DFIG model
Figure 5.3: DFIG model in PSCAD
Vβ by performing Clarke transform. Obtained two-axis voltagesare inte-
grated to obtain corresponding flux values (λα , λβ ). Instantaneous value of
the stator fluxλs , its magnitude and angular position are determined. A sim-
ulation run is performed forPgenre f = 50 MW, Qgenre f = 20 Mvar to obtain
a value of instantaneous stator flux magnitude and angular position. λtotal =
|λs| = 0.075 Wb, whereas the angular position being an instantaneous value it
keeps on varying during the simulation run time.λtotal is the equivalent of a
three-phase magnetic field, whose amplitude remains constant and phase an-
gle varies from -π - π. Thus, we obtain a constant magnitude rotating vector
λs.
2. Perform Park Transform (αβ - dq0): A synchronously rotating framedq0 at
synchronous speedωs is constructed and the stator flux aligned alongd-axis
to obtain|λd| = |λs| = 0.075, and|λq| = 0.
Statord andq voltages are also computed and found to beVd = 0 kV, Vq =
86
0 20 40 60 80 100−0.1
−0.08
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
0.08
0.1
Time in seconds
Flu
x in
web
er
Fluxtotal
Fluxd
Fluxq
λq = 0
λd = λ
s = 0.075
Figure 5.4:|λd| = |λs| = 0.075 and|λq| = 0
28.2 kV. Value forVd can also be obtained analytically from Eq. 3.25, where
ωs = 2 · pi · 60.
3. Assuming that available wind power is sufficient to generate the desired level
of apparent power, reference values for the real and reactive power are set to
sample valuesPgenre f = 50 MW, Qgenre f = 20 Mvar. Value of the reference
currents to be given to the regulated current-source is found out, by compar-
ing the generated power with the reference power values.
4. The reference or command currents thus obtained alongdq-axis (Id, Iq) can be
converted into currents alongαβ -axis (Iα ,Iβ )through inverse park transform
87
0 20 40 60 80 100−20
−10
0
10
20
30
40
Time in seconds
dq a
xis
volta
ge in
kV
VqVd
Vd = 28.2
Vq = 0
Figure 5.5: Voltage alongd-q axis
D +
F
-Pgenref
Pgen
G1 + sT
I
P
Iqcmd
D +
F
-Qgenref
Qgen
G1 + sT
I
P
Idcmd
Active power command
Reactive power command
Figure 5.6: Computing reference currentsId andIq
and eventually into currents alongabc-axis (Irare f , Irbre f , Ircre f ) using inverse
Clarke transform. It can be shown through Eq. 5.1 and Eq. 5.2 developed in
88
vector control theory, that the active power from the generator is controlled
by Iq, while the reactive power byId.
5. The output is measured for different values of the desiredpower and the
power generated is found to track accurately the desired value.
0 20 40 60 80 1000
50
100
150
200
250
300
350
400
450
Time in seconds
Pow
er in
MW
/MV
ar
PgenQgen
Figure 5.7:Pgenre f = Pgen = 50-400 MW in steps of 50 MW,Qgenre f = Qgen = 0MVAr
Further, to establish decoupled or independent control of the real and reactive
power,Qgenre f = 0 MVAr is kept constant andPgenre f = 50 to 400 MW with
steps of 50 MW and correspondingPgen andQgen values are registered. It
is clearly seen from the Figure 5.7 that with step change of 50MW in the
active power, the reactive power remains constant as the desired real power
89
is increased from 50 MW to 400 MW. There are small overshoots during
transient period, but the output settles rapidly. Thus, it is demonstrated that,
the reactive power change is independent of the real power demand.
It can be satisfactorily established from Figure 5.8 that step changes of 20
MVAr in reactive power has no change in the real power output of the DFIG.
Thus, Figure 5.8 confirms independentP andQ control.
0 20 40 60 80 1000
50
100
150
200
250
Time in seconds
Pow
er in
MW
/MV
ar
PgenQgen
Figure 5.8:Qgenre f = Qgen = 50-400 MW in steps of 50 MW,Pgenre f = Pgen = 50MW
5.3 MATLAB/SIMULINK Regulated Current-Source Model
Modeling in SIMULINK involved developing the model in parts:
90
1. Developing theabc-αβ -qd0 and inverse transformation blocks.
2. Using controlled current sources to inject the referencecurrents at stator or
grid frequency.
3. Tuning the PI controllers to computeId andIq the command currents by com-
paringPre f andQre f with Pgen andQgen respectively.
4. Demonstrating successful power tracking and decoupled control ofP andQ.
5. Developing and using a look up table approach to compute a referenceP and
referenceQ for a 1.8 MVA machine, 1.5 MW rated active power at rated wind
speed of 14.2 m/s.
Figure 5.9: Block diagram of DFIG model in SIMULINK
Stator voltage in theabc frame and at the grid frequency of 60 Hz and are
measured and transformed toαβ stationary frame to obtain two axis voltagesVα
91
andVβ fromVabc. Further, the voltage signals are integrated to obtain the flux along
αβ axis. A rotatingqd0 frame is then constructed and theq−axis aligned with
stator field. The newly createdqd0 frame rotates at the grid frequency or stator
frequency. With theqd0 frame constructed and sample input values for voltage
showing proper alignment of theq−axis with stator field, the next part of mod-
eling the DFIG includes, using current-controlled sources(representing induction
machine) to inject currents into the grid.
Figure 5.10: Block diagram forabc−αβ −qd0 tranformation
As such controlled sources are available in SIMULINK. Usingthe current
source blocks available in SIMULINK and an entire block modeling a three phase
voltage source as grid andpi sections representing transmission lines are used.
Given below is the specification for grid parameters and transmission line parame-
ters used initially.
Grid voltage =Vs = 34.5 kV
Grid frequency =fs = 60 Hz
MVA base = 100
92
X/R ratio = 10
Transmission line parameters for a three phase line are usedfor an equivalentpi
model of the line, whereC is the shunt capacitance andL is the series inductance
per km
R = 0.2568Ω/km
L = 2 mH/km
C = 8.6·10−3µF/km
Length of the line = 100 km
0 5 10 15 20−0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Time in seconds
Pow
er in
MW
/MV
ar
PgenQgen
Figure 5.11: Active power excursion
93
Table 5.1: Power trackingWind speed in m/s Active powerP in MW
6 0.1382327 0.3124858 0.5043399 0.69240110 0.86445611 1.0041312 1.1079613 1.1721614.4(rated) 1.215 1.216 1.217 1.218 1.219 1.220 1.2
A 3-φ multi-meter available in SIMULINK was used to measureIabc and
Vabc. A built-in complex power measurement unit is used to measure active and
reactive power. A PI controller is used to generateIqcmd andIdcmd command cur-
rents, by comparing the actual values of active power and reactive power with the
reference values respectively. Tuning of the PI controllers is performed using the
Ziegler Nichols method as explained before.
Once thePI controllers are tuned,Iqcmd and Idcmd command currents are
transformed using Inverse Park and Inverse Clarke transformto obtainIare f, Ibre f,
Icre f reference currents for the controlled current sources. As shown in Figure 5.11
P andQ can be controlled independently to achieve “Power factor correction” or
94
6 8 10 12 14 16 18 200
0.2
0.4
0.6
0.8
1
1.2
1.4
Time in seconds
Act
ive
pow
er in
MW
Pgen
Figure 5.12: Wind active power profile for the DFIG
“voltage regulation”, i.e. the wind turbine is set to maintain a desired power factor
or voltage at its terminals. To demonstrate active power tracking for a given wind
turbine, Table.5.1 is used to plot the power profile shown in Figure 5.12. Table.5.1
shows the amount of active power to be generated for a particular wind speed. The
Wind turbine used to obtain the power profile shown in the table below is rated at
14.4 m/s at+0.165 pitch angle and rated active power for the generator is 1.2 MW
(machine rated for 1.8 MVA). The maximum rated power obtained for the givenCp
vs λr a characteristic is 1.2 MW.
95
5.4 PSCAD/EMTDC complete DFIG Model
A wind turbine driven doubly-fed induction generator (DFIG) using back-
to-back converters is modeled in PSCAD/EMTDC. This section describes the mod-
eling of a back-to-back converter system for the DFIG using field oriented control
(FOC). The converters are modeled to be voltage source converters. The dynamic
performance of the DFIG for the changes in wind speed is demonstrated. The model
includes turbine’s aerodynamic, mechanical, and electrical components. Data for
the rotor, drive-train, and electrical generator are givento allow replication of the
model in its entirety.
Aerodynamic model and the drive train model of the wind turbine remains
the same. A full-blown converter model of the DFIG is implemented. This model
uses hystereris control to generate the switching signals for current regulated volt-
age source rotor side converter (inverter). It uses a PI controller to generate the
switching signals for the grid side converter (rectifier). Adetailed description of
the converter modeling is provided in the succeeding sections.
5.4.1 Rectifier
The two back-to-back converters (rectifier-inverter pair)allow bi-directional
flow of power between the grid and the rotor of the machine. Thegrid side converter
(rectifier) is responsible for balancing the power injectedinto the DC-link capacitor
versus the active power exchanged with the grid [2]. Rectifierat the grid side is
controlled in a manner, so as to achieve a constant link voltage across the DC link
capacitor. A relation between the DC-link voltage and theqd0- axis stator currents
96
and stator voltages is used to model the control and the firingcircuit for the rectifier.
Field oriented control, using Clarke and Park transforms, isused to obtain the actual
qd0-axis stator currents and stator voltages.
The desiredqd0 voltages to keep the DC-link voltage constant, are obtained
by comparing the actual value of the DC-link voltage with the set-point value (5.5
kV). The set-point value for the DC-link voltage is chosen keeping in mind the
peak-to-peak value of the rotor line-line voltage (Vr ). For a stator voltage ofVs =
0.575 kV and with a turns ratio of 0.3. The rotor side voltage is computed to beVr
= 1.9167 kV with a peak-to-peak value ofVrpp = 5.4 kV. Hence, a DC-link voltage
closest to this value is chosen i.e.Vdc = 5.5 kV.
EDCrefPI 1
Xc
PI 2+
-+
EDCactual
Idref
Idactualdq – abc
Transform
QrefPI 1
+
Qactual
Iqref
PI 2
-+
Xc
Iqactual
-
Vterm
+
+
-
-
-
Vdref
Vqref
Vabc_ref
-
PWM
Vabc_actual
IGBT firing
signals
Figure 5.13: Rectifier control [5]
A PI controller is used to obtain the desired values of the statorvoltages
in the qd0 frame as seen in Figure 5.13. The proportional gain (Kp) and integral
gain (Ki) constants for thePI controller are deteremined using the Ziegler-Nicols
method. These desiredqd0 voltages are then transformed to theabc frame by ap-
97
plying the inverse Park and Clarke transforms to fire the IGBTs.Figure 5.14 shows
the step-up transformer connected inwye gounded-wye groundedconfiguration (to
avoid the phase difference between the winding voltages) and the rectifier (mod-
eled with IGBT switches with anti-parallel diodes). Figure 5.15 shows the sim-
ulation block diagram for the rectifier control circuit and the inverse Park-Clarke
transform.
Gnode
A
B
C
A
B
C4.0
#2#1
0.69
1.0
1.0
E6
[oh
m]
IcA
IcB
IcC
VgA
VgB
VgC
VcA
VcB
VcC
D1 T1D1 D1
T1 T1D1 T1D1
T1T1
Ecap
T1g T3g T5g
D1
T4g T6g T2g
Gpos
Gneg
Figure 5.14: Rectifier model in PSCAD
D +
F
+ IdrefEcaprefD +
F
-
G1 + sTEcap G
sT1 + sT
I
P
D +
F
-
Id1
I
P
3.266
B
+
D -
F
+
Iq1
Vdref1
D +
F
-
QgenGref
QgenG
Kpssc
Tissc
I
P
iqref
0.0
*1.6 *1.6
D +
F
-
I
PD -
F
-
Vqref1G
1 + sT
A
B
Ctrl
Ctrl = 1
PI controller stage 1
D +
F
+ IdrefEcaprefD +
F
-
G1 + sTEcap G
sT1 + sT
I
P
D +
F
-
Id1
I
P
3.266
B
+
D -
F
+
Iq1
Vdref1
D +
F
-
QgenGref
QgenG
Kpssc
Tissc
I
P
iqref
0.0
*1.6 *1.6
D +
F
-
I
PD -
F
-
Vqref1G
1 + sT
A
B
Ctrl
Ctrl = 1
PI controller stage 1
PI controller stage 2
Low pass filter
PI controller stage 1
Control for DC link voltage
Control for reactive power
PI controller stage 2
Low pass filter
Vdref1
Vqref1
Y
X
MP
M
PY
XY
X
M X
P Y
MP
vqref
vdref
phi
Varef
Vcref
Vbref
theta
d
qStationary
alpha
beta
(d,q)
(alpha,beta)
Rotating
a
b
c
Inverse
Transform
alfa
beta
Clarke
zero
0.0
qd0 –αβ –abc frame
transformation
Figure 5.15: PSCAD block diagram for rectifier control circuit
98
5.4.2 Inverter
The rotor side converter(inverter) of the DFIG is connectedto the grid side
converter(rectifier) through a DC link capacitor (100 mF). The value of capacitance
is chosen by trial and error. Any value between 10 mF - 1000 mF can be chosen
depending on the stability of the system. Assuming, that therectifier maintains a
constant DC-link voltage, the role of the inverter is to inject rotor frequency (vari-
able) currents into the rotor circuit and thus achieving decoupled active and reactive
power control. As explained in the previous section stator active and reactive power
are proportional to rotorqd0 currents. With change in wind speed, slip changes and
thus the frequency of the rotor currents [2].
Actual active power (Pgen) is compared with the set-point value (Pgenre f)
which is determined by the wind speed. API controller is used, as seen in Figure
5.17, to generate the required value ofIqr. Similarly, for the reactive power, aPI
controller is used to generate the requiredIdr [3]. The proportional gain (Kp) and
integral gain (Ki) constants for thePI controller were determined using the Ziegler-
Nicols method. These values ofIqr andIdr are transformed back into theabcframe
to obtain the required value of rotor currents. Also seen in the Figure 5.17, is a
hysteresis controller used to generate the switching sequence for the IGBT switches
in the rotor side converter. Required rotor currents obtained in theabc frame are
thus generated by using hysteresis control. A hysteresis band of 0.1% is used for
the hysteresis controller.
99
Pref
PI+
+
Pactual
QrefPI
+
Qactual
Iqref
Iar_act
-
+
+
--
-
Iar_ref
Ibr_ref
Ic_ref
dq – abc Transform
-
Ibr_act
Icr_act
IGBT firing signals
Idref
Figure 5.16: Inverter control [5]
Pgen
PgenRef
B
+
F
-I
P
PgenERR Iqr_target
Active power control
Qgen B
+
F
-I
P
QgenERR Idr_target
Qdesired
T1r
T4r
T2r
T5r
T3r
T6r
C-
D +
C-
D +
C-
D +
Ira_ref
Irb_ref
Irc_ref
IrA
IrB
IrC
G1 + sT
G1 + sT
Reactive power control
Hysteresis control
Iripple = 0.1 %
Kp = 1.5Ki = 0.5
Figure 5.17: PSCAD block diagram for inverter control circuit
5.4.3 Grid model
The grid is simulated as an ideal voltage source (R = 0Ω) at 34.5 kV, 10
MVA. A delta-wye groundedtransformer rated at 0.575/34.5 kV and 2 MVA is
used to connect the machine stator to the voltage source representing grid. Figure
5.18 shows the complete PSCAD simulation block diagram for the DFIG (induction
machine, back-to-back converter), circuit breaker, connection transformer and the
100
grid.
1.0
wGenpu
AeroTpu
S
TL
I M
W
Rectifier
Gnode
10
00
00
.0 [u
F]
Vs
R=0#1 #2
WTbrk
4.0252.113
TimedBreaker
LogicClosed@t0
WTbrk
Inverter
Rnode
Is
0.0
01
[oh
m]
Figure 5.18: Block diagram for DFIG using back-to-back converters in PSCAD
5.4.4 Results
Field data for a GE 1.5 MW DFIG turbine [1] has been used to simulate the
model. The output power versus turbine speed set point (tssp) is used to determine
the wind speed versus active power curve for the turbine. Table.?? shows the de-
sired active power at the corresponding wind speed for a tsspvalue. The maximum
allowable turbine speed is 1.4 p.u. The WTGS is rated at 1.5 MW for a rated wind
speed of 14 m/s.
An expected power and speed profile, obtained from Table.?? is plotted in Figure
5.19. A rated active power of 1.5 MW is expected at a rated windspeed of 14 m/s.
As can be seen from the speed profile, maximum allowable generator speed is 1.4
p.u.
The DFIG was simulated for varying wind speed and change inQ require-
101
Table 5.2: GE 1.5 MW DFIG turbine field data [1]
Wind speed in m/s Turbine speed set point in p.u (ωgen) Active power in p.u.
5.5 0.69 06.5 0.78 0.27.3 0.9 0.38 0.98 0.49.1 1.12 0.610 1.17 0.712 1.2 0.914 1.27 1.018 1.38 1.020 1.4 1.0
ment:
• DFIG simulation run for wind speed sweep from 6 m/s to 20 m/s.
• Power factor correction with a step change inQ from 0-1 Mvar in steps of 0.2
Mvar.
DFIG simulation run for wind sweep from 6 m/s to 20 m/s
As seen in the Figure 5.20 the wind speed is varied from cut-inspeed (6 m/s) to
cut-out speed (20 m/s) in steps of 1 m/s. The overshoot transient seen in the power
profile of Figure 5.20 is due to the simulation start-up. Reactive powerQ is main-
tained at 0 Mvar. The active powerP is found to increase till the the wind speed
reaches 14 m/s (rated wind speed), at which rated generator output (1.5 MW) is
obtained. For further increase in wind speed above 14 m/s thegenerator output re-
mains at 1.5 MW as expected. It can be verified that there is decoupled control of
102
6 7 8 9 10 11 12 13 14 15 16 17 18 19 200
0.3
0.6
0.9
1.2
1.5
1.8
Wind speed in m/s
Act
ive
pow
er in
MW
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Wind speed in m/s
ωge
n in
p.u
.
Figure 5.19: Expected active power and speed profile for the DFIG model simula-tion
active and reactive power.
DFIG simulation run for p.f. correction
In Figure 5.21 the wind speed is maintained at a constant value of 14 m/s (rated
wind speed). Power factor correction is simulated by varying the reactive powerQ
from 0 Mvar to 1 Mvar in steps of 0.2 Mvar. From the graphs it is easily verified
that as the reactive powerQ varies the active powerP remains constant. Thus, there
103
0 5 10 15 20 25 30 35 40 45 50−1
0
1
2
P in
MW
0 5 10 15 20 25 30 35 40 45 50−1
0
1
2
Q in
Mva
r
0 5 10 15 20 25 30 35 40 45 50−2
−1
0
1
τ gen in
p.u
0 5 10 15 20 25 30 35 40 45 500.5
1
1.5
ωge
n in
p.u
0 5 10 15 20 25 30 35 40 45 500
7
14
21
Simulation time in seconds
Vw
ind
in m
/s
Figure 5.20: DecoupledP-Q control with variable wind speed, Q = 0 Mvar
is decoupled control of active and reactive power. Comparingthe active power and
speed profile in Figure 5.19 and Figure 5.20 it can be seen thatthe model’s dynamic
performance is as expected.
DC link capacitor voltage and hysteresis control
104
0 5 10 15 20 25 30 35 40 45 50−2
0
2
P in
MW
0 5 10 15 20 25 30 35 40 45 50−1
0
1
2
Q in
Mva
r
0 5 10 15 20 25 30 35 40 45 5013
14
15
Simulation time in seconds
Vw
ind
in m
/s
0 5 10 15 20 25 30 35 40 45 50−1.5
−1
−0.5
0
τ gen in
p.u
Figure 5.21: DecoupledP-Q control with step change of 0.2 Mvar inQ
From Figure 5.22(a) the DC link voltage is maintained at a constant value of 5.5
kV. Figure 5.22(b) shows the rotor current generated when the hysteresis control is
applied. Comparing the actual generated current and the reference wave we see that
the hysteresis controller is working as required and follows the reference signal.
105
0 5 10 15 20 25 30 35 40 45 50−1
0
1
2
3
4
5
6
7
Simulation time in seconds
DC
link
cap
acito
r vol
tage
in k
V
E
cap
(a) DC link capacitor voltage
25 25.5 26 26.5 27 27.5 28 28.5 29 29.5 30−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
Simulation time in seconds
Rot
or c
urre
nt in
kA
Actual rotor current phase aReference rotor current phase a
(b) Rotor currents generated using the hysteresis controller
Figure 5.22: DC link capacitor voltage and the actual rotor current
5.5 Reactive power capability of the DFIG
The operation of a DFIG can be characterized by the active power supplied
to the grid, the total reactive power produced/absorbed from the grid and the stator
voltage. In the preceeding sections, significant work has been done in modeling
106
the DFIG using PSCAD and MATLAB. The models have evolved from being a
regulated currrent-source model to a model, which involvesthe actual machine and
back-to-back converters. As discussed earlier, the chief advantage of a DFIG is its
capability to achieve independent control of active and reactive power. Delivering
reactive power without affecting the active power output toachieve power factor
correction and voltage regulation makes a DFIG far more marketable than its pre-
decessors [22].
Operating limits of the DFIG can be characterized by theP-Q relationship
under constant stator voltage. The stator voltage of the DFIG is assumed to remain
constant at 1 p.u. With this assumption the reactive power capability of the DFIG
and the power converters are limited in terms of rotor current and stator current.
The rotor current and stator current limitations are evaluated for the given machine
data. The relation between the maximum stator/rotor currents and theQ limits have
been derived. TheQ limits are found for the given machine data in Appendix A of
the report. In order to plan the reactive power capability ofwind farms as required
by recent changes in the grid code. It is crucial to determinethe reactive power limit
band (maximumQ - minimum Q) of a DFIG. This section discusses theQ limits
and the parameters affecting theQ limits.
5.5.1 Analysis of Rotor Current Limits
The fundamental steady-state equations for the DFIG [23] are given the Eq.
5.3 - Eq. 5.8.
107
Vs = jωsλs (5.3)
whereVs is the stator terminal voltage,ωs is the stator angular frequency andλs is
the stator flux linkage.
Vr = Rr Ir + j(ωs−ωr)λr (5.4)
whereVr is the rotor terminal voltage,ωr is the rotor angular frequency,Ir is the
rotor current,Rr is the rotor resistance andλr is the rotor flux linkage.
λs = LsIs+LmIr (5.5)
λr = Lr Ir +LmIs (5.6)
whereLs is the stator inductance,Lr is the rotor inductance,Lm is the magnetizing
inductance andIs is the stator current [23]. Substituting the flux relation inEq. 5.3
and Eq. 5.4, we get
Vs = jωs(LsIs+LmIr) (5.7)
Vr = Rr Ir + jsωs(Lr Ir +LmIs) (5.8)
Thus, the equivalent circuit corresponding to Eq. 5.7 and Eq. 5.8 is shown
in Figure 5.23
108
Vs Vr/s
Is Ir
jωLm
jωLσs jωLσrRs Rr
+ +
- -
Figure 5.23: Steady state per phase equivalent circuit of induction machine
By using the flux oriented control theory, in thedq0 frame, rotating at syn-
chronous frequency and by neglecting the stator resistanceRs. The expressions for
active and reactive power are obtained (Eq. 3.37 - Eq. 3.38).From the active power
and reactive power equations indq0 frame, maximum rotor current values along
thedq axis can be obtained as : SubstitutingVqs = -λs · ωs andLs = Lls + Lm in the
active-reactive power equation indq0 frame (Eq. 5.9 - Eq. 5.10)
Ps =32
ωsλsLmirq
(Lls +Lm)(5.9)
Qs =−32
ωsλs(λs−Lmidr
Lls +Lm
)
(5.10)
Simply by rearranging Eq . 5.9 and Eq. 5.10 and rewriting in terms of ird andirq,
Eq. 5.11 and Eq. 5.12 are obtained.
ird =2LsQs
3VqsLm+
Vqs
ωsLm(5.11)
109
irq =2LsPs
3VqsLm(5.12)
Ir =√
i2rd + i2rq (5.13)
From Eq. 5.11, Eq. 5.12 and Eq. 5.13
Irmax≤√
( 2LsQs
3VqsLm+
Vqs
ωsLm
)2+(
2LsPs
3VqsLm)2 (5.14)
wherePs andQs are the stator active and reactive power respectively. FromEq. 5.14
minimum and maximum value of reactive power can be determined for a maximum
rotor current ofIrmax. Generally, a maximum rotor current of 1.2 p.u. is allowed
[22].
Qsmaxr≤−3V2
qs
2ωsLs+
√
(3LmVqsIrmax
2Ls
)2−P2s (5.15)
Qsminr≥−3V2
qs
2ωsLs−
√
(3LmVqsIrmax
2Ls
)2−P2s (5.16)
whereQmaxr is the maximum reactive power that can be delivered by the DFIG,
without exceeding the rotor current limit andQminr is the maximum reactive power
absorbed by the DFIG. Figure 5.24 shows theP-Q relationship calculated for the
DFIG model implemented in PSCAD.Sbase= 2 MVA, Vbase= 575 V, Lm = 2.904
p.u.,Ls = 0.1714 p.u.,Irmax = 1.2 p.u.
110
0 0.5 1 1.5−3
−2
−1
0
1
2
3
Active power in MW
Rea
ctiv
e po
wer
in M
var
Qmaxr
Qminr
Rotor current limit =1.2 p.u.
Figure 5.24:Q limit band for maximum rotor current
Consider the plot obtained in Figure 5.24. It shows the maximum reactive
power produced and maximum reactive power absorbed by the DFIG for a partic-
ular value of stator active power. Since, the rectifier (gridside converter) of the
back-to-back converter pair is operating at unity power factor. Therefore, the sta-
tor of the DFIG produces or absorbes all the reactive power. It can be seen from
the Figure 5.24 for an active power demand ofPs = 0.5 MW, the DFIG can pro-
duce a maximum reactive powerQmaxr = 1.62 Mvar and can absorb a maximum
reactive power ofQminr = -1.62 Mvar. These values of reactive power delivering
and absorbing capacity of the DFIG are calculated under a maximum rotor current
condition.
111
5.5.2 Analysis of Stator Current Limits
Stator current limitation for a DFIG is fairly straight-forward to find, as
compared to rotor current limitation. The total apparent power delivered by the
DFIG stator, assuming stator terminal voltage remains constant is given by :
Ss = VsI∗s (5.17)
The relation between stator apparent power, active and reactive power is :
S2s = P2
s +Q2s (5.18)
From Eq. 5.17 and Eq. 5.18, maximum and minimum reactive power delivered by
the DFIG stator can be computed as:
Qmaxs≤√
(VsIsmax)2−P2s (5.19)
Qmins≥−√
(VsIsmax)2−P2s (5.20)
Eq. 5.19 and Eq. 5.20 form theQ limit band for maximum stator current condition.
Figure 5.25 shows theP-Q relationship plot for a maximum stator currentIsmax=
1.5 p.u.
Consider the plot obtained in Figure 5.25. Similar to the rotor current limit
analysis, the plot shows the maximum reactive power produced and absorbed by the
DFIG for a particular active power demand. For example, the DFIG can produce
112
0 0.5 1 1.5−3
−2
−1
0
1
2
3
Active power in MW
Rea
ctiv
e po
wer
in M
var
Qmaxs
Qmins
Statorcurrentlimit =1.5 p.u.
Figure 5.25:Q limit band for maximum stator current
a maximum reactive power ofQmaxs= 2.06 Mvar and absorb a maximum reactive
power ofQmins = -2.06 Mvar for an active power demand ofPs = 0.5 MW. These
values of the maximum reactive power delivered and absorbedby the DFIG are
obtained under maximum stator current condition.
From Figure 5.24 and Figure 5.25 actual boundaries for reactive power delieverd
by the DFIG can be calculated as :
Qsmax= Minimum Qmaxr, Qmaxs
Qsmin = MaximumQminr, Qmins
Figure 5.26 shows the actual actual boundaries of the reactive power produced/absorbed
by the DFIG, governed by rotor and stator current limits. It is obtained by combin-
ing the maximum rotor and stator current conditions. It can be seen from the Figure
5.26, that a maximum reactive power ofQmax= 1.62 Mvar can be produced, while a
113
maximum ofQmin = -2.06 Mvar absorbed by the DFIG for an active power demand
Ps = 0.5 MW.
0 0.5 1 1.5−3
−2
−1
0
1
2
3
Active power in MW
Rea
ctiv
e po
wer
in M
var
Qmaxr
Qmins
Irmax
<= 1.2 p.u
Ismax
<= 1.5 p.u
Figure 5.26:Q limit band for maximum rotor and stator currents
5.5.3 Verification ofQ limits for the PSCAD DFIG model
For the PSCAD DFIG model two scenarios of wind sweep were considered:
1. Wind speed above rated to cut-out i.e. 14 m/s - 20 m/s.
2. Wind speed from cut-in to rated i.e. 6 m/s - 14 m/s.
The model was run at a fixed wind speed of 14 m/s and the active power
demand changed from 0.1 MW to 1.5 MW in steps of 0.1 MW. The rotor current
limits were imposed to find out the maximum reactive power produced by the DFIG
at a particular active power demand. A maximum rotor currentof 1.2 p.u was set, at
114
Sbase= 2 MVA, Vbase= 0.575 kV, and stator to rotor turns ratio of 0.3. With the given
value of base MVA and base voltage, a maximum rotor currentIrmax = 0.7229 kA
was calculated from Eq. 5.21 Now, maximum the reactive powerproduced (within
rotor current limits) for active power demand from 0.1 - 1.5 MW was recorded as
shown in the Table 5.3.
Irmax = 1.2· 0.3·Sbase√3Vbase
(5.21)
Ps Qsmaxat 14 m/s Qsmaxat 9m/sin MW in Mvar Mvar
0.1 1.6 1.850.2 1.55 1.80.3 1.5 1.750.4 1.42 1.680.4 1.37 1.60.6 1.32 1.520.7 1.28 1.420.8 1.25 1.280.9 1.2 1.11.0 1.1 0.91.1 1.05 NA1.2 0.95 NA1.3 0.9 NA1.4 0.8 NA1.5 0.65 NA
Table 5.3: Maximum reactive produced at 14 m/s and 9 m/s with step change of 0.1MW
Active power limit at 9 m/s wind speed is determined to be 1 MW,hence
the corresponding reactive power limit is not obtained in Table 5.3. For the sake of
115
comparison, Table 5.3 also shows the maximum reactive powerrecorded at a fixed
wind speed of 9 m/s. Such a comparison enables us to investigate the difference
between the reactive power delivering capacity of the DFIG during “flat” active
power profile (above rated wind speed) and during the “power climb” (between
cut-in wind speed and rated wind speed).
Consider, Figure 5.27. A comparative plot showing the calculated limit of
reactive power production capacity of the DFIG with the actual reactive power pro-
duced at two different wind speeds is shown in Figure 5.27. Itcan be seen from the
plot, that the calculated value of reactive power limits is close to the reactive power
limits obtained at 14 m/s. The reactive power limits obtained at 9 m/s wind speed
is higher (maximum reactive power delivered higher) at the same active power de-
mand. This continues tillPs = 0.5 MW. AbovePs = 0.5 MW, if the active power
demand is further increased, the reactive power limit decreases rapidly at 9 m/s, 14
m/s and calculated, in the same chronological order.
A comparative plot shown in Figure 5.27 can prove helpful in determining
the operating mode of the DFIG. For low wind speeds, i.e. below rated wind speed
(Vwind ¡ 14 m/s) the DFIG can be operated at low active power demand and high
reactive power demand. Such, an application will find its useas a STATCOM.
In Figure 5.28 a comparative plot between the calculated andthe recorded
values of the maximum reactive power delivered by the DFIG isshown. The reac-
tive power limit values are determined at 14 m/s (rated wind speed). It can be seen,
that the recorded values are close to the calculated values.
116
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−3
−2
−1
0
1
2
3
Rea
ctiv
e po
wer
in M
var
Active power in MW
Qmax
calculated
Qmax
at 9 m/s
Qmax
at 14 m/sQ
max calculated
Irmax
<= 1.2 p.u
Qmax
at 14 m/sQmax
at 9 m/s
Figure 5.27:Q limit comparison between calculated, at 9 m/s and at 14 m/s windspeed
In Figure 5.29 a comparative plot between the calculated andrecorded val-
ues at 9 m/s wind speed is shown. Comparing Figure 5.28 and Figure 5.29, the
reactive power delivered by the DFIG at wind speed below rated is clearly above
both the calculated values and the ones recorded at 14 m/s wind speed.
Figure 5.30 shows the comparison between reactive power limits at two dif-
ferent wind speeds. In a more general sense, it is the comparison between reactive
power limits above and below rated wind speed. It can be seen,that the reactive
power cabability of the DFIG is certainly higher at low wind speeds. But it only
remains higher tillPs = 0.5 MW, afterPs = 0.5 MW, the maximum reactive power
117
0.2 0.4 0.6 0.8 1 1.2 1.4
0.8
1
1.2
1.4
1.6
1.8
2
Active power in MW
Rea
ctiv
e po
wer
in M
var
Q
max calculated
Qmax
at 14 m/s
Irmax
<= 1.2 p.u
Figure 5.28:Q limit comparison between calculated and at 14 m/s wind speed
available at 9 m/s is lower than that available at 14 m/s. The capability of the DFIG
to produce reactive power at different active power demandshas been verified with
the calculated values. It can be also seen from Figure 5.27, the maximum reactive
power limit of the DFIG increases at lower wind speeds. Such an increase in the
reactive power delivering capacity of the DFIG can be attributed to reduction in
the active power produced. Reactive power limit above rated wind speed for the
PSCAD modeled DFIG is verified against the calculated values.The stator current
limit was never exceeded, as should be the case. The limit forminimum reactive
power delivered by the DFIG could not be verified with the PSCADmodel owing
to model limitations.
118
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Active power in MW
Rea
ctiv
e po
wer
in M
var
Q
max calculated
Qmax
at 9m/s
Irmax
<= 1.2 p.u
Figure 5.29:Q limit comparison between calculated and at 9 m/s wind speed
5.6 Simulation : Regulated Current-Source DFIG model
This section discusses, the simulation process of theRegulated current-
source DFIG model. Understanding the simulation is important in the overall un-
derstanding of model function. It is important, that the simulation steps be described
for a complete understanding of the model results and their significance. It also
helps in getting accoustomed to the software platform in use(MATLAB/SIMULINK).
5.6.1 Objective
This simulation of the current-source model (CSM) of a DFIG has two ob-
jectives :
119
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
Active power in MW
Rea
ctiv
e po
wer
in M
var
Q
max at 9 m/s
Qmax
at 14 m/s
Irmax
<= 1.2
p.u
Figure 5.30:Q limit comparison between 14 m/s and at 9 m/s wind speed
1. To plot the active power profile of the DFIG for the entire wind sweep from
6 m/s - 20 m/s.
2. To demonstrate decoupled control of active (P) and reactive power of a DFIG.
5.6.2 Discussion
A doubly-fed induction generator (DFIG) is a type of induction genrator,
whose rotor is excited by injecting variable frequency current. Since, it is fed both
from stator and rotor, hence the namedoubly- f ed. A DFIG system not only con-
sists of a doubly-fed induction machine, but also of a back-to-back converter pair.
The converter that is connected to the stator is arecti f ier, while the one that is con-
120
nected to the rotor is aninverter. There is also a DC-link capacitor between the two
converters. This DC-link is used to keep the input voltage of the inverter constant
or stiff. Shown in Figure 5.31 is the schematic representation of the DFIG wind
turbine.
Control
System
DFIG
Generator
Grid
Gear Box
Stator
connection
Rotor
connection
AC AC
DC DC
Power Electronic Converters
Figure 5.31: DFIG Wind Turbine Schematic [3]
A DFIG wind turbine is capable of independently controllingthe active and
reactive power output fed to the grid. Such a capablity of theDFIG can be used
for power factor correction and voltage regulation. The DFIG system is fairly com-
plicated. In order to simplify and demonstrate its control mechanism, a regulated
current source model is used. A regulated current-source model of the DFIG mim-
ics the complete model as seen in Figure 5.32. Representing the DFIG as a regu-
lated current-source, helps to focus on field oriented control. Field oriented control
(FOC) is used to obtain the reference currents to be injected into the rotor windings
of the induction machine.
121
AC
AC
AC
pi section of the line
3-Ф AC grid
Regulated current -source representation
of the DFIG
Ia_ref
Ib_ref
Ic_ref
Figure 5.32: Schematic diagram of regulated current-source representation of theDFIG
Field oriented control
Flux-vector control allows the decoupled control of real and reactive power.
The wound rotor induction machines are used in DFIG wind turbines. In the sta-
tionary abc reference frame, the relationships between the voltages, currents and
flux linkages of each phase for a machine of this type are time variant. Analysis
in this reference frame is cumbersome, so time variant quantities are made time in-
variant by transforming them into an appropriate rotating reference frame, i.e. the
rotatingqd0 reference frame.
The currents flowing in the stator are assumed to be balanced.These cur-
rents produce a resultant stator magnetic field which has a constant magnitude and
is rotating at synchronous speed. Since the angular speeds of the stator magnetic
field and theqd0 rotating frame are identical, the vector of the stator magnetic field
is fixed with respect to theq− andd− axes of theqd0 rotating frame. Thed−axis
of the reference frame is oriented in such a way that it alignswith the vector of the
stator magnetic field. The real and reactive power can be controlled by adjusting the
122
statorq− andd−axis current. The statorq− andd−axis currents can be controlled
by adjusting the rotorq− andd−axis currents. The stator real and reactive power
can thus be written as:
Ps = kps· i′qr (5.22)
Qs = −kqs1 +kqs2 · i′qr (5.23)
wherekps, kqs1, andkqs2 are the respective constants for the stator real and reactive
power. Equations 5.22 and 5.23 clearly show that the stator real and reactive power
can be controlled by the rotorq− andd−axis currents independently. An inverse
Park-Clarke transform of theq− andd−axis currents is performed to obtain the
reference currents inabcframe (Iare f, Ibre f, Icre f).
Obtain reference currents
To obtain the reference currents for the current source following steps are
performed :
1. Perform Clarke Transform (abc-αβ ): Grid voltageVsa, Vsb, Vsb are converted
from three-axis (abc) quantities to two-axis quantities (αβ ) Vα andVβ by
performing Clarke transform. Obtained two-axis voltages are integrated to
obtain corresponding flux values (λα , λβ ). Instantaneous value of stator flux
λs , its magnitude and angular position are determined.λtotal = |λs| = con-
stant, whereas the angular position being an instantaneousvalue it keeps on
123
varying during the simulation run time. Thus, we obtain a constant magnitude
rotating vectorλs.
2. Perform Park Transform (αβ - qd0): A synchronously rotating frameqd0 at
synchronous speedωs is constructed and stator flux aligned alongQ axis to
obtain|λq| = |λs| = constant, and|λd| = 0.
3. Value of reference currents to be given to the regulated current-source is
found out, by comparing the generated power with reference power values.
The PI controllers are then fed the error signal (difference between actual
power and reference power). The controllers are tuned usingZieglor nicols
control algorigthm. Figure 5.33 shows the block diagram forobtained the
reference currents.
Pref
PI+
Pactual
QrefPI
+
Qactual
Iqref
-
-
Ia_ref
Ib_ref
Ic_ref
qd0 – abc Transform
Idref
Figure 5.33: Block diagram for obtaining the reference currents
124
5.6.3 To plot the power profile of a DFIG
1. To run the simulation file, open the DFIGregulatedcurrentsource.mdl with
MATLAB
2. In the model window observe the various blocks such as the voltage source,
regulated current source, power measurement block, Clarke-Park transform
block. Double-click on each block and observe the sub-components involved.
Also, note down the transform equations.
3. Take a note of the ratings of the 3-φ voltage source and thecoupled− pi sec-
tion and note down the values
Vll = kV
Phase angle of Phase A =
Frequency = Hz
X/R ratio =
R/km = Ω/
L/km = mH
C/km = µ/km
Total length = km
4. Shown in Figure 5.34 is the model in SIMULINK. Locate the wind speed
variable and set the wind speed to 0 m/s. The value can be set bydouble-
clicking the Wind speed variable block shown in the block diagram.
125
5. Start the simulation by clickingRun located on the runtime toolbar of the
window.
powergui
Continuous
angle
Wind speed
15
Vwind
Vabc
Vabc
Three -Phase Source
A
B
C
Q gain
100000
Power measurement
Field anlge
Active Power
Reactive power
Pi Section Line C
Pi Section Line B
Pi Section Line A
P gain
100000
P and Q
Multimeter
A
B
C
a
b
c
Inverse Park and Clarke Transform
Iqcmd
Idcmd
angle
Ia_ref
Ib_ref
Ic _ref
Iabc
High R in parallel
A B C
A B C
Desired Reactive power
2
Controlled Current Source phase C
s
-+
Controlled Current Source phase B
s
-+
Controlled Current Source phase A
s
-+
Command Currents
Pgenref
Pgen
Qgenref
Qgen
Iqcmd
Idcmd
Clarke-Park Transform
Vabc angle
Active Power profile 1.2 MW
Figure 5.34: SIMULINK block diagram of the DFIG
6. Observe the active power on the display block coming out ofthe power mea-
surement block. The power measurement block measures, active and reactive
power fed to the grid.
7. You can see that, the active power fed to the grid is negative. Now increase
the wind speed in steps of 1 m/s unless you see positive value of active power
8. Wind speed at which active power generated is poisitive isknown as cut-in
wind speed. Note the corresponding value of wind speed. Cut-in wind speed
126
= m/s.
9. Increase the wind speed until rated power is generated, and the active power
display shows (1.2 MW). Note the corresponding wind speed. Rated wind
speed =
10. Increase the wind speed till you reach 20 m/s. At high windspeeds the me-
chanical stresses are very high on the turbine. Consider thisto be the cut-out
wind speed.
11. Generate the active power profile by recording active power values at wind
speeds starting from cut-in to cut-out speed. Plot the active power values
against wind speed in Excel or MATLAB. Record your values in thefollow-
ing table.
5.6.4 To demonstrate decoupled control of active (P) and reactive power (Q)
1. Similar simulation run can be performed to demonstrate decoupled control of
active and reactive power.
2. Open the DFIGregulatedcurrentsource.mdl with MATLAB
3. Run the model at rated wind speed and change the reactive power demand
in steps of 0.1 Mvar. Simultaneousy note down the corresponding value of
active power generated and reactive power generated.
4. Run the model again, at rated wind speed. In this simulationrun, keep the
reactive power demand at 1 Mvar and change the active power insteps of 0.1
127
Wind speed in m/s Active power in MW
MW (note you can only reduce the active power demand from 1.2 MW to 0
MW). Also note down the corresponding values of active and reactive power.
5. You might have observed that, along with the scope there are someTo workspace
blocks connected for measuring the generated active and reactive power. These
blocks transmit the variable to the workspace of MATLAB.
6. Once, in MATLAB workspace, the values are recorded as samples. It means
that you will find a N X 1 vector with the corresponding variable name in
MATLAB workspace. e.g. active power is stored asPgen and reactive power
is stored asQgen.
7. You can plot these sample values ofPgenandQgenagainst a time vector with
128
the same length i.e N X 1.
8. A time vector can be generated by using “t = 0:(time step):len(Pgen)”. Once,
you have the time vector, by using “plot” command on MATLAB command
prompt. Plottimevs Pgen andtimevs Qgen on the same figure.
Conclusion
129
Chapter 6
Summary and Future Work
6.1 Summary
Model implementation of three wind turbine technologies Type-I (fixed speed),
Type-II (dynamic rotor resistance control), Type III (Doubly-fed induction gener-
ator) has been done on PSCAD/EMTDC and MATLAB. As one of the objective,
this thesis has successfully covered topics starting from capture of kinetic energy in
air molecules electricity conversion through induction machine. Aerodynamics re-
lated to the wind turbine rotor, gear-box complexity and finally induction machine
have been explained. Before we start with actual modeling of the wind turbines,
theoretical concepts involved in modeling the rotor, gearbox and the machine itself
have been explained.
Model implementation and simulation run results have also been showcased
to demonstrate the validity of the models. Some PSCAD/EMTDC models were also
replicated in MATLAB/SIMULINK and similar results obtained. In-depth analysis
of Type-I, Type-II and Type-III wind turbines has been performed. Tuning of con-
trollers, through the Ziegler nichols iterative algorithmhas been explained. Some
analysis, showing the differences between “constant power” and “constant current”
strategy for Type-II wind turbine has been performed and results drawn.
130
Doubly-fed induction generators have been given special attention, with one
chapter devoted completely to their theory and modeling. Flux-vector control and
reference frame transformation used for controlling the DFIG has been explained.
Regulated current-source model of the DFIG is implemented inPSCAD and MAT-
LAB. Reactive power capablity of the DFIG has been determined.Its relation to
the rotor current and stator current limits has been established. Such current limits
can be implemented in future models for the sake of completeness and to asses the
utility of DFIG turbines for power factor correction and voltage regulation.
Simulation experiments based on regulated current-sourcemodel of the DFIG
have been created. These experiments can be included in undergraduate coursework
teaching wind turbine modeling and simulation. The simulation experiments have
been designed keeping in mind the basic concepts involved inthe functioning of
the DFIG. They also verify flat active power profile (above rated wind speed) and
independent P-Q control for the DFIG.
6.2 Future Work
There is a lot of scope for future model development and implementation.
Type-IV (full-converter) has not been modeled for this thesis work. Type-IV model
brings along an option of using synchronous machines, whichcan operate at low
rotor speeds (low rpm) thus eliminating the need for a gear-box. Since, for a Type-
IV wind turbine it machine type (synchronous/induction) differences if any, can be
investigated.
Stability limit remains to be applied for determining the reactive power
131
capability of the DFIG. There is still scope for model implementation in MAT-
LAB/SIMULINK. Dynamic rotor resistance control, using a converter on the rotor
side instead of real-resistors can also be implemented. As it replicates real wind
turbine control used in Type-II wind turbines.
132
Appendices
133
Appendix A
Machine specifications
Poles 6Rated voltage (l-l) 690 V
Rated power 1.8 MVABase angular frequency 376.99 rad/sStator/rotor turns ratio 0.379
Angular moment of inertia 0.578 sStator rotor resistance 0.0054 p.u.Wound rotor resistance 10−6 p.u.Magnetizing inductance 6.83309 p.u.
Stator leakage inductance 0.08 p.uRotor leakage inductance 0.04782 p.u.Nominal frequency [Hz] 60 Hz
Nominal mechanical power [MW] 1.5 MWGenerator pole pairs 3
134
Appendix B
Drive-train model Specifications
Jrot Rotor moment of inertia [kgm2] Jrot = 4,950,000 kgm2
Jgen Generator moment of inertia [kgm2] Jgen = 80 kgm2
Jq2 Gearbox moment of inertia [kgm2] Jq2 = 15 kgm2
Krq1 Spring constant rotor shaft [Nm/rad] Krq1 = 9,800,000 Nm/radKq2g Spring constant generator shaft [Nm/rad]Kq2g = 2,950,000 Nm/rad
Drot Damping rotor [Nms/rad] Drot = 0 Nms/radDrot Damping gearbox [Nms/rad] Dq2 = 2.4 Nms/radDrot Damping generator [Nms/rad] Dgen = 0 Nms/radDrot Damping rotor shaft [Nms/rad] Drq1 = 13500 Nms/rad
Drot Damping generator shaft [Nms/rad] Dq2g = 30 Nms/rada Gear ratio a = 70
135
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Vita
Mithunprakash G Vyas was born in Warangal, India on 23 June 1985, son
of Rama Vyas and Govindprasad Vyas. After completion of his high school educa-
tion from Bishop Cotton School, Nagpur, he received the Bachelor of Technology
degree from Motilal Nehru National Institute of Technology(MNNIT), Allahabad
in November 2007. During his undergraduate studies, he worked with major indus-
trial and heavy electrical manufacturers in India including Hindustan Aeronautics
Limited, Nashik and Bharat Heavy Electricals Limited, Bhopal. He was also re-
cruited as graduate engineer trainee (GET) and worked for 1 year (July 2007 - June
2008) with Reliance Energy Limited, Noida. His work as a GET was focussed on
project management of utility scale power generation. In Reliance Energy Limited,
he gained valuable experience in project planning and budgeting. In fall 2008, he
joined the master’s degree program in the Electrical and Computer Engineering de-
partment at The University of Texas At Austin. During his master’s he was involved
in wind power research and modeling projects under the supervision of Dr. Surya
Santoso.
Permanent address: Shri Nilay SA-109 Gyandeep AptsNagpur, India 440013
This thesis was typeset with LATEX† by the author.
†LATEX is a document preparation system developed by Leslie Lamport as a special version ofDonald Knuth’s TEX Program.
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