PhD Thesis_Md. Ayaz Chowdhury
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Impact of Wind Energy Systems on Power System Dynamics and Stability By Md. Ayaz Chowdhury A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy Discipline of Electrical, Electronic and Computer Systems Faculty of Engineering & Industrial Sciences Swinburne University of Technology Hawthorn, Victoria, Australia March, 2013
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Transcript of PhD Thesis_Md. Ayaz Chowdhury
Impact of Wind Energy Systems on Power System Dynamics and Stability
By
Md. Ayaz Chowdhury
A thesis submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
Discipline of Electrical, Electronic and Computer Systems Faculty of Engineering & Industrial Sciences Swinburne University of Technology Hawthorn, Victoria, Australia
March, 2013
To my Parents
They are the reason why I am here
“I will not further anticipate some H. G. Wells of the future with power-producing
windmills; but the power of winds has to be felt to be believed, and nothing is quite
impossible to physicists and engineers.”
Frank Debenham
(Speaking at convention of the British Association for the Advancement of Science in 1935)
i
ABSTRACT
With large wind energy integration into power systems, wind farms begin to
influence power systems in a much more significant manner. As wind energy
systems utilize different generator technologies from the one utilized in the
conventional power plants, the steady-state, transient and small-signal dynamics,
as well as, power system stability will thus be significantly affected. The impact of
wind energy systems on the power system dynamics and stability is thus of
practical importance.
As there is a significant increase in installation of wind turbines equipped with
doubly-fed induction generator (DFIG) in recent years, a dynamic model of the
DFIG wind turbine is firstly developed in this thesis. The model is validated
against field measurement data, and the validation gives confidence about the
accuracy and applicability of the developed model.
DFIG wind farms consist of tens to hundreds of identical DFIG wind turbines
increasing the complexity of the wind farm model and simulation time. A novel
aggregation technique is developed in this thesis that incorporates a multiplication
factor, namely mechanical torque compensation factor (MTCF), to the mechanical
torque of the full aggregated wind farm model. The MTCF is initially constructed
to approximate a Gaussian function by using fuzzy logic method. By optimizing
the MTCF on a trial and error basis, less than 10 percent discrepancy is then
achieved between the proposed aggregated model and the complete model. The
proposed aggregation technique is then applied to a 120 MVA offshore wind farm
comprising of 72 DFIG wind turbines and shows higher accuracy in approximating
the wind farm dynamics as it appears at the point of common coupling (PCC) as
compared to the full aggregated model. The proposed aggregated model computes
ii
faster than the complete wind farm model by 90.3 percent during normal
operations and 87 percent during grid disturbances.
To overcome the adverse effects due to the fluctuating nature of wind, two wind
power smoothing methods are proposed using a fuzzy logic pitch angle controller
for a smooth performance with a minimum drop in output power. One method
performs partial smoothing with only 4.74 percent drop in the output power while
the other method offers complete smoothing with a 8.28 percent drop in output
power.
The impact of wind energy integration on power system transient stability (PSTS)
is studied quantitatively with the transient energy margin (TEM), which is
calculated through the evaluation of the transient energy function (TEF). This
study is carried out in two ways in the thesis. One is to analyse the impact of
transient fault on the DFIG wind turbine as compared to SGs for different factors,
like the fault clearing time, the grid coupling, the inertia constant and the voltage
sag. The study reveals that transient stability of the DFIG wind turbine is hardly
affected by the grid coupling, the inertia constant and the generator terminal
voltage sag variations indicating its consistent transient performance within a wide
range of these factors. The fault clearing time should be almost 11 percent faster for
the system with the DFIG than the synchronous generator (SG).
The other is to investigate the impact of the DFIG wind farm on the PSTS with the
variation of different factors, which are the voltage sag, the fault clearing time, the
load and the wind power penetration level. The study reveals that power systems
integrated with DFIG wind farms are sensitive to transient events with high
voltage sag, high fault clearing time, low load operation and high wind power
penetration level. Machines at different locations individually possess distinct fault
response and suffer from a large-scale power imbalance. As a result, reliable
operation of DFIG wind farm integrated power systems demands upgraded
iii
equipment, such as advanced switchgear, fast breakers/isolators, efficient power
reserve systems and advanced reactive power compensating device, etc.
iv
ACKNOWLEDGEMENTS
First of all, I would like to lay thanks and gratitude to my almighty lord ALLAH
for giving me the strength and composure to complete this thesis.
It is with immense pleasure to express my heartfelt gratitude to my principal
supervisor Dr. Weixiang Shen and external supervisor Dr. Hemanshu Roy Pota for
their encouragement, guidance and continuous support throughout my research
period. I must mention the name of Dr. Nasser Hosseinzadeh, who had been my
principal supervisor for the first two years of my PhD candidature before he left
the university.
Dr. Greg Ayers, Ex Director of Bureau of Meteorology of Melbourne deserves
memorable thanks from me. He helped me providing real time wind speed data. I
thank the wind turbine manufacturing company as well, which would like to stay
anonymous, for providing field measurement data of a DFIG wind turbine with a
confidential agreement in order to validate the developed DFIG wind turbine
model.
I would also like to thank all the staffs from Swinburne ITS, who have always been
helpful in installing or updating software and any other associated technical issues.
Thanks to all of my colleagues at Swinburne for their support and discussion at
times during my research.
The financial contribution by Swinburne University of Technology through
SUPRA scholarship to support my PhD is highly acknowledged.
Finally, I am obliged to convey my thanks to my family and friends for their love,
motivation and support in every aspect. Last but not the least, I thank my wife,
Nuzhat for her constant support and encouragement throughout my PhD tenure.
v
DECLERATION
I hereby declare that I am the sole author of this thesis and to the best of my
knowledge; it contains no material that has been published by others previously
except where references have been made. This is the true copy of the thesis that has
no material accepted for the award of any other degree or diploma at any
university.
I understand that my thesis may be available to others electronically.
Md. Ayaz Chowdhury
March, 2013
vi
LIST OF PUBLICATIONS
Refereed International Journals:
1. M. A. Chowdhury, N. Hosseinzadeh and W. X. Shen, "Smoothing wind power
fluctuations by fuzzy logic pitch angle controller", Renewable Energy, vol. 38,
no. 1, pp. 224-233, February 2012.
2. M. A. Chowdhury, W. X. Shen, N. Hosseinzadeh and H. R. Pota, “A novel
aggregated DFIG wind farm model using mechanical torque compensating
factor”, Energy Conversion and Management, vol. 67, pp. 265-274, March 2013.
3. M. A. Chowdhury, N. Hosseinzadeh, W. X. Shen and H. R. Pota, “Comparative
study on fault responses of synchronous generators and wind turbine
generators using transient stability index based on transient energy function”,
International Journal of Electrical Power and Energy Systems, vol. 51, pp. 145-
152, October 2013.
4. M. A. Chowdhury, N. Hosseinzadeh, and W. X. Shen, “Dynamic validated
model of a DFIG wind turbine”, International Journal of Renewable Energy
Technology, 2013. (the revised version was submitted)
5. M. A. Chowdhury, W. X. Shen, N. Hosseinzadeh and H. R. Pota, “Transient
stability of power system integrated with DFIG wind farm”, submitted to
Renewable Energy, 2013.
6. M. A. Chowdhury, W. X. Shen, N. Hosseinzadeh and H. R. Pota “A review on
transient stability of DFIG integrated power system”, submitted to Renewable
and Sustainable Energy Reviews, 2013.
vii
Peer Reviewed Conference Proceedings:
7. M. A. Chowdhury, N. Hosseinzadeh, and W. X. Shen, “Effects of wind speed
variations and machine inertia constants on variable speed wind turbine
dynamics,” 20th Australasian Universities Power Engineering Conference
(AUPEC), Christchurch, New Zealand, 5-8 Dec 2010.
8. M. A. Chowdhury, N. Hosseinzadeh, M. M. Billah and S. A. Haque, “Dynamic
DFIG wind farm model with an aggregation technique,” 6th International
Conference on Electrical and Computer Engineering (ICECE), Dhaka,
Bangladesh, 18-20 Dec 2010.
9. M. A. Chowdhury, N. Hosseinzadeh and W. X. Shen, “Fuzzy logic systems for
pitch angle controller for smoothing wind power fluctuations during below-
rated wind incidents,” IEEE PES PowerTech Conference 2011, Trondheim,
Norway, 19-23 Jun 2011.
10. M. A. Chowdhury, W. X. Shen, N. Hosseinzadeh and H. R. Pota, “Impact of
DFIG wind turbines on transient stability of power systems – a review,”
accepted for the 8th IEEE Conference on Industrial Electronics and Application,
Melbourne, Australia, 19-21 Jun 2013.
viii
TABLE OF CONTENTS
ABSTRACT ……………………………………………………………………і
ACKNOWLEDGEMENT ……...……………………………………………іν
DECLERATION …………………………………………………………….…ν
LIST OF PUBLICATIONS …………………………………...............................νі
TABLE OF CONTENTS ………………………………………………….. νііі
LIST OF FIGURES ……………………………………………………...xііі
LIST OF TABLES …………………………………….………xνіі
CHAPTER 1 Introduction
1.1. Background and motivation …………………………………………..1
1.2. Wind power generation concepts …………………………………........4
1.3. Literature review …………………………………………………..……..7
1.3.1. DFIG wind turbine modelling: previous works ………………..7
1.3.2. Aggregated DFIG wind farm model ………………………..9
1.3.2.1. Previous works on aggregation technique ..…..…….10
1.3.3. Smoothing DFIG output power fluctuations ……………...13
1.3.3.1. Previous works on smoothing techniques ….............14
1.3.4. Transient stability of DFIG integrated power system ……...20
1.3.4.1. Transient stability assessment ……………………...21
1.3.4.1.1. Qualitative assessment ………………...…21
1.3.4.1.2. Quantitative assessment ………………….22
1.3.4.2. Transient phenomena with DFIG wind turbines ……23
ix
1.3.4.3. Previous works on transient stability of DFIG integrated
power system ……………………….…………………………28
1.3.4.4. Transient energy function (TEF) ………..….................30
1.4. Power system dynamics simulation ……………………...………..31
1.5. Major contributions of the thesis ……………………………………..33
1.6. Thesis outline …………………………………………….…...……….34
CHAPTER 2 DFIG Wind Turbine Model
2.1. Introduction …………….………………………………………..……....36
2.2. Dynamic model of DFIG wind turbine ……..……………………..36
2.2.1. Turbine rotor aerodynamic model …….. …………………37
2.2.2. Drive train model …………………………….……………39
2.2.3. Generator model .…..…………………………………………41
2.2.3.1. Reference frame transformation ..………………...42
2.2.3.2. Space-vector model …………………….....43
2.2.3.3. Generator model in the dq reference frame ……...45
2.2.4. Power converter model ……………………….……………46
2.2.5. Control system model ………………………….………………47
2.2.5.1. Speed controller model ..…………………………...48
2.2.5.2. Converter controller model ……………………………...50
2.2.5.2.1. RSC controller ……...……………………...50
2.2.5.2.2. GSC controller ……...……………...……....53
2.2.5.3. Operating regions ……...…………………...…………55
2.2.5.3.1. Partial load region ………………….......56
2.2.5.3.2. Full load region …………………….......57
2.2.6. Protection system model ….…………………….…………….58
2.3. Model validation …………..…………………………………………60
2.4. Summary ……………………………………………………………….64
x
CHAPTER 3 Aggregated DFIG Wind Farm Model
3.1. Introduction ………………………………………………………….......65
3.2. Formation of a complete DFIG wind farm model ………...……66
3.3. Proposed aggregated DFIG wind farm model …….……...……..…68
3.3.1. Full aggregated DFIG wind farm model ……………………...69
3.3.2. Basis of MTCF calculation ..………………………….............69
3.3.3. MTCF calculation by fuzzy logic system …………...................71
3.3.4. Equivalent internal electrical network ……………………...76
3.3.5. Model simplification ….…………………………...................76
3.4. Simulation results …………………………………...…………………77
3.4.1. Normal operation ..…………………………………...............79
3.4.2. Grid disturbance ..………………………………………..…...81
3.5. Evaluation of the proposed aggregation technique ……………...83
3.5.1. Accuracy in approximating the collective responses at the PCC …83
3.5.2. Simulation computation time ..………………………........84
3.6. Summary ..…………………………………………………………………85
CHAPTER 4 Smoothing DFIG output power fluctuations
4.1. Introduction ……………………………………………………………...86
4.2. Fuzzy logic pitch angle controller …….….…………...………………..87
4.2.1. FLS-A ...……………………………………………………………88
4.2.2. FLS-B ...……………………………………………………………90
4.2.2.1. Method one ....…………………………………...91
4.2.2.2. Method two .... ……….……………………..…...97
4.3. Simulation results ...……….………………………………………….101
xi
4.3.1. Evaluation of FLS-A …………………..….…………………......102
4.3.2. Evaluation of FLS-B …………………..….…………………......103
4.3.2.1. Evaluation of the proposed method one ….……..103
4.3.2.2. Evaluation of the proposed method two ….……104
4.3.3. Numerical validation of the proposed methods .……….......104
4.4. Summary ..………………………………………………………………..106
CHAPTER 5 Transient stability of DFIG integrated power system
5.1. Introduction ………………………………………………………….....107
5.2. Description of the TEF method ………………………………….....108
5.2.1. TEF formulation in power system ……...…………………..110
5.2.2. Approximation of accurate UEP ……...……………………..114
5.2.3. TEM calculation ….……..……...…………………….……....115
5.3. Fault response of DFIG wind turbines …………………………….118
5.3.1. Test system ………………………………………….................118
5.3.2. Case design …..………………………………………...............119
5.3.3. Simulation results …….....……………………………………120
5.3.3.1. Impact of fault clearing time ………………..120
5.3.3.2. Impact of grid coupling …………………….122
5.3.3.3. Impact of inertia constant …………………….122
5.3.3.4. Impact of generator terminal voltage sag ...…..124
5.4. Impact of DFIG wind farm on transient stability …………………..128
5.4.1. Test system ………………………………………….................128
5.4.2. Case design …………………………………………………….130
5.4.3. Simulation results …….....……………………………………131
xii
5.4.3.1. Impact of voltage sag ….…………………….131
5.4.3.2. Impact of fault clearing time …………….134
5.4.3.3. Impact of load demand ………….……………..137
5.4.3.4. Impact of wind power penetration level ………….140
5.5. Summary ………………………………………………………………143
CHAPTER 6 Conclusions and future works
6.1. Conclusions ………………………………………………………........146
6.2. Future works ……………………………………………….................152
REFERENCES ……….………………………………………………………154
xiii
LIST OF FIGURES
Figure 1-1: Installed wind power capacity worldwide in the last decade …………..2
Figure 1-2: FSIG wind turbine ……………………………………..………………...........5
Figure 1-3: DFIG wind turbine ………….………………………..………………..............5
Figure 1-4: DDSG wind turbine …………………..……………………………….…..6
Figure 1-5: Block diagram of a complete DFIG wind farm model …...…….……...9
Figure 1-6: Block diagram of (a) full aggregated and (b) semi aggregated DFIG wind farm
models ………………………………………………………………………...…...………11
Figure 1-7: Operating regions of the DFIG wind turbine ………………………..11
Figure1-8: Approximation of collective responses at the PCC by the full aggregated and
semi aggregated wind farm model in the partial load region ....……………….12
Figure 1-9: Smoothing performance of different smoothing methods ……………….18
Figure 1-10: Numerical evaluation of different smoothing methods: (a) Smoothing function
and (b) Maximum energy function …………………………………………………..19
Figure 1-11: A test system suffering a short circuit fault ……………………..…23
Figure 1-12: Thevenin equivalent circuit: (a) Pre-fault operation and (b) Post-fault
operation …………………………………………………………………………….24
Figure 1-13: Fault responses of the DFIG wind turbine: (a) Terminal voltage, (b) Active
power, (c) Torques, (d) Generator rotor speed, (e) Stator current and (f) Rotor current
…………………………………………………………………………………..…………………..27
Figure 1-14: Variations of TKE and TPE along a post-fault trajectory ………..……31
Figure 2-1: Configuration of a DFIG wind turbine ……………………………….....37
Figure 2-2: Drive train model ...……………………………………………………40
xiv
Figure 2-3: Reference frame for the generator equations …………………………42
Figure 2-4: Equivalent circuit of an induction generator dynamic model .……...44
Figure 2-5: Power converter in DFIG wind turbine …...………………………….46
Figure 2-6: Power coefficient curve for different tip speed ratio for the wind turbine model
(at β =0°) …………………………………………………………………………………...48
Figure 2-7: Pitch angle controller …………………………...…………………………...49
Figure 2-8: Stator flux oriented control of RSC …………………………………50
Figure 2-9: Stator flux oriented control of GSC …………………………………53
Figure 2-10: Turbine power characteristics at β =0°for different wind speed and transfer
characteristic ……………………………………………………………………………...55
Figure 2-11: Configuration of a crowbar ………………….………………………58
Figure 2-12: Measured (solid lines) and simulated (dashed lines) responses from the DFIG
wind turbine: (a) Wind incident, (b) Generator rotor speed, (c) Pitch angle, (d) Active
power and (e) Reactive power …..……………………………………………………….62
Figure 3-1: A 120 MVA offshore DFIG wind farm model …...…………………...66
Figure 3-2: Block diagram of the proposed aggregated DFIG wind farm model …...68
Figure 3-3: Torque curves of the complete and full aggregated model in the partial load
region ……………………………………………………………………………………..70
Figure 3-4: Gaussian distribution of MTCF (α) with respect to average wind speed (VWagg) ..
………………………………………………………………………………………………………71
Figure 3-5: Block diagram of a FLS …..………………..……………………………..72
Figure 3-6: Membership functions: (a) VWagg, (b) V
Wσ and (c) α ………………………..74
Figure 3-7: First order approximation (dashed line) of transfer characteristic (solid line) of
DFIG wind turbine ……………………………………………………………………77
xv
Figure 3-8: Wind speed received by the first DFIG wind turbine in each group ……78
Figure 3-9: Evaluation of the proposed aggregated wind farm model during normal
operation at the PCC: (a) Active power and (b) Reactive power …………………..80
Figure 3-10: Evaluation of the proposed aggregated wind farm model during grid
disturbance at the PCC: (a) Active power and (b) Reactive power ………………..82
Figure 4-1: Control scheme of the proposed fuzzy logic pitch angle controller ……88
Figure 4-2: Fuzzy sets and their corresponding membership functions during above rated
wind incidents: (a) eA, (b) ∆eAand (c) βcA ………………...……………………………..89
Figure 4-3: Distribution of EMA weights ….……………………………...…………..92
Figure 4-4: Fuzzy sets and their corresponding membership functions for determining a
proper correction factor: (a) eB1, (b) Pg_ref and (c) k …………………………………93
Figure 4-5: Obtaining command output power from EMA command output power by the
generation of correction factor (k) ……………….………………………………….95
Figure 4-6: Fuzzy sets and their corresponding membership functions during below rated
wind incidents using Method one: (a) eB1, (b) ∆eB1 and (c) βcB1 ……………...………...96
Figure 4-7: Fuzzy sets and their corresponding membership functions during below rated
wind incidents using Method two: (a) eB2, (b) ∆eB2 and (c) βcB2 ………….…………..99
Figure 4-8: Evaluation of the proposed methods: (a) Wind speed, (b) Pitch angle, (c) Active
power and (d) Reactive power ………………..…………………………………….102
Figure 4-9: Numerical validation of the proposed fuzzy logic controllers: (a) Smoothing
function and (b) Maximum energy function …….…………………………………..105
Figure 5-1: A ball rolling on the inner surface of the bowl ………………………109
Figure 5-2: Equivalence of transient energy method with equal area criterion ….110
Figure 5-3: Single-machine infinite bus system ……………………………………118
xvi
Figure 5-4: Fault responses of (a) SG, (b) DFIG and (c) TEM for different values of fault
clearing time (tc) …………………………………………………………………..121
Figure 5-5: Fault responses of (a) SG, (b) DFIG and (c) TEM for different values of PMFSO_sy
…………………………………………………………………………………………………………………………………….123
Figure 5-6: Relationship between line impedance and PMFSO_sys for SG and DFIG ….124
Figure 5-7: Fault responses of (a) SG, (b) DFIG and (c) TEM for different inertia constant
(H) values (the values inside the brackets corresponding to inertia constant (H) values for
DFIG) …………………………………………………………………………..................125
Figure 5-8: Fault responses of (a) SG, (b) DFIG and (c) TEM for different values of PMFSO_sys
(the values inside the brackets corresponding to PMFSO_sys values for DFIG) ………….126
Figure 5-9: Relationship between terminal voltage sag and PMFSO_fault for SG and DFIG ..127
Figure 5-10: Single line diagram of IEEE New England power system ...….……128
Figure 5-11: TEM for different voltage sags ………………………………………...132
Figure 5-12: Standard deviation of TEM (TEMσ ) for different voltage sags ………..134
Figure 5-13: TEM for different fault clearing times (tc) ……………………... 135
Figure 5-14: Standard deviation of TEM ( TEMσ ) for different fault clearing times (tc)
……………………………………………………………………………………………………..137
Figure 5-15: TEM for different load demands …………………………………...…138
Figure 5-16: Standard deviation of TEM ( TEMσ ) for different load demands ……...140
Figure 5-17: TEM for different wind penetrations: (a) G10, (b) G2, (c) G4 and (d) G9 …142
Figure 5-18: Standard deviation of TEM (TEMσ ) for different wind penetrations
……………………………………………………………………………………………………..143
xvii
LIST OF TABLES
Table 1-1: Wind turbine products with DFIG concept …………………………..…7
Table 1-2: Overview of wind energy storage devices ……………………………..16
Table 2-1: Simulated DFIG wind turbine parameters …….…………...…………...59
Table 3-1: DFIG wind farm parameters ………………………………………………..67
Table 3-2: Rules of the FLS ……….…………………………………………………..75
Table 3-3: Accuracy in approximating the collective responses at the PCC ………83
Table 3-4: Comparison of simulation computation time ………………………..84
Table 4-1: Rules of FLS-A …………………………………………...…………………90
Table 4-2: Rules for determining correction factor ………………………………....94
Table 4-3: Rules of FLS-B (Method one) ………………………………………….97
Table 4-4: Power stages ……………………….……………………………………….98
Table 4-5: Command pitch angle range for FLC-B (Method two) ..………………...100
Table 4-6: Rules of FLS-B (Method two) ……………………………………….100
Table 5-1: Test system parameters ……………….…………………..…………….118
Table 5-2: Simulation parameters ……………….………………………………….119
Table 5-3: Load flow data of New England power system ……………………..129
Table 5-4: The rate of change of TEM (∆T) for increment in voltage sag ……………133
Table 5-5: The rate of change of TEM (∆T) for increment in fault clearing time (tc)
……………………………………………………………………………………………………..136
Table 5-6: The rate of change of TEM (∆T) for increment in load demand ……..139
1
CHAPTER 1
Introduction
1.1. Background and motivation
The accessibility of electrical energy is a prerequisite for the functioning of a
modern society. Without electrical energy, we cannot think of information and
communication technology, transportation, lighting, food processing and storage
as well as a great variety of industrial processes, which combine to form the
modern society. Research shows that there is a significant relationship between
socio-economic growth and electricity consumption [1].
Electricity is an energy carrier. It is generated by converting primary energy
sources, such as fossil fuels (coal, oil, natural gas, etc.) or nuclear fission, into
electrical power. An important drawback of generating electricity from fossil fuels
and nuclear fission is the environmental impacts, such as the greenhouse effect
caused by the increase in carbon emission and the nuclear waste disposal problem.
Moreover, fossil fuels and uranium reserves are finite. Large scale hydro power
plants converting the energy in falling or flowing water into electricity are
potential alternatives to thermal and nuclear power plants, but the construction of
dams and basins for hydro power generation causes the flooding with a long term
impact on ecosystems.
Other electricity generation technologies using renewable energy sources
overcome the disadvantages of thermal and nuclear generation. Examples are
wave and tidal power, solar power and wind power. The renewable power
generation has the advantage of being sustainable energy sources with less severe
environmental consequences. On the other hand, most of the renewable energy
generation technologies have two principal disadvantages. These are: high initial
2
cost and lack of controllability. Many governments tend to value the advantages of
renewable power generation more than those of conventional power generation,
and they promote technological advancements and policies to make renewable
energy projects profitable in order to support the expansion of the renewable
energy generation capacity. These initiatives will eventually overcome the
disadvantages associated with the renewable energy generation.
Figure1-1: Installed wind power capacity worldwide
Among various renewable energy sources, wind power is a relatively cheap
source. The promotion of wind energy systems by governments of many countries
in the world has led to a strong exponential growth over the last decade (Figure 1-
1). Wind power capacity has reached 254 GW (3 percent of global electricity
consumption) worldwide with a growth rate of 16.4 percent percent in the mid of
2012 (273 GW is expected by the end of 2012). With this growth rate, wind power
capacity shall double every three years. Based on this accelerated development and
future policies, it is predicted that 12 percent of global electricity demands (1900
GW) will be provided by wind energy systems in the year 2020 [2]. Australian
3
government has also paid attention to wind power generation as a part of ‘Zero
carbon energy plans’ [3], where current installed wind power capacity is 2.476 GW,
which is aimed to be increased to 10 GW by next 10 years.
With the increasing penetration of wind power, wind farms begin to influence
power systems in a significant manner. Wind power generation must provide a
certain reliability of supply and a certain level of stability. The traditional concepts,
which have been used in the analysis of stability and quality of power system, may
not be suitable for the analysis of the power system integrated with wind farms.
A number of challenges we may encounter are [4]:
• Wind power is variable and difficult to predict; power systems may
adversely be affected due to the requirement of scheduling of spinning
reserves and energy storage.
• Wind farms utilize different generator technologies as compared to the
conventional power plant. As generators mainly govern the power system
dynamics and stability, power system has a different steady-state, transient
and small-signal dynamics, as well as, stability with wind energy
integration.
• Wind power may have problems of frequent occurrence of voltage dips,
grid frequency variations and low power factor due to the location and
intermittent nature of wind turbine generators.
• Wind farms require the design of a strong transmission grid. This is due to
the fact that wind turbines are mainly installed in places with good wind
resources, which are usually low consumption areas, and as a result, a large
amount of power is required to be exported.
• Wind farms have higher operating and maintenance cost.
4
As a part of the promotion of wind energy, millions of dollars are being invested in
wind energy research every year. We had a fascinating decade with a significant
advancement in this arena. We are still in need of further technological
advancements if we wish to establish wind energy as one of the most prominent
energy alternatives in the near future.
1.2. Wind power generation concepts
Wind power generation technologies can be distinguished according to their
operation and control principles. Three types of wind turbine generators are
available in the wind turbine industries. They are:
• Wind turbine equipped with fixed speed induction generator (FSIG),
termed as FSIG wind turbine
• Wind turbine equipped with doubly-fed induction generator (DFIG),
termed as DFIG wind turbine
• Wind turbine equipped with direct drive synchronous generator (DDSG),
termed as DDSG wind turbine
A FSIG wind turbine comprises of a squirrel cage induction generator (SCIG) or a
wound rotor induction generator (WRIG), whose rotor is mechanically coupled to
the wind turbine through a drive train. A reactive source is also connected at the
generator terminal (Figure 1-2). The connection between the FSIG and the grid
does not allow for much variation in the blade rotation speed (only 1 to 2 percent)
and hence, it is termed as a fixed speed wind turbine. In order to prevent the
induction generator from being damaged, at high wind speeds, the turbine blade is
either designed to operate at lower efficiency (stall control) or blade angle is
adjusted (pitch angle control) [5].
5
Figure 1-2: FSIG wind turbine
A DFIG wind turbine comprises of a WRIG, whose rotor is mechanically coupled
to the wind turbine rotor through a drive train. A back-to-back voltage source
converter is also connected to the generator (Figure 1-3). The converter controls the
stator voltage and current, as well as, enables variable speed operation of the wind
turbine. With the converters and pitch angle control, the DFIG is free from being
overloaded at high wind speed.
Figure 1-3: DFIG wind turbine
A DDSG wind turbine comprises of a synchronous generator (SG), whose rotor is
mechanically coupled to a wind turbine rotor. A back-to-back voltage source
converter is also connected directly to the generator (Figure 1-4). The grid side of
this converter is a voltage source converter while the generator side can either be a
6
voltage source converter or a converter rectifier. This also enables variable speed
operation. The generator is excited using either excitation windings or permanent
magnets [6].
Figure 1-4: DDSG wind turbine
Although variable speed wind turbines are more expensive due to additional
power electronic components and control systems, they are technically more
advanced than the constant speed wind turbines in a number of ways [7, 8]:
• Variable speed wind turbines adjust to continuously changing wind
velocity, which means they can be operated at peak performance nearly all
the time. Over the span of a year, the annual energy production might
increase by 10 percent.
• Variable speed wind turbines handle the mechanical stress of the torque
pulsation caused by the back pressure of the tower in an efficient manner.
This is done by absorbing and storing the energy of wind gusts in the
mechanical inertia of the turbine, creating a resilience that reduces torque
pulsation and minimize flickers. This improves the power quality.
• Variable speed wind turbines reduce acoustic noise and mechanical load
stress because low speed operation is possible at low power condition.
These facts influenced many manufacturers to switch from conventional constant
speed wind turbines to variable speed wind turbines, which led to a significant
7
increment in the installation of DFIG wind turbines in the wind farms in recent
years. The DFIG wind turbine has special feature of independent regulation of
active and reactive power. It also decouples generator frequency from grid
frequency and efficiently maintains the terminal voltage. Table 1-1 shows examples
of DFIG wind turbine products from a number of manufacturers [9, 10].
Table 1-1: Wind turbine products with DFIG concept
Manufacturers Power
(MW)
Rotor
diameter
(m)
Swept
area
(m2)
Turbine
speed
(rpm)
Gear
ratio
ENERCON E-126 7.5 127 14,527 5-11.7 Gearless
ENERCON E-101 3 101 8,012 4-14.5 Gearless
Gamesa G90 2.5 82.5 5,945 9-19 1:100.5
Vestas V80-2.0 2 80 5,620 9-20.7 1:92.6
GE 1.5 1.5 77 5,160 12-22.2 1:72
A lot of research works has been carried out to meet the challenges associated with
DFIG wind turbines. The main idea of this thesis is to identify current research
gaps and contribute to the knowledge of the two following issues: (1) output
power fluctuations of the DFIG wind turbine and (2) transient stability of DFIG
integrated power systems.
1.3. Literature review
1.3.1. DFIG wind turbine modelling: previous works
A detailed DFIG wind turbine model for power system stability studies is
proposed with the inclusion of stator flux transient in [11]. However, this
8
representation possesses difficulty for positive sequence fundamental frequency
simulation tools due to a very small time step stipulation and incompatibility with
standardised power system components.
A reduced order model of a DFIG wind turbine is proposed in [12], where the
stator transient is neglected during a normal simulation. However, the
involvement of a current controller still requires a small step-size for simulation. A
simplified DFIG wind turbine model compatible with the fundamental frequency
representation is proposed in [13]. This simplified model excluded both stator and
rotor flux dynamics from the DFIG model, which is equivalent to a steady state
representation. However, the rotor current controller is still assumed to be
instantaneous. An iteration procedure is needed to solve algebraic loops between
the generator model and the grid model, which is not desirable for the model
implementation. The time lags, which represent delays in the current control, are
introduced to avoid algebraic loops in [14]. Another simplified model is
introduced for the DFIG wind turbine by modelling the generator as a current
controlled source in [15]. Thus, the rotor dynamics are omitted.
This thesis presents the modelling of a DFIG wind turbine, which is based on
recent work reported in Refs. [8, 16-24]. The emphasis is given on the facts that the
model must meet the following three criteria:
• The model must be compatible with the standardised positive sequence
fundamental frequency representation.
• The model can be validated against more detailed representations or
measured data.
• The model must be computationally efficient.
9
1.3.2. Aggregated DFIG wind farm model
One of the goals of this thesis is to study the impact of large wind energy
integration on the dynamic behaviour of large power systems. This justifies the
need of a wind farm model that may consist of tens to hundreds of wind turbine
models, leading to model complexity and computation burden [25, 26]. Figure 1-5
shows a complete DFIG wind farm model with n number of DFIG wind turbines.
Figure 1-5: Block diagram of a complete DFIG wind farm model
To simplify the complete wind farm model, an aggregated wind farm model is
required to reduce the size of the power system model, the data requirement and
the simulation computation time [18, 27, 28], where this aggregated model can (1)
represent the behaviour* of the wind farm during normal operations, characterized
by small deviations of the grid quantities from the nominal values and the
occurrence of wind speed changes and (2) represent the behaviour of the wind
farm during grid disturbances, such as voltage drops and frequency deviations.
*Behaviour of the wind farm consists of active and reactive power exchanged with the power
system at the point of common coupling (PCC).
10
1.3.2.1. Previous works on aggregation technique
Two types of wind farm aggregation techniques have been proposed: the full
aggregated and the semi aggregation techniques. Figure 1-6 shows the full
aggregated and semi aggregated DFIG wind farm models.
The full aggregated model consists of one equivalent wind turbine and one
equivalent generator for a wind farm with one operating point at an average wind
speed for all the wind turbines in the wind farm [28-33]. The semi aggregated
model consists of all the wind turbines in the wind farm and one equivalent
generator [8, 34].
For a DFIG wind farm, the ability of the full or semi aggregated model to
approximate the complete model depends on the operating region of the DFIG
wind turbines. The operating regions of the DFIG wind turbine can be segmented
into two parts: a partial load region and a full load region (see Figure 1-7), which is
discussed in more detail, in Chapter 2.
The nonlinear relationship between the turbine speed and the turbine power in the
partial region corresponds to the nonlinear relationship between the wind speed
(VW) and the mechanical torque (T
m).
The full or semi aggregated model can represent the complete model when DFIG
wind turbines in the wind farm operate in the full load region regardless of the
differences in the operating points of the wind turbines in the wind farm. This is
due to the fact that all generators produce the same current at its maximum rating
in this region.
11
Figure1-6: Block diagram of (a) full aggregated and (b) semi aggregated DFIG wind farm
models
Figure 1-7: Operating regions of the DFIG wind turbine
12
Figure1-8: Approximation of collective responses at the PCC by the full aggregated and
semi aggregated wind farm model in the partial load region
The full aggregated model cannot provide an accurate approximation of a
complete model when DFIG wind turbines in the wind farm operate in the partial
load region as shown in Figure 1-8. This is due to the fact that the full aggregation
technique does not consider the operating points of all corresponding wind
turbines in the wind farm and the nonlinear relationship between the wind speed
and the mechanical torque in the partial load region.
13
The semi aggregated model, on the other hand, improves the approximation of a
complete model in the partial load region by considering the operating points of all
corresponding wind turbines in the wind farm. However, the use of an average
generator rotor speed (ωg) for all of the wind turbines still contributes to
discrepancies in the magnitude of mechanical torque and consequently
electromagnetic torque (see Figure 1-8).
Therefore, this thesis aims for a novel approach for an aggregation technique with
the incorporation of a mechanical torque compensation factor (MTCF) into a full
aggregated wind farm model to deal with the nonlinearity of wind turbines in the
partial load region and to make it behave as closely as possible to a complete
model of the wind farm.
1.3.3. Smoothing DFIG output power fluctuations
Air energy density is very low (1/800 as compared to that of water energy) that
causes wind speed to be fluctuating. This results in wind power fluctuations in a
significant manner because wind power is proportional to the cube of the wind
speed. The sources of wind power fluctuations can be categorized into followings
[35]:
• Cyclic components (tower shadow, wind shear, mechanical vibration, etc.)
• Wind farm weather dynamics (turbulence, boundary layer atmospheric
stability, micrometeorological dynamics, etc.)
• Events (connection or disconnection of the turbine, change in generator
configuration, etc.)
The problems of the DFIG integrated power system originated with output power
fluctuations are as follows:
• Wind power fluctuations cause the grid frequency to fluctuate.
14
• Amount of absorbed reactive power by the induction generator from power
grid is directly related to the active power generation. The variation in wind
speed causes the fluctuation of the active power generation and thus the
absorbed reactive power, leading to voltage flicker at the buses of the power
grid.
• Grid frequency fluctuation and voltage flicker contribute to poor power
quality and originate instability problems in the power system, especially
when there are loads sensitive to high voltage and frequency variations.
The importance of smoothing output power fluctuations becomes significant with
the increasing wind energy integration into the power system.
1.3.3.1. Previous works on smoothing techniques
Wind turbines have the natural tendency of smoothing output power fluctuation
due to the synchronization phenomena (when the blades of different wind turbines
have the same rotational speed) [36]. However, this tendency of the smoothing
may be lost due to a typical situation of changing weather pattern every few
seconds.
Several promising methods for smoothing of output power fluctuation have been
reported in the literature. These are:
• Energy storage
• Rotor inertia control
• Pitch angle control
There are a number of possible technologies for energy storage for smoothing, such
as flywheel, supercapacitor, superconducting magnetic energy storage (SMES) and
battery. These energy storage devices can be readily integrated into the design of
the DFIG using a bidirectional DC/DC converter coupled with the DC bus [37] and
can smooth wind power fluctuations based on a command output power. The
15
command output power may be a constant value compliant with the machine
rating [38]. An exponential moving average (EMA) method is more suitable for a
wide range of power fluctuation [39]. In the EMA method, the energy storage
devices are equipped with a controller, which enables these devices to follow the
command output power by absorbing or providing real power.
The two most promising short term storage devices are flywheel and
supercapacitor. Both offer similar characteristics and both are suitable for storing
wind energy and hence the smoothing. Flywheels store energy with the help of a
rotating mass in a form of rotating energy while supercapacitors provide higher
storage capacity in a double layer, mostly known as an electric double layer
capacitor [40, 41]. The energy capacitor system (ECS) combines power electronic
devices with the electric double layer capacitor for efficient smoothing method of
wind power fluctuation [39, 42]. SMESs store energy in the magnetic field of a coil
and are regarded as an exciting method for smoothing, though the resulting
magnetic field is threatening to the environment. Batteries are long term energy
storage systems and provide an efficient smoothing of output power fluctuation.
Sodium sulphur batteries, possessing very good technical characteristics, are used
for storage of a large amount of wind energy [43]. An overview of energy storage
devices for wind systems is summarized in Table 1-2.
The smoothing principle of the rotor inertia control can be realized from
continuous adjustment of power coefficient (Cp) through the process of charging
and discharging of kinetic energy in response to the wind speed in the large rotor
inertia that acts itself as an energy storage device. Charging occurs when the wind
turbine rotational speed accelerates as the wind speed increases while discharging
follows the deceleration of the wind turbine as the wind velocity decreases [44, 45].
This method helps to mitigate torque ripple on the shaft.
16
Table 1-2: Overview of wind energy storage devices
Technology People Advantage Disadvantage
Flywheel Cardenas et al.[46]
Takahashi et al.[47]
• Long life
• High energy
density
• Short access time
• Environmentally
friendly
• Short term
storage
• Expensive
Capacitor Kinjo et al.[40]
Shishido et al.[41]
Muyeen et al.[39]
Kamel et al.[42]
• Long life
• Short access time
• High storage
capacity
• Environmentally
friendly
• Short term
storage
• Expensive
SMES Zhou et al.[48]
Nomura et al.[49]
Ali et al.[50]
• Long life
• Long term
storage
• Small energy
density
• Environmentally
threatening
• Stability problem
• Expensive
Battery Mokadem et al.[51] • Large energy
density
• Fast access time
• High storage
capacity
• Expensive
• Significant
environmental
impact
• Expensive
17
On the other hand, T. Senjyu and his team had set up an excellent contribution in
the smoothing of output power fluctuation with pitch angle control method [52-
55]. Pitch angle controller performs smoothing by shedding mechanical power so
that the output power follows the command power value. The command power
value may be formed by the EMA method [42] or the output power approximate
equation at zero pitch angle [55].
Different methods have been applied to control pitch angle controllers, such as PI
control [56], minimum variance control [52], adaptive control [53], H∞ control [54],
minimax linear quadratic Gaussian control [57], fuzzy logic control (with single
fuzzy logic system (FLS)) [42, 58] and generalized predictive control [55].
Figure 1-9 shows the smoothing performance of the ECS, rotor inertia control, and
pitch angle control with and without fuzzy neural network (FNN) correction factor
(which adjusts command output power value continuously to handle the rapid
changes in the operating points providing stability in the system [55]). These
smoothing methods are compared with a maximum power point tracking (MPPT)
method, which does not involve in any sort of smoothing. Machines are of
different MVA-ratings in different literature. For the proper comparison, the
output powers are expressed in per unit (p.u.).
Though the smoothing strategies through energy storage methods are very
effective and provide almost complete smoothing when power quality is
concerned for high sensitive loads, they are mostly highly expensive. The rotor
inertia control and the pitch angle control are cheaper alternatives. The pitch angle
control has become the most popular smoothing method due to its reliable
operation, but the rotor inertia control or the pitch angle control can only perform
partial smoothing and hence offer the partial solution to the problems originated
by the output power fluctuations. In addition, they cause a large drop in output
power. This keeps the compensation role of the power storage system for proper
smoothing still significant.
18
Figure 1-9: Smoothing performance of different smoothing methods
The smoothing performance can be evaluated numerically by smoothing function
(Pe_smooth) and maximum energy function (Pe_max) which are expressed as [55]
( )dt
dt
tdPP
te
smoothe ∫=0
_ (1-1)
( )dttPPt
ee ∫=0
max_ (1-2)
The values of Pe_smooth and Pe_max are calculated from a DFIG wind turbine of 1.667
MVA-rating. The smoothing function (Pe_smooth) is an indication of smoothing
performance. The output power fluctuation is small if the value of the smoothing
function (Pe_smooth) is small. Figure 1-10a shows the smoothing performance of the
pitch angle control is 55.55 percent better than that of the rotor inertia control and
is elevated by another 24.36 percent when the pitch angle control is incorporated
with a FNN correction factor.
19
Figure 1-10: Numerical evaluation of different smoothing methods: (a) Smoothing function
and (b) Maximum energy function
On the other hand, the maximum energy function (Pe_max) indicates the maximum
energy produced from the DFIG wind turbine at a particular time. Figure 1-10b
shows that the DFIG wind turbine produces the highest amount of power in
association with the ECS. As compared to the ECS, the rotor inertia control and the
pitch angle control without and with FNN correction factor have the output power
drop approximately equal to 29.19 percent, 30.2 percent and 34.97 percent,
respectively.
20
The numerical studies show that a better smoothing performance is achieved at the
expense of larger drop in output power. Therefore, this thesis aims to achieve a
better smoothing performance of the DFIG wind turbine with a minimum drop in
output power by limiting mechanical power to a predetermined value according to
the instantaneous wind incident. For this accomplishment, a fuzzy logic pitch
angle controller is used. The robust and energy efficient fuzzy logic control method
is chosen due to its ability to reason precisely with imprecise, uncertain,
incomplete and nonlinear data from a wind farm even without a thorough
knowledge on its ambiguous dynamics.
Frequency and voltage fluctuations of grid may also be originated from load
variations. This thesis only deals with the frequency and voltage fluctuations
caused by power fluctuations at the generation point, which is a common
phenomenon in wind energy systems.
1.3.4. Transient stability of DFIG integrated power system
Power system transient stability (PSTS) is the capability of a power system to
return to a stable operating point after the occurrence of a disturbance that changes
its topology [59]. Examples of topology changes of a power system are:
• Tripping of a generator or a line
• Sudden change of a load, including a load trip
• Occurrence of a fault, i.e., a short circuit
Higher installation capacity of the DFIG wind farm brings about wider influence of
wind power on the grid and causes a major change in the operating conditions of
the power systems during transient events [60]. This is due to the fact that transient
stability is largely dominated by generator technologies in the power system, and
dynamic characteristics of DFIG wind turbines are different from that of the SGs in
21
the conventional power plants. This brings new challenges in the stability issues
and, therefore, it is very important and imperative to study these wind turbine
models in the DFIG integrated power systems elaborately and systematically.
1.3.4.1. Transient stability assessment
Transient stability assessment of the power systems integrated with the DFIG
turbines has been mainly reported in the following two aspects in the literature: (1)
Qualitative assessment and (2) Quantitative assessment.
1.3.4.1.1. Qualitative assessment
Qualitative assessment is carried out by observing post-fault state of different
generator variables. The variables are:
Rotor angle: when the rotor angle of the generator drops out of phase, the
generators are likely to lose the synchronism, leading to system instability.
Rotor speed/active power: when the rotor speed/active power continuously
increases without limitation or experiences fast undamped oscillations after the
fault; the system is referred to as unstable.
Terminal voltage: quicker restoration of generator terminal voltage after the fault
gives a good confidence on the system being stable.
Reactive power: when there is a heavy reactive power demand on the grid
followed by the fault, the system may suffer from transient instability. This may be
due to a voltage collapse of the network from the reduction of the reserves of the
reactive power.
22
1.3.4.1.2. Quantitative assessment
Quantitative assessment is carried out by the following transient state
measurement units:
Critical clearing time (CCT): the CCT is the maximal fault duration for which the
system possesses transient stability. The CCT is a complex function of pre-fault
system conditions (operating point, topology, system parameters), fault structure
(type and location) and post fault conditions that depend on the protective
relaying plan employed. The CCT is conventionally calculated from equal area
criterion theory [61, 62]. Another method computes the CCT through the
computation of a trajectory on the stability boundary [63, 64].
Transient rotor angle stability index (TRASI): the TRASI is a comparative
measure of rotor angle separation following a transient fault and defined as
follows [65]
−
−=
pre
post
max
max
2
2TRASI
δπ
δπ (1-3)
where post
maxδ and pre
maxδ are the maximum post-fault (typically measured from the first
swing of post-fault trajectory) and pre-fault rotor angle difference (in radian) in the
network respectively, with respect to a reference machine.
The TRASI index varies from 0 to 1. With the TRASI value closer to 1, the system is
considered to be more stable.
Transient stability index (TSI): the TSI (η) is defined as follows [66, 67]
1002
2
max
max ×
+
−=
δπ
δπη (1-4)
where maxδ is the maximum angle separation (in radian) between any two
machines in the system at the same time in the post-fault response.
23
The TSI varies from -100 to +100. With the TSI value greater than 0, the system is
considered to be stable.
1.3.4.2. Transient phenomena with DFIG wind turbines
This section gives a brief highlight of the transient phenomena of the power
systems integrated with DFIG wind turbines. Detailed descriptions can be found in
[18, 68, 69].
To assess the transient phenomena with a DFIG wind turbine, the simplest and
most widely used test system is adopted from [18, 70-72] (Figure 1-11). The DFIG
wind turbine is added to the original network at Bus E, and a short circuit fault is
simulated on one of the lines between Bus A and Bus D, which is cleared after 9
cycles (0.15 s).
Figure 1-11: A test system suffering a short circuit fault
The Thevenin equivalent circuit, seen from Bus B, is shown in Figure 1-12. This is
generally called the driving point impedance at Bus B found from the ZBus matrix of
the power system network.
24
With reference to the simplified diagram below (Figure 1-12), the Thevenin
impedance before the fault is
( )ABBottomADTopADeFTh ZZZZ +⊥= __Pr_ (1-5)
where ZTh_PreF is the Thevenin impedance before the fault between Bus D and Bus
B, ZAD_Top and ZAD_Bottom are the impedance of the lines between Buses A-D;
ZAB=ZAC+ZBC is the impedance between Bus A and Bus B.
Figure 1-12: Thevenin equivalent circuit: (a) Pre-fault operation and (b) Post-fault
operation
The Thevenin impedance after the fault is cleared is
ABBottomADPostFTh ZZZ += __ (1-6)
where ZTh_PostFis the Thevenin impedance between Bus D and Bus B after the
removal of the fault line.
25
It is clear that ZTh_PreF is less than ZTh_PostF, which weakens the system after fault. The
weaker system results in a large voltage drop across the generator terminal (vt)
immediately after the fault initiated at 0.1 s (Figure 1-13a).
The terminal voltage drop leads to the corresponding flux decrease in both rotor
and stator, resulting in generator demagnetizing process. The active power (Pe), as
well as, the electromagnetic torque (Te) of the generator is consequently reduced
(Figure 1-13b). Mechanical torque (Tm) gets higher as compared to the
electromagnetic torque at a point (Figure 1-13c) and the generator rotor speed (ωg)
starts accelerating (Figure 1-13d). High transient currents (is and ir) appear in the
stator and rotor windings (Figure 1-13e and 13f). To prevent the converters from
these high currents, the crowbar is triggered, the rotor side converter (RSC) is
blocked, and the grid side converter (GSC) is not alone able to transfer the whole
power from the rotor through the converter further to the grid. As a result, the
additional energy goes into charging the DC bus capacitor rapidly.
The shaft system between the wind turbine and the DFIG is extremely flexible,
which causes to accumulate potential energy during normal operations. When a
fault occurs, the energy is released, and it causes the rotating mass of the shaft to
excite oscillations [29].
When the fault is cleared at 0.25 s, the voltage cannot recover immediately because
the blocked RSC cannot provide necessary reactive power to the generator for its
magnetization process. The generator thus needs to absorb reactive power from
the grid and this action delays the recovering process of the grid voltage and
frequency. The GSC successfully controls the DC voltage back to its nominal value.
The crowbar is removed, as soon as, the grid voltage recovers over a certain value
and the generator currents and voltages start to converge to their pre-fault values
and the RSC retains its control over the active and reactive power.
26
27
Figure 1-13: Fault responses of the DFIG wind turbine: (a) Terminal voltage, (b) Active
power, (c) Torques, (d) Generator rotor speed, (e) Stator current and (f) Rotor current
28
1.3.4.3. Previous works on transient stability of DFIG integrated power
systems
Transient phenomena on wind energy integrated power system open the doorway
of two basic research streams. One is to analyze the impact of wind energy systems
on the PSTS, and the other is to improve the fault ride through (FRT) capability of
wind turbine generators as a means of enhancing transient stability so that the grid
code requirements are met [73, 74].
For wind energy systems with the DFIG, the generators are usually required to be
disconnected from the grid so that these are prevented from high transient current
flow, oscillations excited to rotating mass of the drive train, rotor overspeed and
dip in grid voltage due to the fault, but the DFIG wind turbines would, unlike the
conventional power plants, not be able to support the voltage and the frequency of
the grid during and immediately after the grid disturbance prior to disconnection.
With larger wind energy integration in the grid, DFIG wind turbines are required
to ride through the fault; otherwise this would cause serious problems for the
system stability [59]. However, the technology of the FRT capability of DFIG wind
turbines is significantly advanced for last few years. A number of methods are
adopted, such as:
• Limiting rotor overcurrent [10, 24, 75, 76]
• Shedding aerodynamic power [57, 69, 77, 78]
• Damping torsional oscillations [79, 80]
• Compensating reactive power [20, 57, 81-86]
This thesis mainly focuses on the impact of wind energy systems on the PSTS. V.
Akhmatov and J. G. Slootweg had pioneered to spot limelight on this hot research
of today [11, 87]. From their qualitative studies, it is known that fault response of
DFIG wind turbines for the largest part is determined by the settings of the
protective system. Later, the impact of grid integration of wind power on the PSTS
29
in terms of generator types, power system topologies, fault types and location is
studied. The study advocates that the PSTS will be enhanced if some traditional
SGs are replaced with DFIGs of the same capacity [28, 88]. Further research reveals
that the PSTS can be either improved or reduced when some traditional SGs are
replaced with DFIGs of the same capacity [89]. This finding is affirmed with the
identification of electromechanical mode of oscillation using eigenvalue analysis
that influences the PSTS beneficially or detrimentally with increasing integration of
DFIG turbines into power systems [67]. However, the qualitative study is unable to
point to any definite transient status of power system. Rather, it can only provide a
comparison of transient state between two different cases of transient events.
Hence, no accurate and precise action can be taken from the limited qualitative
study to significantly enhance the transient stability for the power system
integrated with the DFIG wind farms.
Results obtained from the qualitative study are verified quantitatively by means of
the CCT [90], the TRASI [65] and the TSI [66]. A more extensive study has also
been carried out that reveals the followings:
• The PSTS increases first and then decreases with the increasing capacity of
DFIGs.
• DFIG integration improves the system response to small disturbances, but it
may have an adverse impact on the response to larger ones.
• A fault initiated close to DFIG wind farms results in more adverse effects on
transient stability than a fault initiated near SGs.
Results in the above-mentioned articles are still limited to simplified network
structures, a few fault scenarios, and etc. The parameters used for the
quantification of the PSTS have limitations, as well. The concept of the CCT is of
limited value as far as a DFIG is concerned because protection system is activated
during fault negating transient stability assessment within the statutory limits [71].
30
The calculation of the post-fault rotor angle in the TRASI and the TSI can only
measure the status of the PSTS followed by a fault.
This thesis hence aims to study the impact of various influential factors on the
PSTS in a greater depth. Two types of quantitative research are mainly focused in
this thesis: one is to analyse the transient behaviour of the DFIG wind turbine, and
the other is to investigate the impacts of the DFIG wind farm on the PSTS. The
quantitative analysis is carried out by means of the transient energy margin (TEM),
which is calculated through the evaluation of the transient energy function (TEF).
The TEM determines not only the status but also the degree of the PSTS by
yielding the information on the absorbing capability of the transient energy within
the stability limit (if the post-disturbance system is stable) or the requirement of
absorbing capability for switching into a stable state (in case of the post-
disturbance system being unstable). Thus, the TEM can provide deeper insight into
the PSTS with a quicker decision, which makes it highly suitable to be
implemented in the dynamic security assessment.
1.3.4.4. Transient energy function (TEF)
The TEF is based on the Lyapunov function and LaSalle’s invariance principle,
which is proposed by Athay, Kakimoto et al. [91, 92] in the end of 1970s. Ideally,
the TEF is the sum of kinetic and potential energies of all the generators of the
power system. According to the law of energy conservation, the TEF is
conservative (remains unchanged) during the post-fault period, i.e., transient
kinetic energy (TKE) and transient potential energy (TPE) are equally exchanged
after fault is removed [91]. The TEF conservation is violated, due to the separation
of a number of critical machines (machines that are likely to lose synchronism from
the rest of the system) from the remaining machines immediately after a fault [93].
The system simulation result in Figure 1-14 shows that the total TKE never reaches
zero, even though the system transient is stable [93, 94]. It means not all TKEs
31
participate in system’s first swing separation. It also shows that not all TPEs are
responsible for absorbing TKEs during a first swing transient; a part of TPEs
balances that portion of TKEs which does not contribute to the first swing
separation [95]. This justifies the modification of the TEF.
Figure 1-14: Variations of TKE and TPE along a post-fault trajectory
Therefore, this thesis aims to modify the TEF by accounting the separation of the
critical machines from the remaining machines followed by a transient fault so that
accurate transient stability assessment is assured.
1.4. Power system dynamics simulation
A power system comprises of a large number of components: overhead lines and
underground cables, transformers, generators and loads. Most of these
components are mathematically described by differential equations, which might
result in hundreds or thousands of differential equations in case of a large power
system. As a result, numerical integration method is only a practical approach to
analyse the behaviour of a power system instead of analytical solutions.
32
Matlab/Simulink V.7.6 (R2010b) and PSS/E V.32 have been used in this thesis,
which are exciting software packages for power system dynamics simulation
approach. A fixed time step forward Euler method has been used for the numerical
integration of differential equations describing the power system. Some technical
issues associated with model implementation in this thesis are addressed as
follows:
• The simulation tool approaches fundamental frequency simulation or
electromechanical transient simulation to study the phenomena. The higher
harmonics are neglected. It helps to alleviate difficulty associated with time
response discrepancy among different power system components.
• It operates with positive sequence equivalents of the power systems, which
requires symmetrical three-phase network. The generators are modelled by
their positive sequence equivalents, as well.
• The fundamental frequency transients, i.e., the DC offset in the network are
omitted to make simulation of unbalanced disturbance like tripping of
three-phase line possible.
• The DC offset in the line current is also neglected at a balanced disturbance
like three-phase symmetrical fault. This simplification is justified from the
fact that it does not influence on the voltage profile in the entire power grid,
but allows a relatively large time step speeding up the simulation
computation time significantly.
• State variables and other variables of the dynamic simulation models are
ensured to be properly initialized based on initial load flow data.
Initialization is a crucial step in dynamic simulations. For improper
initialization, the system starts at an unsteady condition. In some cases, the
system may move away from the equilibrium condition after some time
preventing from achieving the desired state according to the initial load
33
flow. In the worst case, the system may become unstable, and the simulation
may come to a halt [10].
1.5. Major contributions of the thesis
The results of the works in this thesis provide a valuable contribution in the
following aspects:
• A DFIG wind turbine model is presented that is compatible with
standardised positive sequence fundamental frequency model and a
validation of the model against field measurement data is carried out.
• A novel aggregation technique is proposed with the incorporation of a
MTCF into the full aggregated wind farm model to deal with the
nonlinearity of wind turbines in the partial load region and to make it
behave as closely as possible to a complete model of wind farms. The
performance of the proposed aggregation technique is evaluated
quantitatively, as well.
• Design of a fuzzy logic pitch angle controller is proposed that sheds the
output power to a target value according to instantaneous wind instant.
Different fuzzy rules are assigned for different target values to enable
dynamic pitch actuation so that proper smoothing of output power
fluctuations is ensured with lesser drop in output power.
• A modified TEF, which accounts the separation of critical machines from
remaining machines followed by a transient fault for the assurance of
accurate transient stability assessment, is formulated.
• The TEM has been defined as a parameter for quantitative transient stability
assessment, which determines not only the status but also the degree of
system stability.
34
• A quantified comparison of the fault response of DFIG wind turbines with
that of the conventional SG is carried out, which outlines necessary actions
on fault incident on the power system integrated with DFIG wind farms.
• The impact of DFIG wind farms on the PSTS is assessed. The studies outline
power system planning and design actions on transient faults prior to large
integration of wind energy into power systems for reliable operation of
power system during transient events.
1.6. Thesis outline
The structure of the thesis reflects the discussions made on this chapter about the
current research stand and research gaps on the selected topics. The thesis is
organized as follows:
Chapter 2 presents the development of DFIG wind turbines. Firstly, the modelling
approach is discussed and developed. A validation of the developed model is then
carried out against the real time measurement.
Chapter 3 presents a novel aggregation technique for DFIG wind farms. Approach
of aggregation technique is first discussed and developed. The effectiveness of the
aggregated wind farm model is then evaluated in terms of accuracy in
approximations of the output powers and simulation computation time.
Chapter 4 presents the design of a fuzzy logic controller for smoothing wind
power fluctuations. Two methods of smoothing techniques are firstly discussed
and developed. The effectiveness of the proposed methods is then evaluated in
comparison with that of the conventional method.
Chapter 5 presents quantitative transient stability assessment of the power system
integrated with DFIG wind farms. Firstly, the TEM is defined by the formulation of
35
the TEF. Transient behavior of the DFIG wind turbine is then analyzed and finally,
the impact of the DFIG wind farm on the PSTS is investigated.
Chapter 6 summarizes the conclusions from the research and discusses the options
for future research.
36
CHAPTER 2
DFIG Wind Turbine Model
2.1. Introduction
An adequate model for wind farms is highly recommended in order to assess
power system dynamic behaviour and transient stability with wind energy
integration. The first step in this regard would be to develop a dynamic model of a
DFIG wind turbine, the basic unit of a DFIG wind farm, which is described in this
chapter.
The model should be simplified to enable faster simulation time. However, the
model should not be too simple so that it is unable to provide reliable results with
an optimum accuracy. The model should be compatible with the standardised
positive sequence fundamental frequency representation, as well.
This chapter describes various subsystems of the DFIG wind turbine and their
corresponding equations. Simulation results obtained from the models are
compared with the field measurement data. It is concluded that the model
developed in this work is reasonably accurate and can be used to represent wind
turbines in power system dynamics simulations.
2.2. Dynamic model of DFIG wind turbine
A DFIG wind turbine comprises of a wound rotor induction generator (WRIG) and
a wind turbine connected through two shafts with a gearbox in between with the
generator stator directly connected to the grid and the generator rotor connected to
the grid through two back-to-back insulated gate bipolar transistors (IGBT) pulse
37
width modulator (PWM) converters with an intermediate DC link capacitor. It
means that the generator is fed from both stator and rotor sides. In this chapter, the
dynamic wind turbine model is represented in terms of behaviour equations of
each of the subsystems, mainly the turbine rotor, the drive train, the induction
generator, the power converters and associated control systems and a protection
system, namely ‘crowbar’ (Figure 2-1).
Figure 2-1: Configuration of a DFIG wind turbine
2.2.1. Turbine rotor aerodynamic model
The wind turbine rotor that extracts the kinetic energy from the wind is a complex
aerodynamic system. For the state-of-the-art modelling of the turbine rotor, blade
element theory is used [96], but it causes a number of drawbacks [16]
• Instead of one wind speed signal, an array of wind speed signals has to be
applied.
• Detailed information of the rotor geometry should be available.
• Computations become complicated and lengthy.
38
To overcome these problems, a simplified way of modelling the wind turbine rotor
is usually used when the electrical behaviour of the system is the main point of
interest. An algebraic relation between the wind speed (VW) and the mechanical
power (Pm) extracted by the wind turbine is assumed, which is expressed as [97]
2
3
Wp
m
VACP
ρ= (2-1)
where ρ is the air density, A is the swept area of the blades and Cp is the power
coefficient.
The power coefficient corresponds to maximum mechanical power extraction from
the wind and is a function of tip speed ratio (λ) and pitch angle (β). The tip speed
ratio is obtained from
W
t
V
Rωλ = ` (2-2)
where R is the turbine radius.
There are alternatives for modelling the aerodynamic system of a wind turbine
such as using the blade element method, Cp(λ,β) lookup table, analytical
approximation and the wind speed-mechanical power lookup table [96]. Analytical
approximation proves to be the simplest method with higher accuracy. In this
method, Cp(λ,β) characteristic of a turbine aerodynamic model is approximated by
a nonlinear function from data provided by the manufacturer. One such function
given in [68] is in the following form
( ) ieCi
p
λβλ
βλ
5.12
54.0116
22.0,
−
−−= (2-3)
where
1
035.0
08.0
113 +
−+
=ββλλi
(2-4)
39
The mechanical torque (Tm) applied to the shaft can be computed as
t
m
m
PT
ω= (2-5)
where ωt is the turbine rotor angular speed.
2.2.2. Drive train model
Mechanical dynamics of a wind turbine may influence electrical responses, such as
3p effect, tower vibration effect and torsional dynamics. The 3p effect is the
occurrence of the largest periodic power pulsations in three-bladed turbines
caused by wind shear and tower shadow [98, 99]. For power system stability
studies, the 3p and the mechanical vibration effects are of secondary importance
since the magnitude of the oscillation generated by these dynamics is negligible.
Hence, only torsional dynamics is taken into account in stability studies.
A wind turbine drive train can be seen as a three-mass system consisting of three
inertias, which include the generator rotor, the turbine hub, and the blades [100,
101]. The representation of a wind turbine drive train as a three-mass model
increases the complexity of the model. In power system stability studies, it is
justified to include a two-mass model of the drive train [102-104]. Two-mass model
includes only the relatively soft low-speed shaft neglecting the gearbox and the
high speed shaft of the wind turbine, which is assumed to be infinitely stiff [87].
A two-mass model of the wind turbine drive train is used in this thesis, in which
the rotor is conventionally treated as two lumped masses, i.e., turbine mass and
generator mass are connected together by a shaft with a certain damping and
stiffness coefficient values. Turbine mass includes lumped inertia of the turbine,
part of the gearbox and the low-speed shaft and generator mass includes generator
40
rotor mass, high speed shaft along with its disk brake and the rest part of the
gearbox [22].
Figure 2-2: Drive train model
As shown in Figure 2-2, the structure of the drive train consists of two inertias. The
different damping components are present in the model, namely the turbine self-
damping (Dt), the generator self-damping (Dg) and the mutual damping (Dm). The
turbine self-damping represents the aerodynamic resistance that takes places in the
turbine blade. The generator self-damping represents mechanical friction and
windage. The mutual damping represents balancing dynamics that occur because
of different speeds between the generator rotor and the turbine shaft. The
mathematical equations of a two-mass drive train model obtained by neglecting Dt
and Dg are given as [10]
( ) ( )tgmtgsm
t
t DKTdt
dH ωωθθ
ω−−−−=2 (2-6)
( ) ( )tgmtgse
g
g DKTdt
dH ωωθθ
ω−+−+−=2 (2-7)
t
t
dt
dω
θ= (2-8)
41
g
g
dt
dω
θ= (2-9)
where H is the inertia constant, Ks is the shaft stiffness, θ is the rotor angle and T
e is
the electromagnetic torque. Suffixes t and g denote the turbine and the generator
parameters, respectively.
2.2.3. Generator model
An induction generator (IG) can be represented in different ways depending on the
level of the detail of the model, which is mainly characterized by the number of
phenomena included in the model, like the stator and rotor flux dynamics,
magnetic saturation, skin effect and core and iron losses. The dynamics of
magnetic saturation, skin effect and core losses have a little influence on the
stability analysis. Iron losses have an insignificant impact on machine torques and
currents while these make the model too complex [105]. Main flux saturation is
only of importance when the flux level is higher than the nominal level. The skin
effect should be taken into account for a very large slip operating condition only,
which may not be required in case of a DFIG wind turbine. A 5th order induction
generator model (also known as the electromagnetic transient (EMT) model) is
used in this thesis that includes both stator and rotor flux dynamics because it can
provide detailed approximation of the transient [22].
In the modelling of the IG, the following conventions are considered:
• The generator structure is symmetrical and three-phase balanced
• Magnetic saturation is neglected
• Flux distribution is sinusoidal
• All losses are neglected except for copper losses
• The sum of the three stator currents equals zero
42
• Generator convention is considered, i.e., positive real and reactive powers
are fed into the grid
• All parameters are given in p.u. quantities
A number of reference frames have been proposed over the years. A
synchronously rotating dq reference frame with arbitrary rotating speed ω is
chosen to model the IG in this thesis. The IG space-vector model is first detailed,
which is composed of three sets of equations: voltage equations, flux linkage
equations and motion equations. Then, the dq-axis model of the IG is obtained
from the space-vector model.
2.2.3.1. Reference frame transformation
Variables in the abc stationary frame are transformed to the dq rotating frame with
an arbitrary speed ω, which relates to θ, the rotation angle of the dq-frame with
respect to the stationary frame, by
dt
dθω = (2-10)
The reference frame transformation is done by deriving simple trigonometric
functions from the orthogonal projection of the variables xa, xb and xc to the dq-axis
variables xd and xq. Figure 2-3 shows that the d-axis component is oriented along
the phase a at t=0, which starts rotating at a speed of ω at t=0+. The q-axis
component is 90˚ ahead of the d-axis with respect to the rotation direction [22].
Figure 2-3: Reference frame for the generator equations
43
The transformation of abc variables in the dq-frames can be expressed as [106]
( ) ( )( )3/4cos3/2coscos3
2πθπθθ −+−+= cbad xxxx (2-11)
( ) ( )( )3/4sin3/2sinsin3
2πθπθθ −+−+−= cbaq xxxx (2-12)
A coefficient of 3
2is added to the equation so that the magnitude of the two-phase
voltage is equal to that of the three-phase voltage after the transformation.
2.2.3.2. Space-vector model
The voltage equations for the stator and rotor of the generator in the arbitrary
reference frame are given by [106]
s
s
sssdt
diRv φω
φj++= (2-13)
( )rg
r
rrrdt
diRv φωω
φ−++= j (2-14)
where v, i and R are voltage, current and resistance, respectively, and φ is the flux
linkage. Suffix s and r denote the stator and the rotor side of the generator,
respectively.
The voltage vectors can be decomposed into d and q-axis as
qsdss vvv j+= (2-15)
qrdrr vvv j+= (2-16)
44
The flux linkage equations for the stator and rotor of the generator in an arbitrary
reference frame are given by [106]
( ) rmsmlss iLiLL ++=φ (2-17)
( ) smrmlrr iLiLL ++=φ (2-18)
where Ll is the leakage inductance and Lm is the mutual inductance.
Drive train equations along with the electromagnetic torque (Te) equation are
termed as motion equations. The electromagnetic torque can be expressed as
( )*jRe
22
3rre i
pT φ= (2-19)
where p is the number of poles.
The above equations constitute the vector-space model of the IG, whose equivalent
circuit representation is given in Figure 2-4. The generator model is in an arbitrary
reference frame, rotating in space at the arbitrary speed ω.
Figure 2-4: Equivalent circuit of an induction generator dynamic model
45
2.2.3.3. Generator model in the dq reference frame
The dq-axis model of the IG can be obtained by decomposing the space-vectors into
their corresponding d and q-axis components as
qd xxx j+= (2-20)
where x can be voltage or current or flux linkage in the stator or rotor side of the
generator.
The dq-axis voltage equations of the IG are thus obtained as [106]
qs
ds
dssdsdt
diRv ωφ
φ−+= (2-21)
ds
qs
qssqsdt
diRv ωφ
φ++= (2-22)
( )qrg
dr
drrdrdt
diRv φωω
φ−−+= (2-23)
( )drg
qr
qrrqrdt
diRv φωω
φ−++= (2-24)
where
( ) drmdsmlsds iLiLL ++=φ (2-25)
( ) qrmqsmlsqs iLiLL ++=φ (2-26)
( ) dsmdrmlrdr iLiLL −+=φ (2-27)
( ) qsmqrmlrds iLiLL −+=φ (2-28)
The electromagnetic torque is expressed in [107] as
( )dsqsqsdse ii
PT φφ −=
22
3 (2-29)
46
The stator power equations can be written as [107]
( )qsqsdsdss ivivP +=2
3 (2-30)
( )qsdsdsqss ivivQ −=
2
3 (2-31)
2.2.4. Power converter model
The power converter is made up of two back-to-back DC linked converters,
namely: the rotor side converter (RSC) and the grid side converter (GSC), which is
connected to the rotor winding and grid, respectively. This is known as ‘Scherbius
scheme’. The converters are typically made of voltage-fed current regulated
inverters, which enable a two-directional power flow. The inverter valves make the
use of IGBTs provided with freewheeling diodes (Figure 2-5) [10].
Figure 2-5: Power converter in DFIG wind turbine
The RSC acts on rotor current components so that the independent regulation of
stator real power (Ps ) and stator reactive power (Q
s) is ensured. The GSC helps to
47
keep DC link capacitor voltage (VDC) constant acting on grid current components. It
also regulates the reactive power exchange from the converter to the grid (Q1)
during voltage re-establishment after a grid disturbance condition. Both the RSC
and the GSC are modelled as current controlled voltage sources. The switching
dynamics of the converters are neglected since the PWM modulation frequency is
much higher than the system frequency. These converters are assumed lossless and
hence, the DC link capacitor dynamics can then be described as [10]
−=
DC
rDC
V
PP
Cdt
dV 11 (2-32)
where C is the DC link capacitance, Pr is the rotor power and P
1 is the converter
power.
The DC chopper consists of a resistor and a switch connected in parallel to the DC
bus with the DC link capacitor. This is controlled by an IGBT when a DC
overvoltage is detected. It dissipates the excess of energy that cannot be
transmitted to the grid during a fault. When the DC chopper is activated, Eq. 2-32
becomes
−
−=
DC
DC
DC
rDC
R
V
V
PP
Cdt
dV 11 (2-33)
where RDC is the equivalent resistance of the DC chopper.
2.2.5. Control system model
There are two levels of control in the wind energy conversion system. The high
level control or speed control actuates the pitch angle of the rotor blades and gives
torque reference signals to the converter. The low level control or converter control
drives the converter IGBTs to meet its control objectives.
48
2.2.5.1. Speed controller model
Speed controller has two different objectives depending on the region where the
machine is operating. In the partial load region, its mission is to maximize the
power extracted from the wind referencing the proper electromagnetic torque
signal to the converter. The electromagnetic torque reference is calculated using
[108]
2* * tCpe KT ω= (2-34)
where KCp is the parameter that depends on the geometry of the wind turbine.
Figure 2-6: Power coefficient curve for different tip speed ratio for the wind turbine model
(at β =0°)
Eq. 2-34 gives the expression of the equilibrium electromagnetic torque as a
function of the equilibrium speed of the turbine rotor. The power coefficient (Cp)
curve in Figure 2-6 shows that maximum power coefficient (Cpmax) corresponds to
optimum tip speed ratio (λopt). The turbine rotor speed is always adjusted through
variable-speed mode of the wind turbine so that optimum tip speed ratio is
49
maintained to meet maximum power coefficient for extracting maximum
mechanical power.
When the system reaches the full load region, the task of the speed controller is to
keep extracting the nominal power varying the pitch angle (β) to reduce power
coefficient (Cp) so that a constant electromagnetic torque (Te) is maintained. It is
expected that the rotor speed will eventually be controllable before the rotor speed
reaches its upper limit.
Figure 2-7 shows a conventional simplified PI controller for the purpose of
controlling pitch angle. Pitch angle controller regulates the output in accordance
with the error between generator rotor speed and its upper limit (reference) value.
The error signal is then sent to the PI controller generating the command signal (βc)
for the mechanical servo system.
Figure 2-7: Pitch angle controller
The choice of the reference value is system dependent. This is chosen in such a way
that minimum possible reference value enables generation of maximum possible
power (1 p.u.) as higher generator rotor speed is vulnerable to power system
instability. For the specific wind turbine system in [109], this reference value (ωg_ref)
is chosen as 1.21 p.u.
The mechanism governing the pitch angle is usually a hydraulic actuator or a
servomotor that can be modelled using a first order delay system with a time
constant (Td) as [110]
50
c
d sTββ
+=
1
1 (2-35)
The inclusion of the servomotor along with the rate limiter provides a realistic
response from the controller. The concept of pitch rate of change is very important
because it decides how fast the mechanical power can be reduced in order to
prevent over-speeding of the generator rotor during both strong wind incidents
and grid disturbances. It depends on the servo motor that drives the blade and
mechanical properties of the material chosen for the blade construction.
2.2.5.2. Converter controller model
2.2.5.2.1. RSC controller
Figure 2-8: Stator flux oriented control of RSC
The RSC acts on rotor current components so that the independent regulation of
stator powers (Ps and Qs
) is ensured. Figure 2-8 shows stator field oriented control
of the RSC.
Aligning the d axis of the reference frame to be along the stator flux linkage will
result in
0=e
qsφ (2-36)
51
and
e
qr
mls
me
qs iLL
Li
+−= (2-37)
where superscript e identifies the synchronously rotating reference frame.
The electromagnetic torque thus becomes
e
qr
e
ds
mls
me
e iLL
LPT φ
+−=
22
3 (2-38)
For e
dsφ to remain unchanged to zero, e
dsv must be zero [111]. The stator power
equation then becomes
( )e
qs
e
qs
e
s ivP2
3= (2-39)
( )e
ds
e
qs
e
s ivQ2
3= (2-40)
Therefore, the above equations show that active and reactive powers of the stator
can be controlled independently.
The reference stator active power ( e
refsP _ ) can be generated from the instantaneous
generator rotor speed (ωg). On the other hand, the reference stator reactive power
( e
refsQ _ ) can be generated from e
refsP _ and the desired stator side power factor
(cosφs_ref) [17].
refs
refse
refs
e
refs PQ_
_
2
__cos
cos1
ϕ
ϕ−= (2-41)
Any changes in the voltage component in d or q axes result in changes in both
current components. It leads to the conclusion that the wind energy system is
coupled. But, implementation with current controlled PWM inverter using stator
52
flux oriented approach requires decoupling scheme. Equations are required to be
redeveloped in order to compensate for these cross couplings between d and q
axes.
The leakage component (σ) in the induction generator is defined as [112]
( )( )mlrmls
m
LLLL
L
++−=
2
1σ (2-42)
The rotor flux linkage equations become [107]
( ) e
ds
mls
me
drmlr
e
drLL
LiLL φσφ
+++= (2-43)
( ) e
qrmlr
e
qr iLL += σφ (2-44)
The reference rotor voltage equations can be written as [107]
e
compdr
e
refdr
e
dr vvv __ += (2-45)
e
compqr
e
refqr
e
qr vvv __ += (2-46)
where
( )t
iLLiRv
e
dr
mlr
e
drr
e
drd
d++= σ (2-47)
( )t
iLLiRv
e
qr
mlr
e
qrr
e
qrd
d++= σ (2-48)
( ) ( ) e
drmlrgs
e
ds
mls
me
compdr iLLtLL
Lv +−−
+= σωω
φ
d
d_
(2-49)
( ) ( ) ( ) e
drmlrgs
e
ds
mls
m
gs
e
compqr iLLLL
Lv +−+
+−= σωωφωω_
(2-50)
where ωs is the supply angular speed. Suffix comp stands for compensating factor.
53
Inclusion of these compensating terms to the corresponding uncompensated
voltage terms enables the decoupled performance of the stator flux-oriented
control of the RSC.
The reference rotor voltage equations are again aligned to its natural reference
frame by [17]
( ) ( )gs
e
qrrs
e
drdr vvv θρθρ −−−= sincos (2-51)
( ) ( )gs
e
qrrs
e
drqr vvv θρθρ −+−= cossin (2-52)
where ρs is the stator flux-linkage space phasor with respect to stationary d axis.
These two-phase rotor voltage signals are transformed to three-phase signals by
transformation of dq-frames into abc variables before feeding to the PWM by [106]
θθ sincos qrdrar vvv −= (2-53)
( ) ( )3/2sin3/2cos πθπθ −−−= qrdrbr vvv (2-54)
( ) ( )3/4sin3/4cos πθπθ −−−= qrdrcr vvv (2-55)
2.2.5.2.2. GSC controller
The main objective of the GSC is to maintain the DC link voltage constant
irrespective of the magnitude and direction of the slip power. A current controlled
PWM scheme is used, where d and q axes currents are used to regulate DC link
voltage and reactive power. Figure 2-9 shows stator field oriented control of the
GSC.
54
Figure 2-9: Stator flux oriented control of GSC
The reference values for the DC link voltage and reactive power exchange between
the GSC and the grid are taken as 1200 V and 0 p.u. for the simulation studies of
this thesis [109].
Stator voltage equations can be written as follows[107]
e
d
e
qss
e
dse
ds
e
ds vLit
iLRiv 1
d
d+−+= ω (2-56)
e
q
e
dss
e
qse
qs
e
qs vLit
iLRiv 1
d
d+−+= ω (2-57)
where v1, R and L are the voltage, the resistance and the inductance of the input
filter connected in between the GSC and the grid, respectively.
Therefore, reference values for GSC can be written as
e
qss
e
dse
ds
e
refd Lit
iLRiv ω+−−=
d
d_1
(2-58)
( )e
qs
e
dss
e
qse
qs
e
refq vLit
iLRiv −+−−= ω
d
d_1
(2-59)
55
The reference GSC voltage equations are again aligned to its natural reference
frame, and two-phase rotor voltage signals are transformed to three-phase signals
by transformation of dq-frames into abc variables before feeding to the PWM.
The main task of the control scheme in the PWM converters is to force the current
to follow their reference signals prior to the error signal generated from the
reference and actual signal fed into the PI controllers. PI controllers are tuned
using the internal mode control (IMC) method as [113]
τ
LK P = (2-60)
τ
RK I = (2-61)
where KP is the proportional gain, K
I is the integral gain of the PI controller and τ is
the desired current loop time constant.
2.2.5.3. Operating regions
The power converters must be controlled in collaboration with the speed controller
so that the control forces wind turbines to follow a predefined power-speed
characteristic, known as tracking characteristic. This is to ensure optimal energy
capture when the mechanical power is extracted by the rotor in both partial and
full load regions. In Figure 2-10, a transfer characteristic is illustrated by the red
curve, superimposed on the mechanical power characteristics of the turbine
obtained at different wind speeds for the system simulated in this work [87, 106,
109].
56
Figure 2-10: Turbine power characteristics at β =0°for different wind speed and transfer
characteristic
The tracking characteristic curve mostly follows the maximum power tracking
points for different wind speeds. Power reaches 1 p.u. at minimum generator rotor
speed value of 1.21 p.u., which is held constant for any higher rotor speed than this
value in the simulations. The actual speed of the turbine is measured, and the
corresponding mechanical power of the tracking characteristic is used as the
reference power for the power control loop.
Several operating regions of a DFIG wind turbine can be defined based on transfer
characteristic. These are described in the following sections [10].
2.2.5.3.1. Partial load region
The partial load region is chosen when the turbine rotates at a speed between 0.7
p.u. and 1.21 p.u. (i.e., when wind speed ranges between 4.5 ms-1 and 14.5 ms-1).
The partial load region comprises of three parts:
• Minimum speed operating region (MinSOR)
• Optimum speed operating region (OSOR)
57
• Maximum speed operating region (MaxSOR)
The MinSOR is chosen when the turbine rotates at a speed between 0.7 p.u. and
0.71 p.u. In the MinSOR, the generator speed is kept constant at its minimum
speed, which is usually around 30 percent below synchronous speed.
The OSOR is chosen when the turbine rotor rotates at a speed between 0.71 p.u.
and 1.2 p.u. In the OSOR, the speed of the turbine rotor is adjusted to capture a
maximum power at a given wind speed. This principle is appropriate in
circumstances where the rated power of the wind turbine is not reached. This
strategy is also called the 'wind-driven mode’. However, this operation may cause
generator output power fluctuations due to variations in wind speed. Generator
speed is electromagnetically controlled by the RSC.
The MaxSOR is chosen when the turbine rotates at a speed between 1.2 p.u. and
1.21 p.u. In the MaxSOR, generator speed is not able to follow optimum operation
continuously since generator speed is not allowed to exceed a certain limit. At this
point, the controller attempts to maintain generator speed at maximum speed,
typically around 15 to 20 percent above synchronous speed. As a consequence,
wind power conversion is no longer optimized. Still, this maximum speed
regulation is mainly achieved by means of the RSC [10].
2.2.5.3.2. Full load region
The full load region is chosen when the turbine rotates at a speed above 1.21 p.u.
(i.e., when wind speed exceeds 14.5 ms-1). In the full load region, the RSC is no
longer able to keep generator speed below the maximum value. Alternately,
generator speed must be limited by reducing aerodynamic torque, which can be
achieved through the action of a pitch angle controller. This region is also termed
as power limitation operating region.
58
2.2.6. Protection system model
DFIG wind turbines are also equipped with advanced protection devices like
crowbar [28]. A crowbar is designed to bypass the RSC in order to avoid
overcurrent on the RSC, as well as, overvoltage on the DC link capacitor subject to
a fault. The crowbar can be constructed by using a combination of a diode bridge
and a thyristor with an external resistor (Figure- 2-11).
Figure 2-11: Configuration of a crowbar
The crowbar resistance value typically ranges between 1 to 10 times the rotor
resistance [114], the exact value is dependent on machine parameters. A higher
crowbar resistance value is favourable to dampen rotor transient current quickly,
but after a threshold it may lead to the risk of overvoltage on the converter.
Therefore, the value of the resistance must be designed as a compromise between
these two factors. The maximum value for the crowbar resistance (Rcbmax) is
estimated by [115]
2
max
2
'
max
max
7.1 rs
sr
cb
vv
XvR
−
= (2-62)
where vrmax is the maximum allowable rotor voltage, X
s’ is the stator transient
reactance and vs is the stator voltage vector.
59
The crowbar action can be triggered either when the DC link voltage reaches
approximately 12 percent above the nominal value [116, 117] or when the current
in the RSC exceeds 1.8 p.u. [118].
Parameters of the DFIG wind turbine along with its control system used in the
simulation studies of this thesis are shown in Table 2-1 [87, 106, 109].
Table 2-1: Simulated DFIG wind turbine parameters
Parameter Symbol Value Unit
Wind turbine
Nominal mechanical output power Pm 1.5 MW
Inertia constant Ht 2.5 s
Generator
Nominal power Pe 1.5*0.9 MW
Nominal voltage (line to line) VL-L
690 V
Stator leakage resistance Rls 0.0084 p.u.
Stator leakage inductance Lls 0.167 p.u.
Rotor leakage resistance Rlr 0.0083 p.u.
Rotor leakage inductance Llr 0.1323 p.u.
Mutual inductance Lm 5.419 p.u.
Inertia constant Hg 0.5 p.u.
Friction factor F 0.01 p.u.
Number of poles p 4 -
Converter
Converter maximum power Pcmax 0.5 p.u.
Grid side coupling inductor inductance Lc 0.15 p.u.
Grid side coupling inductor resistance Rc 0.0015 p.u.
Nominal DC voltage VDC
1200 V
DC capacitance C 10 mF
60
Controller
Grid voltage regulator gain KP 1.25 -
KI 300 -
Droop Xs 0.02 p.u.
Power regulator gain KP 2 -
KI 10 -
DC bus voltage regulator gain KP 0.002 -
KI 0.05 -
GSC current regulator gain KP 1 -
KI 100 -
RSC current regulator gain KP 0.3 -
KI 8 -
Pitch angle regulator gain KP 100 -
KI 10 -
Maximum pitch rate of change dβ/dt ±3 deg ⋅ s-1
System servo delay Td 0.25 s
2.3. Model validation
The responses of the simulated model to a particular wind speed sequence (VW) are
investigated and compared to actual measurements (Figure 2-12a). The field
measured data is obtained from a wind turbine manufacturing company under a
confidential agreement.
The variables considered for the comparison are: generator rotor speed (ωg), pitch
angle (β), active power (Pe) and reactive power (Q
e). All values are in p.u., and
confidentiality is maintained by not indicating their base values, except for the
wind speed and pitch angle.
61
62
Figure 2-12: Measured (solid lines) and simulated (dashed lines) responses from the DFIG
wind turbine: (a) Wind incident, (b) Generator rotor speed, (c) Pitch angle, (d) Active
power and (e) Reactive power
From the simulated responses of the DFIG wind turbine in Figure 2-12, it is
observed that the DFIG wind turbine operates in the full load region during two
periods, one is between 11 s and 16.5 s and the other is between 32 s and 37 s, when
the generator rotor speed exceeds 1.21 p.u. due to the higher wind speed for a
reasonable period (Figure 2-12b). As a result, the pitch angle controller is activated
to limit the mechanical power extraction (Figure 2-12c) and hence, the generator
rotor speed is maintained to its control speed value. Therefore, power coefficient
63
(Cp) is no more a constant; it is rather a nonlinear function of the tip speed ratio (λ)
and the pitch angle (β) as given by equation Eq. 2-3.
The DFIG wind turbine thus produces the active power at its maximum rating
value (1 p.u.) and reactive power at -0.0656 p.u. (negative value indicates that the
reactive power is being absorbed by the wind turbine from the grid due to having
capacitive load) (Figure 2-12d and 2-12e).
In the rest of the period, the generator rotor speed never exceeds the upper limit
value 1.21 p.u. (Figure 2-12b) when the DFIG wind turbine operates in the partial
load region. In this situation, there is no actuation of the pitch angle of the rotor
blades (Figure 2-12c) and power coefficient remains constant. As a result, the active
power flow on the grid and reactive power absorbed by the wind turbine from the
grid follow the wind speed curve proportionally (Figure 2-12d and 2-12e).
When the measured responses are compared with the simulated ones, a high
degree of similarity is observed (except during the period between 27 s and 38 s).
Measured responses show that the active power and the reactive power curves
follow the wind speed curve when the DFIG wind turbine operates in the partial
load region.
Measured responses also show that the generator rotor speed exceeds 1.21 p.u.
when the DFIG wind turbine operates in the full load region and enables the
activation of pitch angle controller acting in a similar way with respect to the rate
of change (3 deg ⋅ s-1) as compared with the simulated responses (Figure 2-12c).
The generated active and reactive power saturate at 1 p.u. and -0.0656 p.u.,
respectively, during these times, as well.
On the other hand, two dissimilarities have been observed. One is the time delay in
the measured response, which is due to a finite time taken by the generation
system to produce power according to the wind incident on the turbine blade.
Simulation, on the other hand, gives almost instantaneous response from the wind
64
incident. A manipulation in inertia constant (H) with an arbitrary coefficient may
make for a higher degree of correspondence between the measured and the
simulated responses.
The other is the behaviour of the DFIG wind turbine during the period between 27
s and 38 s, where the rotor speed and output active and reactive powers decrease
with an increasing trend of the wind speed with no actuation of the pitch angle of
the rotor blades as expected. This happens due to two reasons. Firstly, wind speed
is measured with a single anemometer. This prevents the anemometer from
adequate measurement of wind speed acting on the large surface of the rotor.
Secondly, the measured wind speed is severely disturbed by the rotor wake due to
the anemometer locating on the nacelle.
2.4. Summary
This chapter accomplishes the development of a dynamic DFIG wind turbine
model, basic unit of a DFIG wind farm with a goal that the model would be of the
simplest possible design with an optimum accuracy for proper power system
dynamic behaviour and stability investigation with wind energy integration within
an optimum simulation run time. Mathematical descriptions of all subsystems of
the DFIG wind turbine, mainly the turbine, the drive train, the induction generator,
the power converters with associated control systems and the crowbar, are
elaborately explained. Except the period of the inadequacy in measurement with a
single anemometer and the effect of the rotor wake, the results simulated from the
developed model have a high degree of similarity with those obtained from the
field measurement data, which gives good confidence about the accuracy and
applicability of the developed model.
65
CHAPTER 3
Aggregated DFIG Wind Farm Model
3.1. Introduction
Typical utility scale DFIG wind farms may consist of tens to hundreds of identical
DFIG wind turbines. As a consequence, representing a wind farm with each wind
turbine unit for power system stability studies increases the complexity of the
model, and simulation thus requires enormous time. Hence, a simplification of the
wind farm model consisting of a large number of wind turbines is essential.
However, this simplification must not result in incorrect predictions of wind farm
performance during both normal operations and grid disturbances.
The objective of this chapter is to develop a novel aggregation technique with the
incorporation of a mechanical torque compensation factor (MTCF) into the full
aggregated wind farm model that enables the model to mimic the collective
responses at the point of common coupling (PCC) as if they are produced from the
complete wind farm model.
Therefore, this chapter describes the formation of a detailed model of a 120 MVA
offshore wind farm comprising of 72 DFIG wind turbines and proposes the novel
aggregation technique for the 120 MVA offshore wind farm. It first outlines
relevant theories on fuzzy logic system (FLS) and then the construction method of
the MTCF by the FLS, the calculation of equivalent internal electrical network and
further model simplifications are detailed. Finally, a quantitative analysis is carried
out to evaluate the effectiveness of the proposed aggregation technique from the
simulation results obtained from the complete, the full aggregated and the
proposed aggregated wind farm model during both normal operations and grid
66
disturbances. From the comparison, it is concluded that the proposed technique
can provide more accurate results and save computation time.
3.2. Formation of a complete DFIG wind farm model
The model of a DFIG wind farm with all of its electrical networks is presented in
this section, which is a modified version of a 120 MVA offshore wind farm model
implemented by ‘NESA Transmission Planning’ of Denmark for power stability
investigations [29] as shown in Figure 3-1. The wind farm model comprises of 72
DFIG wind turbines. Each DFIG wind turbine comprises of the same mechanical,
electrical and the control system blocks explained in Chapter 2 with the parameters
specified in Table 2-1. Each DFIG wind turbine is connected to the cable sections
through 0.67/30 kV transformer (LV/MV) and line impedance of 0.08+j0.02 p.u.
The wind farm is connected to the power grid through a 30/132 kV tertiary
transformer (MV/HV) and then through a high voltage (132 kV) transmission
network (HVTN) with the impedance value of 1.6+j3.5 p.u.
Figure 3-1: A 120 MVA offshore DFIG wind farm model
67
The internal and external electrical networks including electric lines, transformers
and cables are represented by constant impedances [8]. Short circuit capacity
viewed from the PCC into the HVTN is around 1500 MVA. The power grid is
modeled by an infinite bus with the MVA-rating of 1000 MVA.
A pair of indices identifies the DFIG wind turbine within the wind farm, where the
first index (from 1 to 6) denotes the number of the group (the 30 kV sea cable) and
the second index (from 1 to 12) denotes the number of the DFIG wind turbine
within the group. The parameters of the DFIG wind farm used in the simulation
are shown in Table 3-1 [8, 29].
Table 3-1: DFIG wind farm parameters
Parameter Symbol Value Unit
Internal electrical network
Base power SDFIG 1.5/0.9 MVA
Base voltage VDFIG 575 V
LV/MV transformer - 0.69/30 KV
ST 2 MVA
εcc 6 %
Line impedance ZL 0.08+j0.02 p.u.
External electrical network
MV/HV transformer - 30/132 KV
ST 150 MVA
εcc 8 %
HVTN impedance ZT 1.6+j3.5 p.u.
Short circuit capacity of the PCC SPCC 1500 MVA
X/R ratio of PCC (X/R)PCC 20 p.u.
Short circuit capacity of the grid SG 1000 MVA
68
3.3. Proposed aggregated DFIG wind farm model
Figure 3-2 shows the proposed aggregated DFIG wind farm model that consists of
a mechanical torque compensating factor (MTCF) incorporated into a traditional
full aggregated model. The full aggregated model provides poor approximation of
collective responses at the point of common coupling in the partial load region due
to not considering operating points of all corresponding DFIG wind turbines and
existing nonlinear relationship between the wind speed and the mechanical torque.
The MTCF (α) in the proposed model is a multiplication factor to the mechanical
torque (T’magg) of the full aggregated model that minimizes this inaccuracy in
approximation. The mechanical torque (Tmagg) of the proposed aggregated DFIG
wind farm model is thus calculated by
α*'
maggmagg TT =
(3-1)
The proposed model also involves the calculation of an equivalent internal
network and the simplification of the power coefficient (Cp) function.
Figure 3-2: Block diagram of the proposed aggregated DFIG wind farm model
69
3.3.1. Full aggregated DFIG wind farm model
The full aggregated DFIG wind farm model converts all DFIG wind turbines in the
wind farm into one equivalent unit with the same p.u. value of mechanical and
electrical parameters in the voltage, flux linkage and motion equations [8], which is
driven by an average wind speed (VWagg) [34]
∑=
=n
i
WiWagg Vn
V1
1 (3-2)
where n is the number of DFIG wind turbines in the wind farm and suffix agg
denotes the aggregated wind farm model.
This gives the mechanical torque as
tagg
Waggp
magg
VACT
ω
ρ
2
2
' = (3-3)
where ωtagg is the average turbine rotor speed calculated from V
Wagg.
3.3.2. Basis of MTCF calculation
The full aggregated model can provide an approximation of the complete model
when DFIG wind turbines operate in the full load region (i.e., when VWagg exceeds
14.5 ms-1). Thus, in this region the MTCF takes a value equal to 1.
When the wind turbines operate in the partial load region (i.e., when VWagg ranges
between 4.5 ms-1 and 14.5 ms-1), the adoption of an average operating point for the
DFIG wind turbines causes the discrepancies between the complete and full
aggregated models at different wind speeds and thus different operating points.
Figure 3-3 shows that the torque of the full aggregated model is generally lower
than that of the complete model in the partial load region. Thus, the MTCF takes a
value more than 1 in this region.
70
Figure 3-3: Torque curves of the complete and full aggregated model in the partial load
region
It means that the MTCF increases from the value 1 as VWagg increases from 4.5 ms-1
or VWagg decreases from 14.5 ms-1, which implies that the MTCF may take its
maximum value between 4.5 ms-1 and 14.5 ms-1. On the other hand, the MTCF
maintains a proportional relation with the wind speed deviation (VWσ) and it takes
a value equal to 1 when the operating points of the DFIG wind turbines in the
wind farm are identical (i.e., VWσ =0). Thus, the MTCF is a function of V
Wagg and VWσ
and may be ‘approximated’ by an ideal Gaussian function (see Figure 3-4) in the
partial load region:
( )
σσ
µ
α W
VV
Vle
WWagg
2
2
21
−−
+= (3-4)
According to Eq. 3-4, the maximum value of α is (1+l) when the wind speed is
equal to VWµ (in this thesis, V
Wµ =9.5 ms-1) and σ is the standard deviation from V
Wµ.
From empirical rule of the central limit theorem, it is known that 99.993 percent of
data lie within four standard deviation from their mean value [119]. It gives the
value of σ and l.
71
54 =σ (3-5)
32.02
1==
πσl (3-6)
Figure 3-4: Gaussian distribution of MTCF (α) with respect to average wind speed (VWagg)
3.3.3. MTCF calculation by fuzzy logic system
It is difficult to find the mathematical model for the input-output relationship for
the calculation of the MTCF, due to the complex nonlinear relationship and
ambiguous dynamics of the wind power generation system. However, based on
the expert (operator’s) knowledge, a human operator can express the input-output
relationship of a MTCF by using linguistic rules without knowing the exact
mathematical relationship and this expert knowledge described by linguistic rules
can be used to design the fuzzy logic system (FLS), which makes the FLS a very
good candidate to compute the MTCF. Thus, the FLS is adopted to calculate the
MTCF in this thesis.
A FLS comprises of three basic blocks, namely, Fuzzification, Inference system and
Defuzzification as shown in Figure 3-5 [120].
72
Figure 3-5: Block diagram of a FLS
A FLS handles crisp input signals by describing them in fuzzy terms. Firstly, the
crisp input signals are expressed in terms of membership function of the fuzzy
sets, and then the input variables are processed to determine the degree which the
input variables belong to, known as fuzzification. Membership functions are
applied as a means of controller tuning and range between 0 and 1. Membership
functions are chosen in such a way that these reflect the characteristics of the input
variables and meet the requirements of the controller.
The fuzzy inference includes the process of fuzzy logic operation, fuzzy rule
implication and aggregation. In the fuzzy inference system, the fuzzified input
variables are processed with ‘AND’ fuzzy operators (selecting minimum of the
input membership functions) and the IF-THEN rule implementation, which are
based on expert knowledge of the control problem. These rules are, in fact, the
control strategy of the system and describe the actions that are required for all
conceivable combinations of memberships.
Fuzzy sets representing the outputs of each rule are then combined into a single
fuzzy set, known as aggregation. Several aggregate methods have been proposed
73
in the literature. The maximum aggregate method, taking the maximum value of
all the output fuzzy sets to form a single fuzzy set, has been used in this work.
The desired output signal of the FLS is then transformed into a crisp value, but
several rules will fire at any time. It means each of rules makes a suggestion as to
how the output signal should be changed. Hence, the defuzzification combines the
results of all the rules and finds a crisp value. The Centre of Gravity (CoG) method
is used for defuzzification, which returns the centre of the area under the curve
representing the aggregated output fuzzy set.
The FLS is initially constructed by assigning overlapped triangular membership
functions for the fuzzy sets and setting fuzzy rules based on the ideal Gaussian
function. Triangular membership functions are easy to implement, quicker to
process and give more sensitivity, especially as variables approach zero. Firing of
more than one rule caused by the overlapping is a key feature of fuzzy systems.
The design is optimized by making possible changes in membership functions for
the fuzzy sets and fuzzy rules on trial and error basis to achieve less than 10
percent discrepancy between the proposed aggregated model and the complete
model.
The FLS takes two inputs: average wind speed (VWagg) and wind speed deviation
(VWσ). In the design of the FLS, V
Wagg ranges between 4.5 ms-1 and 14.5 ms-1. VWσ
ranges between 0 and its maximum possible value. The value of VWσ is the
maximum when wind speeds received by the wind turbines are equally spaced
within the specified range of VWagg. For 72 DFIG wind turbines, the maximum
value of VWσ is found by the following calculation:
25.55.9172
5.45.14
72
1 72
1
2
max =
−
−
−= ∑
=iW iV σ
(3-7)
74
Figure 3-6: Membership functions: (a) VWagg, (b) V
Wσ and (c) α
75
Then, according to Eq. 3-4, the MTCF (α) is 2.7 when VWagg = V
Wµ and V
Wσ = 5.25
(takes its maximum value), thus the range of the MTCF should be between 1 and
2.7.
Figure 3-6 shows that triangular membership functions are assigned to each input
or output variable. It has been selected 7 membership functions for VWagg, 7 for V
Wσ
and 8 for output α. Overall 49 (i.e., 7×7) rules are built by crossing the fuzzy sets as
shown in Table 3-2.
Table 3-2: Rules of the FLS
α VWσ
1 2 3 4 5 6 7
VWagg
1 1 1 1 2 3 3 4
2 1 1 2 3 3 4 5
3 1 2 3 3 5 6 7
4 2 3 4 5 6 7 8
5 1 2 3 4 5 6 7
6 1 1 2 3 4 5 6
7 1 1 2 3 3 4 5
The ith fuzzy rule is expressed as [55]
Rule i: if VWagg is Aa and VWσ
is Bb,
then α(n) is Cc. (3-8)
76
a= 1, 2, …., 7; b= 1, 2, …., 7; c= 1, 2, …., 49
where Aa and Bb denote the antecedents and Cc are the consequent part.
The FLS gives the values of the MTCF (i.e., α) by applying CoG method [55]
∑ ∑= =
=49
1
49
1
/)(i i
iciCn ωωα
(3-9)
where ωi denotes the grade for the antecedent, which is the product of grade for
the antecedents of each rule.
3.3.4. Equivalent internal electrical network
The aggregated wind farm must operate at an equivalent internal electrical
network. Thus, the internal electrical network of each individual DFIG wind
turbine in the complete model is required to be replaced by equivalent impedance
in the proposed aggregated wind farm model. The short circuit impedance of the
aggregated wind farm must be equal to that of the complete wind farm, which
gives the calculation of the equivalent impedance (Ze) of the aggregated wind farm
[8]
n
ZZZ wt
awte −=
(3-10)
where Zawt is the equivalent impedance of the internal electrical network of each
individual DFIG wind turbine in the complete model, Zwt is the impedance of DFIG
wind turbine.
77
3.3.5. Model simplification
The detailed representation of wind farms with DFIG wind turbines is quite
complex. However, it can be simplified assuming that the power coefficient (Cp) is
always equal to the maximum value because the control mechanism of the DFIG
wind turbine maintains its power-speed characteristics such that Cp is always
tracking its maximum value (in this thesis, Cpmax=0.48) [87]. The complicated Cp(λ,β)
characteristics from the model (Eq. 2-3) is replaced by the transfer characteristics
by a first order approximation, Due to the adoption of the maximum power
coefficient (see Figure 3-7).
Figure 3-7: First order approximation (dashed line) of transfer characteristic (solid line) of
the DFIG wind turbine.
3.4. Simulation results
Both the proposed aggregated model and the full aggregated model are simulated
to obtain the dynamic responses at the PCC under the following two conditions:
(1) normal operation and (2) grid disturbance. The variables considered for the
comparison are the active (Pe) and reactive power (Qe) exchange between the wind
farm and power system.
78
The reactive power is taken into the calculation for evaluating the effectiveness of
the proposed aggregated model because the reactive power does not solely depend
on active power generation in the DFIG wind turbine. The reactive power and
active power are independently regulated by the converter controllers in the
exchange of reactive power with the grid. In addition, the operation in the dynamic
speed range could demand lower reactive power output due to increased active
power output at strong and gusty wind conditions [121].
Figure 3-8 shows the speed of the wind received by the first DFIG wind turbine in
each group. The time delay and wake effect are accounted for approximating wind
speed for the following DFIG wind turbines in each corresponding group.
Figure 3-8: Wind speed received by the first DFIG wind turbine in each group
Any changes in wind speed upstream have effects on the wind speed downstream
after a certain time delay due to the wind speed transport. The delay is a function
of distance and wind speed. The transport time delay of wind speed (tdelay) passing
between two successive columns can be roughly estimated using [122]
W
delayV
dt =
(3-11)
79
where d is the distance between the two successive turbine columns and WV is the
average wind speed passing the first DFIG wind turbine.
Power extraction on wind flow passing the turbine creates a wind speed deficit in
the area behind the turbine. This phenomenon is known as wake effect. As a
consequence, the turbines that are located downstream obtain lower wind speed
than those that are located upstream. The deficit in wind speed due to the wake
effect depends on several factors, such as the distance behind turbine, turbine
efficiency and turbine rotor size. Wind speed in the wake at a distance x behind the
turbine rotor can be calculated as [123]
( ) ( )
−−
+−= T
w
oW CRxk
RVxV 111
2
(3-12)
where Vo is the incoming free-stream wind speed, CT is the turbine thrust
coefficient whose value is adopted from [10] and kw is the wake decay constant.
3.4.1. Normal operation
The collective responses of the complete, the full aggregated and the proposed
aggregated wind farm models at the PCC during normal operation are shown in
Figure 3-9.
The proposed aggregated model has a higher correspondence in approximating
active power (see Figure 3-9a). Comparing with the complete model, it has the
maximum and average discrepancy of 2.94 percent and 2.35 percent, respectively,
while the full aggregated model has the maximum and average discrepancy of 8.23
percent and 6.58 percent, respectively. The multiplication factor MTCF,
dynamically produced by a well-tuned FLS, manipulates the mechanical torque to
compensate existing nonlinearities in the wind farm in order to have a better
approximation in the proposed aggregated model.
80
Figure 3-9: Evaluation of the proposed aggregated wind farm model during normal
operation at the PCC: (a) Active power and (b) Reactive power
The proposed aggregated model has a higher correspondence in approximating
reactive power, as well (see Figure 3-9b). Comparing with the complete model, it
has the maximum and average discrepancy of 5.45 percent and 4.36 percent,
respectively, while the full aggregated model has the maximum and average
discrepancy of 9 percent and 8.14 percent, respectively. The manipulation of
mechanical torque in the proposed aggregated model enables it to provide a better
performance. However, poor approximation of reactive power is observed during
81
the periods between 13 s and 18 s and between 34.5 s and 38 s. Actions of converter
controllers for each DFIG wind turbine of the wind farm are not taken into
consideration in the full aggregated model that are related to reactive power
exchange between the DFIG wind turbine and the grid. But, reactive power
exchange in the system with DFIG is independent of the active power generation.
This contributes to lesser accuracy in the approximation of reactive power than
that of active power at the PCC.
The full aggregated model cannot respond to the high output power fluctuations
as compared to the complete model. The proposed aggregated model cannot do
either as it performs manipulation on the mechanical torque from the full
aggregated model. This is due to the assumption that high output power
fluctuations can be neglected in the aggregated model as it is a completely
stochastic phenomenon that can smooth over the wind turbines with the square
root of the number of turbines [87].
3.4.2. Grid disturbance
A voltage sag of 50 percent lasting for 0.1 s is originated at the PCC at t=1 s to
evaluate the proposed aggregated wind farm model during grid disturbances, the
collective responses of the complete, the full aggregated and the proposed
aggregated wind farm models at the PCC are shown in Figure 3-10.
Figure 3-10 shows that the active power produced by the wind farm reduces and
goes to negative values for a short time (i.e., the grid supplies active power to the
DFIG to keep it spinning) during grid disturbances. On the other hand, the reactive
power, which is normally negative (which means the wind farm takes reactive
power from the grid), changes sign and increases during the disturbance. This
means the wind farm supplies reactive power to the grid during the disturbance
caused by the voltage sag.
82
It also shows a high correspondence among the collective responses at the PCC of
the complete, the full aggregated and the proposed aggregated wind farm models
with negligible discrepancies on the active and the reactive powers. However, the
active power (Pe) slightly mismatches in both aggregated models right after
clearing the fault when different parameters start retaining their normal values.
This high level of correspondence is partly due to the fact that the grid
disturbances are much faster than the wind speed variations [8] and, therefore, the
discrepancies during normal operations are unimportant during grid disturbances.
Figure 3-10: Evaluation of the proposed aggregated wind farm model during grid
disturbance at the PCC: (a) Active power and (b) Reactive power at the PCC
83
3.5. Evaluation of the proposed aggregation technique
In this section, the effectiveness of the proposed aggregation technique is evaluated
in terms of accuracy in the approximation of the collective responses at the PCC,
such as the active power (Pe) and the reactive power (Qe) and the simulation
computation time.
3.5.1. Accuracy in approximating the collective responses at the PCC
The discrepancy between any instantaneous output power of the proposed
aggregated model and that of the complete model can be calculated by the
following equation [108]
comp
aggcomp
x
xxx
−=∆
(3-13)
where x can be either active power (Pe) or reactive power (Qe). Suffix comp denotes
the complete wind farm model.
Table 3-3: Accuracy in approximating the collective responses at the PCC
Operation type Full aggregated model Proposed aggregated
model
Normal operation nPe (%) 91.3 nPe (%) 100
nQe (%) 87.5 nQe (%) 100
Grid disturbance nPe (%) 95 nPe (%) 95
nQe (%) 100 nQe (%) 100
The results of accuracy in approximating the collective responses are shown in
Table 3-3, where nPe and nQe are the number of instantaneous values of active and
reactive power, respectively. It shows that less than 10 percent discrepancy has
84
been achieved between the proposed aggregated model and the complete model. It
can be seen as well that the proposed aggregated model approximates active
power (Pe) and reactive power (Qe) more accurately than the full aggregated model
by 8.7 percent and 12.5 percent, respectively, during normal operating conditions.
However, both models show the same level of accuracy during grid disturbances.
3.5.2. Simulation computation time
The comparison of computation time for the complete and both aggregated wind
farm models is made, and the results are shown in Table 3-4. The simulations are
carried out on a personal computer with the following specifications: Intel (R)
Pentium (R) Dual CPU E2200, 2.20 GHz, 1.96 GB of RAM.
Table 3-4: Comparison of simulation computation time
Operation
type
Simulation computation time (s) Reduction in simulation
time (%)
Complete
model
Full
aggregated
model
Proposed
aggregated
model
Full
aggregated
model
Proposed
aggregated
model
Normal
operation
1476 110 142 92.5 90.3
Grid
disturbance
2283 235 298 89.7 87
It can be seen that the proposed aggregated wind farm model has higher
simulation computation time than the full aggregated wind farm model by 2.38
percent and 3 percent during normal operation and grid disturbance, respectively.
A slight increase in the computation time is caused by the additional computing
85
block with the FLS to generate the MTCF. However, it has significantly reduced
the simulation computation time by 90.3 percent and 87 percent, respectively, as
compared to the complete model during normal operation and grid disturbance.
3.6. Summary
This chapter describes the development of a novel aggregation technique with the
incorporation of a MTCF into the full aggregated wind farm model to obtain
dynamic responses of a wind farm at the PCC. The aim is to simulate the dynamic
responses of the wind farm with an acceptable level of accuracy while reducing the
simulation time considerably by using the aggregation technique. The MTCF is a
multiplication factor to the mechanical torque of the full aggregated wind farm
model that is initially constructed to approximate a Gaussian function by using
fuzzy logic method. By optimizing the MTCF on a trial and error basis, less than 10
percent discrepancy is then achieved between the proposed aggregated model and
the complete model. The proposed aggregation technique is then applied to a 120
MVA offshore wind farm comprising of 72 DFIG wind turbines. Simulation results
show that the proposed aggregated wind farm model has the average discrepancy
in approximating active power (Pe) and reactive power (Qe) of 2.35 percent and 4.36
percent, respectively, during normal operation as compared to the complete
model. The proposed aggregated model, nevertheless, has 8.7 percent and 12.5
percent more approximation capability of Pe and Qe, respectively, than the full
aggregated model. In addition, the proposed aggregated model can mimic Pe and
Qe with negligible discrepancy during grid disturbance. Computational time of the
proposed aggregated model is slightly higher than that of the full aggregated
model. But, it is faster than the complete model by 90.3 percent during normal
operation and 87 percent during grid disturbance.
86
CHAPTER 4
Smoothing DFIG Output Power Fluctuations
4.1. Introduction
With large wind energy integration in power systems, wind farms begin to
influence power systems in a much more significant manner. The fluctuations of
wind power due to fluctuating wind speed thus have an adverse effect on the grid,
because they lead to frequency fluctuation in the grid and voltage flicker, which in
turn may lead to power system instability.
The objective of this chapter is to develop a fuzzy logic pitch angle controller for
the DFIG wind turbine developed in Chapter 2 on the motivation of better
smoothing performance with a minimum drop in output power. It consists of two
fuzzy logic systems (FLSs): one for partial load region and the other for full load
region. Two smoothing methods are suggested based on the FLS when the
machine is operating in the partial load region. The first method combines the
work in [42, 55], which determines the command output power through the
exponential moving average (EMA) with a proper selection of correction factor by
fuzzy reasoning so that the output power follows the command value by dynamic
pitch actuation. The second method assigns different fuzzy rules for the pitch angle
controller so that the output power is set to follow a target value according to
instantaneous wind instant.
Therefore, this chapter presents the fuzzy implementation of the pitch angle
controller for the DFIG wind turbine for its usual functionality of shedding
mechanical power for preventing the generator rotor from going above its control
speed limit when the machine is operating in the full load region by defining
87
inputs and outputs with their corresponding fuzzy sets, assigning membership
functions of those fuzzy sets and setting the fuzzy rules. Then, the FLS for both
smoothing methods is constructed in the similar way. Finally, simulation results
obtained from the proposed methods (with the fuzzy logic pitch angle controller)
are compared to those of the conventional method (with the proportional integral
(PI) pitch angle controller). It is concluded that the methods provide a better
smoothing with the sacrifice of a little drop in output power.
4.2. Fuzzy logic pitch angle controller
DFIG wind turbines may operate in the partial load region or the full load region.
Two FLSs have been incorporated in the pitch angle controller for the operation of
wind turbine in the full load region (FLS-A) and the partial load region (FLS-B).
In this work, a fuzzy logic pitch angle controller is proposed on the motivation of
better smoothing performance with a lesser drop in output power. Pitch angle
controller with the FLS is advantageous in numerous ways. Wind turbine system
is highly nonlinear with many uncertain factors like meteorological conditions and
continuously varying ac system loads [124]. It also contains some unknown
ambiguous dynamics which makes accurate dynamic modeling of a wind turbine
system difficult or even impossible [125]. However, the rules of the FLS possess
expert adaptability and learning capability to deal with imprecise, uncertain,
incomplete and nonlinear data from a wind turbine system[126]. Moreover, It is
cheap, reliable, robust and energy efficient.
Figure 4-1 shows the proposed controller with two combined FLS: FLS-A and FLS-
B.
88
Figure 4-1: Control scheme of the proposed fuzzy logic pitch angle controller
4.2.1. FLS-A
When the DFIG wind turbine operates in the full load region, the generator rotor
speed exceeds the control speed value. In this mode of operation, the controller has
got nothing to do regarding power fluctuation minimization because the generator
produces currents at its maximum rating irrespective of wind speed fluctuation,
which ensures generation of constant wind power. The only concern of the
controller is to shed mechanical power for preventing the generator rotor from
going above the control speed limit value 1.21 p.u. The FLS-A has been proposed
to incorporate the command pitch angle controller (βcA), which is only active in this
mode of operation.
To obtain command pitch angle from the FLS-A (βcA), generator rotor speed
variation from its reference value (eA) and its variation during a sampled time (∆eA)
are used as inputs. As control action of the FLS-A would be shedding mechanical
power to limit the generator rotor speed to a control speed value, using generator
rotor speed as the control input of the FLS-A is a means of direct control method. It
gives flexible control over the system by enabling constant observation on
generator rotor speed.
89
Figure 4-2: Fuzzy sets and their corresponding membership functions during above rated
wind incidents: (a) eA, (b) ∆eA and (c) βcA
90
In this work, triangular membership functions with overlapping are used. Figure
4-2 shows the input and output membership functions. The linguistic variables are
represented by N (Negative), ZE (Zero), XS (Extra Small), S (Small), M (Medium), L
(Large), XL (Extra Large), NS (Negative Small), NL (Negative Large), PS (Positive
Small) and PL (Positive Large).
The FLS-A has 35 rules that are built by crossing the fuzzy sets. The same weight
has been considered for all the rules. The rules are sorted into groups depending
on the signals they deal with. The rules are formed in a similar way of Eq. 3-5 and
listed in Table 4-1. Correction factor (k) has been crisped by the Centre of Gravity
(CoG) defuzzification method using Eq. 3-6.
Table 4-1: Rules of FLS-A
βcA ∆eA
NL NS ZE PS PL
eA NR ZE ZE ZE ZE ZE
ZE ZE ZE ZE ZE ZE
XS ZE XS XS XS S
S XS S S S M
M S M M M L
L M L L L XL
XL L XL XL XL XL
4.2.2. FLS-B
On the other hand, when the DFIG wind turbine operates in the partial load
region, there is no generation of pitch angle. Any variation in wind speed can
cause high fluctuations in wind power. To smooth the fluctuating wind power,
two methods have been proposed to incorporate the FLS-B controller by
generating command pitch angle (βcB).
91
4.2.2.1. Method one
The smoothing technique of method one is to determine a command output power
(Pe_com) from the reference output power (Pe_ref). The output power from the wind
turbine with the conventional PI controller has been considered as the reference
output power. The pitch angle is generated from the FLS output (βcB1) so that the
generated output power can follow the command output power. To accomplish
this,
• Command output power must be smooth.
• Smoothing is achieved by the generation of pitch angle with some drop
in output power. As the generated output power is always lower than
the reference output power, command output power must be ensured to
be lower than the reference value so that the fuzzy rules for the
generation of pitch angle are effectively set up by ensuring control input
of variation of reference output power from the command output power
in FLS-B falls in the positive domain.
As the initial step, the smoothed version of reference output power, known as
‘EMA command output power (Pe_com’)’ has been generated. This command value
at any instant t is given as [127]
( ) tttcome PCP γγ −+= 1'_ (4-1)
where C is the current value and P is the previous period’s value of the reference
output power and γ is the smoothing constant.
In this work, 12 periods of the average value (each of 1 s) is used in the simulation.
As a result, the EMA starts from 12 s when 12 period’s data are available.
Smoothing constant (γ) is chosen as 0.8, which indicates that 80 percent weight has
been considered for the data of the present period in comparison with 20 percent
weight to the previous period’s data. The trend of weight assigned to the previous
period’s data can be realized by expanding Eq. 4-1.
92
( ) ( )[ ]
( ) ( )
( ) ( ) 1
1
0
1
2
1
11'_
11
11
11
−
−
=−
−−
−−
−+−=
−+−+=
−+−+=
∑ t
tt
i
it
i
ttt
ttttcome
PC
PCC
PCCP
γγγ
γγγγ
γγγγ
(4-2)
The term (1-γ)t indicates that weights of the previous period’s data are
exponentially decreasing. The distribution of the EMA weights for n samples is
shown in Figure 4-3.
Figure 4-3: Distribution of EMA weights
The superiority of the EMA is that the EMA can follow wind speed more rapidly
as compared to other smoothing techniques because it uses its data of previous
periods for the next calculation [42].
93
Figure 4-4: Fuzzy sets and their corresponding membership functions for determining a
proper correction factor: (a) eB1, (b) Pe_ref and (c) k
94
To ensure the command output power (Pe_com) to be lower value than the reference
value, a concept of correction factor (k) has been introduced, which is related to the
command output power (Pe_com) in the following manner
'__ comecome PkP ×= (4-3)
The correction factor has been assessed by applying fuzzy reasoning. Variation of
reference output power from the command output power (eB1) and reference
output power (Pe_ref) are used as inputs. The system has triangular membership
functions with overlapping. Figure 4-4 shows the input and output membership
functions. The linguistic variables are represented by N, ZE, P (Positive), S, M, L,
XS, XL and XXL (Double Extra Large).
The system has got 12 rules, which are formed in the similar way of Eq. 3-5 and
listed in Table 4-2. Correction factor (k) has been crisped by the CoG
defuzzification method using Eq. 3-6.
Table 4-2: Rules for determining correction factor
k eB1
N ZE P
Pe_ref ZE XS S XXL
S XS S XL
M XS S L
L S S L
Figure 4-5 shows that the command output power (Pe_com) achieved is lower than
the reference output power (Pe_ref) over the whole 300 s period except for the
period during the rapid change in operating points from the EMA command
output power (Pe_com’) by the generation of correction factor k, where the role of k is
insignificant because output power simply switches to a different operating point
and needs not to be smoothed. The role of k is not accountable during above rated
95
wind incidents as well because output power is generated at its maximum rating
and needs not to be smoothed either.
Figure 4.5: Obtaining command output power from EMA command output power by the
generation of correction factor (k)
To obtain command pitch angle from FLS-B using method 1 (βcB1), the variation of
reference output power from the command output power (eB1) and its variation
during a sampled time (∆eB1) are used as inputs. The system has triangular
membership functions with overlapping. Figure 4-6 shows the input and output
membership functions. The linguistic variables are represented by NXL (Negative
Extra Large), NL (Negative Large), NM (Negative Medium), NS (Negative Small),
ZE, PS, PM (Positive Medium), PL, PXL (Positive Extra Large), ZEP (Zero Plus),
XXS (Double Extra Small), XS, S, M, L, XL and XXL.
FLS-B has 45 rules, which are formed in the similar way of Eq. 3-5 and listed in
Table 4-3. Command pitch angle (βcB1) has been crisped by the CoG defuzzification
method using Eq. 3-6.
96
Figure 4-6: Fuzzy sets and their corresponding membership functions during below rated wind
incidents using Method one: (a) eB1, (b) ∆eB1 and (c) βcB1
97
Table 4-3: Rules of FLS-B (Method one)
βcB1 ∆eB1
NL NS ZE PS PL
eB1 NXL XXS S ZE S L
NL XS M ZEP M XL
NM S L XXS L XXL
NS M XL S XL XXL
ZE L XXL S XXL XXL
PS XL XXL L XXL XXL
PM XXL XXL L XXL XXL
PL XXL XXL XXL XXL XXL
PXL XXL XXL XXL XXL XXL
4.2.2.2. Method two
Another method is proposed to minimize wind power fluctuations for the FLS-B
when the DFIG wind turbine operates in the partial load region. The following
steps have been carried out as a means of design strategy:
• Generated wind power (Pe) has been categorized into stages with the
steps of 0.05 p.u., which is defined as ‘Power Stage (PS)’ as shown in
Table 4-4. The lower limit value of each corresponding PS is taken as a
target value (Pe_tar) for the controller.
• If the generated wind power falls under a PS, a pitch angle would be
actuated to shed the mechanical power and limit the wind power to
Pe_tar. For instance, if Pe=0.78 p.u. at any instant, a pitch angle is actuated
to make Pe=0.75 p.u. (see PS3 in Table 4-4).
To obtain command pitch angle from FLS-B using method 2 (βcB2), variation of
reference output power from the target value selected by FLS-B (eB2) and its
variation during a sampled time (∆eB2) are used as inputs. Control action of FLS-B
98
would be limiting output power to a certain target value instead of generator rotor
speeds, which make the control design easier because the use of the rotor speed
would cause nonlinearity.
Table 4-4: Power stages
Power stage Range Pe_tar
PS1 0.9<Pe≤0.85 0.85
PS2 0.85<Pe≤0.8 0.8
PS3 0.8<Pe≤0.75 0.75
.
.
.
PS16 0.15 <Pe≤0.1 0.1
PS17 0.1<Pe≤0.05 0.05
PS18 0.05<Pe≤0 0
This system also has triangular membership functions with overlapping. Figure 4-7
shows the input and output membership functions. The linguistic variables are
represented by ZE, ZEP, XXS, XS, S, M, L, XL, XXL, NS, NL, PS and PL.
The range of the command pitch angle output is different for each corresponding
PS. It generally requires more pitch angle generation as wind power falls in the PS
of lower levels. The values of x1 and x2 of Figure 4-7c are listed in Table 4-5. The
same values of x1 and x2 for PS1 and PS18 refer to singleton output membership
function.
FLS-B has 45 rules, which are formed in a similar way of Eq. 3-5 and listed in Table
4-6. Command pitch angle (βcB2) is crisped by the CoG defuzzification method
using Eq. 3-6.
99
Figure 4-7: Fuzzy sets and their corresponding membership functions during below rated
wind incidents using Method two: (a) eB2, (b) ∆eB2 and (c) βcB2
100
Table 4-5: Command pitch angle range for FLC-B (Method two)
Power stage x1 x2 Power stage x1 x2
PS1 0 0.1 PS12 0.5 1.4
PS2 0.2 0.6 PS13 0.5 1.6
PS3 0.3 0.7 PS14 0.5 1.8
PS4-PS7 0.3 0.9 PS15 0.6 2
PS8-PS9 0.4 1.1 PS16 0.8 6
PS10 0.5 1.2 PS17 1.5 15
PS11 0.5 1.3 PS18 0 45
Table 4-6: Rules of FLS-B (Method two)
βcB2 ∆eB2
NL NS ZE PS PL
eB2 ZE XXS S ZE S L
ZEP XS M ZEP M XL
XXS S L XXS L XXL
XS M XL S XL XXL
S L XXL S XXL XXL
M XL XXL L XXL XXL
L XXL XXL L XXL XXL
SL XXL XXL XXL XXL XXL
XXL XXL XXL XXL XXL XXL
101
4.3. Simulation results
To investigate the effectiveness of the proposed methods, a wind turbine
connected to a grid has been simulated. The control action and collective responses
of the conventional method (with PI pitch angle controller) and the proposed
methods (with fuzzy logic pitch angle controller) at the grid have been compared.
A fluctuating wind pattern is considered for simulation as shown in Figure 4-8a.
The effectiveness of the proposed fuzzy logic pitch angle controller is
demonstrated in the following sections.
102
Figure 4-8: Evaluation of the proposed methods: (a) Wind speed, (b) Pitch angle, (c) Active
power and (d) Reactive power
4.3.1. Evaluation of FLS-A
The conventional PI pitch angle controller activates pitch actuation only when the
DFIG wind turbine operates in the full load region (between 102 s and 160.2 s in
Figure 4-8b). In this mode, the proposed controller also activates pitch actuation for
shedding mechanical power to prevent generator rotor from going above the
103
control speed limit value by producing the current at its maximum rating and
maintaining constant output power (Figure 4-8c and 4-8d) regardless of the change
of wind speed.
4.3.2. Evaluation of FLS-B
There is no pitch angle generation by the conventional PI pitch angle controller
when the DFIG wind turbine operates in the partial load region (for the first 102 s
and the last 139.8 s in Figure 4-8b) as there is no point of limiting the generator
rotor speed, which ensures the wind turbine operation at its maximum possible
efficiency. The outputs of active and reactive powers, however, have high
fluctuations due to abrupt variations in wind speed (Figure 4-8c and 4-8d). This is
because wind power depends on the cube of the wind speed and the input torque
cannot be controlled [55]. The smoothing is achieved by the proposed methods and
evaluated in the following sections.
4.3.2.1. Evaluation of the proposed method one
For the control strategy in the proposed method one, a command value is
generated smaller than the reference output power with the proper selection of
correction factor by fuzzy reasoning. The controller actuates pitch to limit the
output power.
It allows the output power to follow the command value. It means power
fluctuation minimization is achievable with the cost of some output power drops.
Figure 4-8c shows that partial smoothing of output power is achieved by the
method one. In Figure 4-8d, negative value of the reactive power refers to the
absorption of reactive power by the induction generator from the power grid (due
to having capacitive loads), which is directly related to the active power generation
104
and thus the absorbed reactive power is partially smoothed with the generation of
partially smooth active power. The generation of pitch angle for method one is
shown in Figure 4-8b.
4.3.2.2. Evaluation of the proposed method two
The proposed method two causes pitch actuation to limit the output power to a
target value (Pe_tar) during the operation of the DFIG wind turbine in the partial
load region. Figure 4-8c shows that the proposed pitch angle controller sheds the
output active power to ensure smoothing output power of 0.7 p.u. as it falls into
PS4 when there is no pitch angle generation for the first 40.5 s. Smooth output
power is achieved (0.65 p.u. in the next 57.6 s, 0.8 p.u. between 161.4 s and 218.4 s
and 0.6 p.u. onwards). The active power is always shed to Pe_tar for smoothing
fluctuations. The reactive power absorbed by the generator is also automatically
smoothed with the generation of smoothing active power (Figure 4-8d). The
generation of pitch angle for method two is shown in Figure 4-8b.
4.3.3. Numerical validation of the proposed methods
The validity of the proposed methods in output power smoothing has been carried
out numerically by smoothing function (Pe_smooth) and maximum energy function
(Pe_max).
Figure 4-9a shows that smoothing function (Pe_smooth) drops to 66.67 percent and 50
percent due to the application of the proposed methods one and two, respectively,
in comparison with the conventional method. The proposed method one
demonstrates the economic benefit by employing power storage system of smaller
capacity besides the controller for partial smoothing purpose. The proposed
method two ensures complete smoothing with a little more drop in output power
105
than the proposed method one. It demonstrates no requirement of compensation of
output power fluctuations by means of power storage system at least during
normal operations ensuring ample economic benefits.
Figure 4-9: Numerical validation of the proposed fuzzy logic controllers: (a) Smoothing
function and (b) Maximum energy function
Figure 4-9b shows that maximum energy functions (Pe_max) for both proposed
methods drop slightly as compared to the conventional method because the pitch
106
angle remains fixed at 0 degree when conventional PI pitch angle controller is
applied. Since the purpose of this work is to smooth the output power, a drop in
the output power cannot be avoided. This drop, however, should be at a minimum
for efficient operation. A drop in output power is approximately equal to 4.7
percent and 8.28 percent for the methods one and two, respectively.
4.4. Summary
This chapter describes the development of a fuzzy logic pitch angle controller,
which is controlled by two mutually exclusive fuzzy logic systems. The main
functions of the controllers are to regulate output power in the full load region and
smooth wind power fluctuations in the partial load region. Two methods have
been depicted for the smoothing of wind power fluctuations. The first method is to
determine the command output power based on the EMA with a proper selection
of correction factor by fuzzy reasoning to make output power to follow that
command value. The second method is to select the target output power values
dynamically according to the wind incident and limit power to obtain the target
output. The performances of the proposed fuzzy logic pitch angle controller with
both methods have been compared with that of the conventional PI pitch angle
controller. The results indicate that the proposed methods smooth output power
fluctuations with significantly smaller drop of output power as compared to the
previous works. The method one performs partial smoothing with only 4.7 percent
drop in output power demonstrating the economic benefit by employing power
storage system of smaller capacity beside the controller for smoothing purpose.
The method two performs complete smoothing with 8.28 percent drop in output
power. This smoothing ability offers economic benefits because there will be no
requirement of compensation of output power fluctuations by means of power
storage system at least during normal operations.
107
CHAPTER 5
Transient stability of DFIG integrated power system
5.1. Introduction
Transient fault plays a significantly vulnerable role in the operation of power
system. With large wind energy integration into power systems, it is justified to
have a thorough study of power system transient stability (PSTS). This is because
PSTS is largely dominated by the generator technology used in the power system
and dynamic response characteristics of DFIG wind turbines in the wind farms are
different from conventional synchronous generators (SGs) in the conventional
power plants.
The objective of this chapter can be segmented into two parts. One is to analyse the
impact of transient fault on the DFIG wind turbine to observe how it behaves
followed by a fault as compared to SGs with the variation of different factors
influential to the PSTS, such as the fault clearing time, the grid coupling, the inertia
constant and the voltage sag. The model of SG is adopted from SimPowerSystems
library of Matlab/Simulink software package. Detailed documentation on SG
modelling with its exciter and governor parameters is available in [128], which is
out of scope in this thesis.
The other is to investigate the impacts of the DFIG wind farm on the PSTS with the
variation of different factors, such as the voltage sag, the fault clearing time, the
load and the wind power penetration level (termed as wind penetration in this
thesis). The PSTS assessment is carried out in a quantitative manner. For such
quantification, transient energy margin (TEM) is defined which is evaluated
through the assessment of transient energy function (TEF).
108
Therefore, this chapter describes the theory of the TEF with its formulation for the
TEM calculation. The developed TEF is a modified version accounting the
separation of critical machines from the remaining machines for accurate transient
stability assessment. Then, the simulation cases and simulation steps are discussed.
Finally, the simulation results are obtained, which show that power systems
integrated with DFIG wind farms are sensitive to severe transient events.
Therefore, it is suggested that the DFIG wind farm integrated power systems must
be equipped with advanced switchgear, faster isolators, more efficient power
reserve systems and advanced reactive power compensating devices so that
reliable operation of power system during transient events is ensured.
5.2. Description of the TEF method
The TEF approach can be described by considering a ball rolling on the inner
surface of a bowl [61] as depicted in Figure 5-1. A stable equilibrium point (SEP) is
located at the bottom of the bowl. The rim of the bowl refers to potential energy
boundary surface (PEBS); a set of unstable equilibrium point (UEP) is located on
the PEBS. The post-fault transient dynamic could be analogous to the ball subject
to injection of some kinetic energy swinging in the bowl. If the ball converts all of
its kinetic energy before reaching the rim, it settles down in the SEP after several
swings and the system is said to be stable. If the ball passes the rim, it starts
swinging near the UEP and will never return to the SEP, and the system is said to
be unstable.
The basis for the application of the TEF method to the analysis of the PSTS is
comprehendible from the incident of a ball rolling in the bowl. At the occurrence of
a fault, the generators accelerate, the power system gains kinetic and potential
energy and moves away from the SEP. After fault clearing, the kinetic energy is
converted into the potential energy in the same manner as the ball rolling up the
109
potential energy surface. The system must be capable of absorbing the kinetic
energy before the generators are forced to operate at a new equilibrium position to
avoid instability. This depends on the energy-absorbing capability of the post-
disturbance system.
Figure 5-1: A ball rolling on the inner surface of the bowl
The method of the TEF analysis can well be realized by making an analogy to the
equal area criterion method for two-machine system as illustrated in Figure 5-2
[61], where the critical clearing angle (θc) is established by the equality of areas A1
and A2. In the TEF method, the critical clearing angle is specified in terms of the
potential and kinetic energy. The transient stability is determined by comparing
the sum of the kinetic energy gained during the fault-on period and the potential
energy at the corresponding rotor angle with the critical potential energy at the
rotor angle (θu) when the system is critically stable.
The above discussions reveal that two kinds of energies are required for the
transient stability assessment. One is the total system transient energy (Ecl), which
is injected into the system during the fault-on period. It consists of both kinetic
energy and potential energy calculated at the instant of fault clearing. The other is
110
the system critical energy (Ecr), a potential energy, which measures the energy-
absorbing capabilities of the post-fault system.
Figure 5-2: Equivalence of transient energy method with equal area criterion
5.2.1. TEF formulation in power system
The dynamic response in classical representation for the ith generator in a power
systems is given by [129]
i
i
tω
δ=
d
d (5-1)
eimi
i
i PPt
J −=d
dω (5-2)
111
where δ is the angle between the rotor flux and the resultant magnetic flux in the
air gap, ω is the generator rotor speed, Pm is the mechanical input power and Pe is
the electrical output power.
The generator rotor speed (ω) is related to its synchronous speed (ωs) by the
following equation
( ) ss ωω −= 1 (5-3)
where s is the slip, the slip of the SG is zero and the slip of the DFIG is generally
taken the values in the range of -0.2 to +0.2 [109].
J is the moment of inertia and is given by
ωHJ 2= (5-4)
where H is the inertia constant.
In Eq. 5-1 and 5-2, the angle difference is used instead of the angle with respect to
synchronously rotating frame of reference, which increases the number of state
variables. This problem is avoided by choosing the center of inertia (COI)
formulation, which references a weighted average of all the angles in the system.
However, the new representation does not change the physical meaning of angles.
The dynamics of the COI for n machines is given by
i
n
i
i
T
o JJ
δδ ∑=
=1
1 (5-5)
i
n
i
i
T
o JJ
ωω ∑=
=1
1 (5-6)
where
∑=
=n
i
iT JJ1
(5-7)
112
Transforming the variables in the COI frame of reference as
oδδα −= (5-8)
oωωω −=' (5-9)
Swing equations in the COI frame of reference for the ith generator are then given
by
'
d
di
i
tω
α= (5-10)
( )∑=
−−−=n
i
eimi
T
i
eimi
i
i PPJ
JPP
tJ
1
'
d
dω (5-11)
To account the separation of the critical machines from the remaining machines,
the rotor speed and the corresponding rotor angle for the group of critical
machines and the remaining machines are calculated separately as follows
'
1
1i
n
i
i
cr
cr
cr
JJ
ωω ∑=
= (5-12)
'
1
1i
n
i
i
sys
sys
sys
JJ
ωω ∑=
= (5-13)
i
n
i
i
cr
cr
cr
JJ
αα ∑=
=1
1 (5-14)
i
n
i
i
sys
sys
sys
JJ
αα ∑=
=1
1 (5-15)
where
∑=
=crn
i
icr JJ1
(5-16)
113
∑=
=sysn
i
isys JJ1
(5-17)
Suffixes cr and sys denote the critical machines and the remaining machines in the
systems, respectively.
Swing equations can now be written as
''
d
dω
θ=
t (5-18)
( ) ( ) ( )θω
i
n
i
eimi
sys
eqn
i
eimi
cr
eq
eq fPPJ
JPP
J
J
tJ
syscr
=−−−= ∑∑== 11
''
d
d (5-19)
where
syscr ωωω −='' (5-20)
syscr ααθ −= (5-21)
syscr
syscr
eqJJ
JJJ
+= (5-22)
Replacement of Eq. 5-18 in Eq. 5-19 results in
( ) θθωω dd ''''
ieq fJ = (5-23)
Integrating Eq. 5-23 with the appropriate upper and lower limits provides the
expression of the TEF for n generators
( ) ( ) ( ) ( )θωθθω θ
θ
θ
θPE
n
i
KEeimi
sys
eqn
i
eimi
cr
eqeqEEPP
J
JPP
J
JJE
sysi
SEPi
cri
SEPi
+=−+−−= ∑∫∑∫== 1
''
1
2''
dd2
(5-24)
where θSEP is the SEP, EKE is the transient kinetic energy (TKE) and EPE is the
transient potential energy (TPE).
114
Electrical output power from the ith row jth column element can be represented as
[61]
( )∑≠=
+=n
ijj
ijijijijei DCP,1
cossin θθ (5-25)
where C and D depend on the induced voltage, resistance and reactance of
machines and impedance of all transmission lines, transformers and loads.
Finally, we have the TEF as follows
( )
( ) ( ) ( )
( ) ( ) ( )
+−−−−+
+−−−−−
=
∑ ∑ ∫∑
∑∑ ∫∑−
= +=
+
+=
−
= +=
+
+=
1
1 11
1
1 11
2''
''
dcoscoscos
dcoscoscos
2,
sys sysji
SEPjSEPi
sys
cr crji
SEPjSEPi
cr
n
i
n
ij
jiijijSEPijijijSEPii
n
i
misys
eq
n
i
n
ij
jiijijSEPijijijSEPii
n
i
mi
cr
eq
eq
DCPJ
J
DCPJ
J
JE
θθ
θθ
θθ
θθ
θθθθθθθ
θθθθθθθ
ωθω
(5-26)
The expression for the TEF of a single-machine is thus given as
( ) ( ) ( ) ∫+−−−−=δ
δ
δδδδδδω
δωs
DCPJ
E ssm dcoscoscos2
,2
(5-27)
5.2.2. Approximation of accurate UEP
For a reliable PSTS assessment through the calculation of the TEM, an accurate
approximation of initial value of the UEP (θu) is very important. Conventionally,
the UEP is calculated by using the equal area criterion [61]
su θπθ −= (5-28)
This equation gives the most conservative value for the UEP, which may not be the
accurate one. As a result, an unstable power system shall always be detected
unstable while a stable power system may sometime be unstable during the PSTS
assessment after a fault.
115
Several steps are followed to find out the accurate UEP [61, 130]:
• A reduced form of the multi-machine power system is found out, which is
defined as [61]
( ) ( ) ( )θθ
i
n
i
eimi
sys
eqn
i
eimi
cr
eqgPP
J
JPP
J
J
t
syscr
=−−−= ∑∑== 11d
d (5-29)
where gi(θ) is called the acceleration power between the COIs of the set of
critical machines and the set of remaining machines.
• Simulation is carried out in the time domain prior to a fault until the post-
fault trajectory reaches the PEBS of the reduced system. The post-fault
trajectory crosses the PEBS if and only if gi(θ) changes its sign from negative
to positive [93]. The intersection point of the post-fault trajectory and the
PEBS is identified as an exit point.
• Considering the exit point as an initial condition, the reduced system
trajectory is integrated until the TPE reaches its first local minimum. The
TPE is approximated as
( ) θθ dgEn
i
iPE ∑∫=
−=1
(5-30)
• Using the minimum TPE value as initial guess, the UEP is obtained by
solving a system of nonlinear equations given by
( ) 0=θig (5-31)
5.2.3. TEM calculation
The TEM calculation for a single-machine involves following steps:
Step 1: Machine parameters like transient reactance (Xg’), H, B, G, etc. are recorded.
Step 2: Simulation is run in normal operating condition with a certain value of Pm.
The values of output powers (Pe, Q
e), terminal voltage (Vt) and terminal load angle
(θL) of the generator and infinite bus voltage (V
B) are recorded.
116
Step 3: Voθ∠ is calculated, which is given by [61]
( )L
L
eefaultpreL
o tV
tV
QPXg
X
V θθ
θ ∠+−∠
−
+
=∠− j*j'j _
(5-32)
where V is the internal voltage of the generator, θo is the pre-fault SEP and the
resultant magnetic flux in the air gap and XL_pre-fault is the pre-fault line reactance.
Step 4: The system initial state governed maximum first swing output (MFSO)
power (PMFSO_sys) is calculated by
T
B
sysMFSOX
VVP
*_ = (5-33)
where
faultpostLgT XXX −+= _
' (5-34)
In Eq. 5-33, XL_post-fault is the post-fault line reactance after clearance of the faulty
line.
Step 5: The post-fault SEP (θs) is calculated using the following equation.
= −
sysMFSO
m
sP
P
_
1sinθ (5-35)
Step 6: The UEP (θu) is calculated by following Section 5.2.2.
Step 7: A fault is simulated with a specific clearing time (tc). The MFSO power
followed by clearing the faulty line (PMFSO_fault) is recorded from the simulation
result. The fault responses are recorded in the time domain, as well.
Step 8: The critical clearing angle (θc) is determined by the equal area criterion [61].
117
( )
+
−= −
m
faultMFSO
omm
cP
Pθ
θθθ cos
*cos
_
1 (5-36)
where
−= −
faultMFSO
m
mP
P
_
1sinπθ (5-37)
Step 9: The system critical energy (Ecr) can be calculated from the pre-fault network
considering the following in Eq. 5-26
uθθ = (5-38)
0=KEE (5-39)
The total system transient energy (Ecl) can be calculated from the pre-fault network
considering the following in Eq. 5-26
cθθ = (5-40)
Finally, the TEM is calculated (denoted T in the Equation) by
%100×−
=cr
clcr
E
EET (5-41)
It provides a quantitative insight into the measure of the PSTS. From Eq. 5-41, if T
is positive, it indicates that the post-fault system is stable with the system’s
capacity for further absorbing T percent of the critical energy; if T is negative, it
indicates that the post-fault system is unstable and the system should be capable of
absorbing an extra T percent of the critical energy for switching into a stable state.
118
5.3. Fault response of DFIG wind turbines
5.3.1. Test system
To study the fault response of the DFIG wind turbine, a single-machine connected
to an impedance through an infinite bus is used as the test system as shown in
Figure 5-3. The test system parameters are given in Table 5-1 [131].
Figure 5-3: Single-machine infinite bus system
Table 5-1: Test system parameters
Parameter Symbol Value Unit
Base power SGEN 1.5/0.9 MVA
Base voltage VGEN 690 V
Transformer - 0.69/30 KV
ST 2 MVA
εcc 6 %
ZTr 0.08+j0.02 p.u.
Line impedance ZL 1.6+j3.5 p.u.
Short circuit capacity of the infinite bus SGRID 1000 MVA
119
5.3.2. Case design
The considered generator/system parameters and the fault characteristics for the
impact studies in this thesis are the fault clearing time, the grid coupling, the
inertia constant and the terminal voltage sag. A short circuit fault is simulated at
the generator terminal after t=1s in each simulation to investigate the fault
response with the TEM. Since transient events are much faster than wind speed
fluctuations, the DFIG is operated with constant wind speed [8]. Table 5-2 shows
the initial simulation parameters for both SG and DFIG running at a constant
mechanical input power of 0.9 p.u. The value of PMFSO_fault is considered for the
system subjected to a three-phase short circuit fault. The lower inertia constant (H)
value is taken for the DFIG than that for the SG with the same capacity, and the
rotor of the same size and material since the shaft between the turbine and the
induction generator is relatively soft [29]. Inertia constant values of the SG and the
DFIG in Table 5-2 is adopted from [87].
Table 5-2: Simulation parameters
Generator characteristics Value
Parameter Symbol Unit SG DFIG
Mechanical power Pm p.u. 0.9 0.9
Initial rotor angle θo rad 0.6992 0.71
System governed MFSO PMFSO_sys p.u. 1.1 1.054
MFSO after clearing fault PMFSO_fault p.u. 1.78 1.076
Fault clearing time tc s 0.05 0.05
Inertia constant H s 3.5 3
Slip s - 0 0.2
Load PL % of Pe 95 95
120
5.3.3. Simulation results
5.3.3.1. Impact of fault clearing time
Fault clearing time is the time interval between the fault inception and the fault
clearance. Industrial and commercial power users are increasingly less tolerant to
outages and fault clearing time has become a very important tool for PSTS studies.
Switchgear equipped with a multifunction microprocessor-based relay is an
efficient means to clear the fault nowadays.
The impact of the fault clearing time (tc) is shown in Figure 5-4. The fault is cleared
after 0.01 s, 0.05 s and 0.09 s, respectively, to observe the impact on the output
power for the SG and the DFIG.
It can be seen that the fault causes mechanical oscillations in the generator rotor
speed, which are reflected on the output power for both generators. It is obvious
that the longer time taken to clear the fault causes higher oscillations of the output
power. The settling time for the SG to damp the oscillations is almost 10 s (not
shown in Figure 5-4a) while the settling times of the DFIG is 1.26 s. The DFIG has
included the fast action of the damping controllers. Moreover, the DFIG is
equipped with two PI controllers in the rotor and grid side. It enables the
decoupled control of the active and reactive power and helps in fast restoration of
the generator terminal voltage and the grid frequency.
The TEM curve in Figure 5-4c shows that the DFIG is more sensitive to the fault
clearing time. The TEM value for the DFIG is larger till tc= 0.0525 s than that for the
SG, but it has got the fastest drop with increasing fault clearing time. The TEM
curve also gives the direct measure of the critical clearing time (CCT), which is the
maximum allowable time to clear the fault.
121
Figure 5-4: Fault responses of (a) SG, (b) DFIG and (c) TEM variation for different values of
fault clearing time (tc)
122
After the CCT, the TEM drops to a negative value, i.e., the system switches to
unstable state. For the particular simulation arrangements stated in Table 5-2, the
CCT for the SG and the DFIG are 0.073 s and 0.065 s, respectively.
5.3.3.2. Impact of grid coupling
Grid coupling has a strong relationship with the MFSO power determined by the
system initial state (PMFSO_sys). From Eq. 5-31, PMFSO_sys is inversely proportional to
the line impedance (ZL), i.e., stronger grid coupling corresponds to higher value of
PMFSO_sys. Simulations are carried out for different values of PMFSO_sys to observe the
impacts of grid coupling on the output power for the SG and the DFIG. The results
are shown in Figure 5-5.
It is clear that the TEM of the DFIG is more influenced by the variation of PMFSO_sys
as shown in Figure 5-5c. However, the variation in the grid coupling only causes a
negligible change in the value of PMFSO_sys as shown in Figure 5-6, where the slopes
of the curves depicting the relationship between ZL (neglecting resistance, RL) and
PMFSO_sys for the SG and the DFIG are -0.035and -0.0085, respectively. Thus, the grid
coupling has very insignificant impact on the TEM of the DFIG.
5.3.3.3. Impact of inertia constant
Figure 5-7 shows the impact of the inertia constant (H). Simulations are carried out
for the inertia constant values (H) of 3 s, 3.5 s and 4 s for the SG and 2.5 s, 3 s and
3.5 s for the DFIG.
It shows that smaller value of inertia constant causes higher oscillations because
the smaller the inertia constant the smaller the rotor. The inertia constant is one of
the most dominating factors for governing the TEM.
123
Figure 5-5: Fault responses of (a) SG, (b) DFIG and (c) TEM for different values of PMFSO_sys
124
Figure 5-6: Relationship between line impedance and PMFSO_sys for SG and DFIG
The TEM curve in Figure 5-7c shows that the system remains highly stable with the
SG connected to the grid since the SG has higher inertia constant value than the
DFIG. The slopes of the TEM curves for the SG and the DFIG are 18.35 percent per
second and 9.65 percent per second, respectively. It indicates that the variation of
the inertia constant has very little impact on the DFIG.
5.3.3.4. Impact of generator terminal voltage sag
Voltage sag is not a complete interruption of power; it is a temporary drop in the
generator or bus terminal voltage level. Voltage sags are probably the most
significant power quality problem being faced by the industrial customers today
and they can be a significant problem for large commercial customers, as well. The
level of voltage sag at a generator or bus terminal depends on the fault type
(magnitude and duration) or the distance of the fault from that terminal and
sensitivity of the equipment.
125
Figure 5-7: Fault responses of (a) SG, (b) DFIG and (c) TEM for different inertia constant
(H) values (the values inside the brackets corresponding to inertia constant (H) values for
DFIG)
126
Figure 5-8: Fault responses of (a) SG, (b) DFIG and (c) TEM for different values of PMFSO_sys
(the values inside the brackets corresponding to PMFSO_sys values for DFIG)
127
The impact of generator terminal voltage sag depends on the fault type and the
distance of the fault initiated from the machine. The generator terminal voltage sag
has a direct proportional relationship with the MFSO power followed by clearing
the faulty line (PMFSO_fault). Thus, the impacts of terminal voltage sag on the fault
responses and the TEM of the SG and the DFIG are analyzed by varying PMFSO_fault.
Simulations are carried out for different values of PMFSO_fault for the SG and the
DFIG according to their corresponding ranges. Results are shown in Figure 5-8.
It can be seen that high oscillations are influenced by severe type of fault and/or
by the fault initiated near to the machine (higher value of PMFSO_sys). The TEM curve
in Figure 5-8c shows that the system remains highly stable with the DFIG
connected to the grid due to proper controller actions for compensating reactive
power and pitch angle generation for damping rotor overspeed.
Figure 5-9: Relationship between terminal voltage sag and PMFSO_fault for SG and DFIG
128
Figure 5-9 shows that the slopes of the curves depicting the relationship between
the generator terminal voltage sag and PMFSO_fault for the SG and the DFIG are
0.0064 p.u. per percentage and 0.00023 p.u. per percentage, respectively. This
means that the variation in generator terminal voltage sag causes a very negligible
change in the value of PMFSO_fault for the DFIG and has the minimum impact on the
TEM of the DFIG.
5.4. Impact of DFIG wind farm on transient stability
5.4.1. Test system
IEEE New England power system is one of the most widely used test systems for
stability studies [91]. This power system consists of a 10 machine 39 bus power
system with 19 loads and 46 transmission lines as shown in Figure 5-10.
Figure 5-10: Single line diagram of IEEE New England power system
129
The reasons for using a test system rather than a practical system are [87]
• Practical power system models are not well documented, and data is partly
confidential. This shifts focus from investigating certain dynamic
phenomena to improve the model itself. Most parameters of the test system
are given in the literature which makes it convenient to use them.
• Practical power system models are usually very large, which make the
development and calculation of numerous scenarios cumbersome and time
consuming and complicates the identification of general trends.
• The results obtained with models of practical systems are less generic than
those obtained with general purpose test systems. The model can be
validated easily and compared with results of other investigations, as well.
Table 5-3: Load flow data of New England power system
Bus
Generator
Bus
Load
Bus
Load
Capacity
(MVA)
Generation
(MW)
P
(MW)
Q
(MVar)
P
(MW)
Q(MVar)
30 300 250 3 322 2.4 23 247.5 84.6
31 700 572.8 4 500 184 24 308.6 -92.2
32 700 650 5 233.8 84 25 224 47.2
33 700 632 8 522 176 26 139 17
34 600 508 12 8.5 88 27 281 75.5
35 700 650 15 320 153 28 206 27.6
36 600 560 16 329 32.2 29 283.5 26.9
37 600 540 18 158 30 31 9.2 4.6
38 900 830 20 680 103 39 950 250
39 1100 1000 21 274 115
Total capacity
6900 MVA
Total generation
6192.8 MW
Total load
5996.1 MW
130
G1-G10 are the groups of a number of SGs. SGs of G10 are modelled as a three
phase infinite source while SGs of the other nine groups are modelled in detail
with the inclusion of the turbine governors and AVR/exciter dynamics. To
improve the damping of the low frequency power oscillations, SGs of G6 are
equipped with a power system stabilizers [61].Their mathematical description is
given in detail in [128]. Load flow data of the system are given in Table 5-3 [132].
5.4.2. Case design
When all the traditional SGs are used in the IEEE New England power system, it is
referred to as ‘base operation’. If G1 is replaced with the DFIG wind farm of the
higher capacity (due to capacity factor of wind farm being lower) and the same
static output in the system, it is referred to as ‘wind operation’. Wind operation
corresponds to the wind penetration of 15 percent. The impact of the DFIG-
equipped wind farm on the PSTS is studied by comparing the fault response of
different SGs at various locations for both base operation and wind operation. A
short circuit fault is simulated at bus 39 which results in 50 percent voltage sag in
G1 terminal, which is propagated to the other SGs of the system. In the post-fault
scenario, G1 to G10 refer to individual group of those generators which remain in
synchronism.
The TEM response of the SGs, namely G10, G2, G4 and G9 (placed according to
ascending order of their distance from G1) is assessed under the variation of
different variables, such as the voltage sag, the fault clearing time, the load and the
wind penetration. The TEM, the rate of change of the TEM (∆T) and the standard
deviation of the TEM ( TEMσ ) are also analysed.
∆T implies how fast the PSTS gets affected adversely immediately after the fault
and is measured by calculating the gradient of the TEM with respect to a
parameter like voltage sag, fault clearing time, etc., which is given by
131
mn
TTT mn
−
−=∆ (5-42)
where Tn and T
m are the TEMs of the SG for the particular parameter values of n
and m, respectively.
TEMσ implies how diverse are the TEMs of different SGs and is calculated by
( )∑=
−=n
i
iTEM TTn 1
21σ (5-43)
whereT is the average TEM of n number of generators.
5.4.3. Simulation results
5.4.3.1. Impact of voltage sag
Simulation results for different voltage sag values are shown for SGs of G10, for
example, in Figure 5-11. The voltage sag crossover point of TEM for base operation
is about 37 percent. It means the wind operation provides more positive impact on
the PSTS if the voltage sag is less than 37 percent. Otherwise, the wind operation is
more vulnerable to power system instability as compared to the base operation.
The crossover points for G2, G4 and G9 are 42 percent, 61.5 percent and 82.5
percent, respectively. The explanation lies in the properties of DFIG wind turbines.
The DFIG wind turbine is equipped with external power electronic devices that
decouple control of active and reactive power and restoration of terminal voltage.
Thus, the system possesses more favorable transient response during the wind
operation than the base operation. On the other hand, the DFIG has a softer and
more flexible shaft system than the SG, it can accumulate a high amount of energy
in the rotating mass of the DFIG wind turbine. This large amount of transient
132
energy is released to the system followed by the fault, which is difficult to be
absorbed by the system due to having limited energy absorbing capability. Thus,
the wind operation becomes more vulnerable to transient instability than the base
operation as voltage sag increases.
Figure 5-11: TEM for different voltage sags
The rate of change of the TEM (∆T) for the increment of voltage sag is investigated
and summarized in Table 5-4. ∆T is calculated as the fall of the TEM for every 10
percent change in voltage sag.
From Table 5-4, it is seen that ∆T possesses higher negative value with the
increasing voltage sag for all SGs during the wind operations as compared to that
during the base operation. This is consistent with the graphical observations in
Figure 5-11.
∆T of the SGs for both modes of operation get more identical with their increasing
distance from G1. This indicates that DFIG wind farm has less impact on SGs that
are at farther distance because those SGs generate a small amount of transient
energy that can be easily absorbed by the system.
133
Table 5-4: The rate of change of TEM (∆T) for increment in voltage sag
Voltage sag
increment (%)
The rate of change of TEM(∆T) for increment in voltage sag
G10 G2 G4 G9
From To Base
operation
Wind
operation
Base
operation
Wind
operation
Base
operation
Wind
operation
Base
operation
Wind
operation
10 20 -0.611 -0.8 -0.511 -0.661 -0.498 -0.659 -0.468 -0.56
30 40 -0.982 -1.284 -0.882 -0.981 -0.863 -0.965 -0.841 -0.945
50 60 -1.204 -1.358 -1.104 -1.226 -1.087 -1.209 -1.033 -1.147
70 80 -1.665 -1.75 -1.565 -1.748 -1.53 -1.71 -1.12 -1.383
90 100 -1.913 -2.167 -1.813 -2.062 -1.8 -2.05 -1.223 -1.443
134
The standard deviations of the TEM (σTEM) of the SGs for both base and wind
operations under different voltage sags are shown in Figure 5-12. It shows that σTEM
is higher among SGs at different locations during wind operation when voltage
sag is above 20 percent. It means a DFIG wind farm integrated into power systems
results in diverse fault response for individual SGs at different locations when
voltage sag is above a certain threshold.
Figure 5-12: Standard deviation of TEM ( TEMσ ) for different voltage sags
5.4.3.2. Impact of fault clearing time (tc)
Simulation results for different fault clearing time (tc) values are shown for G10, for
example, in Figure 5-13. The fault clearing time crossover point of the TEM for base
operation is about 0.048 s. It means the wind operation provides more positive
impact on the PSTS if the fault clearing time is less than 0.048 s. Otherwise, the
wind operation is more vulnerable to power system instability as compared to the
base operation. The crossover points for G2, G4 and G9 are 0.057 s, 0.074 s and
0.082 s, respectively. This is because the system encounters with higher modes of
135
oscillations if the fault clearing time is longer. In such a situation, the natural
damping ability of the SGs due to having higher inertial constant (H) as compared
to the DFIG is more helpful than the decoupled control ability of the DFIG wind
turbine.
Figure 5-13: TEM for different fault clearing times (tc): (a) G10, (b) G2, (c) G4 and (d) G9
The rate of change of the TEM (∆T) for the increment of 0.01 s in fault clearing time
is investigated and summarized in Table 5-5. ∆T is calculated as the fall of the TEM
for every 0.01 s change in fault clearing time.
The results in Table 5-5 demonstrate that PSTS is more severely affected prior to
fault with longer fault clearing time in the power systems integrated with the DFIG
wind farms that is consistent with the graphical observations in Figure 5-13. ∆T of
the SGs for both modes of operation gets more identical with their increasing
distance from G1 indicating lesser impact of DFIG wind farms on those SGs.
136
Table 5-5: The rate of change of TEM (∆T) for increment of in fault clearing time (tc)
Fault clearing time
increment (s)
The rate of change of TEM (∆T) for increment of in fault clearing time (tc)
G10 G2 G4 G9
From To Base
operation
Wind
operation
Base
operation
Wind
operation
Base
operation
Wind
operation
Base
operation
Wind
operation
0.01 0.02 -4.03 -5.29 -2.03 -3.02 -1 -1.73 -0.15 -0.54
0.03 0.04 -9.41 -10.16 -7.41 -8.1 -6.34 -6.74 -5.43 -5.67
0.05 0.06 -14.78 -15.5 -12.78 -13.78 -11.67 -7.98 -10.75 -10.88
0.07 0.08 -20.16 -24.72 -18.17 -19.15 -16.2 -17.83 -14.8 -14.83
0.09 0.1 -25.35 -31.85 -22.53 -28.06 -20.83 -24.47 -20 -20.22
0.11 0.12 -30.95 -41.3 -26.95 -33.89 -24.93 -27.84 -24.51 -30
137
The standard deviations of the TEM (σTEM) of the SGs for both base and wind
operations under different fault clearing times are shown in Figure 5-14. It shows
that a DFIG wind farm integrated into power systems results in diverse fault
response for individual SGs at different locations when fault clearing time is above
0.03 s.
Figure 5-14: Standard deviation of TEM (TEMσ ) for different fault clearing times (tc)
5.4.3.3. Impact of load demand
Load demand is the power consumed momentarily with the generation of power.
It is expressed as the percentage of power consumed to power generated.
Simulation results for different load demand values are shown for G10, for
example, in Figure 5-15. It shows that the SGs possess better transient stability
with higher load demand at bus 39 for both operations. At lower load demand, the
power system suffers from power imbalances prior to the fault and due to this fact
the system cannot absorb the transient energy generated effectively before the
CCT. It results in transient instability of the system, which is indicated by the
negative value of the TEM.
138
Figure 5-15: TEM for different load demands: (a) G10, (b) G2, (c) G4 and (d) G9
The rate of change of the TEM (∆T) for the increment in load demand is
investigated and summarized in Table 5-6. ∆T is calculated as the fall of the TEM
for every 10 percent change in load demand.
It is observed in Table 5-6 that ∆T possesses higher positive value with the higher
load demand for all the SGs during both the base and wind operations. It indicates
that the higher load demand provides a positive impact on the PSTS during both
operations. It also indicates that ∆T is higher during the base operation than the
wind operation at lower load demand even though loads have an almost similar
impact on both modes of operations for all the SGs. This is because of the
intermittent nature of wind power generation that results in power imbalances in a
worse manner during the wind operation.
The standard deviations of the TEM (σTEM) of the SGs for both base and wind
operations under different load demands are shown in Figure 5-16. It shows that
DFIG wind farm integration into power systems results in diverse fault response
for individual SGs at different locations when load demand is below 88 percent.
139
Table 5-6: The rate of change of TEM (∆T) for increment in load demand
Load demand
increment (%)
The rate of change of TEM (∆T) for increment in load demand
G10 G2 G4 G9
From To Base
operation
Wind
operation
Base
operation
Wind
operation
Base
operation
Wind
operation
Base
operation
Wind
operation
10 20 0.482 0.467 0.432 0.427 0.245 0.243 0.253 0.251
30 40 0.65 0.642 0.59 0.585 0.316 0.314 0.361 0.359
50 60 0.858 0.849 0.808 0.803 0.41 0.405 0.41 0.4
70 80 1.078 1.074 0.952 0.903 0.465 0.464 0.463 0.46
90 100 1.2 1.2 1.028 1.008 0.555 0.555 0.553 0.552
140
Figure 5-16: Standard deviation of TEM ( TEMσ ) for different load demands
5.4.3.4. Impact of wind penetration
The wind penetration is the ratio of the installed wind power capacity to the total
power capacity of the grid. It is expressed as the percentage of wind power
capacity to the total power capacity.
Simulation results in Figure 5-17 show that the SGs possess poorer transient
stability with higher wind penetration, which is indicated by the negative slope of
the TEM because higher wind penetration refers a larger number of the soft and
flexible shaft of the DFIG wind turbines. This causes the power system to suffer
from transient instability as discussed earlier.
141
142
Figure 5-17: TEM for different wind penetrations: (a) G10, (b) G2, (c) G4 and (d) G9
It is also seen from Figure 5-17 that the DFIG wind farm plays a positive role on the
PSTS if the wind penetration is below 15.8 percent. Although DFIG wind turbine
features with decoupled controllability and reactive power support at lower wind
penetration, more transient energy is accumulated in its rotating mass at higher
wind penetration while the system has a limited energy absorbing capability.
The critical wind penetration (that value of penetration when the TEM of a
particular SG reaches zero) for G10, G2, G4 and G9 during the wind operation are
about 21.3 percent, 22.5 percent, 25.2 percent and 26.2 percent, respectively. The
reason behind increasing critical value with increasing distance of the SGs from the
fault location is that the transient energy generated by those SGs is less, which can
easily be absorbed by the system to sustain the PSTS.
The standard deviation of the TEM (σTEM) of the SGs for both base and wind
operations for different wind penetrations are shown in Figure 5-18. The σTEM curve
demonstrates that SGs at different locations possess more diverse fault response
for individual with larger DFIG wind farm penetration into power systems.
143
Figure 5-18: Standard deviation of TEM (TEMσ ) for different wind penetrations
5.5. Summary
The works in this chapter can be segmented into two parts. One is to analyse the
impact of transient fault on the DFIG wind turbine to observe how it behaves
followed by a fault with the variation of different factors influential to PSTS, like
the fault clearing time, the grid coupling, the inertia constant and the generator
terminal voltage sag. The other is to investigate the impacts of the DFIG wind farm
on PSTS with the variation of different factors, like the voltage sag, the fault
clearing time, the load and the wind penetration. The assessment of fault response
of the machines is carried out in a quantitative manner. For such quantification, the
TEM is used which is calculated through the evaluation of the TEF.
For the study of the fault response of the DFIG wind turbine as compared to the
SG, a short circuit fault is simulated in a single-machine infinite bus system. The
TEF derived is for single-machine system and is modified that enables the
calculation of the TEM for both the SG and the DFIG.
144
Simulation results demonstrate that the SG possesses higher TEM value implying
more favorable transient behaviour than the DFIG, because the SG has higher
inertia constant (H) value, one of the most dominant factors on transient energy
conversion after a fault occurrence. Higher inertia constant value of the SG should
result naturally in better damping of oscillations than the DFIG wind turbines, but
simulation results show that the DFIG damps oscillations almost 85 percent faster
than the SG, because the DFIG has included the fast action of the damping
controllers. Moreover, the DFIG is equipped with two PI controllers in the rotor
and grid side. It enables the decoupled control of the active and the reactive
powers and helps in fast restoration of the generator terminal voltage and the grid
frequency. The fault clearing time should be almost 11 percent faster for the system
with the DFIG than the SG for the parameters chosen in Table 5-2, otherwise the
TEM of the DFIG reaches a high negative value faster than that of the SG, i.e., the
system becomes highly unstable after the CCT, thus the DFIG must be equipped
with a fast and efficient breaker/isolator. However, it is also advocated that the
grid coupling, the inertia constant and the generator terminal voltage sag
variations have significantly less impact on the DFIG. This implies that DFIG
shows a consistent transient performance within a wide range of these factors.
For the study of the impact of the DFIG wind farm on PSTS, a short circuit fault
simulated at the G1 terminal in the IEEE New England power system and TEM
response of the SGs, namely G10, G2, G4 and G9 (placed according to ascending
order of their distance from G1) in the power system are compared between the
base operation (when all the traditional SGs are used) and the wind operation
(when the SG, namely G1 is replaced with a DFIG wind farm of the same capacity).
The TEF derived is for a multi-machine system and is modified that accounts the
separation of critical machines from the remaining machines for proper transient
stability assessment.
145
Simulation results demonstrate that power systems integrated with DFIG wind
farms are less sensitive to transient events than those without wind farms when
the voltage sag, fault clearing time and wind penetration are below certain
thresholds. They are less sensitive as well when the load demand is above a
threshold value. Outside these thresholds, the wind farms have an adverse effect
on the transient stability. The DFIG wind turbine has softer and more twisted shaft
system than that of the SG, which causes the accumulation of a very large amount
of energy in the rotating mass, which is released to the system followed by the
fault while the system has a limited energy absorbing capabilities. Thus, the result
points out to the fact that power systems integrated with DFIG wind farms must
be equipped with advanced switchgear and faster isolators to ensure its reliable
operation during transient events.
DFIG wind farms have less significant impact on those SGs that are farther from
the location of the fault, but they result in diverse fault responses for individual
SGs at different locations for certain thresholds of variables. The fault response
becomes more diverse with larger wind energy penetration. This fact draws us an
attention to having an advanced protection system with sensitivity of a wide range
of stability (i.e., TEM) connected to each individual machine.
The problem of power imbalances caused by the variability and intermittency of
wind power along with dynamically varying load demands may be prevented
from the use of an efficient power reserve systems or advanced reactive power
compensating device in the power systems integrated with DFIG wind farms.
146
CHAPTER 6
Conclusions and future works
6.1. Conclusions
With large wind energy integration in power systems, wind farms begin to
influence power systems in a much more significant manner. As wind energy is
regarded as a variable energy source from the point of view of the power grid due
to intermittent and fluctuating nature of wind speed, it influences reliable
operation of power grids. As a result, a number of challenges are encountered for
the stable operation of a large power system, such as power quality problems (like
voltage dips, frequency variations and low power factor), power imbalance due to
the unpredictability of wind power generation and load requirements, requirement
of extra reserves and strong transmission grid. Moreover, wind energy systems
utilize different generator technologies from the one utilized in the conventional
power plants. The steady-state, transient and small-signal dynamics, as well as,
power system stability will thus be significantly affected in a different manner at
some points since power system dynamics is governed mainly by the generators.
The thesis mainly focuses on two of several major challenges associated with
power system dynamics with wind energy systems, which are wind power
fluctuations and wind energy dynamic impacts on power system transient stability
(PSTS).
An adequate model for wind farm is of prime necessity before addressing these
issues. Many manufacturers have switched from conventional constant speed
concept to variable speed concept due to less acoustic and mechanical stress,
energy efficiency, decoupled controllability and improved power quality. As a
result, the installation of wind turbines equipped with doubly-fed induction
147
generator (DFIG) in the wind farms has been significantly increased in recent
years. Therefore, the first step in developing of a wind farm model would be to
develop a dynamic model of a DFIG wind turbine, a basic unit of the DFIG wind
farms.
A validated dynamic DFIG wind turbine model
This thesis presents a dynamic DFIG wind turbine model describing operations
and mathematical equations of its various subsystems, mainly the turbine rotor,
the drive train, the induction generator, the power converters and associated
control systems and the crowbar. The factors appropriate for power system
dynamics and stability studies are included in the model. It has been kept in mind
that the model must be compatible with the standardised positive sequence
fundamental frequency representation, validated against measurement data and
computationally efficient.
The developed model shows a high degree of similarity with the field
measurement data, which gives good confidence about the accuracy and
applicability of the developed model.
Aggregated DFIG wind farm model
Typical utility scale DFIG wind farms may consist of tens to hundreds of identical
DFIG wind turbines. As a consequence, representing a wind farm with each wind
turbine unit for power system stability studies increases the complexity of the
model, and simulation thus requires enormous time. Hence, a simplification of the
wind farm model consisting of a large number of wind turbines is essential.
However, this simplification must not result in incorrect predictions of wind farm
behaviours during both normal operations and grid disturbances.
This thesis develops a novel aggregation technique with the incorporation of a
mechanical torque compensation factor (MTCF) into the full aggregated wind farm
148
model to obtain dynamic responses of a wind farm at the point of common
coupling. The aim is to simulate dynamic responses of the wind farm with an
acceptable level of accuracy while reducing the simulation time considerably by
using the aggregation technique. The MTCF is a multiplication factor to the
mechanical torque of the full aggregated wind farm model that is initially
constructed to approximate a Gaussian function by a fuzzy logic method. By
optimizing the MTCF on a trial and error basis, less than 10 percent discrepancy is
then achieved between the proposed aggregated model and the complete model.
The proposed aggregated model is then applied to a 120 MVA offshore wind farm
comprising of 72 DFIG wind turbines. Simulation results show that the proposed
aggregated wind farm model approximates active power and reactive power more
accurately than the full aggregated wind farm model during normal operation
while it shows a similar performance as the full aggregated wind farm model
during grid disturbance. Its computational time is slightly higher than that of the
full aggregated model. But, it is faster than the complete wind farm model by 90.3
percent during normal operation and 87 percent during grid disturbance.
Smoothing DFIG output power fluctuations
Low density of air energy causes the wind to be fluctuating in a significant
manner. With large wind energy integration in power systems, the fluctuations of
wind power due to fluctuating wind speed have an adverse effect on the grid
because they lead to frequency fluctuation in the grid and voltage flicker, which in
turn may lead to power system instability.
This thesis develops a fuzzy logic pitch angle controller on the motivation of better
smoothing performance with a minimum drop in output power. The FLS is chosen
due to its efficient performance in a wind farm even without a thorough
knowledge on its ambiguous dynamics. It proposes two smoothing methods. The
first method combines the work in [42, 55], which determines the command output
power through the exponential moving average (EMA) with a proper selection of
149
correction factor by fuzzy reasoning so that the output power follows the
command value by dynamic pitch actuation. The second method assigns different
fuzzy rules for the pitch angle controller so that the output power is set to follow a
target value according to instantaneous wind instant.
The performances of the proposed fuzzy logic pitch angle controller with both
methods have been compared with that of the conventional proportional integral
(PI) pitch angle controller. The results indicate that the proposed methods smooth
output power fluctuations with significantly small drop of output power as
compared to the previous works. The method one performs partial smoothing with
only 4.7 percent drop in output power demonstrating the economic benefit by
employing power storage system of smaller capacity besides the controller for
smoothing purpose. The method two performs complete smoothing with 8.28
percent drop in output power. This smoothing ability offers economic benefits
because there will be no requirement of compensation of output power
fluctuations by means of power storage system at least during normal operations.
Transient stability of DFIG integrated power system
Higher installation capacity of the DFIG wind farm brings about wide influence of
wind power on the grid and causes a major change in the operating conditions of
the power systems especially during transient events. This is due to the fact that
transient stability is largely dominated by the generator technology used in the
power system, and dynamic response characteristics of DFIG wind turbines in the
wind farms are different from the conventional synchronous generators (SGs) in
the conventional power plants. This brings new challenges in the stability issues
and, therefore, it is very important and imperative to study these wind turbine
models in power system dynamic evaluations with large grid-connected wind
farms elaborately and systematically.
This thesis carries out two types of research on transient stability with wind energy
integrated power systems. One is to analyse the impact of transient fault on the
150
DFIG wind turbine to observe how it behaves followed by a fault with the
variation of different factors influential to the PSTS, like the fault clearing time, the
grid coupling, the inertia constant and the generator terminal voltage sag. The
other is to investigate the impacts of the DFIG wind farm on PSTS with the
variation of different factors, like the voltage sag, the fault clearing time, the load
demand and the wind penetration.
The transient stability assessment is carried out in a quantitative manner. For such
quantification, transient energy margin (TEM) is used which is calculated through
the evaluation of transient energy function (TEF).
Fault response of the DFIG wind turbine
For the study of the fault response of the DFIG wind turbine as compared to the
SG, a short-circuit fault is simulated in a single-machine infinite bus system. The
TEF for a single-machine system has been modified to calculate the TEM for both
the SG and the DFIG. It is demonstrated that the SG possesses higher TEM value
implying more favorable transient behaviour than the DFIG because the SG has
higher inertia constant value, one of the most dominant factors on transient energy
conversion after a fault occurrence. Higher inertia constant value of the SG should
result naturally in better damping of oscillations than the DFIG wind turbines, but
simulation results show that the DFIG damps oscillations almost 85 percent faster
than the SG, because the DFIG has included the fast action of the damping
controllers. Moreover, the DFIG is equipped with two PI controllers in the rotor
and grid side. It enables the decoupled control of the active and the reactive
powers and helps in fast restoration of the generator terminal voltage and the grid
frequency. The fault clearing time should be almost 11 percent faster for the system
with the DFIG than that for the SG for the parameters chosen in Table 5-2;
otherwise the TEM of the DFIG reaches a high negative value faster than that of
the SG, i.e., the system becomes highly unstable after the CCT; thus the DFIG must
be equipped with a fast and efficient breaker/isolator. However, it is also
151
advocated that the grid coupling, the inertia constant and the generator terminal
voltage sag variations have significantly small impact on the DFIG. This implies
that DFIG shows a consistent transient performance within a wide range of these
factors.
Impact of DFIG wind farm on transient stability
For the study of the impact of the DFIG wind farm on the PSTS, a short circuit fault
simulated at the G1 terminal in the IEEE New England power system and the TEM
response of the SGs, namely G10, G2, G4 and G9 (placed according to ascending
order of their distance from G1 and the fault) in the power system are compared
between the base operation (when all the traditional SGs are used) and the wind
operation (when the SG, namely G1 is replaced with a DFIG wind farm of the same
capacity). The TEF derived is for a multi-machine system and is modified that
accounts the separation of the critical machines from the remaining machines for
proper transient stability assessment.
Simulation results demonstrate that power systems integrated with DFIG wind
farms are less sensitive to transient events than those without wind farms when
the voltage sag, fault clearing time and wind penetration are below certain
thresholds. They are less sensitive as well when the load demand is above a
threshold value. Outside these thresholds, the wind farms have an adverse effect
on the transient stability. DFIG wind turbine has softer and more twisted shaft
system than that of the SG, which causes accumulation of a very large amount of
energy in the rotating mass, which is released to the system followed by the fault
while the system has a limited energy absorbing capabilities. Thus, the result
points out to the fact that power systems integrated with DFIG wind farms must
be equipped with advanced switchgear and faster isolators to ensure its reliable
operation during transient events.
152
DFIG wind farms have less significant impact on those SGs that are farther from
the location of the fault, but they result in diverse fault response for individual SGs
at different locations for certain thresholds of variables. The fault response
becomes more diverse with larger wind energy penetration. This fact draws us an
attention to having an advanced protection system with sensitivity of a wide range
of stability (i.e., TEM) connected to each individual machine.
The problem of power imbalances caused by the variability and intermittency of
wind power along with dynamically varying load demands may be prevented
from the use of an efficient power reserve systems or advanced reactive power
compensating device in the power systems integrated with DFIG wind farms.
6.2. Future works
The following prospective topics are proposed for future works, which are relevant
to the works carried out in the thesis:
• A validation method of the DFIG wind turbine against field measurement
data is preferred, which would comprise of more detailed wind data (that
includes wind speed, as well as, wind direction), wind energy dynamics like
rotor wake and tower shadow during both normal operations and grid
disturbances.
• The aggregated wind farm model might be improved by a finer tuning of
the fuzzy logic system (FLS) so that it is able to approximate collective
responses, like active power (Pe) and reactive power (Qe) at the point of
common coupling (PCC) more accurately. A further simplification in the
FLS structure in an optimum way might increase the computation
efficiency.
153
• The unit step response of the pitch angle controller with the proposed fuzzy
logic system as compared to the conventional one may be analysed by
assessing overshoot, rise time, settling time and steady state error.
• The effectiveness of the proposed fuzzy logic system may be studied as
compared to the load frequency controller considering simultaneous
fluctuations at both the generation and the load sides.
• The performance of the proposed fuzzy logic system to enable fault ride
through operation of DFIG wind turbines may be analysed quantitatively as
compared to the conventional one by calculating the TEM.
• The study on the impact of wind energy systems with the DFIG on the PSTS
might be repeated in a number of standard power systems, like IEEE 30 bus
system, CIGRE B4-39 grid etc. and real power systems, like Dutch power
system, Nordic power system etc., which would give more confidence on
the results achieved in this thesis. The study might also be extended by
simulating faults in different locations, integrating wind farms in different
grids, etc.
• The study on the impact of wind energy systems with the DFIG on the PSTS
opens a doorway towards research on inventing a faster and more
intelligent breaker/isolator than the one already in the market for reliable
operation of wind energy integrated power system.
154
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