UNIVERSIDADEFEDERALDO RIO GRANDE DO NORTE
UNIVERSIDADEFEDERAL DORIOGRANDE DO NORTE
CENTRO DETECNOLOGIA
PROGRAMA DEPÓS-GRADUAÇÃO EM
ENGENHARIAELÉTRICA E DECOMPUTAÇÃO
A NOVEL CONTROL STRUCTURE TO ENHANCE THE
DFIG-BASED WIND ENERGY CONVERSION SYSTEM
INTEGRATION TO THE GRID
Filipe Emanuel Vieira Taveiros
Advisor: Prof. Dr. Flavio Bezerra Costa
Thesis presented to the UFRN Graduate Pro-gram in Electrical and Computer Engineering (area: automation and systems) in partial ful-fillment of the requirements for the degree of Doctor in Engineering Science.
Serial Number PPgEEC: D228
Natal, RN, August 2018
Universidade Federal do Rio Grande do Norte - UFRN Sistemas de Bibliotecas - SISBI
Catalogação de publicação na fonte. UFRN - Biblioteca Central Zila Mamede
Taveiros, Filipe Emanuel Vieira.
Uma Nova Estrutura de Controle para Melhorar a Integração do Sistema de Con-versão de Energia Eólica Baseado no DFIG à Rede Elétrica / Filipe Emanuel Vieira Taveiros. - 2018.
215f.: il.
Tese (doutorado) - Universidade Federal do Rio Grande do Norte, Centro de Tec-nologia, Programa de Pós-graduação em Engenharia Elétrica e da Computação. Natal, RN, 2018.
Orientador: Dr. Flavio Bezerra Costa
1. Gerador de indução duplamente alimentado - Tese. 2. Realimentação de estados - Tese. 3. Códigos de rede - Tese. 4. Suportabilidade a faltas e afundamentos - Tese. 5. Amortecimento de fluxo - Tese. I. Costa, Flavio Bezerra. II. Título.
I dedicate this work to my father
Antonio Alves Taveiros
and to my mother
Maria Aureliana Vieira Taveiros.
...whatsoever things are true,
whatsoever things are honest,
whatsoever things are just,
whatsoever things are pure,
whatsoever things are lovely,
whatsoever things are of good report;
if there be any virtue, and if there be any
praise, think on these things.
Philippians 4:8
Acknowledgment
To God, worthy of all honor, all glory and all praise.
To my mother and my father, to whom I dedicate this work and from whom I emanate all the motivation and strength for the accomplishment of this work.
To my wife Priscila for her love, support and all the comfort she provided me so that I could finish this thesis. I would also like to thank her for her significant help and time commitment in setting up the practical experiment.
My thanks and appreciation go to my supervisors, Dr. Luciano Sales Barros and Dr. Flávio Bezerra Costa, for their guidance, support, time, patience and attention to my aspirations. Their advice and opinions have helped me to overcome many problems during the last years, since my undergraduate.
I would like to thank my colleagues Aguinaldo, Dolvim, Flaviano, Marco Aurélio, Mário Guil-herme, Patrício, João Ribeiro and Wellington of the Centro de Lançamento da Barreira do Inferno (CLBI) for all their support.
To the colleagues Rodrigo Prado and João Campos and other graduate colleagues for the shared experiences.
Finally, I would like to thank the Federal University of Rio Grande do Norte, the Graduate Pro-gram in Electrical and Computer Engineering, the School of Sciences and Technology (ECT) and the Brazilian National Research Council (CNPq) for the opportunity.
Resumo
O sistema de conversão de energia eólica baseado no Gerador de Indução Duplamente Ali-mentado (DFIG) atualmente predomina no mercado de energia eólica devido às suas vantagens em relação a outras topologias. O controle apropriado dos conversores back-to-back permite que as turbinas eólicas baseadas no DFIG operem no modo de velocidade variável, cujos bene-fícios incluem máxima extração da potência disponível no vento, injeção de potência reativa e redução do estresse mecânico. Entretanto, o crescente número de sistemas de conversão de energia eólica levou os operadores da rede elétrica a estabelecer regulamentos específicos para conexão destes sistemas à rede. Nestes regulamentos, a suportabilidade a faltas e afundamen-tos de tensão é um dos mais importantes aspecafundamen-tos, além fornecer potência reativa para a rede de modo a dar suporte à rede para restabelecer o nível de tensão durante uma falta. Portanto, é man-datório que estes sistemas mantenham um alto nível de controlabilidade durante tais distúrbios. Esta tese investiga o impacto das estratégias de controle e acionamento no desempenho do sis-tema de conversão de energia eólica baseado no DFIG, sob as perspectivas da máxima extração de potência e da suportabilidade a faltas, de acordo com os regulamentos das redes do Brasil, Canadá, Estados Unidos e Alemanha. É proposta uma nova estrutura de controle por realimen-tação de estados de ordem aumentada com característica preditiva para ser aplicada ao controle do gerador, que considera de maneira integrada a dinâmica das correntes da máquina em con-junto com a formulação geral da perturbação eletromagnética presente durante faltas simétricas e assimétricas, bem como os erros de rastreamento. A estrutura proposta foi desenhada para efetivamente suprimir a dinâmica oscilatória do surto de força contra-eletromotriz que ocorre no caso de uma perturbação na tensão da rede para, desta forma, mitigar oscilações e surtos no torque eletromagnético e nas correntes da máquina, isentando a necessidade de usar estraté-gias de modificação de referência de corrente ou a ativação da proteção física durante faltas de nível intermediário, permitindo assim que o DFIG suporte distúrbios simétricos e assimétricos na rede apresentando oscilações de torque limitadas e fornecendo corrente reativa, conforme demandado pelos códigos de rede. No caso da falta severa, a estrutura proposta permite o efe-tivo rastreio das referências de corrente calculadas para mitigar as oscilações e sobreníveis de corrente e tensão. A estrutura proposta também emprega uma nova técnica de amortecimento de fluxo que acentua a componente de eixo direto da corrente do rotor para reduzir significati-vamente o tempo de estabilização do fluxo do estator após as faltas, enquanto o torque oscila minimamente durante a recuperação pós-falta. Resultados obtidos por meio de simulações dig-itais em tempo real e ensaios experimentais em condições ideais e não ideais demonstram a superioridade da estrutura proposta em relação a técnicas convencionais e anteriores.
Palavras-chave: gerador de indução duplamente alimentado, realimentação de estados, códigos de rede, suportabilidade a faltas e afundamentos, amortecimento de fluxo
Abstract
The doubly fed induction generator (DFIG)-based wind energy conversion system (WECS) currently leads the wind energy market due to its advantages in comparison to other topologies. The appropriate control of the back-to-back power converter scheme allows the wind turbines based on the DFIG to operate in variable speed mode, whose benefits include maximum extrac-tion of the power available in the wind, reactive power injecextrac-tion and mechanical stress reduc-tion. The increasing number of wind energy conversion systems has led the grid operators to develop specific regulations regarding the connection of these systems to the grid. Under these regulations, the fault ride-through and low voltage tolerance are amongst the most important and relevant aspects, as well as to provide reactive power to the grid in order to restore the volt-age level during a fault. Therefore, such systems must maintain a high level of controllability during grid disturbances. This thesis investigates the impact of control and drive strategies on the performance of the DFIG-based wind energy conversion system, under the perspectives of maximum power extraction and fault ride-through, according to the grid regulations of Brazil, Canada, the United States and Germany. It is proposed a new heightened state-feedback con-trol structure with predictive behavior to be applied to the generator concon-trol, which considers in an integrated manner the dynamics of the machine currents in conjunction with the general modelling of the electromagnetic disturbance present during symmetric and asymmetric faults, as well as the tracking errors. The proposed structure was designed to effectively suppress the oscillatory dynamics present in the back electromotive force that occurs in the case of a grid voltage disturbance, in order to mitigate oscillations and surges in the electromagnetic torque and the machine currents, exempting the need to use current reference modification strategies or the activation of physical protection during intermediate level faults, thus allowing the DFIG to ride-through symmetrical and asymmetrical disturbances in the grid featuring limited torque oscillations and contributing reactive current, as required by grid codes. In the severe fault case, the proposed structure allows effective tracking of the current references calculated in order to mitigate the oscillations, overcurrent and overvoltage developments. The proposed structure also employs a novel flux damping technique which accentuates the rotor current direct axis component in order to significantly reduce stator flux settling time after faults, while the torque minimally oscillates during post-fault recovery. Results obtained by means of real-time dig-ital simulations and experimental tests under ideal and non-ideal conditions demonstrate the superiority of the proposed structure in comparison to conventional and previous techniques.
Keywords: doubly-fed induction generator, state-feedback, grid codes, low-voltage ride-through, flux damping
Contents
List of Figures v List of Tables ix List of Symbols xi Abbreviations xvii 1 Introduction 1 1.1 Motivation . . . 3 1.2 Objectives . . . 4 1.3 Contributions . . . 5 1.4 Methodology . . . 6 1.5 Thesis Structure . . . 62 State of the Art 7 2.1 DFIG Drive and Control . . . 8
2.2 LVRT Techniques . . . 13
2.3 Summary . . . 16
I
WIND ENERGY CONVERSION SYSTEMS
19
3 WECS Fundamentals 21 3.1 Main Components . . . 213.2 WECS Topologies . . . 23
3.3 Wind Energy Extraction . . . 26
3.3.1 Harnessed Power Control . . . 29
3.3.2 Maximum Power Point Tracking . . . 32
3.4 Summary . . . 34
4 Conversion System Models 35 4.1 Mechanical System . . . 35
4.1.1 Wind Turbine Torque-Speed Feature . . . 35
4.2 Drive Train Model . . . 36
4.3 Electrical System . . . 37
4.3.1 DFIG Electrical Model . . . 38
4.3.2 Operating Modes . . . 43
4.4 Back-to-Back Converter Model . . . 45
4.5 PWM Schemes . . . 48
4.5.1 Sine-Triangle Modulation . . . 48
4.5.2 Third Harmonic Injection Modulation . . . 50
4.5.3 Space Vector Modulation SV-PWM . . . 50
4.5.4 Trapezoidal Wave Slope Modulation . . . 52
4.5.5 PWM Schemes Comparison . . . 54
4.6 Line Filter Model . . . 58
4.7 DC Link Model . . . 60
4.8 Summary . . . 61
5 DFIG-based WECS Control and Drive 63 5.1 Control Objectives . . . 63
5.2 Energy capture optimization . . . 65
5.3 Low voltage ride-through . . . 67
5.3.1 Grid code requirements . . . 71
5.3.2 Analysis of the doubly fed induction generator (DFIG) during a voltage sag . . . 72
5.3.3 LVRT strategies . . . 84
5.4 Electric power quality . . . 92
5.4.1 Power Quality Regulations Applied to WECS . . . 93
5.4.2 Reactive Power Demand . . . 95
5.5 Attainment of control objectives . . . 98
5.5.1 Rotor-side control . . . 98
5.5.2 Grid-side control . . . 101
5.6 Summary . . . 105
II
THE PROPOSED CONTROL STRUCTURE
107
6 The Proposed Control Structure 109 6.1 The Proposed Heightened State-Feedback Control . . . 1096.1.1 Plant Definition . . . 111
6.1.2 General Control Signal Description . . . 115
6.1.3 Heightened Error-State-Space System . . . 116
6.1.4 Control Law Definition . . . 117
6.1.5 The Predictive Loop . . . 119
6.1.6 The Current-Feedback Loop . . . 120
6.2 Active Flux Damping . . . 121
6.2.1 The Proposed d-FD Technique . . . 124
6.2.2 Controllability and Stability Proof . . . 127
6.3 Summary . . . 131
7 Results 133 7.1 Controller Design Process . . . 133
7.1.1 Proposed HSFC Design . . . 134
7.1.2 Conventional and PI-R2 design . . . 137
7.2 Performance Assessment Under Simulations . . . 140
7.2.1 Severe Voltage Sags . . . 140
7.2.2 Intermediate Voltage Sags . . . 144
7.3 Robustness Assessment . . . 145
7.3.1 Parameter Deviation . . . 145
7.3.2 Grid Frequency Deviation . . . 148
7.4 Experimental verification . . . 151
7.6 Summary . . . 156
III
CONCLUSION
157
8 Conclusions and Future Work 159 8.1 Overview and Conclusions . . . 1598.2 Future work . . . 160
8.3 List of Publications . . . 161
8.3.1 Journal Publications . . . 161
8.3.2 Conference Publications . . . 162
References 164 A A Realistic 2 MW-rated DFIG-based WECS 177 A.1 Turbine Parameters . . . 177
A.2 Generator Parameters . . . 179
A.3 Transformer Parameters . . . 179
A.4 Converter Parameters . . . 181
List of Figures
3.1 Main components of a WECS. . . 22
3.2 Fixed-speed wind turbine with SCIG. . . 23
3.3 Variable-speed wind turbine with DFIG. . . 24
3.4 Variable-speed wind turbine with full-scale power converter. . . 25
3.5 Illustration of wind conditions around the moving blade. . . 27
3.6 Power utilization coefficient for different values of λ. . . 29
3.7 Typical power curve of a wind turbine . . . 30
3.8 Power curve of a passive-stall controlled wind turbine. . . 31
3.9 Illustration of active-stall control on the turbine blade. . . 31
3.10 Illustration of pitch control on the turbine blade. . . 32
3.11 The power-speed characteristic of a wind turbine and the maximum power point tracking. . . 34
4.1 The torque-speed characteristic of a wind turbine and the optimal torque trajectory. 36 4.2 Two-mass model of the drive train. . . 37
4.3 Diagram of a DFIG applied in wind power generation. . . 38
4.4 Diagram of the DFIG electrical model. . . 39
4.5 The power flow in a DFIG-based WECS. . . 44
4.6 Back-to-back converter scheme. . . 45
4.7 The two-level converter. . . 46
4.8 Space-vector αβ voltages of the two-level converter. . . 48
4.9 The sine-triangle modulation scheme. . . 49
4.10 The third harmonic injection modulation scheme. . . 50
4.11 Dwell time calculation in the αβ plane. . . 51
4.12 Operating concept of the SLOPE-PWM technique. . . 53
4.13 ST-PWM scheme performance. . . 55
4.14 3H-PWM scheme performance. . . 56
4.15 SV-PWM scheme performance. . . 56
4.16 SLOPE-PWM scheme performance with maximum switching frequency of 540 Hz. . . 57
4.17 SLOPE-PWM scheme performance with maximum switching frequency of 1560 Hz. . . 58
4.18 Grid line filter model. . . 59
4.19 Grid voltage synchronous reference frame orientation. . . 60
4.20 DC link bus between the back-to-back converters. . . 60
5.1 WECS objective and control subsystems. . . 65
5.2 Power-speed MPPT scheme. . . 66
5.3 Optimal tip speed ratio MPPT scheme. . . 67
5.4 Optimal torque MPPT scheme. . . 68
5.5 Rio do Fogo wind farm power system connection diagram. . . 69
5.6 Typical LVRT curve. . . 70
5.7 PCC voltage sags examples. . . 71
5.8 LVRT requirements of Brazil, Canada, Germany and The United States. . . 73
5.9 BEMF levels as seen from the rotor circuit during a single-phase voltage sag: (a) as a function of the sag depth and the rotor slip; and (b) evaluated for different slip values as a function of time and sag depth. . . 78
5.10 Voltage profile in the simulations. . . 79
5.11 Voltage divider model for the voltage sags. . . 80
5.12 Generator variables during 80% voltage sag due to a three-phase fault. . . 82
5.13 Generator variables during 80% voltage sag due to a single-phase-to-neutral fault. 83 5.14 Crowbar LVRT scheme. . . 87
5.15 Modified crowbar LVRT scheme. . . 87
5.16 Dynamic voltage restorer LVRT scheme. . . 88
5.17 Amplitudes of the theoretically corresponding rotor current and voltage under different kr of CRTC LVRT-CM strategy. . . 91
5.18 Generic strategy for voltage support. . . 92
5.19 Brazilian grid code requirements for steady-state generation/absorption of reac-tive power at the point of connection of the generating plant. . . 96
5.20 Brazilian grid code reactive current requirements for under- or over-voltage
sit-uations. . . 97
5.21 Brazilian grid code frequency operation range and disconnection requirements. 98 5.22 Rotor side control schematic. . . 103
5.23 Grid side control schematic. . . 104
6.1 Rotor voltage defined by the HSFC control law in (6.38) . . . 118
6.2 HSFC control error predictive regulator loop. . . 120
6.3 Proposed HSFC Structure. . . 121
6.4 Flux trajectory evolution during 80% voltage sag due to a single-phase-to-ground fault. . . 123
6.5 Flux trajectory evolution during 80% voltage sag due to a two-phase-to-ground fault. . . 124
6.6 Flux trajectory evolution during 80% voltage sag due to a three-phase-to-ground fault. . . 125
6.7 Proposed HSFC structure with d-FD flux damping technique. . . 126
6.8 Proposed HSFC closed-loop diagram: (a) complete system; (b) interchange of summation blocks; and (c) simplified system. . . 129
7.1 Time performance of the ITAE and Bessel system prototypes. . . 135
7.2 Frequency performance of the ITAE and Bessel system prototypes. . . 135
7.3 C code implementation of the proposed HSFC. . . 138
7.4 Theoretical step response of PI, PI-R2 and proposed HSFC compared. . . 139
7.5 Frequency response of the proposed heightened state-feedback predictive con-trol structure (HSFC) compared to PI and PI-R2 concon-trollers (designed to be equivalent below the grid frequency). . . 140
7.6 Real-time 2 MW WECS simulation comparison of low-voltage ride through performance of the classical PI, PI-R2 and proposed HSFC during 80% voltage sag due to a single-phase-to-ground fault using the CRTC LVRT-CM strategy. . 142
7.7 Real-time 2 MW WECS simulation comparison of low-voltage ride through performance of the classical PI, PI-R2 and proposed HSFC during 80% voltage sag due to a three-phase fault using the CRTC LVRT-CM strategy. . . 144
7.8 HSFC low-voltage ride through real-time simulation results without the usage of LVRT-CM techniques during 40% symmetrical and asymmetrical voltage sags with rotor direct current switched to 1 pu and quadrature current switched to 0.5 pu. . . 146
7.9 HSFC robustness assessment: pole-zero map of DFIG closed-loop system un-der positive and negative parameter variation. . . 147 7.10 HSFC performance under concomitant -7% grid frequency deviation and
asym-metrical voltage sags of intermediate and severe levels. . . 149 7.11 HSFC performance under concomitant +5% grid frequency deviation and
asym-metrical voltage sags of intermediate and severe levels. . . 150 7.12 Scheme of the experimental small-scale DFIG-based WECS test bench . . . 152 7.13 Test bench supervisory system developed in LabVIEW. . . 153 7.14 Experimental results of HSFC low-voltage ride through without the usage of
LVRT-CM techniques during symmetrical and asymmetrical voltage sags with rotor direct current switched to 3 pu. . . 154 A.1 Vestas V90 side-view. . . 178 A.2 Vestas V90-VCS DFIG-based WECS power characteristics . . . 178
List of Tables
2.1 State-of-the-art review summary . . . 18
3.1 Coefficients for the analytical approach of Cp . . . 28
4.1 Output voltages of the two-level power converter. . . 47
4.2 Possible αβ voltages in the two-level converter as a function of Sa, Sb and Sc signals. . . 49
4.3 PWM schemes comparison. . . 57
5.1 Normalized values of voltages and initial flux . . . 76
5.2 Voltage sags tests according to IEC 61400-21. . . 85
5.3 Post-Fault Rotor Current References in Different LVRT-CM Schemes . . . 89
5.4 Global harmonic distortion limits set by the ONS. . . 95
5.5 Individual limits of harmonic distortion for the generating units. . . 96
7.1 System prototypes pole locations normalized for Tst= 1 s. . . 134
7.2 Controllers gains and step response performance for the simulation and experi-mental systems. . . 139
7.3 Small-scale WECS test bench parameters. . . 155
A.1 2 MW WECS V90-based turbine parameters. . . 179
A.2 2 MW WECS V90-based generator parameters. . . 180
A.3 2 MW WECS V90-based transformer parameters. . . 181
A.4 2 MW WECS V90-based converter parameters. . . 182
A.5 2 MW WECS V90-based protection circuit-breakers parameters. . . 182
List of Symbols
Turbine symbols
α Angle of attack
Cp Power utilization coefficient
c1-c9 Cpmodel coefficients
CT Torque coefficient DT Friction coefficient
JG Lumped inertia of the generator JT Lumped inertia of the turbine
KS Drive train stiffness
λ Tip speed ratio
λo Optimal tip speed ratio
nHS High-speed gear number of teeth nLS Low-speed gear number of teeth ωHS High-speed shaft speed
ωLS Low-speed shaft speed
ωT Rotational speed [rad/s]
φ Angle of incidence pm Mechanic power [W] R Blade length [m] ρ Air density [kg/m3] θLS Low-speed shaft angle
θT Rotor angle
THS High-speed shaft torque TLS Low-speed shaft torque
TO Optimal torque
TT Mechanic torque [N.m]
#»
Vrel Relative wind speed vector #»
Vtip Blade tip speed vector #»
Vw Wind speed vector Vw Wind speed [m/s]
DFIG symbols
DG Friction coefficient ira Rotor current in phase a irb Rotor current in phase b irc Rotor current in phase c ird Rotor direct axis current irq Rotor quadrature axis current
irabc Rotor currents array irdq Rotor dq currents array
irdq,w Rotor current parcel due to the distur-bance
isa Stator current in phase a isb Stator current in phase b isc Stator current in phase c isd Stator direct axis current isq Stator quadrature axis current
isabc Stator currents array isdq Stator dq currents array kd BEMF parallel coefficient xi
kq BEMF vertical coefficient Kr Rotor winding factor Ks Stator winding factor Λ Stator flux rated value λra Rotor flux in phase a
λrb Rotor flux in phase b
λrc Rotor flux in phase c
λrd Rotor direct axis flux
λrq Rotor quadrature axis flux
λrabc Rotor fluxes array
λrdq Rotor dq fluxes array
λsa Stator flux in phase a
λsb Stator flux in phase b
λsc Stator flux in phase c
λsd Stator direct axis flux
λsq Stator quadrature axis flux
λsabc Stator fluxes array
λsdq Stator dq fluxes array
Lm Magnetizing inductance Lr Rotor inductance
Lrabc Rotor inductance matrix Ls Stator inductance
Lsabc Stator inductance matrix Lσr Rotor leakage inductance Lσs Stator leakage inductance Lsr,abc Mutual inductance matrix
Msr Stator-to-rotor mutual inductance
Nr Rotor windings number or turns
Ns Stator windings number or turns ωm Rotor mechanic speed
ωr Rotor electric speed
ωsr Slip speed
Pr Power-conservative Park transform matrix (rotor)
Ps Power-conservative Park transform matrix (stator)
PF Power factor
φr Unknown phase variable of the rotor
current
Pp Number of pole pairs
pr Rotor active power ps Stator active power
Ψ Initial amplitude of the stator flux tran-sient component
qr Rotor reactive power qs Stator reactive power Rc Crowbar resistance Rr Rotor resistance
Rs Stator resistance
s Slip factor
σ Machine leakage coefficient τs Stator time constant
Tem Electromagnetic torque θm Rotor mechanic angle
u Stator-to-rotor standstill turn ratio Vpk,maxMaximum RSC peak voltage vra Rotor voltage in phase a vrb Rotor voltage in phase b vrc Rotor voltage in phase c
vrd Rotor direct axis voltage vrq Rotor quadrature axis voltage vrabc Rotor voltages array
vrdq Rotor dq voltages array vsa Stator voltage in phase a vsb Stator voltage in phase b
vsc Stator voltage in phase c vsd Stator direct axis voltage vsq Stator quadrature axis voltage vsabc Stator voltages array
vsdq Stator dq voltages array
VsN Stator voltage negative-sequence com-ponent magnitude
VsP Stator voltage positive-sequence
com-ponent magnitude # »
BEMF Back electromotive force vector #»i
m Magnetizing current vector
#»i
r Rotor current vector #»ir= ird+ jirq
#»i
s Stator current vector #»is= isd+ jisq
#»
λr Rotor flux vector
#»
λr= λrd+ jλrq
#»
λs Stator flux vector
#»
λs= λsd+ jλsq
#»
λsn Natural stator flux vector
#»v
s Stator voltage vector #»vs= vsd+ jvsq
#»v
sN Stator voltage vector
negative-sequence component #»v
sP Stator voltage vector positive-sequence
component #»v
r Rotor voltage vector #»vr = vrd+ jvrq
Converter symbols
δ Angle between #»vgand #»v f
Ec Energy stored in the DC-bus capacitor ftri Triangular carrier frequency
h Modulation sampling period if d Filter direct axis current if q Filter quadrature axis current iga Grid current in phase a igb Grid current in phase b igc Grid current in phase c
idg Grid direct axis current iqg Grid quadrature axis current Lf Filter inductance
ma Amplitude modulation index
mf Frequency modulation index
ωcarr Carrier frequency
pf Filter active power
pGSC Power through the grid-side converter pRSC Power through the rotor-side converter qf Filter reactive power
Rf Filter resistance
Sa Switch signal of the phase a Sb Switch signal of the phase b Sc Switch signal of the phase c t0-t2 Space vectors dwell time
θvg Grid voltage angle
Vcarr Carrier signal
VDC DC-bus voltage
vf a Filter voltage in phase a vf b Filter voltage in phase b vf c Filter voltage in phase c vf d Filter direct axis voltage vf q Filter quadrature axis voltage vf abc Filter voltages array
Vg Grid voltage magnitude vga Grid voltage in phase a vgb Grid voltage in phase b
vgc Grid voltage in phase c
vgd Grid direct axis voltage vgq Grid quadrature axis voltage vtri Triangular carrier
# »
#»v
f Filter voltage vector
#»v
g Grid voltage vector
HSFC symbols
Af System matrix of the stator flux state-space model
α1-α5 General control signal coefficients
β Element of Fhdefined in (6.34)
Bf Input matrix of the stator flux state-space model
c0-c2 Unknown amplitude variables of the
disturbance
c3-c5 Unknown amplitude variables of the
rotor current reference
Cc Predictive loop actual-input selection
matrix
∆h(z) Closed-loop system characteristic polynomial
Ds f(z) State-feedback part closed-loop trans-fer function denominator
ε Error state vector
erdq[k] Rotor current control error
η(z) Polynomial which describes the distur-bance and references specificities F Discrete-time model system matrix Fh Heightened error-state-space system
matrix
G Discrete-time model input matrix Γ Element of Fhdefined in (6.34)
Gc Predictive loop error weighing vector
Gh Heightened error-state-space input ma-trix
Gp(z) Predictive loop part closed-loop
trans-fer function
Gr(z) Rotor circuit disturbance-detached
model transfer function
Gs f(z) State-feedback part closed-loop trans-fer function
iλd Rotor current direct axis contribution for stator flux damping
iλq Rotor current quadrature axis contribu-tion for stator flux damping
Kε Error samples gain
K Heightened error-and-state feedback gain vector
Kλ Flux feedback gain matrix kr CRTC tracking coefficient
Kξ Rotor current state gain
µ Heightened error-state-space input Np(z) Predictive part closed-loop transfer
function numerator
Ns f(z) State-feedback part closed-loop trans-fer function numerator
ωs Synchronous reference frame speed
φ1-φ2 Unknown phase variables of the BEMF
disturbance
φ3-φ4 Unknown phase variables of the rotor
current reference
S(z) General control signal complex repre-sentation
Ts Sampling period
uc Predictive loop states
udq Rotor voltage parcel due to the control error (predictive loop output)
w Disturbance input
w(z) Disturbance signal complex model ξ Rotor current dynamics state Superscripts
a Variable represented in the generic ref-erential
0
Actual rotor variable (without being re-ferred to stator side)
∗ Reference value
r Variable represented in the rotor SRF s Variable represented in the stator flux
SRF Subscripts [k] k-th discrete sample DC DC-bus variable f Filter-related variable g Grid-related variable h Heightened system variable λ Flux-related variable r Rotor-related variable s Stator-related variable
Referentials
c Variable represented in the stationary (Clarke) referential
ωa Generic referential speed
ωar Rotor speed in the generic referential
θa Generic referential angle
θr Rotor electric angle
θs Stator flux SRF angle
θsr Slip angle
Other symbols
s Continuous complex frequency vari-able
z Discrete complex frequency variable j Complex number j =√−1
Abbreviations
3H-PWM Third harmonic injection PWM
ABNT Brazilian association of technical standards AC Alternating current
ANSI American National Standards Institute BEMF Back electromotive force
CNPQ Brazilian National Research Council CRTC Current reversely tracking control
d-FD Proposed rotor current d-axis flux damping technique DC Direct current
DFIG Doubly fed induction generator DPC Direct power control
DSP Digital signal processor
DTHTS Total harmonic distortion indicator DVR Dynamic voltage restorer
EPQ Electric power quality ESS Energy storage system FCB Full control boundary
FERC Federal Energy Regulatory Commission FPGA Field Programmable Gate Array
FRT Fault ride-through GSC Grid-side converter
GWEC Global Wind Energy Council xvii
HSFC Proposed heightened state-feedback predictive control structure IEA International Energy Association
IEC International Electrotechnical Commission IEEE Institute of Electrical and Electronics Engineers IGBT Insulated-gate bipolar transistor
ITAE Integral of time multiplied by the absolute value of the error LMI Linear matrix inequality
LPV Linear parameter-varying LQR Linear quadratic regulator LVRT Low voltage ride-through LVRT-CM Current-modify LVRT strategy MISO Multiple input single output MPP Maximum power point
MPPT Maximum power point tracking NBR Brazilian standard defined by ABNT ODE Ordinary differential equation
ONS Brazilian national electric system operator PCC Point of common connection
PI Proportional-integral controller
PI-R Proportional-integral-resonant controller
PI-R2 Proportional-integral doubly-resonant controller PLL Phase locked loop
PMSG Permanent magnet synchronous generator
PROINFA Brazilian alternative energy sources incentive program PWM Pulse width modulation
RMS Root mean square RSC Rotor-side converter
SIN Brazilian national integrated system SLOPE-PWM Trapezoidal-wave slope PWM SMC Sliding-mode control
SRF Synchronous reference frame ST-PWM Sine-triangle PWM
SV-PWM Space vector PWM THD Total harmonic distortion TSO Transmission system operator
U-PWM Double-sided uniform-sampled PWM
UFRN Universidade Federal do Rio Grande do Norte VCS Vestas conversion system
Chapter 1
Introduction
Wind energy has become one of the most widely used sources of renewable energy in the world. Between 2001 and 2017, the installed wind generation capacity in the world increased from 23.900 to 539.123 GW1. In Brazil, it jumped from 0.235 to 12.767 GW2 between 2006 and 2017 and, according to a prospecting study, the installed capacity in Brazil will reach about 18 GW2 in 2023. This growth is mainly due to the decrease in sustainability of fossil fuels, caused by increased costs, limited reserves, and severe environmental impacts and, therefore, wind generation has drawn great attention from researchers, governments and industry. Such growth reflects the global effort to seek energy sustainability and reduce environmental impacts, especially the pollution and emission of greenhouse gases.
Brazil is ranked among the ten largest wind energy producers in the world, with an installed capacity of about 13 GW2, even though it has a small capacity compared to other countries of the same economic and geographical size. Wind energy currently accounts for about 8 percent of the electricity generation in Brazil, but it has been increasing its participation in the energy matrix in recent years. This percentage may seem small, however, it is very significant when compared to other much older sources in terms of exploration in Brazil, such as biomass (9.2 percent / 14.56 GW)2, oil (6.5 percent / 10.17 GW)2and coal (2.5 percent / 3.73 GW)2. Among the Brazilian states, the Rio Grande do Norte is the main provider of wind energy in terms of installed capacity (3.72 GW), number of wind farms and power under construction [Associação Brasileira de Energia Eólica 2017].
Even though Brazil is a country with a fairly large wind potential which features about 143 gigawatts3,4, the progress of wind power generation is slow due to the national energy matrix being predominantly made up of hydropower generation (61.3%)2 which, despite the environ-mental impact it causes, can be considered a clean form of generation of energy [Barros 2006, Barros 2011]. In the early 2000 years, the need to complement and supplement the brazilian energy sources has become more and more evident, when the country electricity sector expe-rienced lower flows than the historical average and a continuous process of depletion of water
Statistical data obtained from
1The Global Wind Report [Global Wind Energy Council 2017]
2The Wind Generation Annual Bulletin [Associação Brasileira de Energia Eólica 2017] 3The Brazilian Electrical Energy Atlas [Agência Nacional de Energia Elétrica 2005]
2 CHAPTER 1. INTRODUCTION
storage reservoirs, in addition to an aggravation of the financial crisis and lack of investments in the energy generation, transmission and distribution segments. Moreover, over the last few years, environmental pollution has become a major concern to mankind. A probable energy crisis brought the Brazilian government and researchers to seek new technologies for the gen-eration of clean and renewable energy. In this context stand out the wind energy conversion system (WECS), usually referred to as wind turbine, which presents the fastest growth rate in the energy industry while run into several obstacles towards large-scale integration and, there-fore, require continuous research.
Wind turbines can operate in two modes: fixed or variable speed. For a fixed speed turbine, the generator is connected directly to the electric grid, and its speed is determined according to the grid frequency. For a variable speed turbine, the generator speed is controlled by a sophisticated power electronic device. There are several reasons to use variable-speed turbines, among them the greater use of the available energy, the reduction of stress in the mechanical structure, the reduction of noise and the possibility of controlling the active and reactive power of the generator [Barros 2006]. Currently, the wind turbine manufacturers are producing large turbines, with a capacity of 3 to 6 MW, featuring variable-speed mode and pitch angle control. Fixed speed generators are considered unsuitable for these large turbines [Chen & Li 2008, Cheng & Zhu 2014]
Variable-speed turbines are connected directly (without gearboxes) to a synchronous gen-erator, or indirectly (with gearboxes) to a DFIG. Also known as a wound rotor gengen-erator, the DFIG is an electric machine with both stator and rotor electrical terminals. The DFIG features attractive attributes as a wind generator in view of its operation in the variable-speed mode. However, the most exceptional feature of the DFIG, which hand over its commercial preference, is that the power processed by the power converter is only a fraction of the total power rating of the wind generator. Currently, this topology represents about 50 percent of the wind market, and is the predominant generator used in the wind power generation industry for large-power turbines on land [Abad 2011, Shafiei 2012, Ackermann 2012, Cardenas et al. 2013, Yaramasu et al. 2015, Li et al. 2018]. Considering the advantages of the DFIG-based WECS, this thesis focuses on this type of generator and provides a detailed study and contributions to this wind generation topology.
To operate the DFIG under high performance requirements aiming to produce electric power with quality, reliability, continuity and high efficiency, it is necessary to study and adopt robust and appropriate strategies for this type of generator. For this reason, this topic has been exten-sively investigated by researchers all over the world, with the objectives of controlling the DFIG to (i) track the point of maximum extraction of wind power, (ii) be capable of overcoming faults and grid voltage problems, and (iii) provide support to the electrical network in terms of voltage level, frequency, power factor and reduction of harmonic content. These targets are known as maximum power point tracking (MPPT), low voltage ride-through (LVRT), and electric power quality (EPQ), respectively [Abad 2011].
Due to the expressive integration of wind power generation into the grid, the transmission system operator (TSO) of several countries, among them Brazil, now requires a more active management of wind farms, and several of them have incorporated the LVRT into their grid codes. The LVRT feature can be divided into two parts: (i) in the event of a voltage sag, the
1.1. MOTIVATION 3
wind turbines must remain connected to the grid for a certain time, that is, support the fault; and, (ii) the turbines must contribute actively to maintaining the stability of the system during and after the fault, namely, to provide support to the grid [Rahimi & Parniani 2010]. Disturbances in the electrical grid, even far distant from the turbine site, can lead to an undercutting of voltage at the connection point of the wind turbine. The abrupt voltage drop in the supply voltage causes overcurrents and overvoltages in the generator and also in the power converters, as well as may cause an increase in the turbine speed. Without an adequate control and/or protection strategy, this phenomenon certainly leads to the destruction of system components.
To comply with the LVRT requirements imposed to WECS, three problems need to be ad-dressed: (i) limit the currents in the system; (ii) limit the capacitor voltage of the converters; and, (iii) limit the oscillation and the peak of the transient response present in the DFIG variables, such as the electromagnetic torque, the induced back electromotive force and the currents in the rotor and the stator of the machine. The strategies that aim to achieve these objectives can be divided into two main categories: (i) hardware strategies, which use additional equipment such as a power dissipation resistor arrangement known as crowbar, temporary energy storage sys-tem (ESS), dynamic voltage restorer (DVR), pitch angle control, etc.; and (ii) control strategies, which aim to apply different approaches in a way that the generator acts in its own protection and network support [Ezzat et al. 2013].
The above mentioned LVRT control strategies share a common characteristic: both depend on a reliable and efficient control of the machine currents [Huang et al. 2016]. Despite many strategies for DFIG control have been published in recent years, it is still not consolidated as a reference in addition to classical strategies based on the proportional-integral controller (PI). In general, despite the robust and promising nature of these techniques, they produce undesirable effects in the control efforts that often become harmful or even impossible to be synthesized by the actuator, which is the power converter in this case [Taveiros et al. 2015]. In addition, conven-tional strategies erroneously: (i) consider the dynamics of direct and quadrature axes as being independent and the effect of one over the other as disturbances automatically compensated by the conventional controller or feedforward compensated; (ii) consider the dynamics of the magnetic flux induced by the stator as being a disturbance of little expression [Abad 2011, Zhu et al. 2018].
The above points play a fundamental role in the control of the DFIG-based WECS, because, in the light of what will be demonstrated, this generator is particularly sensitive to disturbances in the electrical network, since part of its power supply is directly connected to the network. Such considerations are held for the purposes of project simplicity, however, in accordance with recent demands for support and active behavior during disturbances, the incorporation of particular dynamics that arise during a fault to the control models becomes a technological challenge to be overcome.
1.1
Motivation
Aside from the cleanliness and sustainability, wind energy is one of the most abundant and regular renewable resources available, and therefore stands out among other sources of energy
4 CHAPTER 1. INTRODUCTION
as one of the fastest growing. The conversion of kinetic energy of winds into electric energy is a multidisciplinary science and comprises a vast field of knowledge, such as aerodynamics, me-chanical systems, electrical machines, power electronics, control systems and power systems.
At the beginning of the decade of 2000, following the energy crisis in the whole country, it was created the Incentive Program for Alternative Electric Energy Sources (PROINFA), whose aim is to promote the diversification of the Brazilian Energy Matrix, seeking alternatives to increase security in the supply of electric energy, in addition to allowing the valorization of regional and local characteristics and potentialities. Since the creation of the PROINFA, the production of wind energy in Brazil increased from 27 MW in 2005 to 900 MW in 2010, and about 9 GW in 2015. Considering the wind potential installed and the projects under construc-tion, the country will be able to reach the 15 GW mark by the end of 2018. According to the Brazilian Wind Potential Atlas, published by the Eletrobrás Electric Energy Research Center, the Brazilian territory has the capacity to generate up to 143 GW, in which the Rio Grande do Norte is one of the states with the greatest wind potential [Marques et al. 2013].
These factors reiterate the need for continuous investments in generation, transmission and distribution, in order to promote greater security of the electrical system for the coming years. The study of new technologies and methods to improve the use of this vast energy potential represents a great importance, and has attracted the attention of researchers, academics and society on a global scale.
1.2
Objectives
The general practical objective of this work is to provide a dynamic control structure based on hightened order state-space design as a solution for the wind energy conversion system based on the DFIG, in order to (i) allow the turbine to remain connected to the grid during symmetrical and asymmetrical faults, either intermediate or severe, featuring limited currents, minimum oscillation in power and electromagnetic torque waveforms while contributing reactive current in compliance with the grid codes; and (ii) to provide the DFIG to recover and settle promptly after the fault.
Based on a multi-criteria unitary approach that efficiently combines optimization require-ments (MPPT, control effort, losses), in accordance with the requirerequire-ments that depend on the real application (LVRT and EPQ), the specific objectives of this thesis are:
1. to set up and experimentally evaluate a wind energy conversion system, with a digital control and supervision system, using the computer, the digital signal processor (DSP), the Field Programmable Gate Array (FPGA) and the LabVIEW software;
2. to study the impact of the intermittent faults on the grid voltage, both symmetrical and asymmetrical, on the DFIG active and reactive power, electromagnetic torque, rotor and stator currents;
1.3. CONTRIBUTIONS 5
3. to evaluate the existing control techniques for DFIG in literature, both conventional and modern, designed to cope with these situations;
4. to evaluate, in addition, the impact on the power quality caused by the use of different control and action strategies for the DFIG generator, based on realistic parameters, fea-tures and constrains of commercially-available wind turbines; and
5. to propose, design and evaluate experimentally the provided control structure technique, in order to identify the improvements achieved and to compare with other existing meth-ods, on the aspects of MPPT, LVRT and EPQ.
1.3
Contributions
The contributions attained and reported in this thesis are:
1. it was performed an extensive evaluation of the DFIG operation during disturbances in the electrical grid, toward determining the weaknesses to which the machine and the control are subject during such disturbances, and how the control may compensate the generator to ride through-these disturbances;
2. it was proposed a new control termed as HSFC with predictive behavior to regulate the rotor current loops, which is able to effectively suppress back electromotive force surge oscillating dynamics that occur in the event of a disturbance in the grid voltage and to track oscillatory post-fault current references accurately;
3. the proposed structure also employs a novel flux damping technique, which performs full state-feedback of the stator flux, however, accentuating the damping contribution in the rotor current d-axis. In this fashion, most of the oscillation and amplitude level required to damp the stator flux more quickly is transferred to the d-axis current, while the q-axis current also contributes to damping but minimally oscillates. In this fashion, the proposed structure is able to drive the generator to steady conditions after the fault faster than usual featuring minimal torque ripple; and
4. the proposed structure was validated by means of real-time digital simulations and exper-imental results of symmetrical and asymmetrical conditions, which revealed the proposed solutions advantages over classical and previous strategies, namely: (i) the proposed method proved able to mitigate surge and oscillations in currents during intermediate-level symmetrical and asymmetrical disturbances in the grid, while provide the DFIG to still contribute active and reactive current featuring bounded torque oscillations; (ii) the proposed method proved able to provide efficient tracking of the necessary oscillatory post-fault current references during severe-level symmetrical and asymmetrical distur-bances in the grid, which allowed the DFIG to remain connected and ride through the fault.
6 CHAPTER 1. INTRODUCTION
1.4
Methodology
This work was carried out in compliance with the following methodology:
• literature review of the most relevant work in the dynamic analysis and modeling of wind turbine generators connected to power systems, in order to determine the state of the art with regard to the theme of the work;
• in order to realistic represent and assess the characteristics and phenomena experienced by real-world systems, an extensive research was carried out in order to determine the parameters, features and constrains of a realistic MW-rated DFIG-based WECS;
• extensive simulations of the control and drive strategies for DFIG encountered in the literature including the proposed strategies;
• sizing, specification, design and assembly of components to equip a wind energy research laboratory, namely: continuous current machine, wound rotor induction machine, three-phase rectifiers, power inverters, voltage and current transducers, encoder, data acquisi-tion boards and software, among others; and
• experimental evaluation of the control strategies for the DFIG encountered in the literature and, also, of the proposed strategies; stressing the generator to realistic values of gusts and random wind speed conditions, as well as non-ideal conditions of the network to which the generator is connected.
1.5
Thesis Structure
Chapter 2 presents a review of the state of the art with the most relevant work in the domain of control and drive of electrical generators. Chapter 3 presents the fundamentals, components and topologies of wind energy conversion systems, as well as the dynamics of wind energy extraction. Chapter 4 presents the model of a wind energy conversion system based on the DFIG, including the turbine torque-speed characteristic, the generator models, the drive train, the power converters and the electric grid. The parameters and features of realistic 2 MW-rated DFIG-based WECS are also presented.
Chapter 5 presents a comprehensive analysis of the control and drive objectives of the WECS generator. Concepts of the tracking of the maximum power extraction point of the winds, support to faults and voltage sags, grid codes and, also, the power quality regulations imposed to the WECS by the National Operator of the Brazilian Electric System are presented. An extensive evaluation of the DFIG performance during power grid disturbances is also pre-sented. Finally, the chapter presents the achievement of the objectives of the WECS by means of control.
Chapter 6 minutely presents the proposed heightened state-feedback control structure. Chap-ter 7 presents the results and following assessment obtained by means of real-time digital sim-ulations and laboratory test bench experiments. Finally, chapter 8 presents the conclusions and future works.
Chapter 2
State of the Art
In the last decades, several works with studies on DFIG-based WECS have been published as a result of a global effort in the search for energy efficiency and clean energy production, in which different solutions have been proposed to obtain the required dynamic performance of the machine operating in WECS, i.e., control systems with focus on maximum power extraction, operation on balanced and unbalanced grids, faults and voltage problems support, sensor-less control, network frequency support in large wind farms, and stand-alone operation.
In particular, the response of the DFIG-based WECS to grid disturbances is an important topic nowadays, considering the steadily increasing number of installations of this type of wind generators and their integration in the power grid. Thereby, the transmission system operator of several countries formulated grid codes for effective operation of grid-connected WECS, de-manding the generator units to have efficient performance and robust behavior under abnormal conditions, such as symmetrical or asymmetrical voltage sags, which comprises the LVRT fea-ture of the WECS. The studies are basically divided into two strands: (i) novel control strategies or design processes; and (ii) LVRT techniques.
The recent proposed control solutions design special schemes aiming to calculate the opti-mal rotor voltage to counteract the back electromotive force, which significantly increases and oscillates in the rotor circuit due to stator flux variations during grid disturbances, in order to keep providing the DFIG to contribute active and reactive currents to the grid, thus increasing the utilization efficiency of the rotor-side converter (RSC) output capacity. Due to the band-width restrictions of the conventional PI control, the DFIG is not able to effectively counteract oscillatory disturbances when using this strategy. Therefore, recent papers proposed different strategies, ranging from sliding-mode control (SMC), frequency-domain design, proportional-integral-resonant controller (PI-R), repetitive control, linear parameter-varying (LPV), feedfor-ward of references and/or disturbances, among others.
Still in the first strand, attention is also drawn to the DFIG actuator, which imposes the arbitrary voltages at the machine terminals. The static power converter back-to-back scheme, usually comprised by inverters with insulated-gate bipolar transistor (IGBT) switches, is the device which, in fact, allows to input to the machine voltages of variable amplitude and fre-quency, enabling, therefore, the control of the other variables of the electromechanical system. In contrast, the power converters are also one of the main sources of restrains related to control bandwidth and issues related electric power quality (EPQ).
8 CHAPTER 2. STATE OF THE ART
Depending on the severity of the fault, the resulting back electromotive force (BEMF) in the rotor terminals considerably exceeds the RSC voltage output capacity. In this situation, the RSC no longer can freely control the rotor currents, but only limit its rising rate by outputting its maximum voltage, thus overcurrents and torque oscillations are inevitable. Therefore, other recent proposals put up a second-best objective: to suppress the overcurrents and mitigate me-chanic oscillations. Termed as current-modify LVRT (LVRT-CM) strategies, they consist in modifications of rotor current references in the event of a fault in order to reduce the required rotor voltage within RSC permissible range, while mitigate mechanic oscillations by driving the torque to zero. The post-fault current references of LVRT-CM techniques contains the same frequency components present in the BEMF, which are related to the grid frequency.
In this chapter, an overview is presented of the most relevant studies of DFIG generator op-erating in wind energy conversion systems, in the following topics: (i) DFIG drive and control; and (ii) LVRT techniques.
2.1
DFIG Drive and Control
To control voltages imposed at machine terminals, a pulse width modulation (PWM) scheme is used to control the IGBTs switching. This modulation technique is widely used for elec-tric drives, and different approaches have been proposed in the literature. Currently, the most consolidated PWM strategy for the electrical machinery drive is the space vector PWM (SV-PWM), which allows for less state changes of the switches and more efficient use of the DC voltage [Yaramasu et al. 2015]. While essential for the drive, the usage of electronic power con-verters also present disadvantages. These devices constitute the most important class of non-linear loads in power systems, being one of the main sources of harmonic distortion [Sampaio et al. 2013].
The effects of harmonic distortion are numerous, such as: (i) overheating that may lead to reduced life of service; (ii) increased electrical losses; and (iii) limited operation of control systems. For low to medium power isolated systems, harmonics and losses caused by convert-ers are not a major problem. Generally, the problem of harmonics in these systems is solved by using high frequency switching (> 10 kHz), which would theoretically increase the losses. However, for these systems, the switching losses are negligible. Meanwhile, in high power systems, these are limiting factors, both in terms of losses and overheating of the components, which significantly reduces the lifespan of the components. As a consequence, in high-power WECS (> 2 MW) the switching frequency is typically low (< 2 kHz) [Wu 2006]. Regardless of only dealing with a fraction of the power of the system, the power converters used in the DFIG based WECS also draw attention to this fact, due to the harmonic distortion and to the losses caused by the switching.
[Kwasinski et al. 2003] and [Zhou & Wang 2002] provided a comparison between PWM modulation schemes. The following analysis indicates that SV-PWM modulation is functionally identical to the double-sided uniform-sampled PWM (U-PWM). Consequently, straightforward conclusions are drawn about harmonic distortion, losses, use of the CC, and ease of implemen-tation. As the U-PWM modulation is conceptually simple and involves very few steps, it is
2.1. DFIG DRIVE AND CONTROL 9
possible that the computational effort, in practice, is reduced in comparison to SV-PWM. The U-PWM algorithm also can eliminate the need for sector and switching sequence definition of SV-PWM modulation. The linear modulation region, inherent to SV-PWM, is derived from the third harmonic injection PWM (3H-PWM) and, therefore, does not present advantages over the original. Based on this statement, the authors uphold the superiority of the U-PWM technique.
[Vargas-Merino et al. 2009] proposed a PWM technique that uses a trapezoidal modulating signal and a sinusoidal carrier whose frequency is proportionally variable to the slope of the modulating signal. The tuning of two parameters, which are the slope of the trapezoid and a frequency proportionality constant, allows adjusting the output voltage and the number of switching operations per cycle. As a result, a signal modulated with few switching and low harmonic content was achieved, ideal for static drives. In the meantime, this technique has the drawback of not producing instant references, but rather a reference of frequency and amplitude. Such investigations are of great importance for the control system, since the switching technique used may impact on the practicability of the employed control signals. This is further convoluted by unpermissive grid codes demanding the turbine to remain connected in the event of faults and to generate reactive power to assist the grid voltage to recover, which require large bandwidth controllers with fast dynamic response [Zhu et al. 2018].
In order to control the electromagnetic torque and the active and reactive power of the gener-ator, the conventional control strategies on DFIG generators perform the control of the currents in the machine rotor based on PI loops associated to the feedforward compensation of non-linear dynamics, which are not considered for the controller design [Rocha et al. 2008, Shafiei 2012, Abad 2011, Taveiros 2014, Taveiros et al. 2015, Zhu et al. 2018]. However, these un-modeled dynamics represent a strong parametric dependence and of estimation/measurement, which makes this practice not very robust. These controllers present satisfactory performance in steady state, however, they alone do not compensate for the effects of disturbances in order to meet the design requirements during the machine drive and during electrical disturbances.
In the viewpoint of maximum energy extraction available in the wind, the effects of distur-bances may not cause so much impact, since they are of a transient nature and, during steady conditions of the wind, the control will guarantee the maximum extraction. However, even in normal operation conditions an efficient strategy is desired, since it operates on electric currents that feature fast dynamics and, in addition, the turbine may be subject to strong wind variations, in which case the usage of modern control techniques provide superior MPPT performance [Taveiros 2014, Taveiros et al. 2015]. Conversely, from the point-of-view of fault ride-through and voltage support, a robust and reliable control strategy is fundamental to maintain the gener-ator in operation during faults. In this context, LVRT operation enhancement is the main subject of this thesis.
[Cardenas et al. 2013] presented a review of the most recent trends in DFIG control, with particular interest in MPPT, LVRT and the use of DFIG in micro-networks. These are the main set of objectives of the machine control. For a variable speed wind turbine, the maximum aerodynamic efficiency trajectory corresponds to a cubic function relating to the power captured with the angular speed. Various strategies were proposed in the literature aiming the MPPT, which acts on the control of the speed or the electromagnetic torque produced by the machine. If the machine parameters are well known, a very simple control strategy can be used. Conversely,
10 CHAPTER 2. STATE OF THE ART
if these are not known, or even if they vary with time (which is the case of DFIG), an additional control loop may be necessary, as discussed in [Tapia & Tapia 2005] and [Tapia et al. 2003]. This type of configuration requires cascaded controllers, that is, an internal and an external loop, where the bandwidth of the latter is a fraction of the former. The main advantage of this strategy is that the parametric errors are compensated by means of an integrator in the external loop, however, the relationship between the power produced in the machine stator and the square of the rotor current is, according to the MPPT strategy, dependent on the rotational speed and, therefore, some compensation strategy becomes necessary, for example, gain scheduling.
[Lei et al. 2013] presented a more detailed model of the DFIG-based WECS, focused on power turbines in the order of megawatts. This study presents a 4.5 MW turbine with pitch angle control. It also includes a detailed explanation of the control of the DC bus voltage, whose model is frequently dealt with in an abstract manner in other studies. It also evaluates the relationship between the pitch control and the torsional oscillation in the turbine shaft. [Ko et al. 2008] presents a study on the detailed model of a DFIG-based wind turbine connected to the electricity grid. The model includes the control of the generator, the converters on the rotor side and on the grid side, and the control of DC bus voltage. In conjunction with the classic con-trol scheme based on the rotating reference frame dq, the work presents as a contribution a new control scheme that takes into account the power limits of the converters. However, the strate-gies for controlling the currents of both converters remain based on PI loops with feedforward compensation of disturbances. To address parametric uncertainties, these controllers are tuned using the Nyquist stability criteria. In this work, however, the back-to-back converters were not modeled, but were represented by ideal voltage sources. This representation implies in uncon-vincing results from the realistic operational point-of-view, since power converters represent the main restraints source of DFIG control.
[Barambones et al. 2009] and [Kassem et al. 2013] proposed a control scheme based on sliding-mode control (SMC) to overcome problems of parametric uncertainties, unmodeled dy-namics and tuning of PI controllers. The SMC offers many advantages, among them the high performance in the presence of unmodeled dynamics, insensitivity to parametric variations, re-jection to external perturbations and fast dynamic response. The work aims to take advantage of the SMC features in controlling the active and reactive power of the DFIG connected to the network. The project of the SMC controller concisely consists of two main steps: select a sliding surface that models the dynamic performance desired for the closed-loop system and establish a control law such that the trajectory of the dynamic system states is forced for the sliding surface. [Pande et al. 2013] presented a similar approach, however, with the discrete model of SMC applied to the discrete model of DFIG.
[Ebrahimkhani 2016] proposed a fractional order sliding-mode controller applied to the DFIG-based WECS. In order to increase the robustness of the control system, the uncertainties and disturbances are calculated using a fractional order estimator. The proposed control strategy is developed to achieve a control signal free of chattering, without knowledge of uncertainties and disturbances or their limits. The author also proposes the use of a fractional order uncer-tainty estimator. The convergence of the control system is proven using the Lyapunov stability theory. Simulation results of the DFIG were obtained in the presence of several uncertainties in order to evaluate the proposed control scheme. The proposed method achieved outstanding
2.1. DFIG DRIVE AND CONTROL 11
results regarding disturbance estimation while the generator was operating subject to severe wind speed variations. However, grid disturbances investigations was not carried out, while experimental verification is still needed.
Simulations show that SMC presents better results than the conventional strategy with PI controllers. However, some criticisms are to be made. The trajectory of the states before reach-ing the slidreach-ing surface is referred to as reachreach-ing phase. Durreach-ing this phase, the dynamics of the system is still affected by uncertainties. The frequency of the SMC control signal should be ideally infinite so that the system reaches the sliding surface and remains in place. In prac-tice, the frequency is not infinite, but it remains very high, leading to the so-called chattering, a highly undesired effect. Chattering is the high-frequency switching of the control signal, which is undesired because it excites high-frequency dynamics of the plant, and these can cause unforeseen instability. Moreover, the back-to-back scheme that drives the DFIG has limited bandwidth, which makes it impractical to apply a control signal of ideally infinite frequency, although softening techniques have been proposed to reduce this problem in [Abdeddaim & Betka 2013] and [Martinez et al. 2013]. While promising, the simulations carried out did not include a realistic model of the wind speed. Moreover, the efficiency of the controllers is not proven since the back-to-back converter model is usually not taken into consideration, which is represented by ideal voltage sources. Also, no solution was presented in the above mentioned works for the control of the converter on the grid side, which in its place was used a bridge rectifier. The control effort was also not presented in the results.
Although the range of sliding-mode based controllers has been highlighted in recent years, its application to high-power WECS becomes offside because of the inherent system con-straints: bandwidth limitation and power losses. Reducing the high-power converter switching frequency is the main approach to reduce the losses of power converter, however, it will cause the increase of PWM output harmonic content, which affects the control performance and the power quality. The direct control is a trend approach to address the power converter switching frequency in the controller design. In order to reduce switching frequency, based on the pre-dictive model of DFIG, [Yunfei Wang et al. 2016] proposed a model prepre-dictive direct power control (DPC), which directly regulates rotor current through an optimization function with se-lecting appropriate voltage vector. This optimization function mainly achieves two targets: the first objective is to track rotor current references rapidly and the other is to reduce switching fre-quency. The most prominent feature of this proposal is that the switching frequency is reduced up sharply, and it achieves better dynamic and steady-state characteristics at lower switching frequency. However, experimental verification was not provided in this study.
In the same line of direct control, [Zhang et al. 2014] proposed a simple but very effec-tive method to achieve the prediceffec-tive DPC for DFIG-based WECS, which is able to operate at low switching frequency and provides accomplished steady-state and dynamic performances. The proposal is aimed to reduce both active and reactive power ripples while the switching fre-quency can be significantly reduced by appropriately arranging the switching sequence. The influence of one step delay caused by digital implementation is also investigated. The possi-bility of operating the proposed strategy under unbalanced grid voltage is verified by means of simulation results from a 2 MW DFIG system and experimental results from a scaled-down laboratory setup.
