Doctoral School of the Universitat Jaume I
Doctoral Programme in Industrial Technologies and Materials
Control strategies of VSC converters towards their massive deployment
A dissertation submitted by Carlos Díaz Sanahuja to obtain the degree of Doctor of Philosophy from the Universitat Jaume I
AUTHOR
Carlos Díaz Sanahuja
ADVISORS
Dr. Ignacio Peñarrocha Alós Dr. Ricardo Vidal Albalate
Castellón de la Plana, January 2023
Escuela de Doctorado de la Universitat Jaume I
Programa de Doctorado en Tecnologías Industriales y Materiales
Estrategias de control de convertidores VSC para su uso masivo.
Memoria presentada por Carlos Díaz Sanahuja para optar al grado de doctor por la Universitat Jaume I
AUTOR
Carlos Díaz Sanahuja
DIRECTORES
Dr. Ignacio Peñarrocha Alós Dr. Ricardo Vidal Albalate
Castellón de la Plana, Enero 2023
CARLOS|
DIAZ|
SANAHUJA
Firmado digitalmente por CARLOS|DIAZ|SANAHUJA Nombre de reconocimiento (DN):
cn=CARLOS|DIAZ|SANAHUJA, serialNumber=20477657K, givenName=CARLOS, sn=DIAZ SANAHUJA, ou=CIUDADANOS, o=ACCV, c=ES Fecha: 2022.12.26 17:44:45 +01'00'
IGNACIO PEÑARROCHA ALOS - NIF:19002690K
Firmado digitalmente por IGNACIO PEÑARROCHA ALOS - NIF:19002690K Nombre de reconocimiento (DN):
cn=IGNACIO PEÑARROCHA ALOS - NIF:19002690K, serialNumber=19002690K, givenName=IGNACIO, sn=PEÑARROCHA ALOS, ou=CIUDADANOS, o=ACCV, c=ES Fecha: 2022.12.26 19:06:24 +01'00'
RICARDO|
VIDAL|
ALBALATE
Firmado digitalmente por RICARDO|VIDAL|
ALBALATE Fecha: 2022.12.26 20:03:19 +01'00'
Escola de Doctorat de la Universitat Jaume I
Programa de Doctorat en Tecnologies Industrials i Materials
Estratègies de control de convertidors VSC per al seu ús massiu.
Memòria presentada per Carlos Díaz Sanahuja per a optar al grau de doctor per la Universitat Jaume I
AUTOR
Carlos Díaz Sanahuja
DIRECTORS
Dr. Ignacio Peñarrocha Alós Dr. Ricardo Vidal Albalate
Castellón de la Plana, Gener 2023
Funding | Financiación
Contrato predoctoral
• Beca Predoctoral de Formación del Profesorado Universitario (FPU) del Ministerio de Educación, Cultura y Deporte (MECD), Gobierno de España (Ref. FPU16/03505).
Participación en actividades
• Proyecto de Investigación “Control descentralizado y protección para un sistema eléc- trico futuro resiliente basado en convertidores” del Ministerio de Ciencia e Innovación (Ref. TED2021-130120B-C22).
• Proyecto de Investigación “Gestión de sistemas renovables con almacenamiento y con- trol de sus convertidores para contribuir a la operación del futuro sistema eléctrico” del Ministerio de Ciencia e Innovación (Ref. PID2021-125634OB-I00).
• Proyecto de Investigación “Control grid forming para operación avanzada de sistemas eléc- tricos con gran penetración de energía renovable” del Ministerio de Ciencia e Innovación (Ref. PID2020-112943RB-I00).
• Proyecto de Investigación “Desarrollo de metodologías para el diseño de software de control distribuido mediante la norma IEC 61499” de la Universitat Jaume I. (Ref. UJI-B2021-45).
• Proyecto de Investigación “Adapatación de algoritmos de control PID al contexto de la industria 4.0” de la Universitat Jaume I. (Ref. UJI-B2018-39).
• Proyecto de Investigación “Interacción entre convertidores y red en sistemas HVDC y HVAC con alta penetración de generación renovable” del Ministerio de Economía, Indus- tria y Competitividad (Ref. DPI2017-84503-R).
• Proyecto IDIFEDER/2018/036.
Control strategies of VSC converters towards their massive deployment
© 2023 by Carlos Díaz Sanahuja is licensed under CC BY-SA 4.0.
To my grandparents Paco, Pura, José and Upe
“Between grief and nothing I will take grief.”
William Faulkner, The Wild Palms
Abstract
Power systems based on large synchronous generators are moving towards systems dominated by power electronics. One of the reasons for this change is the increase in Distributed Generation, in which the generation sources are located close to the consumption points, thus reducing transmission losses and improving the local voltage regulation. On the other hand, concern for the environment, the need for sustainable generation, as well as favourable policies and cost reductions mean that the use of renewable energy sources such as photovoltaic or wind power has also increased in recent years and the forecasts for the near future are to increase even more. In this new scenario, power electronics devices are used as an interface between different elements of the power system. In particular, the voltage source converters (VSCs) are one of the most widely used technologies due to its flexibility. They permit to regulate the output voltage and the active and reactive power flows through the control of both, the magnitude and phase of the output voltage. Power electronics dominated systems allow to propose more advanced control strategies to improve the performance and stability margins of the system. However, they also present some problems as, for instance, the low mechanical inertia they have compared to traditional power systems or the interaction between different energy sources with intermittent production. Thus, engineers have to deal with new problems related to the synchronization, power flow control, power quality control, fault-ride-through or islanding detection as it is already set in grid codes.
The main objective of this thesis is to develop control strategies that facilitate the integration and widespread deployment of the VSCs into the power grid and to develop control design techniques to obtain controller parameters that guarantee stability and certain performance and robustness requirements. With this aim, different control strategies are proposed in this thesis.
First, starting from vector current control (VCC) strategy based on standard PI controllers, we propose an slight change on this control structure that improves the performance and robust- ness when operating in weak grids. We also propose a design method that guarantees certain performance and robustness requirements.
Second, we propose other control strategy based on a state-feedback control that takes into account the multivariable nature of the problem and, in which we develop a mechanism for avoiding the use of a phase-locked loop (PLL), which is a source of instability issues. With this control strategy, we have more degrees of freedom than with the standard PI control and we
I
can achieve better stability and robustness margins when the converter is connected to weak grids. In addition to this, we also propose a controller design procedure that guarantees specific performance and robustness requirements.
Finally, with the same aim, we apply the proposed control strategies to a particular appli- cation as it is the control of the electrical grid of an offshore wind farm, where several VSCs are involved and in which new control problems arise. Therefore, we propose different control strategies that takes into account the optimal power reference dispatch, the influence of the local design on the global behaviour, or the robustness against the number of operating VSCs when different VSCs are the responsible of controlling the voltage at the point of common coupling, i.e., when different VSCs have the same control objective.
Resumen
Los sistemas eléctricos de potencia basados en grandes generadores síncronos están sufriendo un cambio hacia sistemas en los que cada vez hay más electrónica de potencia involucrada. Una de las razones de este cambio es el incremento de la Generación Distribuida, con la que las fuentes de generación se localizan cerca de los puntos de consumo y , por tanto, se reducen las pérdidas debidas al transporte y se mejora el control de la tensión. Por otra parte, la preocupación por el medio ambiente, la necesidad de una generación sostenible, las políticas favorables y la reducción de costes, hacen que el uso de energías renovables como la fotovoltaica o la eólica hayan crecida también y que los pronósticos para el futuro cercano sean que crezca todavía más.
En este nuevo escenario, los dispositivos de electrónica de potencia se usan como interfaz entre los diferentes elementos que componen el sistema eléctrico. Concretamente, los convertidores en fuente de tensión (VSCs) son una de las tecnologías más usadas debido a su flexibilidad.
Permiten regular la tensión de salida y los flujos de potencia activa y reactiva a través del control tanto de la magnitud como la fase de la tensión de salida. Los sistemas eléctricos de potencia dominados por la electrónica de potencia permiten el uso de controles más avanzados para conseguir mejores márgenes de estabilidad e índices de desempeño, sin embargo, también presentas algunos problemas como, por ejemplo, su baja inercia si se comparan con los sistemas eléctricos de potencia tradicionales o la interacción entre diferentes fuentes con una producción intermitente. Así pues, y como ya viene recogido en los códigos de red, los ingenieros tienen que hacer frente a nuevos problemas relacionados con la sincronización, el control del flujo de potencia, el control de la calidad de la potencia, la capacidad de reponerse de faltas o la operación en modo isla.
El objetivo principal de esta tesis es desarrollar estrategias de control que faciliten la inte- gración y uso de forma generalizada de VSCs en la red eléctrica, así como, desarrollar técnicas de diseño para obtener parámetros de los controladores que garanticen ciertas especificaciones de rendimiento y robustez. Con este objetivo, se proponen diferentes estrategias de control.
En primer lugar, partiendo de la estrategia de control de corriente vectorial (VCC) basada en controladores PI estándar, se proponen pequeños cambios en su estructura de control que mejoran tanto su desempeño como robustez cuando se opera en redes débiles. Además, se propone también un método de diseño que garantiza el cumplimiento de ciertas especificaciones de robustez y rendimiento desde la fase de diseño.
En segundo lugar, se propone una estrategia de control basada en un control por reali- mentación de estados que tiene en cuenta la naturaleza multivariable del problema de control
III
y en la que se desarrolla un mecanismo para prescindir del uso de la PLL, que es una fuente de problemas de estabilidad. Con esta estrategia, se tienen más grados de libertad que con el con- trol PI estándar y se consiguen mejores márgenes de estabilidad y robustez cuando se trabaja en redes débiles. Adicionalmente, también se propone un proceso de diseño de controladores basado en garantizar requisitos de desempeño y robustez específicos desde la fase de diseño.
Finalmente, con el mismo objetivo, las estrategias de control propuestas se implementan en a una aplicación concreta como es el control de la red eléctrica de corriente alterna de un parque eólico marino, donde varios VSCs operan de forma conjunta y donde aparecen nuevos problemas de control. Así pues, se proponen nuevas estrategias de control que tienen en cuenta, entre otros aspectos, el reparto óptimo de las potencia entre los diferentes VSCs, la influencia del diseño local de los controladores sobre el comportamiento global a nivel de parque, o la robustez frente al número de VSCs operativos cuando diferentes VSCs se encargan de controlar la tensión del punto común de conexión, es decir, cuando varios VSCs tienen el mismo objetivo de control.
Resum
Els sistemes elèctrics de potència basats en grans generadors síncrons estan patint un canvi cap a sistemes en els qual cada vegada hi ha més electrònica de potència involucrada. Una de les raons d’aquest canvi és l’increment de la Generació Distribuïda, amb la qual les fonts de generació es localitzen a prop dels punts de consum i, per tant, es redueixen les pèrdues degudes al transport i es millora el control de la tensió . D’altra banda, la preocupació pel medi ambient, la necessitat d’una generació sostenible, les polítiques favorables i la reducció de costos fan que l’ús d’energies renovables com la fotovoltaica o l’eòlica també hagen crescut i que els pronòstics per al futur proper siguen que cresca encara més. En aquest nou escenari, els dispositius d’electrònica de potència es fan servir com a interfície entre els diferents elements que composen el sistema elèctric. Concretament, els convertidors en font de tensió (VSCs) són una de les tecnologies més utilitzades a causa de la seua flexibilitat. Permeten regular la tensió d’eixida i els fluxes de potència activa i reactiva mitjançant el control tant de la magnitud com de la fase de la tensió d’eixida. Els sistemes elèctrics de potència dominats per l’electrònica de potència permeten l’ús de controls més avançats per aconseguir millors marges d’estabilitat i índexs de rendiment, però també presenten alguns problemes com, per exemple, la baixa inèrcia si es comparen amb els sistemes elèctrics de potència tradicionals o la interacció entre diferents fonts amb una producció intermitent. Així doncs, i com ja ve recollit als codis de xarxa, els enginyers han de fer front a nous problemes relacionats amb la sincronització, el control del flux de potència, el control de la qualitat de la potència, la capacitat de refer-se de faltes o l’operació en mode illa.
L’objectiu principal d’aquesta tesi és desenvolupar estratègies de control que faciliten la integració i l’ús de forma generalitzada de VSCs a la xarxa elèctrica. Amb aquest objectiu, es proposen diferents estratègies de control.
En primer lloc, partint de l’estratègia de control de corrent vectorial (VCC) basada en controladors PI estàndard, es proposen petits canvis en la seva estructura de control que milloren tant el rendiment com la robustesa quan s’opera en xarxes dèbils. Es proposa també un mètode de disseny que garanteix el compliment de certs requisits de robustesa i prestacions des de l’etapa de disseny.
En segon lloc, es proposa una estratègia de control basada en un control per realimentació d’estats que té en compte la naturalesa multivariable del problema de control i en la que es desenvolupa un mecanisme per prescindir de l’ús de la PLL, que és una font de problemes
V
d’estabilitat. Amb aquesta estratègia, es tenen més graus de llibertat que amb el control PI estàndard i s’aconsegueixen millors marges d’estabilitat i de robustesa quan es treballa en xarxes dèbils. A més a més, també es proposa un procés de disseny de controladors basat en garantir requisits de robustesa i prestacions específics des de l’etapa de disseny.
Finalment, amb el mateix objectiu, les estratègies de control proposades s’implementen en una aplicació concreta com és el control de la xarxa elèctrica de corrent altern d’un parc eòlic marí, on diferents VSCs operen de manera conjunta i on apareixen nous problemes de control.
Aleshores, es proposen noves estratègies de control que tenen en compte, entre d’altres aspectes, el repartiment òptim de les potències entre els diferents VSCs, la influència del disseny local dels controladors sobre el comportament global a nivell de parc, o la robustesa davant el nombre de VSCs operatius quan diferents VSC s’encarreguen de controlar la tensió del punt comú de connexió, és a dir, quan diversos VSC tenen el mateix objectiu de control.
Acknowledgements | Agradecimientos
En estas líneas me gustaría expresar mi agradecimiento a las personas que, de un modo u otro, me han acompañado en el proceso de realización de la tesis y que termina con este documento como resultado tangible del mismo.
En primer lugar a Nacho, por su dedicación y por la paciencia que ha tenido conmigo. Por todo lo que me ha enseñado y por todo lo que he podido aprender de él. Por tener siempre las palabras exactas que me han hecho seguir hacia delante, sobretodo, en los momentos en los que me apetecía gritar: ¡Motivation such an aggravation! Por ser un ejemplo de no conformismo, de que a veces no basta un porque sí, y de que siempre es mejor no jugar al empate, presentar batalla y no empezar cada combate, tirando la toalla.
A Ricardo, por ser un ejemplo de que el talento no está reñido con el trabajo, el orden, la disciplina y la humildad.
A Agustí, por su amabilidad y por acogerme para hacer la estancia a distancia. A veces “la vida te da sorpresas...” y haberlo conocido ha sido una de las buenas.
A mis colegas de doctorado Ester, Oscar, Rubén y David por compartir los momentos buenos y los no tan buenos, los momentos de locura y algunos momentos raros y difíciles de explicar.
En definitiva, por vivir juntos esta experiencia y hacerme sentir que valió la pena.
A mis amigos, que no son muchos, ni tampoco pocos, pero piensan en mi. Esos amigos que han sabido ver mis momentos de dificultad, que han sido capaces de hacer que deje el ordenador a un lado y con los que he tenido la suerte de vivir experiencias inolvidables.
A Ana, por aparecer en mi vida y haberse querido quedar.
A Lourdes y Paco, mis padres, porque si hay algo bueno en mi, se lo debo a ellos.
Y por último a Laura, mi hermana pequeña. Por apoyarme en todo, por hacerme sentir querido aunque no lo merezca, por demostrarme y hacerme saber que está y va a estar siempre a mi lado, por ser la persona más importante en mi vida, y es que, desde el primer momento que la vi, en una cesta, tapada y con los ojos todavía cerrados, ya intuí que la iba a querer más de lo que me quiero a mi.
VII
Contents
Abstract I
Acknowledgements VII
List of figures XVIII
List of tables XIX
1 Introduction 1
1.1 Motivation . . . 1
1.2 Challenging problems . . . 4
1.3 Thesis outline and contributions . . . 9
1.3.1 List of contributions . . . 13
2 Background 15 2.1 Basics of Voltage Source Converters . . . 15
2.2 Weak grids . . . 19
2.3 Operation of the electrical grid . . . 20
2.4 Grid-level VSC control strategies . . . 21
2.4.1 Grid-following converters . . . 21
2.4.2 Grid-forming converters . . . 23
2.5 Synchronization . . . 23
2.5.1 Synchronous Reference Frame Phase-Locked Loop (SRF-PLL) . . . 24
2.6 Grid-following control strategies . . . 26
2.6.1 Vector current control (VCC) in the synchronous dq0 reference frame . . 27
2.6.2 Vector current control (VCC) in the stationary αβ0 reference frame . . . 30
2.6.3 Equivalent structures in the abc frame . . . 31
2.6.4 Grid Voltage Modulated Direct Power Control (GVM-DPC) . . . 32
2.7 Grid-forming control strategies . . . 35
2.7.1 Droop-based controls . . . 35
2.7.2 Synchronous machine-based control . . . 40
2.7.3 Virtual Oscillator Control . . . 41
2.7.4 Conclusions . . . 41
IX
3 Inner current loop PI design for the connection of VSCs to a weak AC grids 43 3.1 Introduction . . . 43 3.2 Problem statement . . . 45 3.3 Proposed approach . . . 47 3.4 Closed-loop dynamics . . . 49 3.4.1 Steady state . . . 50 3.4.2 Transient . . . 51 3.4.3 High frequency behaviour . . . 55 3.5 Dimensionless performance evaluation . . . 55 3.5.1 Change of variables . . . 55 3.5.2 Nominal performance analysis . . . 57 3.5.3 Weak grid analysis . . . 60 3.5.4 Predicting the closed-loop behaviour and limitations . . . 64 3.6 Design rules . . . 66 3.6.1 Outer loop design (Kd) . . . 66 3.6.2 Inner loop design . . . 67 3.6.3 Cancellation controller . . . 69 3.6.4 Internal model control . . . 71 3.7 Simulation results . . . 74 3.7.1 Controller design example . . . 79 3.8 Conclusions . . . 81 4 Multivariable phase-locked loop free strategy for power control of grid-connected
voltage source converters 83
4.1 Introduction . . . 83 4.2 Problem statement . . . 85 4.2.1 Vector current control . . . 85 4.2.2 Grid voltage modulated direct power control . . . 87 4.3 Proposed approach . . . 88 4.3.1 Controller design . . . 89 4.3.2 Anti-windup design . . . 89 4.3.3 Frequency deviations . . . 90 4.3.4 Comparison with VCC and GVM-DPC approaches . . . 92 4.4 Robustness analysis under weak grids . . . 92 4.5 Simulation results . . . 95 4.6 Conclusions . . . 100
CONTENTS XI 5 Alternative control approach for the offshore grid of wind power plants 103 5.1 Introduction . . . 103 5.2 Problem statement . . . 104 5.2.1 Model and control of an offshore wind farm . . . 104 5.2.2 Variables and goals of the offshore AC network control . . . 105 5.2.3 Mathematical modelling . . . 106 5.3 Proposed approach . . . 107 5.3.1 Frequency control . . . 107 5.3.2 Controller structure . . . 108 5.3.3 Controller parameters design . . . 108 5.3.4 Offshore grid voltage control . . . 109 5.3.5 Wind turbines power control . . . 111 5.4 Simulation results . . . 111 5.4.1 Change in power references . . . 112 5.4.2 Disconnection of wind turbines . . . 113 5.5 Conclusions . . . 114 6 Controllers design of a wind farm: Influence of the local design on the global
behaviour. 117
6.1 Introduction . . . 117 6.2 Offshore wind farm model . . . 120 6.2.1 Electrical model . . . 120 6.2.2 State-space representation . . . 121 6.3 Control strategy . . . 124 6.4 Controller design . . . 126 6.4.1 Local controllers . . . 126 6.4.2 Global performance analysis . . . 133 6.5 Centralized controller . . . 136 6.5.1 Dispatch function . . . 136 6.5.2 Global power Co controller . . . 138 6.6 Numerical examples and simulation results . . . 141 6.6.1 Local controllers . . . 142 6.6.2 Global analysis . . . 143 6.6.3 Simulations . . . 146 6.7 Conclusions . . . 169
7 Robust local controllers design for the AC grid voltage control of an offshore
wind farm 171
7.1 Introduction . . . 171 7.2 Problem statement . . . 173 7.2.1 Offshore wind farm model and control objectives . . . 173 7.2.2 Offshore AC grid model . . . 173 7.3 Proposed approach . . . 175 7.3.1 Frequency control . . . 175 7.3.2 Offshore AC grid voltage control . . . 175 7.3.3 Outer voltage controller design. . . 178 7.4 Simulation results . . . 179 7.5 Conclusions . . . 182
8 Conclusions and future research 183
8.1 Conclusions . . . 183 8.2 Future research . . . 186
A Reference frame transformations 189
A.1 Natural abc frame . . . 189 A.2 Stationary αβ0 reference frame . . . 190 A.3 Synchronous rotating dq0 reference frame . . . 191 A.4 Active and reactive powers . . . 192 A.5 Scaling factors for Clarke transformations . . . 192 A.6 Transformations over differential equations . . . 194 B Considerations regarding the proposed MIMO PLL-free strategy 195 B.1 Avoiding the use of the PLL . . . 195 B.2 Implications of using a fixed frequency for the controller . . . 196 B.3 Antiwindup mechanism (synchronizer) . . . 198 B.4 Fault-ride through capability . . . 199 B.5 Use of a three-phase 2-level VSC (PWM-based) . . . 201 B.6 Multivariable PLL-free approach with a LCL filter . . . 204 B.6.1 Electrical and mathematical model . . . 204 B.6.2 Control strategy . . . 205 B.6.3 Simulation results . . . 213
Bibliography 217
List of Figures
1.1 Global weighted average total installed costs, capacity factors and Levelized Costs of Energy of newly commissioned utility-scale solar PV, onshore and offshore wind, 2010-2021. Source: IRENA (2021), Renewable Power Generation Costs in 2020, International Renewable Energy Agency. . . 2 1.2 Renewable electricity generation by technology, 1990-2026. Source: World Energy
Outlook 2021, International Energy Agency (IEA). . . 3 1.3 Evolution of the electrical system from a centralized generation system (left)
towards the Smart Grid paradigm (right). Source: IEEE. . . 4 1.4 Renewable power plants and energy storage systems interfaced with the grid
through power electronics. . . 5 1.5 Offshore wind farm scheme connected to the onshore grid through a HVDC link. 7 1.6 Estimated new offshore installations per year (MW). Source: GWEC Market
Intelligence, June 2022. ∗ Compound Annual Growth Rate. . . . 8 2.1 2-level VSC with a L output voltage filter. . . 15 2.2 Output voltage of a 2-level VSC before and after a LC filter. . . 16 2.3 Operation principle of multilevel converters. . . 17 2.4 Modular multilevel converter structure. . . 17 2.5 MMC output voltage. . . 18 2.6 Back-to-back configuration. . . 18 2.7 Averaged model of a VSC. . . 18 2.8 VSC connected to a weak grid modelled as the Thevenin equivalent. . . 19 2.9 Operation principle of VSCs. . . 24 2.10 Three-phase PLL in the synchronously rotating reference frame (SRF-PLL). . . . 24 2.11 Block diagram of the linearised SRF-PLL. . . 25 2.12 Model of a VSC with a L filter connected to the AC grid. . . 27
XIII
2.13 VCC controller in dq reference frame and PI controllers. . . 28 2.14 Grid-supporting controls. . . 30 2.15 VCC controller in αβ reference frame and PR controllers. . . 31 2.16 GVM-DPC controller. . . 33 2.17 P /ω and Q/V droop control. . . 36 2.18 Electrical scheme of two VSC connected in parallel to a load. . . 36 2.19 Graphical representation of the droop P /ω. . . 37 2.20 Relationship between the P/Q circle and P/ω and Q/V droop primary control. . 38 2.21 Secondary frequency and voltage control. . . 38 2.22 Graphical representation of the secondary frequency control. . . 39 2.23 Droop control with inner current and voltage control loops. . . 40 2.24 Synchronverter. . . 41 3.1 Electrical model of a VSC connected to a weak grid with measurable and modi-
fiable variables . . . 46 3.2 Proposed control scheme of a VSC connected to a weak grid. . . 48 3.3 (Left) Voltage levels at PCC. (Right) Maximum derated power levels. . . 52 3.4 Block diagram of the control approach with 2DOF PIs. . . 53 3.5 Damping and real part of dominant poles of transfer function φN1,1(s0) . . . 58 3.6 Normalized bandwidth ωa0 of φN1,1(s0)for different values of bd. . . 58 3.7 Nominal performance IE0 (×102) for different values of bd under step reference
changes. . . 59 3.8 Nominal performance IAE0 (×102) for different values of bd under step refernece
changes. . . 59 3.9 IAE0 (×102) for step disturbance changes. . . 60 3.10 Stability regions for injection (left) and absorption (right). . . 61 3.11 (left) Effect of bd, (right) Effect of bqKd0. . . 62 3.12 SCR0 for different values of bd and bq. (for Kd0 = −20) . . . 63 3.13 Block diagram of the control approach with 2DOF PIs. . . 64 3.14 Nyquist diagram of F1,1N(s0) for different values of Kd’ (with SCR0 = 30 and
bd= bq = 1) . . . 65 3.15 MT for different values of bd. . . 65 3.16 (Left) Voltage levels at PCC. (Right) Maximum derated power levels. . . 67 3.17 Cancellation curves. . . 69
LIST OF FIGURES XV 3.18 SCR0 curves in the case of cancellation controllers (for bq= bd). . . 70 3.19 IE and IAE (×102) curves for step reference changes and step disturbance changes
in the case of cancellation controllers. . . 71 3.20 Normalized bandwidth ωbw0 in the case of IMC. . . 73 3.21 IE’ and IAE’ in the case of IMC (step reference changes and step disturbances). . 73 3.22 Minimum SCR admissible for IMC design. . . 74 3.23 SCR0 in the case of IMC (Kd= −20). . . 74 3.24 Power tracking: (top) Connected to stiff grid and (bottom) to a grid with SCR=2. 76 3.25 SCR step changes from 2 to 1.7 (at 0.5 s) and from 1.7 to 1.4 (at 1.0 s) . . . 76 3.26 Effect of bd in tracking active power references (at 0.1 s) and SCR step changes
from 2 to 1.75 (at 0.5 s) and from 1.75 to 1.5 (at 1 s). . . 77 3.27 Effect of Kdin tracking power references connected to a grid with SCR=2. . . . 78 3.28 SCR step change from 2 to 1.75 (Effect of Kd). . . 79 3.29 Tracking power references connected to a grid with SCR=2 with the product
bqKdconstant. . . 80 3.30 SCR change from 2 to 1.75. Product bqKd constant. . . 80 4.1 Model of the system and controller structure. . . 85 4.2 VCC controller block diagram. . . 86 4.3 GVM-DPC controller block diagram. . . 87 4.4 Proposed MIMO controller block diagram. . . 88 4.5 Small gain theorem modelling needs and application to VCC. . . 93 4.6 GVM-DPC approach block diagram in a weak grid. . . 94 4.7 MIMO proposal block diagram in a weak grid. . . 95 4.8 Behavior tracking power references (a) and facing a voltage sag of 70% (b). . . . 96 4.9 Power and current tracking when there are frequency deviations. . . 97 4.10 Errors due to grid voltage deviations. . . 98 4.11 Maximum singular values of T∆i. . . 99 4.12 Comparison of ¯σ(T∆5) for original and optimized controllers. . . 100 4.13 Step change in P∗ when VSC is connected to a weak grid with SCR=2. . . 101 5.1 Offshore wind farm model with a HVDC link. . . 104 5.2 Offshore wind farm model with a HVDC link. . . 105 5.3 Proposed offshore grid voltage control scheme. . . 109
5.4 Proposed wind turbines power control scheme. . . 111 5.5 Dominant eigenvalues for closed-loop systems. . . 112 5.6 Change in power references. . . 113 5.7 Disconnection of wind turbines. . . 115 6.1 Wind farm scheme. . . 118 6.2 Single-phase equivalent electrical scheme. . . 120 6.3 Input/Output scheme for each subsystem. . . 122 6.4 Control structure of the overall system. . . 124 6.5 Local controller structure. . . 126 6.6 Local state-feedback current controller . . . 127 6.7 Pole placement in region S(α, θ, ρ). . . 130 6.8 System GP Q to be controlled by the Co controller. . . 139 6.9 Step response of GP Q from the inputs Po∗∗, Q∗∗o (dashed lines) to the outputs Po,
Qo (solid lines) . . . 140 6.10 Global power Co controller structure. . . 140 6.11 Step response of GWcli. . . 143 6.12 Obtained settling time ts98, damping ζ and norms kKik, kGre(s)k∞, kGrq(s)k2,
depending on ρ. . . 144 6.13 Step response of the transfer function matrix from IT∗idq to ITidqfor different values
of ρ. . . 145 6.14 Relationship between kGre(s)k∞and kGyodo(s)k∞ . . . 145 6.15 Relationship between kGre(s)k∞and kGreτ(s)k∞
f . . . 146 6.16 Step response from current references IT∗1dq and IT∗6dq to voltages VF1dq and VF6dq . 147 6.17 Global power reference tracking: comparison of Co1, Co2, Co3, Co4, Co5 controllers.148 6.18 Global power reference tracking: comparison of Co6, Co7, Co8, Co9, Co10 controllers.149 6.19 Optimal dispatch: power reference tracking for each WTG for the Co7. Pi, Qi
signals represented in solid lines and Pi∗, Q∗i signals in dotted lines. . . 149 6.20 Disturbances rejection: connection of a load (with controller Co). . . 151 6.21 Disturbances rejection: connection of a load (without controller Co). . . 151 6.22 Disturbances rejection: step change in the frequency of the VP CC voltage from
50 Hz to 48 Hz (with controller Co). . . 152 6.23 Disturbances rejection: step change in the frequency of the VP CC voltage from
50 to 48 Hz (without Co controller). . . 152
LIST OF FIGURES XVII 6.24 Disturbances rejection: power references tracking when there are variations on
the parameters of the system of w.r.t the nominal values (with Co controller). . . 153 6.25 Disturbances rejection: global power references tracking when there are variations
on the parameters of the system w.r.t the nominal values (without Co controller). 154 6.26 Connection/disconnection of WTGs: state si of the different WTG. . . 154 6.27 Connection/disconnection: global power reference tracking. . . 155 6.28 Connection/disconnection: local power reference tracking. Pi, Qi(solid lines) Pi∗, Q∗i
(dotted lines). . . 155 6.29 Connection/disconnection: module of the currents ITi control actions Ui∗ and
voltages at points of connection of each WTG VFi. . . 156 6.30 Wind power limitations: available wind power si (in p.u.) for each WTG . . . 157 6.31 Wind power limitations: global power references tracking. . . 158 6.32 Wind power limitations: active powers dispatch. . . 158 6.33 Phase variations: global power references tracking when each local controller has
each own angle. . . 159 6.34 Phase variations: generated currents and control actions in the dq frame (syn-
chronized angles). . . 160 6.35 Phase variations: generated currents and control actions in the dq frame (non
synchronized angles). . . 161 6.36 Phase variations: generated current and control action of the WTG5 in the abc
frame and the module of their dq components. . . 162 6.37 Frequency variations: generated currents and control actions in the dq frame and
their modules . . . 163 6.38 Frequency variations: errors in tracking current references. . . 164 6.39 Frequency variations: generated current and control action of the WTG5 in the
abc frame and the module of their dq components (frequency deviation of -1.33 Hz w.r.t 50 Hz). . . 164 6.40 Fault-ride through: Current references tracking (top) with antiwindup and (bot-
tom) without antiwindup. Module of currents (solid lines) and references (dotted lines). . . 165 6.41 Fault-ride through: Detail of the fault (D1) and the restoration (D2). Module of
currents (solid lines) and references (dotted lines). . . 165 6.42 Fault-ride through: Power references tracking (top) with antiwindup and (bot-
tom) without antiwindup. . . 166 6.43 Fault-ride through: Integral terms of the controller Co. . . 167
6.44 Fault-ride through: Applied and computed control actions of Co (top) with anti- windup and (bottom) without antiwindup. . . 168 7.1 Offshore wind farm model with a HVDC link. . . 172 7.2 Single-phase equivalent electrical scheme of the AC offshore grid. . . 173 7.3 Offshore AC grid voltage control scheme. . . 175 7.4 Cascade control scheme in each front-end inverter. . . 176 7.5 Change of the voltage references. . . 180 7.6 Disturbance rejection. . . 181 7.7 Connection/Disconnection of wind turbines. . . 182 A.1 Voltage vabc in the natural abc coordinate system. . . 189 A.2 Voltage vabc in the natural abc coordinate system and vαβ in the stationary αβ
reference frame. . . 190 A.3 Projections of vαβ on d and q axis. . . 191 B.1 fault-ride through capability . . . 200 B.2 PWM signal. . . 201 B.3 Power tracking and disturbance rejection with PWM . . . 201 B.4 Three phase voltage at point of connection vgabc and currents and generated
currents iabc (fsw = 5kHz). . . 202 B.5 Voltage at point of connection and generated current for different fsw (phase a). 202 B.6 Reference control actions for the VSC in dq and abc frames. . . 203 B.7 Electrical model with LCL filter. . . 204 B.8 Block diagram of the control system. . . 205 B.9 Block diagram of the control system. . . 205 B.10 Block diagram of the control system with option 1 for the outer controller. . . 207 B.11 Block diagram of the control system with option 2 for the outer controller. . . 209 B.12 Block diagram of the control system with option 3 for the outer controller. . . 210 B.13 Block diagram of the control system with option 4 for the outer controller. . . 211 B.14 Option 4 for the outer controller with outputs decoupler Cdec. . . 212 B.15 Active and reactive powers. . . 214 B.16 Module of currents i1dq, i2dq and the voltage vcdq. . . 215 B.17 Module of computed u0dq and applied uappdq control actions. . . 215
List of Tables
1.1 Thesis outline. . . 13 2.1 Classification of grid-forming control strategies. . . 35 3.1 Parameters used in simulations. . . 75 3.2 Effect of bd and bq. . . 75 3.3 Effect of bd. . . 75 3.4 Effect of Kd. . . 78 3.5 Product of bqKd constant. . . 79 3.6 Controllers for case 1. . . 81 3.7 Controllers for case 2. . . 81 3.8 Controllers for case 3. . . 81 4.1 Comparison of the different control approaches. . . 92 4.2 Interconnection transfer matrices in weak grid analysis. . . 94 4.3 Parameters used in simulations. . . 95 5.1 Simulation Parameters . . . 112 6.1 Simulation Parameters. . . 142 6.2 Local controllers design. . . 142 6.3 Comparison of different Co controllers . . . 147 6.4 Comparison between the losses (in W) for the proposed optimal dispatch and a
1
n dispatch . . . 150 6.5 Variations on the parameters w.r.t the nominal values (in p.u.). . . 153 6.6 Phase angle used in each WTG (in◦). . . 158 6.7 Frequency variations in each WTG ∆f (in Hz) w.r.t the frequency of the PCC
voltage (50 Hz). . . 159 7.1 Simulation Parameters . . . 180 B.1 Parameters used in simulations. . . 213 B.2 Inner current controllers design. . . 213
XIX
Chapter 1
Introduction
This chapter is a general overview of the research done during the PhD and exposes the moti- vation, contributions and works related with this thesis.
1.1 Motivation
In the last two decades there have been significant changes in the energy scenario. The global energy consumption has increased globally, and also the greenhouse gases due to our carbon- based energy generation system [81]. The climate change has become a major concern for society and, recently, in the Glasgow Climate Pact most of the countries agreed to limit the global average temperature rise to 1.5◦C. To reach this goal a rapid and large-scale reduction of all greenhouse gases is needed [167]. This involves a substantial reduction in fossil fuel use, widespread electrification and improving the energy efficiency among other measures.
In order to reduce the dependence on the carbon-based generation, and due to a cost re- duction (see figure 1.1) and favourable policies, as well as advances in digital technologies [83], there has been a great progression in the use of Renewable Energy Sources (RES) since the early 2000s and it is expected a bigger deployment in the next years [80] (see figure 1.2). Among all the RES, hydropower is the one with higher total installed capacity worldwide followed by the wind energy systems and solar photovoltaic (PV). However, forecasts for the next few years show that higher total additions in wind and PV sources are expected.
In addition to moving from fossil carbon-based energy sources to RES, other steps are also being taken in order to achieve a more efficient power system. A change of the operation paradigms of power systems is being produced, moving from Centralized Generation (CG) to Distributed Generation (DG).
On the one hand, a traditional CG power system consists of facilities to generate, transmit and distribute electrical power to consumers or loads. Usually, in CG systems, energy sources are big synchronous generators which are located far from the consumption points. This requires that the generated electricity is transmitted long distances and thus, there are high energy losses. Although there are often interconnections at the transmission level to form a strong grid, electricity flows uni-directionally from generation to loads.
1
Figure 1.1. Global weighted average total installed costs, capacity factors and Levelized Costs of Energy of newly commissioned utility-scale solar PV, onshore and offshore wind, 2010-2021. Source: IRENA (2021), Renewable Power Generation Costs in 2020, International Renewable Energy Agency.
On the other hand, DG provides an alternative to the CG by generating electricity near to the consumption points, i.e., at the distribution levels, with the employment of small power generating units. There are different possibilities for operating DG systems, such as: (i) con- necting DG systems directly to the grid (ii) creating micro grids before being connected to the utility grid.
A microgrid can be considered as a small grid, formed by DG systems, Electrical Energy Storage (EES) systems, and loads, being all the components interconnected and controlled in a hierarchical way with the capability to operate either as a grid connected or as an islanded system [31, 136, 147, 148]. The concept of microgrid has appeared in the last years and seems to be the candidate to reduce the dependence on the fossil fuel based generation, towards a more environmentally friendly energy paradigm. Figure1.3 shows the schemes of the current centralized electrical power system and the one expected in the future based on the Smart Grid concept.
Although non-renewable based power systems like gas or diesel generators can be integrated into microgrids because their generation profile can be easily controlled, in order to reduce the greenhouse gases emissions, the use of RES is usually preferred. Among the RES, PV and wind power plants are especially appropriate to be integrated as generators in microgrids. They are smaller and more scalable than centralized power plants, and they can be connected to any point of the power system [57,106,136]. However, they are characterized by having a stochastic and intermittent behaviour, and thus, the EES systems are also claimed to have particularly important role in microgrids [2,37,189].
Power electronic converters enable the efficient and flexible interconnection of the differ- ent elements, i.e., RES, EES, flexible alternating current transmission systems (FACTS) and
1.1. Motivation 3
Figure 1.2. Renewable electricity generation by technology, 1990-2026. Source: World Energy Outlook 2021, International Energy Agency (IEA).
controllable loads, to the electric power system. For integrating both, wind and PV sources, power electronic converters are needed, in the case of wind turbines, to allow the variable-speed operation, and in the case of the PV systems, for converting Direct Current (DC) produced by PV cells into Alternating Current (AC) and pour it into the electricity distribution network.
Power electronic converters are also needed for connecting the EES systems or a microgrid to the AC grid (see figure 1.4). Another application in which power electronic converters are being used is for facing High Voltage Direct Current (HVDC) links [14]. They are used, for instance, to transport the electrical energy from the AC grid of an offshore wind farm to the onshore grid [53] (see figure 1.5).
The electrical power system is moving towards a power electronics dominated system. How- ever, one of its inherent problems is that they have an extremely low mechanical inertia com- pared with traditional power systems composed by large synchronous generators and the impact that this has on rate of change of frequency (ROCOF) during grid events. Moreover, control engineers will have to deal with new problems related to the synchronization, power flow con- trol, power quality control, fault-ride-through or islanding detection, as already is defined in grid codes. Such as systems, based on semiconductors and signal processing allows to propose advanced control strategies to improve the performance and stability margins of the system.
The massive deployment of power electronic converters represents an opportunity, but also a responsibility for control engineers because the stability and performance of the system depend on the proposed control strategy.
Figure 1.3. Evolution of the electrical system from a centralized generation system (left) towards the Smart Grid paradigm (right). Source: IEEE.
1.2 Challenging problems
This thesis is devoted to the development of control strategies for Voltage Source Converters (VSC) for their massive use in power systems. The main concerns and issues that have been addressed are briefly described and listed below.
The change of the electrical power scenario involves, among others, the use of power con- verters as well as the change in the electrical power system structure with the microgrids. In contrast with the strong grids dominated by big synchronous machines, power electronics dom- inated grids can result in weak grid issues [137]. A weak grid is a grid with a low short circuit power with respect to the generation source rated power, which results in a low Short Circuit Ratio (SCR). In this kind of grids, variations in load demands or power injections by generation sources can significantly affect the local bus voltage and thus affect the quality of delivered power, nearby converters and the stability of the entire system [156]. The stability issues in weak grids makes the tuning of the controllers very important [181]. This is challenging as the local SCR may change due to, for instance, a connection/disconnection of generators or events such as line trips.
In this context, the most extended way of converter control is the Vector Current Control (VCC) [184]. Conventional VCC is composed of two cascaded control loops. On the one hand, in the inner current loop, a feedback linearisation is done for both, decoupling the Multiple Input Multiple Output (MIMO) system and also cancelling non linear terms. With this, we have two Single Input Single Output (SISO) systems that will be controlled by, usually, two equal Proportional Integral (PI) controllers. On the other hand, the outer loop is devoted to control active and reactive powers or active power and the voltage of the point of connection or Point of Common Coupling (PCC). VCC has been the industry standard for many decades due to its simplicity in implementation and its good performance in stiff grids. However, it shows poor performance an stability issues in weak grids. As the use of VSC grows in weak grids,
1.2. Challenging problems 5
Bateries
Photovoltaic cells Wind turbines
Figure 1.4. Renewable power plants and energy storage systems interfaced with the grid through power elec- tronics.
it becomes essential to seek control alternatives that improve its performance and ensure its stability.
In this thesis, we wonder if it would be possible to propose a control strategy using the VCC structure, taking advantage of its simplicity in implementation, that is, introducing slight changes that do not increase its complexity, and at the same time improve its performance and stability margins when VSCs are connected to weak grids. Therefore, the first challenging problem that we face can be formulated as
P1. To make slight modifications to the standard VCC structure to improve the performance of VSCs connected to weak grids while ensuring certain stability margins.
The performance and stability depend on the control structure used, but also on the par- ticular value of the parameters of the physical elements such as resistances, inductances or capacitances, as well as on the particular value of the controller parameters, such as the gains of the PI controllers or the time constant of the filters. There are many degrees of freedom and this makes it difficult to give general solutions. In fact, the usual thing in most of works in literature is to propose solutions for particular cases and, in some of them, to sweep for different values or situations and, in this way, provide more general solutions.
We consider that, for a given control structure, it would be interesting to obtain a formal description of the control problem in such a way that the dependency on the particular param- eters is avoided. With this, we would have a clear understanding of the limitations of such a control approach and we would be able to propose general design rules. Motivated by this fact and complementing the challenge P1 we can formulate the challenging problems P2, P3 and P4 as
P2. To model the control problem of a VSC connected to a weak grid avoiding its parameter dependency.
P3. To analyse the control problem of a VSC connected to a weak grid and understand its limitations.
P4. To propose general design rules for this control structure that guarantee some given per- formance requirements and stability margins.
In conventional VCC, the synchronization of the control actions with the voltages at the PCC is needed. It is done by using a Phase Locked Loop (PLL), which determines the synchronisation angle employed by the controller. The PLL is part of the control loop, it must be tuned, and its dynamics must be considered for analysing the stability and performance of the whole system. Hence, the PLL is an instability source. Reducing PLL dynamic capabilities affects de entire controller and, usually, it is effective at avoiding instability, however, it compromises the controller’s responsiveness because PLL dynamics is coupled with the control closed-loop. For this reason, many works in the literature have been focused on proposing modifications of the basic PLL structure or tunning mechanisms to improve its performance and contributing to get a more robust behaviour [10, 111, 185, 193]. Although these strategies improve some aspects of the performance, they also add complexity to the control problem. Some other works propose solutions for avoiding the use of the PLL [71, 187, 188]. In this sense and in line with the idea behind P1, P2, P3 and P4 of reducing the complexity of the control problem we state the next challenging problem to be covered in this thesis as
P5. To develop an alternative proposal for the synchronization in which the PLL is avoided.
The inherent nature of the VSC control problem is multivariable. Dynamics can be formu- lated as a coupled MIMO system in which all the inputs affect all the outputs. However, in the VCC, the inputs or control actions are defined in such way that the closed-loop behaviour becomes decoupled, and it can be seen as the sum of two SISO systems that can be controlled independently, usually by means of two equal PI controllers. This simplifies a lot the controller tuning and implementation, but it has some important drawbacks too.
On the one hand, the decoupling terms used in the control action makes it difficult to define suitable and effective control action saturation and antiwindup mechanisms. In [117] different alternatives for saturating the control action are analysed and in [72] a MIMO antiwindup mechanism is proposed. There exist a lot of works with analysis and proposals for the linear regime of the controllers, however non linear behaviours such as saturation and antiwindup are far from being studied in depth.
On the other hand, the decoupling mechanism in the VCC strategy is appropriate and effective in stiff grids, however, it ceases to be suitable when the VSC is connected to a weak grid due to the non-neglecting impedance associated to the grid.
Therefore, feedforward terms in the control law, changes in the grid impedance (related to the stiffness of the grid), transient errors due to PLL dynamics in the estimation of the grid voltage angle, as well as delays in the reconstruction of the control action can be considered as instability sources. Related to this, three more challenging problems can be defined as
P6. To analyse the different instability sources and study their individual influence on the overall stability.
1.2. Challenging problems 7 P7. To propose an alternative control strategy that avoids the decoupling terms used in the VCC, considers the multivariable nature of the control problem and optimizes the robustness against grid impedance changes without increasing the complexity.
P8. To propose effective saturation and antiwindup MIMO mechanisms.
P CC
Converter Front-End Converter
Back-End
Converter Front-End Converter
Back-End
TRANSMISSION HVDC Offshore
rectifier
Onshore inverter
.. .. ..
Offshore grid Onshore grid
Figure 1.5. Offshore wind farm scheme connected to the onshore grid through a HVDC link.
VSCs can operate in different modes, namely grid following and grid forming. It depends on whether the VSC is devoted to deliver some active and reactive power (grid following) or, in contrast, it is the responsible of generating and maintaining the local bus voltage under control while delivering the active and reactive demanded by the loads (grid forming). The control problem becomes more challenging when various VSCs are interconnected with a particular topology. A growing field in which it is possible to find several interconnected VSCs is in offshore wind farms, as shown in figure 1.5. Moreover, in this kind of systems the VSCs themselves have to create and control the electrical grid. According to [32], it is expected that over 315 GW of new offshore wind capacity will be added over the next decade (2022-2031), bringing the total offshore wind capacity to 370 GW by the end of 2031 (see figure 1.6). The volume of annual offshore wind installations is expected to more than double from 21.1 GW in 2021 to 54.9 GW in 2031, bringing offshore’s share of global new installations from 23% in 2021 to 32% by 2031.
This scenario motivates the following challenging problem:
P9. Applied to a particular offshore wind farm structure, to study the behaviour of the MIMO control approach derived from P7 and P8 when several VSCs are connected to the PCC operating in grid following and also grid forming modes.
As wind farms increase their generation capacity, they are more demanded to contribute to the power grid operation. To do it optimally, a holistic perspective is required rather than an individual control of each wind turbine that does not take into account their interactions.
Therefore, the trend is moving from the control of individual wind turbines towards hierarchical control structures. Generally, these structures are made up of two levels: the wind turbines level and the wind farm level. The wind turbine level is in charge of carrying out the local control of each wind turbine, while the control carried out at the wind farm level is in charge of sending the references to the local controllers and ensuring the correct balance between the power requested and delivered for the complete wind farm. The control of the entire wind farm is a complex problem due to the several factors that are involved, such as, for instance, the different time scales, coupling or interactions between wind turbines from electrical and hydrodynamic
Figure 1.6. Estimated new offshore installations per year (MW). Source: GWEC Market Intelligence, June 2022.
∗Compound Annual Growth Rate.
perspectives or the variable wind power availability among others. In line with simplifying the design procedure, we wonder if it is possible to break down the entire wind farm control problem into smaller and more manageable problems while ensuring that all the requirements in terms of robustness and performance are fulfilled. This makes us to pose three new challenging problems:
P10. To propose a design procedure for the local controllers that guarantees the fulfilment of some requested performance and robustness requirements.
P11. To evaluate how the local controller design affects the global performance.
P12. To propose a controller at wind farm level to achieve zero steady-state error in tracking global power references while it is done in an optimal way.
In grid following operation, the converters are connected to an existing electrical grid in which the voltage and frequency are controlled by other generators or VSCs. In the first renew- able power plants, grid following converters were only requested to control the active and reac- tive powers delivered to the grid, however, as the penetration of RES increase, grid-supporting functionalities such as, voltage support, synthetic inertia or fault ride-through capabilities have been progressively included to those converters for a safer electrical grid operation. Although these functionalities allow for a large penetration of RES into the power system without jeop- ardizing it, they still need that other power plants create the AC grid. Therefore, grid following converters are not able to restore the grid after a black-out or operate in islanded mode. In this context appear the grid forming converters. Although nowadays it is not mandatory, it will be necessary to include these capabilities to the converters in order to get a massive integration of the RES.
The grid forming converters control the magnitude and angle of the output voltage to reg- ulate the power exchanged with the grid. Thus, if there are several grid forming converters connected, we have multiple actuators with the same goal, which is a problem that may lead us to instability issues. In addition, it is usual that the number of connected converters changes
1.3. Thesis outline and contributions 9 due to the variable behaviour of the wind. Hence, the system to be controlled change depending on the number of connected converters. In this sense, we wonder if it is possible to design the same controller for all the converters, without the need to retune them depending on how many of them are connected and guaranteeing the grid stability and some performance requirements.
Related to this, we pose the last challenging problem as follows:
P13. To control voltage at PCC by using the same controller (computed offline) in all the con- verters guaranteeing robust stability against parameter changes and the number of connected wind turbines, while some performance requirements are also fulfilled.
1.3 Thesis outline and contributions
The main objective of the thesis is to develop VSC control strategies that contribute to its massive deployment in the electrical network in the near future. The thesis base line is as follows.
First, Chapter 2 introduces the basics of VSC control. Second, in Chapter 3 we include an analysis of the VCC and propose some modifications on its structure for improving the be- haviour when a VSC is connected to a weak grid in order to give design rules for the current controllers. Chapter 4 shows a comparison between VCC, Grid Voltage Modulated Direct Power Control (GVM-DPC) and a proposed multivariable state-feedback type controller in which mul- tivariable saturation and antiwindup mechanisms are included and the use of a PLL is avoided.
In addition we show an analysis of the uncertainties that may cause instability issues and how, with our proposal, we can design more robust controllers against some of these uncertainties. In Chapter 5, we show a proposal for the control of an offshore wind farm in which the converters of the wind turbines are operating as grid-following converters and the converter of the HVDC link is the responsible for controlling the voltage at the PCC. In Chapter 6 we develop a control for an offshore wind farm with a hierarchical structure in which the wind turbine converters work as grid-following converters, the voltage at PCC is assumed to be controlled by the VSC rectifier of the HVDC link and a centralized controller is in charge of controlling that the total delivered powers fits the requested ones. Then, we use it for studying how the local control design affects to the global behaviour and how we can modify the local controllers in order to achieve some global desired behaviour. Finally, in Chapter 5 we show a proposal for the control of an offshore wind farm in which the converters of the wind turbines are operating as grid-forming converters and the converter of the HVDC link is the responsible for controlling the delivered power to the HVDC link.
Note that each chapter is self-consistent and can be read mostly independently of the others.
Some of the content of the thesis is derived from published or peer-reviewed material, and therefore there may be repetitions of background explanations or some differences in notation between chapters. Let us now present a brief summary of the thesis with references to the publications related to each chapter.
Chapter 2: Background
This chapter aims to give a common framework for the studied problems. First, we present an explanation of the the Clarke and Park transformations. Second, we show basic concepts on the electrical grid operation. Third, we introduce two grid-level VSC control strategies: grid following and grid forming. Finally, we present and briefly explain some examples of each control strategy.
Chapter 3: Inner current loop PI design for the connection of VSCs to weak AC grids
In this chapter we propose slight modifications on the conventional VCC structure to improve the behaviour when we connect a VSC to a weak grid. We propose a controller structure where an outer loop controls the injected/absorbed power and the voltage at the PCC, and where an inner current controller is in charge of achieving the currents demanded by the outer loop.
With our proposal, the inner current controller has more degrees of freedom than standard PI control, and we demonstrate that the extra degree of freedom is useful to face weaker grids while keeping the stability (P1). We do an analysis with a normalization procedure that allows us to present tractable expressions that helps the user to predict the behaviour of the controller (P2, P3) and to design a controller that guarantees some given performance and robustness requirements (P4). We also present three design strategies with various levels of degrees of freedom and achievable performance (P2, P3). Finally, we validate the performance prediction expressions through simulations, and we apply the design procedure in a numerical example.
The results of this chapter are mainly addressed in:
• Carlos Díaz-Sanahuja, Ignacio Peñarrocha-Alós, Ricardo Vidal-Albalate and Agustí Egea- Álvarez. Inner current loop PI design for the connection of VSCs to weak AC grids. CSEE Journal of Power and Energy Systems. (Submitted for journal publication)
Chapter 4: Multivariable phase-locked loop free strategy for power control of grid- connected voltage source converters
In this chapter, we propose a multivariable control strategy in a dq reference frame for grid- connected voltage source converters without using a PLL (P5, P7). First, common VSC controls such as VCC and GVM-DPC are analysed, and their main drawbacks are identified (P3).
Then, the multivariable control strategy is presented, including the implementation of saturation and antiwindup mechanisms, and limitation of overcurrents (P8). Next, different uncertainty channels that may lead to instability in each approach are analysed, showing the drawbacks related to the use of a PLL, which are avoided in our proposal (P6). The effectiveness of the three strategies is compared by means of simulations, showing that the proposal presents a more robust behaviour, specially in weak grids.
The results of this chapter are mainly addressed in [38]:
• Carlos Díaz-Sanahuja, Ignacio Peñarrocha-Alós, and Ricardo Vidal-Albalate. Multivari- able phase-locked loop free strategy for power control of grid-connected voltage source con- verters. Electric Power Systems Research, vol. 210, art. 108084, September 2022.
1.3. Thesis outline and contributions 11
Chapter 5: Alternative control approach for the offshore grid of wind power plants This chapter describes the problem of control of the electric grid of an offshore wind farm that pour their power to the onshore electrical grid through a HVDC link (P9). The wind turbines converters are operating as grid-following converters while the converter of the HVDC link is in charge of controlling the voltage at the PCC. For these controllers it is proposed to use state- feedback controllers with multivariable saturation and antiwindup mechanisms and in which it is proposed to use a fixed frequency to carry out the dq transformations of the signals. In this way we dispense with the use of the PLL (P5, P7, P8).
The results of this chapter are mainly addressed in [40,41]:
• Carlos Díaz-Sanahuja, Ignacio Peñarrocha, Ricardo Vidal-Albalate and Ester Sales-Setién.
Alternativas para el control de la red eléctrica aislada en parques eólicos marinos. In Actas de las XXXVIII Jornadas de Automática (JJAA2017), pages 38–-45, 2017.
• Carlos Díaz-Sanahuja, Ignacio Peñarrocha-Alós, and Ricardo Vidal-Albalate. Alternative control approach for the offshore grid of wind power plants. 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, pp. 1945-1950.
Chapter 6: Controllers design of a wind farm: Influence of the local design on the global behaviour
In this chapter we design the control system of an offshore wind farm with a particular structure in order to be capable of delivering the power requested by some external agent guaranteeing some performance and robustness requirements (P9). Here, the wind turbine converters work as grid-following converters and the voltage at PCC is assumed to be under control. We use a hierarchical structure of two levels. On the one hand, the bottom level is composed of the local controllers of each wind turbine, in which it is carried out a current control. On the other hand, for the top level we propose a centralized controller for correcting the deviations between the requested and delivered powers and a dispatch function for computing the references for the local controllers in an optimal way (P12). For the local controllers, we propose a state- feedback type structure in which we add a multivariable antiwindup mechanism that works also as a synchronizer since it leads us to be synchronized with the voltage of the point where the VSC is going to be connected (P7, P8). This, added to the proposal of using a fixed frequency for obtaining the angle for the dq transformations makes us to not use a PLL (P5).
We develop a design procedure for the local controllers based on guaranteeing the fulfilment of certain performance and robustness requirements expressed as norms (P10). Then, we study the global behaviour and how the local design affects to it (P11). Finally, we show some numerical examples and simulations in different situations that prove the validity of our proposal.
The results of this chapter are mainly addressed in:
• Carlos Díaz-Sanahuja, Ignacio Peñarrocha-Alós and Ricardo Vidal-Albalate. Controllers design of a wind farm: Influence of the local design on the global behaviour. IEEE Journal of Emerging and Selected Topics in Power Electronics. (Submitted for journal publication)