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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: IEEE Press
- Sprache: Englisch
Presents the principles, derivations, and equations of renewable energy power plants, including MATLAB code
Advanced Control of Grid-Integrated Renewable Energy Power Plants presents a comprehensive introduction to the power system dynamics and stability of renewable energy power plants (RPPs), such as wind turbines, wind power plants, and photovoltaic systems. The author—a noted expert on the topic—takes a rigorous approach to the analysis and modelling of RPPs, such as turbine rotors, PV cells, electronic converters, transformers, and aggregated grid models. This approach allows for the validation of requirements for sustainable power systems based on formal methods.
The text deals with nonlinear model-based observer and control design techniques in the Takagi-Sugeno (TS) framework. It explores the Takagi-Sugeno fuzzy (TSF) models which are nonlinear systems, in which the consequent part of a fuzzy rule is a mathematical formula, representing local dynamics or limited nonlinearities by sector functions. The strong property of the TSF finds several applications modelling dynamical systems that can be described by differential equations. The book’s practical exercises use MATLAB code to help model simulation models of single large-scale wind turbines, wind farms, and photovoltaic plants. This important book:
- Provides a complete introduction to the power system dynamics and stability of renewable energy power plants
- Includes a detailed discussion of how to design model model-based controllers for RPPs
- Takes a rigorous approach to the analysis and modelling of RPPs, including turbine rotors, PV cells, electronic converters, transformers, aggregated grid models, and more
- Includes MATLAB code to model simulation models of single large-scale wind turbines, wind farms, and photovoltaic plants
Written for students and researchers of renewable energy, Advanced Control of Grid-Integrated Renewable Energy Power Plants offers an authoritative text to the topic.
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Seitenzahl: 345
Veröffentlichungsjahr: 2024
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Table of Contents
Cover
Table of Contents
Title Page
Copyright
Preface
Acronyms
Notation
1 Introduction
1.1 Energy Transition
1.2 Problem Description
1.3 Methodological Framework
1.4 Topics of this Book
Notes
2 Modeling of Wind Turbines
2.1 Introduction
2.2 First‐Principle Modeling
2.3 Control‐Oriented Models in TS Form
2.4 Summary
2.5 Problems
2.6 Bibliography
Notes
3 Control of Wind Turbines
3.1 Introduction
3.2 Baseline Generator‐Torque and Blade‐Pitch Controller
3.3 Model‐Based Control of WTs
3.4 Model‐Based Power Tracking
3.5 Summary
3.6 Problems
3.7 Bibliography
Notes
4 Modeling and Control of Photovoltaic Power Plants
4.1 Introduction
4.2 Modeling of PV Generators
4.3 DC–DC Converter Modeling
4.4 Voltage Control of PV Generators
4.5 Demanded Power Tracking
4.6 Summary
4.7 Problems
4.8 Bibliography
Notes
5 Modeling and Control of Voltage Source Converters
5.1 Introduction
5.2 Three‐Phase Signals and Systems
5.3 Average and Instantaneous Power
5.4 Reduced‐Order VSC Model
5.5 Power Injection in the Steady State
5.6 Voltage Drop in the Steady State
5.7 Selected Control Concepts
5.8 Summary
5.9 Problems
5.10 Bibliography
Notes
6 Advanced Grid Integration of PV and Wind Power Plants
6.1 Introduction
6.2 Description of Test Scenarios
6.3 Integration of Wind Power Plants
6.4 Integration of PV Power Plants
6.5 Summary
6.6 Problems
6.7 Bibliography
Note
A Modeling in the Takagi–Sugeno FrameworkModeling in the Takagi–Sugeno Framework
A.1 Introduction
A.2 Constructing TS Systems
B LMI Conditions for Stability Analysis and Controller DesignLMI Conditions for Stability Analysis and Controller Design
B.1 Introduction
B.2 Linear Matrix Inequalities
B.3 Stability Analysis of TS Systems
B.4 Relaxations
B.5 State Feedback Design for TS Systems
B.6 Observer Design for TS Systems
C Renewable Energy SourcesRenewable Energy Sources
C.1 Wind Energy Systems
D Parameters of Renewable Energy Power PlantsParameters of Renewable Energy Power Plants
D.1 Physical Constants
D.2 Wind Power Plant Parameters
D.3 PV Power Plant Parameters
D.4 VSC Parameters
D.5 Equivalent Grid Model Parameters
E Control Concept for Bumpless Transition Between Operating RegionsControl Concept for Bumpless Transition Between Operating Regions
References
Index
End User License Agreement
List of Tables
Chapter 3
Table 3.1 Lower and upper bounds of the operating regions of baseline contr...
Table 3.2 Baseline Controller parameters of NREL 5‐MW wind turbine.
Table 3.3 Comparison of LMI‐solver synthesis results for different pole reg...
Chapter 5
Table 5.1 Matrix of primary and secondary power conversion control scheme
D
Table D.1 Physical constants.
Table D.2 Parameters of NREL 5‐MW reduced wind turbine model (part I).
Table D.3 Parameters of NREL 5‐MW reduced wind turbine model (part II).
Table D.4 Parameters of a generic 3 MW photovoltaic power plant.
Table D.5 Parameters of the voltage source converter.
Table D.6 Parameters of the equivalent grid model.
List of Illustrations
Chapter 1
Figure 1.1 Single‐phase equivalent circuit of a line with
Figure 1.2 Which technology will provide ancillary grid services in the futu...
Figure 1.3 Functional diagram of grid‐integrated renewable power plant with ...
Figure 1.4 – curve of PV solar modules in pu with variation of irradiation...
Figure 1.5 – curve of wind turbi...
Chapter 2
Figure 2.1 Structure of a modern wind turbine with key components
Figure 2.2 Example of a horizontal‐axis wind turbine (HAWT)
Figure 2.3 Stream‐tube without (a) and with (b) actuator disc
Figure 2.4 Power coefficient as a function of (a) and (b)
Figure 2.5 Thrust coefficient as a function of (a) and (b)
Figure 2.6 Schematic 3D representation of a wind turbine rotor blade compris...
Figure 2.7 Lift force and drag force ...
Figure 2.8 Blade twist (a) and chord (b) parameter ...
Figure 2.9 Rotor blades of a HAWT with typical twist angle
Figure 2.10 Lift coefficient and drag coefficient of an airfoil (NACA64‐...
Figure 2.11 Illustration of the influence of an additional control angle o...
Figure 2.12 Lift coefficient (a) and drag coefficient (b) of the NACA 63...
Figure 2.13 – (a) and ...
Figure 2.14 – curve of NREL 5‐MW wind turbine related to rotor pitch angle...
Figure 2.15 Pitch drive testbed system at HTW Berlin, Control Engineering Gr...
Figure 2.16 Schematic diagram of a horizontal‐axis wind turbine with collect...
Figure 2.17 Schematic diagram of a wind turbine drive train with gear box
Figure 2.18 Validation of the 1‐DOF model (2.57) by FAST with 5‐MW NREL turb...
Figure 2.19 Validation of the 4‐DOF model (2.57) by FAST using 5‐MW NREL Tur...
Figure 2.20 Wind turbine with wind measurement mast in front
Figure 2.21 An upwind scanning spinner LIDAR installed on a turbine axis in ...
Figure 2.22 Membership function to join two single region models given in (2...
Chapter 3
Figure 3.1 as a function of the generator speed .
Figure 3.2 Controller coefficients and of the gain‐scheduling control la...
Figure 3.3 Simulation results of baseline controller validation with the FAS...
Figure 3.4 Simulation results of baseline controller validation with the FAS...
Figure 3.5 Simulation results of baseline controller validation with mechani...
Figure 3.6 Overview of model‐based wind turbine control scheme.
Figure 3.7 Overshoot vs. damping ratio for the second‐order system 3.20 ...
Figure 3.8 Overshoot vs. region parameter (see Figure 3.9) related to th...
Figure 3.9 Pole region defined by , , and .
Figure 3.10 Eigenvalues of error Eq. (3.18).
Figure 3.11 Comparison of the estimated wind speed for m/s by the true w...
Figure 3.12 Comparison of the estimated wind speed for m/s by the true w...
Figure 3.13 Comparison of the estimated wind speed for m/s by the true w...
Figure 3.14 Comparison of the estimated wind speed with (3.23) by the true...
Figure 3.15 Control scheme for partial‐load with state feedback, integral ac...
Figure 3.16 Control scheme for full‐load operating region with state feedbac...
Figure 3.17 Eigenvalues of related to the open‐loop system (3.31).
Figure 3.18 Eigenvalues of related to the closed‐loop system (3.38).
Figure 3.19 Simulation results of full‐load region controller validation (3....
Figure 3.20 Simulation results related to Figure 3.19: Mechanical motion of ...
Figure 3.21 Eigenvalues of related to the open‐loop system (3.44) with the...
Figure 3.22 Calculated eigenvalues of related to the closed‐loop system (3...
Figure 3.23 Simulation results of controller validation with reduced 1‐DOF w...
Figure 3.24 Simulation results of controller validation with the FAST wind t...
Figure 3.25 Weighting functions for with the overlapping factor .
Figure 3.26 Weighting functions for with the overlapping factor .
Figure 3.27 Power curve of a wind turbine (controlled FAST NREL 5‐MW turbi...
Figure 3.28 Control scheme for power tracking above the rated wind speed.
Figure 3.29 Control scheme for power tracking below the rated wind speed.
Figure 3.30 Visualization of for the set point calculation .
Figure 3.31 Calculation of difference reference power as a function of req...
Figure 3.32 Eigenvalues of related to the open‐loop system (3.73).
Figure 3.33 Eigenvalues related to (3.38).
Figure 3.34 Simulation results of power‐tracking controller validation (cont...
Figure 3.35 Zoom into simulation of Figure 3.34 in time interval .
Figure 3.36 Simulation results related to Figure 3.34: Mechanical motion of ...
Figure 3.37 Power‐tracking controller validation ( control scheme in Figure...
Figure 3.38 Control scheme for power tracking with power feedback controller...
Chapter 4
Figure 4.1 Two‐stage power conversion with centralized maximum power point t...
Figure 4.2 Rooftop system at HTW Berlin (H building).
Figure 4.3 PV power plant at the railroad line Buchloe–Munich.
Figure 4.4 Simplified single‐diode model (SSDM) of a PV cell.
Figure 4.5 Irradiation profile from April 3, 2021, in Berlin (sunny day).
Figure 4.6 Equivalent circuit of a PV generator aggregated from single‐dio...
Figure 4.7 Aggregated – (a) and ...
Figure 4.8 Aggregated – (a) and ...
Figure 4.9 DC–DC buck converter with static transfer function (4.10).
Figure 4.10 DC–DC boost converter with static transfer function (4.14).
Figure 4.11 DC–DC buck–boost converter with static transfer function (4.15)....
Figure 4.12 Buck converter combined with a PV generator.
Figure 4.13 DC–DC buck converter system states with , , and PV generator c...
Figure 4.14 Comparison of the DC–DC buck converter system states and bet...
Figure 4.15 Piecewise linear weighting functions of type “lower boundary fun...
Figure 4.16 TS model with compared to the original nonlinear system: valid...
Figure 4.17 Inner‐loop control scheme of PV generator voltage controller.
Figure 4.18 Pole locations in the complex plane of the open‐loop system (a) ...
Figure 4.19 Pole locations in the complex plane of the open‐loop system (a) ...
Figure 4.20 Validation of the linear controller designed with one model wh...
Figure 4.21 Validation of the Takagi–Sugeno PDC controller designed with m...
Figure 4.22 Variation of the membership function values of the controller ...
Figure 4.23 Comparison between the Takagi–Sugeno PDC controller (TS) and a l...
Figure 4.24 PV power plant controller of the primary conversion with inner v...
Figure 4.25 Calculation of the difference reference power as a function of...
Figure 4.26 Intersections of the generic power curve with constant reference...
Figure 4.27 Inside the power‐tracking controller from Figure 4.17 based on t...
Figure 4.28 Power‐tracking performance with decreasing and increasing power ...
Figure 4.29 Power‐tracking performance with mismatch (4.79) between the meas...
Figure 4.30 Power‐tracking performance with mismatch (4.80) between the meas...
Figure 4.31 Switchable ESC for MPPT and DPT (demanded power tracking).
Figure 4.32 – (a) vs. transformed – (b) curve for model‐free DPT.
Figure 4.33 – (a) vs. transformed – (b) curve for model‐free DPT.
Figure 4.34 Maximum power point tracking with changing cell temperature.
Figure 4.35 Demanded power tracking with step‐change reference power .
Chapter 5
Figure 5.1 Topology of three‐phase voltage source converter with PCC (point ...
Figure 5.2 Voltage source converter with controller board and LCL filter (HT...
Figure 5.3 Scheme of the reduced‐order voltage source converter model
Figure 5.4 Single‐phase equivalent circuit of a line with and
Figure 5.5 Single‐phase equivalent circuit of a line terminated with a load ...
Figure 5.6 Phasor diagram of a single line for , . The direct‐ axis voltag...
Figure 5.7 Control scheme of voltage source converter for grid‐following (GF...
Figure 5.8 Control scheme of voltage source converter for grid‐forming (GFM)...
Figure 5.9 Grid‐forming VSC scheme with inner‐loop current controller
Chapter 6
Figure 6.1 Schematic of the test setup with a voltage source given in 6.1, (...
Figure 6.2 Test Case 1: System response after step change of active power re...
Figure 6.3 Test Case 1: States and system inputs (controller outputs) after ...
Figure 6.4 Test Case 2: System response after wind speed step at s: (a) sh...
Figure 6.5 Test Case 2: System states and inputs (controller outputs) after ...
Figure 6.6 Test Case 3: System response after step change of reactive power ...
Figure 6.7 Test Case 3: System states and converter outputs after step chang...
Figure 6.8 Test Case 4: System response after voltage magnitude drop at s:...
Figure 6.9 Test Case 4: System states and controller outputs after voltage m...
Figure 6.10 Test Case 5: Disturbance rejection after voltage phase shift at
Figure 6.11 Test Case 5: Disturbance rejection after voltage phase shift at
Figure 6.12 Test Case 1: System response after step change of active power r...
Figure 6.13 Test Case 2: System response after irradiation step at s relat...
Figure 6.14 Test Case 3: System response after step change of reactive power...
Figure 6.15 Test Case 4: System response after voltage magnitude drop at s...
Figure 6.16 Test Case 5: System response after voltage phase shift at s re...
A
Figure A.1 Curve of equilibrium points related to the NREL 5‐MW wind turbi...
Figure A.2 Test‐functions (A.17) of four linearization points
B
Figure B.1 Feasible set of (B.3) (hatched area)
Figure B.2 Parameterized stripe‐shaped pole region
Figure B.3 Parameterized pole region
E
Figure E.1 Weighting functions for with the overlapping factor
Figure E.2 Weighting functions for with the overlapping factor
Guide
Cover
Table of Contents
Title Page
Copyright
Preface
Acronyms
Begin Reading
A Modeling in the Takagi–Sugeno Framework
B LMI Conditions for Stability Analysis and Controller Design
C Renewable Energy Sources
D Parameters of Renewable Energy Power Plants
E Control Concept for Bumpless Transition Between Operating Regions
References
Index
End User License Agreement
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Advanced Control of Grid‐Integrated Renewable Energy Power Plants
LMI‐based Design in the Takagi-Sugeno Framework
Horst Schulte
Head of Control Engineering GroupHTW Berlin, Germany
This edition first published 2024
© 2024 John Wiley & Sons Ltd
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.
The right of Horst Schulte to be identified as the author of this work has been asserted in accordance with law.
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MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This work's use or discussion of MATLAB® software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software. While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
Library of Congress Cataloging‐in‐Publication Data:
Names: Schulte, Horst, author.
Title: Advanced control of grid‐integrated renewable energy power plants :
LMI‐based design in the Takagi‐Sugeno framework /
Horst Schulte.
Description: Hoboken, NJ : Wiley, 2024. | Includes bibliographical
references and index.
Identifiers: LCCN 2024017996 (print) | LCCN 2024017997 (ebook) | ISBN
9781119701392 (hardback) | ISBN 9781119701408 (adobe pdf) | ISBN
9781119701286 (epub)
Subjects: LCSH: Power‐plants. | Renewable energy sources. | Automatic
control. | Convex functions.
Classification: LCC TJ164 .S345 2024 (print) | LCC TJ164 (ebook) | DDC
621.042–dc23/eng/20240517
LC record available at https://lccn.loc.gov/2024017996
LC ebook record available at https://lccn.loc.gov/2024017997
Cover Design: Wiley
Cover Image: © zhihao/Getty Images
Preface
Over the past 20 years, there has been a considerable growth in the installation capacity of renewable energy sources (RES) in power systems all over the world [IRENA, 2020]. In contrast to conventional power plants such as coal‐fired or nuclear power plants with large synchronous machines, power plants with RES are much smaller and integrated into the grid via power electronic (PE) interfaces. This leads to a highly distributed structure and heterogeneous integration across all voltage levels into the power grid.
Currently, most renewable energy (RE) systems feed as much power as possible into the grid, but provide little or no grid support (i.e. ancillary services). In the future, this will no longer be sufficient to stabilize the grid due to the decreasing share of synchronous machine‐based units. However, it is clear that the decentralized regenerative generators must be able to adapt the power quickly to the demand for frequency and voltage regulation via a suitable mix of grid‐following and grid‐forming converters, even without or less additional costs arising from battery energy storage systems (BESS) and as few additional control units as possible, such as FACTS and STATCOMS.
There is, still today, no common road map on how to systematically address this problem of grid operation with power‐electronically coupled RES in practice. The book aims to contribute to this scientific question using methods of physical modeling, mathematical systems theory, and control engineering. Emphasis is on the development of model‐based control concepts for photovoltaic and wind power plants, which are also intended to provide auxiliary services for grid frequency and voltage stabilization.
This book is useful for readers who want to gain knowledge of wind and photovoltaic (PV) power plant modeling and control with a deep understanding of model‐based control concepts for optimal resp. flexible energy conversion and grid integration by inverters with grid‐following and grid‐forming operation. It is suitable for students from the fifth semester onward, experts from industry and academics, and PhD students who want to get an overview and possible ideas on an exciting research topic. The intention was to provide a book with well‐understandable description of the design models, the controller functions, and their validation presented in a unified control theory framework. The model and controller validation is done with high fidelity models (used for wind turbine control) or scenarios with measurement uncertainties (considered for PV systems).
This book is based on the results of research projects I have worked on and mostly managed over the past 10 years. The aim was to make the results available to the community in a closed and understandable form, for both professionals and graduate students working on control systems or electrical power systems. I thank my wonderful colleagues and collaborators Prof. S. M. Esmailifar, Prof. J. Fortmann, E. Gauterin, Dr. S. Goerg, N. Goldschmidt, Prof. N. Klaes, Dr. S. Kusche, Dr. Z. R. Labidi, and Dr. F. Pöschke for the many valuable discussions and exchanges without which this book would not have taken the form it has.
Berlin
Horst Schulte
September 2023
Acronyms
AC
alternating current
AGC
automatic generation control
APC
active power control
AS
ancillary services
AVR
automatic voltage regulator
BMI
bilinear matrix inequality
CIG
converter‐interfaced generation
DC
direct current
DER
distributed energy resource
DFIG
doubly fed induction generator
DOF
degree of freedom
DPT
demanded power tracking
DSO
distribution system operator
DVPP
dynamic virtual power plant
EMT
electromagnetic transient
EPS
electrical power systems
ESC
extremum‐seeking control
FACTS
flexible alternating current transmission system
FAST
Fatigue, Aerodynamics, Structures, and Turbulence model
FLL
frequency‐locked loop
HAWT
horizontal‐axis wind turbine
HC
hill climbing
HIL
hardware in the loop
HPP
hybrid power plant
HV
high voltage
HVDC
high‐voltage direct current
IBR
inverter‐based resource
iff
if and only if
IGBT
insulated‐gate bipolar transistor
IOS
input‐to‐output stability
ISS
input‐to‐state stability
LDI
linear differential inclusion
LHS
left‐hand side
LIDAR
light detection and ranging
LMI
linear matrix inequality
LQR
linear quadratic regulator
LPV
linear parameter variable
LTI
linear time invariant
MATLAB
®
Matrix Laboratory
MPP
maximum power point
MPPT
maximum power point tracking
MIMO
multiple‐input multiple‐output
NREL
National Renewable Energy Laboratory
PE
power electronic
PCC
point of common coupling
PDC
parallel distributed compensation
PLL
phase‐locked loop
PMSG
permanent magnet synchronous generator
P&O
perturbation and observation
PI
proportional‐integral
pu
per unit
PV
photovoltaics
RPP
renewable energy power plant
RES
renewable energy source
RHS
right‐hand side
RMS
root mean square
SISO
single‐input single output
SL
sector‐nonlinearity (approach)
STATCOM
static synchronous compensator
s.t.
such that
STC
standard test condition
TS
Takagi‐Sugeno
TSO
transmission system operator
VPP
virtual power plant
VSC
voltage‐sourced converters
WPP
wind power plant
WT
wind turbine
WTG
wind turbine generator
Notation
Italic denotes scalar physical quantities (e.g. ) or numerical variables (e.g. ).
Italic boldface denotes a matrix (capital letters) or a vector (small letters), e.g. , and .
Unit symbols are written using roman type (e.g. Hz, A, and kV).
Standard mathematical functions are written using roman type (e.g. e, sin, cos, and arctan).
Lowercase symbols normally denote instantaneous values (e.g. and ).
Uppercase symbols normally denote RMS or peak values (e.g. and ), exception: active and reactive power denoted as and .
Subscripts and refer to the direct‐ and quadrature‐axis components.
Subscripts and refer to and components of a three phase system.
Italic underline type denotes a phasor (e.g. , and ).
Lowercase symbol with upper arrow denotes a space vector .
1Introduction
1.1 Energy Transition
Public discussion about the energy transition is dominated by the need to accelerate the planning and installation of wind farms and photovoltaic (PV) plants, as well as the grid expansion by new lines and deferrable loads. That is obvious and quite understandable. Far less known and not a subject of public debate is that the transition to renewable energy also means that the traditional use of synchronous machines, which still regulate frequency and voltage in the grid [Machowski et al., 2008], is being replaced by power electronic (PE)–based converter‐interfaced renewable energy sources (RES). The transition to a massive integration of PE‐based power plants [Peng et al., 2018a], also called inverter‐based (IBG) [Joi, 2018] or converter‐interfaced generators (CIG), which began in the decade of the new millennium, enables relatively flexible and efficient power conversion. Such a transition implies all areas within power systems and may be considered a paradigm shift in the sense of Kuhn [1962]. Because power systems fundamentally change in power generation, transmission, and distribution, this has significant implications for the associated engineering and scientific disciplines, as questions of stability, control, and reliability must be addressed in new ways.1
Symptomatic of the fundamental change in power systems is the distributed generation by many heterogeneous units feeding power to different grid levels by power electronic interfaces. At the transmission level, for example, offshore wind farms feed in, at the sub‐transmission level the onshore wind farms or large PV power plants are integrated, and at the distribution level medium‐sized PV power plants. Instead of generators connected to the grid via stator windings, rotating units in renewable energy systems are decoupled from the grid: these cannot contribute to system inertia without additional active control. Until now, the frequency and voltage stability characteristics of power systems have been strongly determined by large synchronous generators driven by steam or gas turbines.
Let us first consider the frequency dynamics in conventional power systems. Assuming a common frequency in the AC network,2 the instantaneous rate of change of frequency (RoCoF) after the disconnection of a generator (generator tripping) or load from a power system before any control becomes active can be computed as follows [ENTSO‐E, 2018]
with as derivative of the difference frequency related to the nominal system value , where is the inertia constant
of each generator , where is the kinetic energy of the generator running at synchronous (nominal) speed . Each turbine's total moment of inertia plus the generator rotor is denoted as . The variable is the rated apparent power of each generator. Here, the inertia constant describes the property of the synchronous machine to maintain the system state of uniform rotary motion when no external torque is applied. A typical value of for a synchronous generator can range from two to nine seconds. The active power deviation in (1.1) is defined by the summation of all mechanical shaft power input to the generator units for and the electrical air‐gap power caused by system loads in the grid and controlled by the power angle or load angle , both expressed in watts
where denotes the total number of generator units. For the interpretation of (1.1) it must be noted that RoCoF is triggered by unplanned load shedding or generator tripping. In case of generator tripping (i.e. ) the remaining generators () provide a frequency change inversely proportional to . This behavior results from the swing equation of each generator represented by two first‐order equations [Machowski et al., 2008]
with , where denotes the electrical rotor speed, denotes the electrical synchronous speed resp. synchronous angular frequency, denotes the power angle, and is the damping coefficient. Introducing an aggregated3 rotor speed and in (1.4), and after summation
and by neglecting the damping term, we obtain the RoCoF index (1.1). It is evident that the RoCoF value increases caused by a decrease of due to the substitution of synchronous generators by inertia‐less (PV power plants) or inertia‐decoupled (wind turbines4 ) generator units. In summary, the energy transition with a high penetration of CIGs with over 80% and more in the future has the effect that the RoCoF value of electrical power systems (EPS) significantly increases which leads to a stronger fluctuation of the grid frequency and an increase of the probability of frequency instability.
In addition to frequency regulation, the voltage control of grids with a high percentage of PE‐based converter‐interfaced generators must also be addressed. In contrast to grid frequency, which can be modeled as a global quantity, the voltage in power grids has to be considered as a local quantity, which can vary strongly in the permitted bounds from node to node. The voltage level could be changing due to factors related to generation, transmission, and distribution. However, the variability of the load is one of the most important factors. The voltage must remain within a specified range because over‐voltage implies an increase in active power losses and, as a long‐term effect, can increase the probability of insulation failure. Thus control is needed to maintain the grid voltage in a permissible range, and if a short circuit occurs, it must be ensured that voltage drops are limited.
In AC networks with typically overhead transmission line parameters (see [Kundur, 1994], Table 6.1) the voltage states are strongly coupled with the reactive power fluxes. For example, the longitudinal voltage drops in the networks are caused by the reactive power currents. For the line element shown in Figure 1.1, the reactive power flow of a single‐phase system5 is given by
Figure 1.1 Single‐phase equivalent circuit of a line with
with the impedance , where denotes the angle between the voltage phasor of the generator resp. converter and V at the reference point to the right of the line inductance
with the root mean square (RMS) voltage values and . The associated active power of a line element of a single‐phase system is determined by
It can be seen that the active power depends on the product of phase voltages and the sine of the angle between their phasors. Because in power systems the node voltages are only within a small percentage of their nominal values, the large changes in active power result from the power angle [Machowski et al., 2008]. Note that with the power relations (1.6), (1.8), and the swing equation (1.4) power dynamics of networks with one, two, and multiple generators can be studied in the control loop and under consideration of power plant interactions. In Chapters 5 and 6 such investigations are presented after model‐based control concepts of renewable energy (RE) generation (wind and solar) were presented and discussed in Chapters 2–4.
In summary, for reliable power system operation, the provision of ancillary services (AS) will have to be provided to a large extent by renewable energy systems in the future. A possible transformation of how AS will be provided in the future is shown in Figure 1.2 from Komarnicki et al. [2023]. In this process, AS from large synchronous generators are first provided by flexible alternating current transmission system (FACTS), STATCOMS, and high‐voltage direct current (HVDC), which are increasingly being replaced by massive distributed inverter‐coupled RE generation up to half. Since these are primarily installed in the distribution grid, it will be a significant challenge to make those AS from the distribution also available to the transmission grid. Note that Figure 1.2 from Komarnicki et al. [2023] also includes system recovery and system control services, such as black start capability [DENA, 2014], which are not addressed in this study. The focus of this book is, that in addition to the important regular feed‐in control operation, that wind and PV power plants are able to provide flexible services for frequency regulation, such as instantaneous reserve, primary frequency control, and voltage regulation. As shown in Figure 1.2, a share of at least 50% and possibly more should be reliably achieved from 2040. A detailed formal problem description of how wind power and solar PV power plants are able to provide AS is given in Section 1.2.
Figure 1.2 Which technology will provide ancillary grid services in the future?
1.2 Problem Description
Renewable energy systems, such as wind and photovoltaic systems, should either feed as much power as possible into the grid or, if needed but also available, follow a requested power demand. It should be considered that the maximum power that can be fed into the grid obviously depends on the currently available power if no additional storage is used. The power plants are connected to the grid via electronic‐based converters and power transformers. The latter is needed to increase the converter's low‐voltage level to the grid's medium‐voltage level, i.e. between 10 and 35 kV. The grid‐side converter is connected to the primary winding of the transformer with an LCL filter. The reference power is generated locally or by an external higher‐level controller.
The generic structure of a generation unit to be considered is illustrated in Figure 1.3. The scheme shows the relationships of both wind and photovoltaic (PV) power plants concerning the power flow, measurements, and control signals. Here, the regenerative energy resource as the wind flow in the rotor disc or the irradiation per area is converted into the electrical power of the wind turbine generator or the aggregated DC power of a solar power plant. The wind turbine (WT) generator and PV array, also called PV generator, feed power into the DC link, which is assigned to the “secondary power conversion” block. The secondary block contains a voltage‐source converter (VSC) that generates a three‐phase AC system from the DC link voltage by a suitable switching logic. For this purpose, the standard space vector modulation (SVM) is applied. In combination with an LCL filter to reduce the current harmonics caused by switching, power is fed into the grid.
Figure 1.3 Functional diagram of grid‐integrated renewable power plant with primary, secondary power conversion, control system, and external reference signals
The two subsystems, the primary and secondary power conversion, are automatically regulated where the controller of the primary conversion subsystem aims to regulate the internal states (rotor speed or PV voltage ) in relation to the states of external resources. The control objective is to either extract the maximum possible power from the renewable resource or to follow a reference power signal, taking into account the achievable limits of the resource. The desired behavior is represented by two modes: (a) generation of the maximum possible electrical power and (b) follow, if possible, the power request and .
To clarify the control task of the primary conversion in renewable energy systems, we will use the – curves. Solar PV power plants' primary conversion is characterized by the power–voltage curve (– curve) parameterized via the irradiation as power per area in . Similarly, for wind turbines, the production by the WT generator is given as power over rotor speed (– curve) parameterized with the effective wind speed in front of the rotor. In grid‐feeding mode, the task of “primary converter control” is to feed as much power as possible into the grid. In addition, other tasks must be covered by the power plant controller in Figure 1.3. For example, the generated power of wind turbines at high wind speeds should not permanently exceed the rated power of the generator. Therefore, at or above the rated wind speed, the wind turbines are operated at a constant speed (rated speed) with constant torque (rated torque). To achieve this, the pitch angle of the rotor blades is regulated to reduce the rotor's torque and adapt it to the nominal torque of the generator. To provide flexible power control for AS, the strategies described above must be superimposed with a deloading procedure. For a formal problem description of the control task of the primary conversion systems, some known characteristic curves for solar PV and wind turbines are now utilized.
Figure 1.4– curve of PV solar modules in pu with variation of irradiation and cell temperature . The power is related to the maximum power by standard test conditions (STC) and the voltage is related to the open‐circuit voltage by STC
First, to characterize the basic control problem of wind turbines, the power–rotor speed curve (– curve) is shown in Figure 1.5. It can be noticed, the point of maximum power changes with varying wind speed. Therefore, to reach the point of maximum power with fluctuating wind speed, the rotor speed must be adjusted according to the – curve. To achieve this, the rotor speed is changed by the generator torque. Depending on whether the generator torque at the low speed shaft is greater or less than the instantaneous rotor torque, the generator speed increases or decreases. Unless the generator torque reaches the nominal torque limit, the speed can be adjusted within the nominal speed range , where denotes the cut‐in and the nominal rotor speed. If the rotor speed increases to the nominal speed due to the increasing wind speed, the control goal of maximum power tracking is left and the rotor speed is kept on the nominal speed using set point control by increasing generator torque. If the nominal generator torque is reached here as well, the increase in speed is controlled by adjusting the pitch angle of the rotor blades instead.
Figure 1.5– curve of wind turbines in pu for pitch angle , where denotes the design also called the rated wind speed . Further details are presented in Chapter 2
The scheme described so far is the conventional control scheme without active power control. Additional flexible power change for grid supporting can be achieved by a superimposed generator torque adjustment whereby the operating point related to the rotor torque is not left by adapting the rotor torque by means of pitch angle control. This means that the decoupling of the control problem into two single input single output (SISO) designs6 can no longer be utilized. Instead, a multi‐variable control method must be used. Indeed, the control system proposed in this book follows a rigorous model‐based approach, where the controller design is performed by solving an optimization problem with linear matrix inequality (LMI) constraints. The modeling of wind turbines for the design is described in Chapter 2. The controller concepts for an optimal and flexible power control and model‐based controller synthesis are presented in detail in Chapter 3.
Second, for solar PV systems, the essentials of power optimization will be described by the illustration in Figure 1.4. In power‐feeding mode the control objective is to track the point of maximum power, also called maximum power point (MPP). Due to the change in radiation W/ and the cell temperature , see Figure 1.4, the MPP position in the curve changes. To track the MPP, the voltage is adjusted by a DC–DC converter. For AS, particularly grid support with negative regulating power, the solar PV generator must also be able to reduce the generated power as fast as possible. This is achieved by leaving the MPP. For positive regulating power, the plant can be permanently derated by 10% to 15%. As a result, this percentage is then available without additional storage to increase the generated power. To be seen in the curve of Figure 1.4, increasing or decreasing the voltage set by the DC‐DC converter results in a flexible power adjustable output.
Both modeling the controller concepts and synthesis for MPP and flexible power control are presented in detail in Chapter 4.
In addition to the primary conversion presented in PV and wind power systems, the problem of secondary conversion is now described for both systems together. As shown in
