Economic engineering modeling of liberalized electricity markets [Elektronische Ressource] : approaches, algorithms, and applications in a European context / von Florian U. Leuthold

Economic engineering modeling of liberalized electricity markets [Elektronische Ressource] : approaches, algorithms, and applications in a European context / von Florian U. Leuthold

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Economic Engineering Modeling of LiberalizedElectricity Markets: Approaches, Algorithms, andApplications in a European ContextDissertationzur Erlangung des akademischen GradesDoctor rerum politicarum (Dr. rer. pol.)vorgelegt an derFakult at WirtschaftswissenschaftenderTechnischen Universit at Dresdenam29. Mai 2009vonDipl.-Wi.-Ing.Florian U. Leutholdgeb. am 06. Juli 1980 in KoblenzVerteidigt am 08. Januar 2010Betreuender Hochschullehrer: Gutachter:Prof. Dr. Christian von Hirschhausen Prof. Dr. Christian von HirschhausenTechnische Universit at Dresden Prof. Dr. Udo BuscherDREWAG-Stiftungslehrstuhlfur EnergiewirtschaftAcknowledgementsThe process of writing a dissertation is an interesting experience and fruitfulprocess. On my way to complete the work at hand, I encountered manydi culties and problems. However, I also found helping hands from variouspeople that supported and encouraged me to take on and overcome at leastsome of the di culties and problems. Many of them have become goodfriends.Regarding work-related support, I wish to express my deepest gratitude toProf. Dr. Christian von Hirschhausen and Prof. Dr. Steven A. Gabriel;Christian von Hirschhausen for making me believe I could do the job andSteven A. Gabriel for actually me do the job. Furthermore, I amparticularly indebted to Hannes Weigt who was a coruscating wit that scru-tinized my ideas and approaches which was a constant form of quality controlfor me.

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Economic Engineering Modeling of Liberalized
Electricity Markets: Approaches, Algorithms, and
Applications in a European Context
Dissertation
zur Erlangung des akademischen Grades
Doctor rerum politicarum (Dr. rer. pol.)
vorgelegt an der
Fakult at Wirtschaftswissenschaften
der
Technischen Universit at Dresden
am
29. Mai 2009
von
Dipl.-Wi.-Ing.
Florian U. Leuthold
geb. am 06. Juli 1980 in Koblenz
Verteidigt am 08. Januar 2010
Betreuender Hochschullehrer: Gutachter:
Prof. Dr. Christian von Hirschhausen Prof. Dr. Christian von Hirschhausen
Technische Universit at Dresden Prof. Dr. Udo Buscher
DREWAG-Stiftungslehrstuhl
fur EnergiewirtschaftAcknowledgements
The process of writing a dissertation is an interesting experience and fruitful
process. On my way to complete the work at hand, I encountered many
di culties and problems. However, I also found helping hands from various
people that supported and encouraged me to take on and overcome at least
some of the di culties and problems. Many of them have become good
friends.
Regarding work-related support, I wish to express my deepest gratitude to
Prof. Dr. Christian von Hirschhausen and Prof. Dr. Steven A. Gabriel;
Christian von Hirschhausen for making me believe I could do the job and
Steven A. Gabriel for actually me do the job. Furthermore, I am
particularly indebted to Hannes Weigt who was a coruscating wit that
scrutinized my ideas and approaches which was a constant form of quality control
for me. Also, for helping to shape my understanding of the European
electricity sector, I would like to thank Dr. Christian Todem in particular and
2the entire crew of EE in general.
Regarding other support, I am deeply indebted to my family and friends. I
would like to thank my good friend Till Huesmann for his constant e orts
to broaden my horizon. The same is valid for my parents who have always
supported me. They taught me to be self-reliant and that knowledge is the
greatest commodity that you can acquire yourself. Furthermore, I would like
to thank my beloved wife Marie that gave up a large part of her everyday
life in order to give me the opportunity to complete my dissertation and to
follow my research interests. She is a great mother of our well-loved son
Alexander to whom I dedicate this work.Abstract
This dissertation focuses on selected issues in regard to the mathematical
modeling of electricity markets. In a rst step the interrelations of
electric power market modeling are highlighted a crossroad between operations
research, applied economics, and engineering. In a second step the
development of a large-scale continental European economic engineering model
named ELMOD is described and the model is applied to the issue of wind
integration. It is concluded that enabling the integration of low-carbon
technologies appears feasible for wind energy. In a third step algorithmic work
is carried out regarding a game theoretic model. Two approaches in order
to solve a discretely-constrained mathematical program with equilibrium
constraints using disjunctive constraints are presented. The rst one
reformulates the problem as a mixed-integer linear program and the second one
applies the Benders decomposition technique. Selected numerical results are
reported.If you want to build a ship, don’t drum
up people to collect wood and don’t
assign them tasks and work, but rather
teach them to long for the endless
immensity of the sea.
Antoine de Saint-ExuperyContents
List of Figures viii
List of Tables ix
List of Abbreviations xii
I Overview 1
1 Introduction and Summary 2
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Classi cation and Research Area . . . . . . . . . . . . 3
1.2.2 Large-Scale Perfect Competitive Economic
Engineering Modeling . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.3 Game Theoretic Economic Engineering Modeling . . . 5
1.2.4 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Literature on Modeling Electricity Markets 8
2.1 General Framework . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.2 Delimitation . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Modeling Liberalized Electricity Markets . . . . . . . . . . . . 19
2.2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Perfect Competition Modeling . . . . . . . . . . . . . 23
2.2.3 Imperfect Competition Modeling . . . . . . . . . . . . 27
2.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
vCONTENTS vi
II Large-Scale Perfect Competitive Economic
Engineering Modeling 32
3 ELMOD - A Model of the European Electricity Market 33
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 Model Description . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Mathematical Notation . . . . . . . . . . . . . . . . . 36
3.2.2 Optimization Problem . . . . . . . . . . . . . . . . . . 37
3.2.3 DC Load Flow Model . . . . . . . . . . . . . . . . . . 39
3.2.4 Time Constraints, Unit Commitment, and Optimal
Dispatch . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2.5 Modeling Pumped Storage and Wind Energy Plants . 42
3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.1 Network . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3.2 Generation . . . . . . . . . . . . . . . . . . . . . . . . 46
3.3.3 Demand . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.4 Applications of ELMOD . . . . . . . . . . . . . . . . . . . . . 52
3.4.1 Network Constraints and O shore Wind . . . . . . . . 52
3.4.2 Locating Generation Investments . . . . . . . . . . . . 53
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4 When the Wind Blows over Europe: An Application of
ELMOD 54
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2.1 Mathematical Notation . . . . . . . . . . . . . . . . . 56
4.2.2 Assumptions . . . . . . . . . . . . . . . . . . . . . . . 57
4.2.3 Optimization Problem . . . . . . . . . . . . . . . . . . 58
4.2.4 Grid Extension Algorithm . . . . . . . . . . . . . . . 59
4.2.5 Investment Costs . . . . . . . . . . . . . . . . . . . . . 60
4.3 Data and Scenarios . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.2 Three Scenarios . . . . . . . . . . . . . . . . . . . . . . 63
4.4 Results and Interpretation . . . . . . . . . . . . . . . . . . . . 64
4.4.1 Price Results . . . . . . . . . . . . . . . . . . . . . . . 64
4.4.2 Comparison . . . . . . . . . . . . . . . . . . . . . . . . 66
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69CONTENTS vii
III Game Theoretic Economic Engineering Modeling 71
5 Solving Discretely-Constrained MPEC Problems Using
Disjunctive Constraints and Discrete Linearization with an
Application in an Electric Power Market 72
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.2 Literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.3 General Mathematical Formulation . . . . . . . . . . . . . . . 75
5.4 Numerical Example for an Electricity Market . . . . . . . . . 78
5.4.1 Mathematical Notation . . . . . . . . . . . . . . . . . 79
5.4.2 Formulation . . . . . . . . . . . . . . . 80
5.4.3 The Disjunctive Constraints Constants . . . . . . . . . 88
5.4.4 Computational Results . . . . . . . . . . . . . . . . . . 89
5.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 Solving Discretely-Constrained MPEC Problems Using
Disjunctive Constraints and Benders Decomposition with an
Application in an Electric Power Market 98
6.1 Introduction and Literature . . . . . . . . . . . . . . . . . . . 98
6.2 General Mathematical Formulation . . . . . . . . . . . . . . . 100
6.2.1 Benders Decomposition: A Primer . . . . . . . . . . . 100
6.2.2 General Problem Setting . . . . . . . . . . . . . . . . . 104
6.3 Numerical Example for an Electricity Market . . . . . . . . . 108
6.3.1 Mathematical Notation . . . . . . . . . . . . . . . . . 109
6.3.2 Formulation . . . . . . . . . . . . . . . 110
6.3.3 Computational Results . . . . . . . . . . . . . . . . . . 117
6.3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
Bibliography 126
A Mathematical Proofs and Remarks (Chapter 5) 146
vA.1 Result that Shows that q 2 [0; 1] is Valid . . . . . . . . . 146nsu;i
A.2 Formal Determination of the Disjunctive Constants . . . . . . 148
B Input Data and Further Model Results of the Numerical
Examples (Chapter 5) 151
C Two-Pass Process: Mathematical Justi cations (Chapter 6)
157CONTENTS viii
D GAMS Codes 161
D.1 GAMS Code for Chapter 3 . . . . . . . . . . . . . . . . . . . 161
D.2 Code for 4 . . . . . . . . . . . . . . . . . . . 172
D.3 GAMS Code for Chapter 5 . . . . . . . . . . . . . . . . . . . 180
D.4 Code for 6 . . . . . . . . . . . . . . . . . . . 185List of Figures
2.1 The process of mathematical model building . . . . . . . . . . 10
2.2 Fundamental features of electric power market equilibrium
and optimization models . . . . . . . . . . . . . . . . . . . . . 20
3.1 ELMOD representation of the European high voltage grid . . 35
3.2 Welfare in an electricity market . . . . . . . . . . . . . . . . . 38
3.3 Partial load e ciency . . . . . . . . . . . . . . . . . . . . . . 48
4.1 Average prices before and after the network extension, 20
d/t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67CO2
4.2 Average prices before and after the network extension, 50
d/t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68CO2
5.1 Three-node test network . . . . . . . . . . . . . . . . . . . . . 89
5.2 Stylized network of the Western European grid . . . . . . . . 92
ixList of Tables
4.1 Beta factors of selected German energy companies . . . . . . 62
4.2 Conventional power plant capacities in Europe . . . . . . . . 63
4.3 Wind generation capacities in 2020 forecasts per scenario . . 65
4.4 Generation costs ind per MWh . . . . . . . . . . . . . . . . . 66
4.5 Results overview Chapter 4 . . . . . . . . . . . . . . . . . . . 70
5.1 Correspondence between general formulation and speci c case
study formulation . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.2 Pro t of strategic player in the three-node network . . . . . . 91
5.3 Model results of the three-node network . . . . . . . . . . . . 95
5.4 Resulting pro ts in the fteen-node Western European network 96
5.5 prices in fteen-node Western European network . 96
5.6 Strategic generation Test Ebel . . . . . . . . . . . . . . . . . 97
5.7on Test EDF . . . . . . . . . . . . . . . . . 97
5.8 Strategic generation Test EON . . . . . . . . . . . . . . . . . 97
5.9on Test RWE . . . . . . . . . . . . . . . . . 97
6.1 Data for tests of the three-node example using Benders
decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.2 Results for tests of the three-node example using Benders
decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3 Results per iteration for Test1 of three-node example using
Benders decomposition . . . . . . . . . . . . . . . . . . . . . . 119
6.4 Results per iteration for Test2 of three-node example using
Benders decomposition . . . . . . . . . . . . . . . . . . . . . . 120
6.5 Data for further tests of three-node example using Benders
decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.6 Results for further tests of three-node example using Benders
decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
x