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Canada Archives Canada Published Heritage Direction Du Branch Patrimoine De I'edition OPTIMIZING EXPANSION OF LOW VARIABLE COST CAPACITY IN COMPETITIVE ELECTRICITY MARKETS: VALUATION OF WIND GENERATION USING STOCHASTIC COMPLEMENTARITY PROGRAMMING By Paul G. Dabrowski A thesis submitted in conformity with the requirements for the degree of Master of Applied Science Graduate Department of Mechanical and Industrial Engineering University of Toronto © Copyright by Paul G. Dabrowski (2008) Library and Bibliotheque et 1*1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A0N4 Ottawa ON K1A0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-45126-7 Our file Notre reference ISBN: 978-0-494-45126-7 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par Plntemet, prefer, telecommunication or on the Internet, distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, electronique commercial purposes, in microform, et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in et des droits moraux qui protege cette these. this thesis. Neither the thesis Ni la these ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent etre imprimes ou autrement may be printed or otherwise reproduits sans son autorisation. reproduced without the author's permission. In compliance with the Canadian Conformement a la loi canadienne Privacy Act some supporting sur la protection de la vie privee, forms may have been removed quelques formulaires secondaires from this thesis. ont ete enleves de cette these. While these forms may be included Bien que ces formulaires in the document page count, aient inclus dans la pagination, their removal does not represent il n'y aura aucun contenu manquant. any loss of content from the thesis. Canada 11 OPTIMIZING EXPANSION OF LOW VARIABLE COST CAPACITY IN COMPETITIVE ELECTRICITY MARKETS: VALUATION OF WIND GENERATION USING STOCHASTIC COMPLEMENTARITY PROGRAMMING Master of Applied Science 2008 Paul G. Dabrowski Department of Mechanical and Industrial Engineering University of Toronto Abstract We study capacity expansion in imperfectly competitive electricity markets by presenting two decision support models formulated as complementarity programs, with wind capacity as the expansion technology. WCAPCOMP 1.0 is a deterministic model with a single-price wind capacity market and separate electricity market, the latter approximating a year of competition. WCAPCOMP 2.WOM is stochastic with nuclear capacity uncertainty between the two markets, and an added "wind output market" (WOM) for contracts-for-difference, where conventional gencos can buy financial rights to wind output from a wind entrant competitor. All gencos behave strategically, anticipating how other gencos will react to their decisions, using an anticipation approach. Results show that conventional gencos with coal on the margin have incentive to purchase WOM contracts and reduce their coal output to the market, and that this increases the total amount of wind capacity constructed, the ratio of coal energy displaced to wind energy added, and profits for the wind entrant. n Ill Acknowledgements To my supervisor, Dr. J. Scott Rogers, for perspective, advice, and accepting nothing less than my best work. To the committee members, Dr. Roy Kwon & Dr. Daniel Frances, for their constructive comments. To members of industry who provided helpful suggestions. To Kevin Au, for document assembly advice, and crib. To my wife Anne, for unconditional love. To my mother, for her support, patience and understanding. 111 IV Table of Contents 1.0 Introduction 1 1.1 Motivation 3 1.2 Purpose and Methodology 5 1.3 Literature Review 7 1.3.1 Electricity Market Equilibrium Models 7 1.3.2 Investment in Capacity Models 13 1.3.3 Comparison To Asl, Rogers 2004 15 1.3.4 Comparison to Yao et. al. 2007 16 1.3.5 Comparison to Murphy, Smeers 2005 17 1.4 Thesis Overview 18 1.4.1 Chapter Two Summary 18 1.4.2 Chapter Three Summary 19 1.4.3 Chapter Four Summary 21 1.4.4 Chapter Five Summary 22 2.0 Analytical Derivation of Value of Wind in Competitive Markets for Open-Loop and Closed-Loop Knowledge 24 2.1 WCM-EM Model: Wind Capacity Market and Electricity Market with Two Gencos 26 2.1.1 Cournot Wind Capacity Market and Open-Loop Electricity Spot Market 30 2.1.2 Cournot Wind Capacity Market with Closed-Loop Electricity Spot Market.... 3 5 2.1.3 Summary of WCM-EM Model Findings 42 2.2 WOM-EM Model: Wind Output Market and Electricity Spot Market with Two Gencos 43 2.2.1 Effect of WOM Contract from Wind-On-Margin Gw to Conventional-On- MarginGl 44 2.2.2 WTP of Gl For WOM Contract Using Total Derivatives 47 2.2.3 WTS of Gw For WOM Contract Using Total Derivatives 50 2.2.4 Verifying Existence of a Mutually-Acceptable Closed-Loop Price for Wind Output Contract in WOM 52 2.2.5 Pitfalls with Standard CP Formulation of WOM 53 IV V 2.2.6 Generalizing WTP and WTS for Imperfect Knowledge Cases 56 2.3 Conclusion 56 3.0 WCAPCOMP 1.0 - Deterministic Capacity Expansion Model for Ontario-like Market 59 3.1 WCAPCOMP 1.0 Model Structure 60 3.1.1 Description of WCAPCOMP 1.0 model 60 3.1.2 Electricity Spot Market 62 3.1.3 Use of Anticipation in Electricity Spot Market 64 3.1.4 Wind Capacity Market 65 3.1.5 Use of Anticipation in Wind Capacity Market 66 3.1.6 Representation of Wind Generation 68 3.2 WCAPCOMP 1.0 Model Notation 68 3.3 WCAPCOMP 1.0 Model Formulation 71 3.3.1 Conventional Genco Primal Formulation 71 3.3.2 Wind-Only Genco Primal Formulation 75 3.3.3 EMO Primal Formulation 75 3.3.4 WMO Primal Formulation 76 3.3.5 Primal Linking Constraints 77 3.3.6 WCAPCOMP 1.0 Dual Constraints 78 3.3.7 Complementarity Programming Formulation of WCAPCOMP 1.0 79 3.3.8 KKT Analysis of WCAPCOMP 1.0 80 3.4 Numerical Results 85 3.4.1 Wind Capacity Allocation and Willingness-to-Pay 86 3.4.2 Electricity Market Outputs 89 3.4.3 Coal Displacement 91 3.4.4 Electricity Market Price and Profits 93 3.5 Conclusion 96 4.0 WCAPCOMP 2.WOM - Stochastic Two-Stage Capacity Expansion Model for Ontario-like Market 98 4.1 WCAPCOMP 2.WOM Model Structure 99 4.1.1 Stage Two Wind Output Contract Market (WOM) 101 v VI 4.1.2 Use of Anticipation for Effect of WOM Contracts on Electricity Market Equilibrium 103 4.1.3 Use of Anticipation of WOM Price 105 4.2 WCAPCOMP 2.WOM Model Notation 106 4.3 WCAPCOMP 2.WOM Model Formulation 108 4.3.1 Conventional Genco Primal Formulation 108 4.3.2 Wind-Only Genco Primal Formulation 110 4.3.3 EMO Primal Formulation 111 4.3.4 WMO Primal Formulation 112 4.3.5 Primal Linking Constraints 112 4.3.6 WCAPCOMP 2.WOM Dual Constraints 112 4.3.7 Complementarity Programming Formulation of WCAPCOMP 2.WOM 114 4.3.8 KKT Analysis of WCAPCOMP 2.WOM 114 4.4 Numerical Results 124 4.4.1 Wind Capacity Allocation and Wind Output Market Activity 125 4.4.2 Coal Displacement 128 4.4.3 Electricity Market and Wind Output Market Contract Prices 130 4.4.4 Genco Profits 132 4.5 Conclusion 134 5.0 Market Structure Sensitivity 136 5.1 Effect of Cross-Market WOM Knowledge and Fossil Generation Ownership 137 5.2 Numerical Results for Sensitivity to WOM Knowledge & Fossil Ownership 140 5.3 Effect of Demand Curve Slope 144 5.4 Numerical Results for Sensitivity to Demand Curve Slope 147 5.5 Note on Stability of the WCAPCOMP Models 150 5.6 Conclusion 151 5.7 Recommendations for Future Work 152 6.0 References 154 7.0 Appendices 158 7.1 Appendix A: Constructing Demand Curves 158 7.2 Appendix B: GAMS Implementation of WCAPCOMP 1.0 160 VI Vll 7.3 Appendix C: Calculation of Seasonal Hydro Parameters 165 7.4 Appendix D: Parameters Used for Chapter Three Numerical Examples 166 7.5 Appendix E: Determining Basic and Advanced Knowledge Cross-Market WOM Anticipation Coefficients 169 7.6 Appendix F: GAMS Implementation of WCAPCOMP 2.WOM 170 7.7 Appendix G: Parameters Used for Chapter Four Numerical Examples 176 7.8 Appendix H: Parameters Used For Sensitivity Examples in Chapter Five 178 vii viii List of Figures Figure 1-1: Valuation of new capacity in a traditional cost-minimizing utility paradigm 4 Figure 2-1: Diagram of the analytical WCM-EM model 27 Figure 2-2 - Solution to the open-loop WCM-EM model using some simple test parameters, with WTP for Gl and Gw indicated 34 Figure 2-3: Diagram of the WOM-EM model 44 Figure 2-4: Comparison of electricity market equilibria, with and without a contract-for- difference on A units of wind output from Gwto Gl 46 Figure 3-1: Diagram of WCAPCOMP 1.0 model 61 Figure 3-2: Converting a seasonal LDC into a discretized load block, and fitting a demand curve 63 Figure 3-3: Illustration of electricity market anticipation and perception of residual demand curve slope 65 Figure 3-4: Illustration of wind capacity market anticipation and perception of residual supply curve slope 67 Figure 3-5: Total wind construction and allocation amongst spot market gencos for low, medium and high nuclear cases 87 Figure 3-6:: Hourly WTP (dual variable on wind output constraint) for wind output in selected blocks, for each genco, defined as the mariginal
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