Hedging Strategy and Electricity Contract Engineering - IFOR

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ö ö õ õ ìj 1Ü õ ìj 0Ü j 1Ü õ õ ö ö õ è ö S f S dS E S aëj Ü j 1Ü á?á@á õ á á 136 Power portfolio optimization ÷uø max r K p max r iâ á á 1 s t K p max r r iâ 1 ë õ i iâ 1 ë õ i aëi K p min ö i bëi K ë p min õ ìj aìj (6.24) 1 jâ jâ 1 õ ë i 0Ü i 1Ü 1Ü ìj bìj Ü r W á?á@á Üuô á@á?á jâ 1 ¦ Define to p min p max 0 and again Wú W K p max . Then (6.24) becomes equivalent ÷uø max ÙˆÚ r ã ÷ ý ÙˆÚ¥¤ s á t á r iâ 1 ië aëi ¦ è jâ 1 ìj aìj (6.25) r r iâ 1 iâ 1 ë õ i ¦ bëi ë õ i jâ 1 õ ìj bìj Wú õ ë i 0Ü i 1Ü 1Ü Ü r ìj jâ 1 1Ü õ ìj 0Ü j 1Ü á?á@á ÜÑô Now by definition á@áaá aìj S f S dS S f S dS S£ S ý j S Sù S ý j ÜÑô and similarly
ìj Û 1 bë j Ý?Ü j 1Ü á?á@á ö ö õ ìj 1Ü õ ìj 0Ü j 1Ü ö á 6.5 Analysis of optimal dispatch strategy 137 ÜÑôkÜ where j denotes an index from the set of pumping thresholds r opposed to an index from the set of production thresholds Sëi iâ 1 . Sìj ö 1 as jâ Using these expressions in (6.25) results in ÷uø max ÙmÚ r ã ÷ ý ÙˆÚ¥¤ s á t á r iâ 1 ë õ i aëi ¦ è õ ìj aëj E S (6.26) 1 jâ r r iâ 1 iâ 1 ë õ i ¦ bëi ë õ i õ ìj bë j Wú ¦ 1 jâ õ ë i 0Ü i 1Ü 1Ü Ü r á@á?á Ükô á@á?á jâ 1 § ¨ Again a is concave and monotone increasing in b as shown by Theorem 6.1 and hence we can conclude Corollary 6.6 In the solution of (6.26) (i) Wú If bë1 then ë1 1 and õ ì 1 1 is optimal õ (ii) If Wú ¦ é bër ¦ bë ö then the problem is infeasible (iii) Else at most two adjacent production weights õ i 1 and ë i and at most ë õ ì two adjacent pumping weights ìj 1 and ìj will be non-zero. õ õ ì A proof is given in Appendix A on page 196. To actually derive the solution we however need to study the dual problem. Consider the dual to the productionpumping problem (6.26)
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Diss. ETH No. 14727 Hedging Strateg
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Abstract This thesis studies risk m
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Zusammenfassung Die vorliegende Sch
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Contents Acknowledgements ¡ ¢ ¡
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Contents xi 5.1 Overview . . . . .
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List of Figures 2.1 Illustration of
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List of Figures xv 7.6 Marginal val
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List of Tables 2.1 Spot market bid.
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Chapter 1 Introduction 1.1. Motivat
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1.3 Structure of the thesis 5 hedge
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Chapter 2 The electricity market 2.
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2.1 Overview 9 Generation ¥ Distri
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2.2 Liberalization of the electrici
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duction cost Marginal pro © 2.3 Su
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2.4 Transmission costs 15 10 Peak l
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2.4 Transmission costs 17 destinati
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2.5 Demand 19 2.5. Demand Compared
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2.6 Special characteristics of elec
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2.7 Electricity contracts 23 tions.
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0& K $ 0& K K % + $ 2.7 Electricity
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2.7 Electricity contracts 27 2.7.2.
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04 04 2.7 Electricity contracts 29
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2.8 Power exchanges and pricing mec
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2.8 Power exchanges and pricing mec
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S 0 eH aIKJ 2.9 Price dynamic 35 To
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2.9 Price dynamic 37 400 2000 350 1
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2.9 Price dynamic 39 simple sinus f
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2.9 Price dynamic 41 1800 1800 1600
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2.10 Summary 43 To deal with the un
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Chapter 3 Risk management 3.1. Over
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3.3 The risks in the electricity ma
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3.3 The risks in the electricity ma
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3.4 Traditional risk management mod
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l H xg yLihkjml f 3.5 The need for
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3.5 The need for a new risk measure
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R S x GaRKV is convex and continuou
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R P 3.6 Multi period risk managemen
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“ “ “ 3.7 Valuation models 67
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3.7 Valuation models 69 storability
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3.7 Valuation models 71 by introduc
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“ 3.7 Valuation models 73 formula
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Chapter 4 Contract engineering 4.1.
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4.2 Gas turbine 77 2000 1800 1600 1
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4.2 Gas turbine 79 220 200 Capped l
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4.3 Hydro storage plant 81 facilita
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¢ 4.3 Hydro storage plant 83 I k L
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Page 103 and 104: 4.4 Coal plant and oil plant 87 4.4
Page 105 and 106: 4.4 Coal plant and oil plant 89 cor
Page 107 and 108: 4.5 Nuclear plant 91 of 1000 MW. Ov
Page 109 and 110: 4.7 All production plants 93 possib
Page 111 and 112: 4.8 Transmission lines 95 Unit type
Page 113 and 114: 4.9 Real option theory 97 The scien
Page 115 and 116: 4.10 Value of different production
Page 117 and 118: 4.12 Summary 101 like the capped sp
Page 119 and 120: Chapter 5 Hedging strategies 5.1. O
Page 121 and 122: È È È È È 5.2 Traditional hedg
Page 123 and 124: É È É È Ì 5.2 Traditional hedg
Page 125 and 126: 5.3 Relevance for electricity hedgi
Page 127 and 128: 5.4 Best Hedge 111 that the expecte
Page 129 and 130: 5.4 Best Hedge 113 that they alread
Page 131 and 132: Chapter 6 Power portfolio optimizat
Page 133 and 134: 6.3 Power portfolio optimization in
Page 135 and 136: 6.3 Power portfolio optimization in
Page 137 and 138: 6.4 Modeling of plants and their op
Page 141 and 142: x k xëk x ìk Ü xë k 0Ü x ìk 0
Page 145 and 146: gìi Û S í SÜ D í DÜ I a í I
Page 147 and 148: õ õ 6.5 Analysis of optimal dispa
Page 149 and 150: õ Ü r á 6.5 Analysis of optimal
Page 151: ¢ é á 6.5 Analysis of optimal di
Page 155 and 156: u ¦ j Ü è è aëj ¦ bë j u j
Page 157 and 158: õ õ õ á á 6.5 Analysis of opti
Page 159 and 160: 6.6 Power portfolio optimization wi
Page 161 and 162: è á 6.6 Power portfolio optimizat
Page 163 and 164: x Û x p Ü x c Ý Û xë1 Ü á@á
Page 167 and 168: ááá ááá ááá ááá ááá
Page 169 and 170: F Û 0Ü 3Ý í è F Û 0Ü 1Ý?Ü
Page 173 and 174: ö 6.6 Power portfolio optimization
Page 175 and 176: ö Ü 6.6 Power portfolio optimizat
Page 177 and 178: ö S kã j á 6.6 Power portfolio o
Page 179 and 180: ¢ ¢ 6.6 Power portfolio optimizat
Page 181 and 182: î yú1 î é yú1 á ¢ 6.6 Power
Page 183 and 184: 6.7 Summary 167 opportunity set wou
Page 185 and 186: Chapter 7 Case study In this chapte
Page 187 and 188: 171 3200 140 3000 2800 120 2600 240
Page 189 and 190: S7 D7 min 8 0 if S i or D p otherwi
Page 191 and 192: 175 Production Spot price Demand [C
Page 193 and 194: 7.1 Efficient frontier 177 lG x 6 9
Page 195 and 196: 7.2 Spot position 179 of the old po
Page 197 and 198: 7.3 Hedging value of water 181 The
Page 199 and 200: 7.4 Value decomposition 183 expecte
Page 201 and 202: MWh CHF/ P 7.4 Value decomposition
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7.6 Summary 187 2500 2000 Dispatch
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7.6 Summary 189 We have quantified
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Chapter 8 Conclusions The special c
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a4q V a4q G 1 V H a4q 6 Appendix A
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8 _ 195 Proof The results follow im
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g b4i d G9:7j b4 j G 1 9j7j H b4 j
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Ax 3 V AxK1 G 1 V H AxK2 V b 1 G 1
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Bibliography [ABA98] [AD80] [ADEH97
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Bibliography 203 [BS73] [BS98] [BT0
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Bibliography 205 [GR92] H. Gravelle
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Bibliography 207 [Mer76] R. C. Mert
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Bibliography 209 [SC89] [Sch90] [Sc
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Curriculum Vitae Personal Data Name
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