Hedging Strategy and Electricity Contract Engineering - IFOR

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õ õ ö õ ë ì ö ì V end á 156 Power portfolio optimization 0 V kã j V 0 Ü iã iã iã iâ iâ iâ JÜ 1Ü Ü 1Ü Ü Ü á?á@á á@á?á V kã j V 0 iã Ü iã iã iâ iâ iâ I j L j x j (6.48) k k k 1 1 1 k K j I j L j x j V max (6.49) k k k 1 1 1 k L kã j 0Ü k 1Ü 1Ü Ü K Ü j 1Ü Ü JÜ á?á@á á@á?á Ü K Ü j 1Ü Ü J á Further as in Chapter 6.5 we impose a constraint on the average end-water level to avoid a myopic solution of an empty water dam at the end of the horizon á@á?á á@á?á V K J ì 1 J V 0 K I iã j K L iã j K x iã j (6.50) jâ 1 iâ 1 iâ 1 iâ 1 j Ü xëKã j and x ì 1ã j Ü Ü x á?á@á ìKã j denote generating and pumping respectively xë1ã in each period in scenario j [MWh], which as before are given á@á?á Ü by xëkã j r Ü J (6.51) iâ 1 ë Û õ kã Ü Ü kã jÝaÜ kã 1Ü i gëi S j D j I a k Ü K Ü j 1Ü á@á?á á@á?á x ìkã j iâ 1 iì i S kã j Ü D kã j Ü I a kã j k ÝaÜ 1Ü gì Û á@á?á Ü K Ü j 1Ü Ü J á (6.52) The exercise gì functions gëi and i are given by the step functions (6.31) and (6.32). The weighting factors, i. e. the decision variables building up the dispatch from the individual exercise functions are denoted by Ü õ Ü õ ë1 r Ü õ 1 . As in the static case, the hydro storage plant has yet another component of decision variables, namely the spill over losses, á@áaá Ü Ü á@á?á L kã j. á@á?á
ö 6.6 Power portfolio optimization with CVaR 157 Similarly to the static case, we would like to take advantage of the superior computational aspects of linear programming and want to reduce our optimization problem (6.1) to (6.34). The assumptions needed in the static case also have to be fulfilled for . The constraints on (6.18) and (6.19) are obviously linear. Also the loss function is linear in õ , since it can be written in the following form õ x õ õ Ü Y Ý n 2K iâ lÛ 1 x i f Ü i Y Ý r iâ 1 õ ë i f Û n i Û Y Ý ë ë 1 ì i f iâ n r ë i Û YÝ , where the functions f i Û Y Ý only depends on the stochastic ë factors Y . The assumptions are obviously fulfilled and a simultaneous optimization of the dynamic hydro dispatch and the contract portfolio in a CVaR õ and profit framework as in (6.34) will thus be given by the solution of the following linear program
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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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x k xœk x «k š xœk 0 š x «k 0
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4.4 Coal plant and oil plant 87 4.4
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4.4 Coal plant and oil plant 89 cor
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4.5 Nuclear plant 91 of 1000 MW. Ov
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4.7 All production plants 93 possib
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4.8 Transmission lines 95 Unit type
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4.9 Real option theory 97 The scien
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4.10 Value of different production
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4.12 Summary 101 like the capped sp
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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 and 152: ¢ é á 6.5 Analysis of optimal di
Page 153 and 154: ìj Û 1 bë j Ý?Ü j 1Ü á?á@á
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 165 and 166: 6.6 Power portfolio optimization wi
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 171: 6.6 Power portfolio optimization wi
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
Page 203 and 204: 7.6 Summary 187 2500 2000 Dispatch
Page 205 and 206: 7.6 Summary 189 We have quantified
Page 207 and 208: Chapter 8 Conclusions The special c
Page 209 and 210: a4q V a4q G 1 V H a4q 6 Appendix A
Page 211 and 212: 8 _ 195 Proof The results follow im
Page 213 and 214: g b4i d G9:7j b4 j G 1 9j7j H b4 j
Page 215 and 216: Ax 3 V AxK1 G 1 V H AxK2 V b 1 G 1
Page 217 and 218: Bibliography [ABA98] [AD80] [ADEH97
Page 219 and 220: Bibliography 203 [BS73] [BS98] [BT0
Page 221 and 222: 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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