Hedging Strategy and Electricity Contract Engineering - IFOR

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è aëj Ü j 1Ü á?á@á bëi uÝ é 138 Power portfolio optimization min Û Wú ¦KÝ u (6.27) s á t á bëi u aëi Ü i 1Ü Ü r uÙmÚOã©@ÙˆÚOã ÙˆÚ u 0 á bë j u ¦ è ¦ á?á@á Ükô Define maxÛ aëi i and max ¦ Û j aëj Û uÝ bë á uÝ uÝaÜ Û Û uÝ?Ü uÜ>Ý Û Û Ý uÜ j Evidently u 0 forms the lower envelope of the feasible region 2 , as illustrated in Figure 6.3. Similarly u 0 forms the lower envelope of the feasible region 2 . Û uÝ Observe that Û uÝ can be specified by the points u 1 0Ü aë1 (6.28) u i Ü aëi bëi u i Ü i 2Ü Ü r u r ë 1 aër bër á?á@á Ü 0 Ü where u i is the solution to aëi ì 1 bëi ì 1 u aë i bëi u, given by u aëi 1 aëi i ì bëi 1 bëi ì Ü i 2Ü Ü r á á@á?á Following from Theorem 6.1 it is easy to see zÛ uÝ that is specified by these points by observing that the point u 1 u é 2 u é r 1, the intersection ë á?á@á
u ¦ j Ü è è aëj ¦ bë j u j Ü j 2Ü ö è ö á 6.5 Analysis of optimal dispatch strategy 139 a 1 + a 2 + ← (u 1 ,v 1 ) ← (u 2 ,v 2 ) v a i + ← (u i ,v i ) v(u) Fig. 6.3: Lower envelope of the dual variable . u î aër 0 and the slope bë1 î bë2 î aë1 î aë2 î î bër 0. The lower envelope Û uÝ has similar properties and can be specified by áaá@á á@á?á u ¦ 1 0Ü è aë1 (6.29) Ükô á@á?á ë 1 aë Ü 0 Ü uö where bë u j 1 aëj ì 1 bë j ì 1 aëj bë j Ü j 2Ü Ükô Hence the dual (6.27) can be reduced to áaá@á min uù 0 zÛ uÝ Û Wú ¦KÝ u Û uÝ Û uÝ (6.30)
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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
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 and 152: ¢ é á 6.5 Analysis of optimal di
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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
Page 203 and 204: 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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