Hedging Strategy and Electricity Contract Engineering - IFOR

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ë ì á 130 Power portfolio optimization r 1â 1 ì õ 1Ü õ ì i 0Ü i 1Ü i (6.19) Ükô Through (6.16)-(6.19) the constraints 0 xëk p max and 0 x ìk p min k 1Ü Ü K will be fulfilled and the dispatch will be able to take the Ü extreme values hence allowing the dispatch to cover its full technical range. á@á?á á?á@á The decision to produce or pump is solely determined by the spot price, demand, aggregated inflow and time. Even though it seems reasonable that the dispatch should be a function of those variables, we do not know the shape of these functions. The key in this dynamic approach is therefore to let the Û õ weighting factors ë1 Ü õ r Ü õ ì 1 Ü Ü õ õ ö Ý be the decision variables, á?á@á Ü á?á@á instead of letting the dispatch x k in itself be a decision variable, as is the case in the static dispatch strategy. The optimization problem will thus give us the best convex combination of the, exogenously given, exercise functions gëi and i . gì One could let gëi and gìi be functions of also other variables, such as volatility or jump frequency. However, these variables are in this work assumed to be deterministic and for a given volatility and jump frequency, the state variable time is actually sufficient to take these possibly time varying variables into account. If we change the volatility or jump frequency, the weighting factors, building up the optimal exercise condition, may however change. 6.5. Analysis of optimal dispatch strategy A crucial issue is to derive the correct type of exercise function. We state that the step function is a natural choice. A step function is a function that can only take two values. It is hence easy to interpret, it is limited and can fulfill the conditions (6.14)-(6.17). But more important, we can show that under certain assumptions the step function is indeed the correct one. Consider the hydro dispatch problem, where the expected profit is maximized under the sustainability constraint that the expected end-water level must exceed or equal a threshold
õ õ 6.5 Analysis of optimal dispatch strategy 131 ÷ max lÛ õ Ü YÝ E (6.20) s á t á V K V end á We hence assume that the water constraint (6.10) is non-binding. Since risk is of no concern, the hydro dispatch is independent of the contract portfolio and naturally only depends on the spot price and time. To simplify we assume that the distribution function of the spot price f S is constant over time, why the dispatch only depends on the spot price. 6.5.1. Hydro production strategy To start with, we consider a hydro storage plant with no pumping capacity. The exercise functions are given as step functions gëi p max if S Sëi 0 otherwise Ü i 1Ü áaá@á Ü rÜ where é 0 é é á@á?á Së1 Së2 Sër is a given ordered set of spot prices. The dispatch problem (6.20) can then be formulated as ÷uø max r ÙˆÚ K s á t á K E r E S r r iâ 1 iâ 1 ë i gëi (6.21) ë õ i gëi W iâ 1 ië 1Ü õ i 0Ü i 1Ü ë Ü rÜ á@á?á iâ where W V 0 V end K 1 I i denotes the average available water for production. To facilitate reading denote
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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
Page 95 and 96: 4.2 Gas turbine 79 220 200 Capped l
Page 97 and 98: 4.3 Hydro storage plant 81 facilita
Page 99 and 100: ¢ 4.3 Hydro storage plant 83 I k L
Page 101 and 102: 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: gìi Û S í SÜ D í DÜ I a í I
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 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
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Page 177 and 178: ö S kã j á 6.6 Power portfolio o
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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
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7.3 Hedging value of water 181 The
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7.4 Value decomposition 183 expecte
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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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