Hedging Strategy and Electricity Contract Engineering - IFOR

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ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá ááá 160 Power portfolio optimization Eq. õ x c L z # á (6.54) áá á (6.55) á á á áá á (6.56) áá á (6.57) áá á (6.59) áá á á á á á á á á á á á á á á á (6.60) áá á (6.61) á á á á áá ô # r n 2K K J J 1 1 J K J K J 1 1 1 á á lar, matrix. á Tab. 6.2: Structure of the A á matrix. áá denotes a diagonal á á and á á á á denotes a full, á áá á denotes a triangu- á á denotes a diagonal band sub- As seen in Table 6.2 the constraint (6.56) and (6.57) and the spill over variables regulating the water level build up the majority of the matrix. One could however relax some of these constraints. For example, in a short horizon optimization in the winter, when the dams are basically full, the constraint that the water level must be non-negative could be excluded from the problem. Further, in the summer when the water level is low, the upper constraint on the water level can be relaxed and the spill over variables could be eliminated. This would dramatically reduce the size of the problem. The feasibility of the solution, although very probable, must then be checked ex-post. To keep the size of the problem within reasonable boundaries, the proposed relaxation of the water level constraints and the corresponding spill-over variables should however be done whenever possible. Another possibility to decrease the size of the problem is to aggregate a number of periods into one. This would however only serve as an approximate solution. The hydro storage plant’s options would then have an average spot price as underlying and not the actual spot price. This should hence preferably be done during times when the stochastic factors are fairly stable, for example, by dividing each day into only one peak period and one off-peak period. The well known fact that the value of a portfolio of options is greater than the value of an option on a portfolio, however implies that an aggregation of periods would underestimate the value
ö S kã j á 6.6 Power portfolio optimization with CVaR 161 of flexible production units, as shown in Example 4.2. One should therefore proceed with care when aggregating periods. 6.6.8. Analysis of dynamic solution As a solution from the optimization (6.53)-(6.62) we will obtain the optimal contract portfolio xú2K 1 Ü á@á?á xún . We will also get the optimal weighting ë factors Ü ú 1 Ü õ Ü õ ë ú r Ü õ ì ú 1 , Ü ë õ ì ú building up the optimal dispatch strategy, i. e. the optimal exercise conditions. á@á?á In any instant within the time horizon á@áaá we can measure the state variables S, D, I a and t and with these variables as input to the exercise functions (6.51) and (6.52) get the optimal dispatch. In this dynamic dispatch strategy we are allowed to react to new information and, for example, meet unexpected high demand by producing more or meet a price peak in a typical off-peak period. This flexibility offers an excellent way to manage these type of uncertain events, which is yet another wording for the hydro storage plant’s superb hedging capacity. An interesting question is what is this flexibility worth. One way to quantify this value would be to compare the average price of produced electricity S h given by S h 1 J J jâ 1 K K kâ 1 S kã j kâ 1 r iâ ë õ gëiã kã ë õ gëiã kã iâ 1 i j r 1 i j ¨1 ö 1 õ ì i iâ ö 1 õ ì i iâ iã kã j gì gìiã kã j Ü (6.63) with the average spot price given by S 1 J K J K 1 kâ 1 jâ (6.64) The difference between the average price of produced electricity, S h and the average spot price S actually gives us the total value of having a flexible
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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
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È È È È È 5.2 Traditional hedg
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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 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: ö Ü 6.6 Power portfolio optimizat
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
Page 223 and 224: Bibliography 207 [Mer76] R. C. Mert
Page 225 and 226: Bibliography 209 [SC89] [Sch90] [Sc
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