Hedging Strategy and Electricity Contract Engineering - IFOR

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u ø j 1 u ì ø j 1 ì u ø i 1 u ì ø i 1 ì 140 Power portfolio optimization and solved by checking the functional value at u i i Ü u j j 1Ü Ükô 1. Ü Ü r 1 and at 1Ü á?á@á áaá@á Ü zÛ Ý ë At u i either j such that u i u j u j 1 and u i is given by û where given by u i u j , or else u i î uö ë 1 Û u i Ý 0 and zÛ u i Ý is consequently zÛ u i Ý Û Wú ¦KÝ u i Û u i Ý û Û u j Ý Û 1 ûüÝ Û u j ë 1Ý Ü zÛ Ý Wú zÛ Û Ý ¦KÝ á Ü Ý zÛ ë u i u i u i Similarly, at u j either i such that u j u i u i 1 and u j is given by û where by u j u i , or else u j î u r ë 1 Û u j Ý 0 and zÛ u j Ý is hence given zÛ u j Ý Û Wú ¦KÝ u j û Û u i Ý Û 1 û}Ý Û u i ë 1Ý Û u j Ý?Ü zÛ u j Ý Û Wú ¦bÝ u j Û u j Ý á The optimum is consequently found by choosing the minimum among u zÛ i r 1ãåäæä ä ã Ý 1Ü zÛ u iâ j jâ 1ã ä äæä ã ö Ý ë á With the help of the dual we can now sharpen the results of Corollary 6.6. Proposition 6.7 In the solution of (6.26) at the most three weights are non-zero and given by (i) In the trivial case, where there is abundant water õ ë1 ë 1 ì õ 1 1. (ii) In the general case where water is scarce, either one production weight equals one, ë i. e. i 1 for 1Ü an Ü i r , and two adjacent pumping weights õ ìj á@á?á 1 and ìj for a j 2Ü are non-zero and given by õ õ ì Ükô á@á?á
õ õ õ á á 6.5 Analysis of optimal dispatch strategy 141 õ ìj Wú ¦ bëi ¦ bë j ì 1 ¦ Û bë j bë j ì 1 Ý Ü õ ìj ì 1 1 õ ìj Or else one pumping weight equals one, i. e. ìj 1 for an 1Ü j and two adjacent production õ weights i õ 1 and õ ë i for an i 2Ü ë are non-zero and given by ì á@á?á Ükô r Ü á?á@á i ë ¦ bë j bëi 1 Wú ¦ Ü ë bëi bëi 1 ë i ë 1 1 ì i ë The proposition is proven in Appendix A on page 197. To further exploit the production and pumping problem (6.26), we study the special case, ô where r and S 1 Së1 ö áaá@á Sì1 . Ü S Ü r Sì Sër Corollary 6.8 The pumping decision is related to the production decision by the marginal value of water and (i) Assume production at price S i , then the marginal value of water is u i . Pumping occurs below price S j j é iÝ , where the marginal value of Û water u j u è i u j 1. ë (ii) Assume pumping at price S j with marginal value of water u j . Then production occurs at price S i Û j é iÝ where è u i u j è u i ë 1. The corollary is proven in Appendix A on page 198. 6.5.3. Conclusion and choice of exercise functions We have in this section, for the special case, where the probabilistic water constraints and the risk constraint are inactive, derived a number of results and showed that step functions indeed are the correct exercise functions. In the general case, where risk and intermediate water level is of concern we can rely
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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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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
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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 159 and 160: 6.6 Power portfolio optimization wi
Page 161 and 162: è á 6.6 Power portfolio optimizat
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Page 167 and 168: ááá ááá ááá ááá ááá
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Page 173 and 174: ö 6.6 Power portfolio optimization
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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
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
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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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