Hedging Strategy and Electricity Contract Engineering - IFOR

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166 Power portfolio optimization Efficient frontier Attractive (2) Expected profit (1) (3) Inattractive Risk Fig. 6.7: Positioning of contracts and plants. with the same arguing as before go short in that contract reducing the risk by prof it one unit, but also penalizing the expected profit with . The reduced risk risk utilization would however allow us to further leverage on the contracts made available in the original optimization and increase the expected profit with prof it yú1 î 0. risk The efficient frontier 6 can be very helpful in positioning contracts and plants according to the marginal value of risk, since the slope of the efficient frontier gives the marginal price of risk. Corollary 6.13 The efficient frontier zÛ CÝ is piecewise linear and concave. A proof is given in Appendix A on page 199. Assume that our optimal portfolio conditioned on the investment opportunity set is given by Û 1Ý in Figure 6.7. A contract or plant added to the investment 6 The efficient frontier is the plot z0 C1 C . The term efficient frontier is normally used for a whole market and not as in this case for a specific player.
6.7 Summary 167 opportunity set would then be attractive if the portfolio, consisting of the original portfolio Û 1Ý including the new contract or plant is located above the original efficient frontier Û 2Ý . A new portfolio located below the efficient frontier Û 3Ý , on the other hand, would be unattractive. One is with this arguing tempted to define the price of a contract or a plant such prof it that risk yú1 , since this is the price making the utility indifferent between buying or selling the contract or plant. We do not go that far, since that price would then depend on the current portfolio and hence the current investment opportunity set. The order in which contracts are added to the investment opportunity set would consequently matter. We however believe that a utility can get additional information on the attractiveness of contracts and plants by investigating the marginal value of risk. And by doing that the utility can get a guidance on which contracts or plants that it should consider to acquire or sell. Operationally the attractiveness of a new contract or plant could be determined by simply calculating the new portfolio’s (consisting of the original portfolio and the new contract or plant) expected profit and risk, and compare it with the efficient frontier of the original portfolio. An example of such a positioning is presented in the case study in the next chapter. 6.7. Summary The proposed power portfolio optimization model using CVaR manages to incorporate the production assets and allows us, through the dynamic dispatch strategy, to take advantage of the hydro storage plant’s operational flexibility. We have also shown how a simultaneous optimization of the contract and the production portfolio can be carried out. As already stated in Chapter 3.5, we believe that CVaR is an appropriate risk measure in heavy-tailed portfolios, such as power portfolios, and we have shown how the non-normal and heavy-tailed feature of power portfolios can be captured by our optimization approach using CVaR. The probabilistic constraints on the water level could also be handled by working with scenarios, which also allows us to incorporate and model the, for the electricity market typical, complex contracts.
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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
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5.3 Relevance for electricity hedgi
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5.4 Best Hedge 111 that the expecte
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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
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
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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: î yú1 î é yú1 á ¢ 6.6 Power
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
Page 227: Curriculum Vitae Personal Data Name
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