Hedging strategy and operational flexibility in the electricity market Characteristics of the electricity market • Non-storability • Transmission constraints • Very complex contracts • Physical production WS Budapest 10.-13..9.2003, 1 Prof. H.-J. Lüthi European Energy Exchange Profit in 2002 (for FPD): 5'127 €/MWh Profit in 2003 (for FPD): -15'434 €/MWh WS Budapest 10.-13..9.2003, 2 Prof. H.-J. Lüthi Introduction Focus of the Study Risk management in the electricity market Interaction between physical production and contracts Operational flexibility as hedging tool WS Budapest 10.-13..9.2003, 3 Prof. H.-J. Lüthi Hydro plant and Options Is In each period we have the option to produce Ls Es Payoff K xs WS Budapest 10.-13..9.2003, 4 Electricity price K = marginal cost of production Prof. H.-J. Lüthi • If we produce today the possibility to produce tomorrow will be affected • In each period we have the option to produce if Es > 0 Max capacity, 500MW Time (hourly buckets) Min capacity, -50MW High spot prices Low spot prices Storage almost empty A series of interdependent options WS Budapest 10.-13..9.2003, 5 Prof. H.-J. Lüthi Inflow (I) Demand (D) Portfolio optimization Production portfolio Contract portfolio Strike Availability Exercise flexibility Marginal costs Volume uncertainty Fixed costs Flexibility Interaction Interruptability Contract engineering & Portfolio optimization Portfolio optimization Optimal dispatch strategy Optimal contract portfolio Engineering thinking Financial thinking Spot price (S) Fuel prices WS Budapest 10.-13..9.2003, 6 Prof. H.-J. Lüthi Optimal (static) portfolio • Maximize expected profit – Given risk constraint (measured as CVaR) max E -l(x, ) xX s.t. CVaRx C • Large problems can be handled if X is a polyhedral set – “static model” – Besides production decisions (pump or produce) we model the amount of futures positions to be hold given the written bilateral contracts WS Budapest 10.-13..9.2003, 7 Prof. H.-J. Lüthi Case study portfolio Long positions Short positions Hydro plants Swing options Future contract Spot contracts WS Budapest 10.-13..9.2003, 8 Prof. H.-J. Lüthi Modeling the Stochastics Spot Price Electricity Inflow (European Energy Exchange) 4000 120.00 3500 Inflow (in m3/s) 100.00 80.00 60.00 3000 2500 2000 1500 40.00 1000 20.00 500 • Jumps • Yearly seasonality • Mean reversion • Daily variations Modeling the Stochastics? Risk measure? Prof. H.-J. Lüthi S A J J Month Month WS Budapest 10.-13..9.2003, 9 M A M F J D S A J J M A M F J D N O N 0 0.00 O Spot Price (in Euro/MWh) 4500 140.00 WS Budapest 10.-13..9.2003, 10 Prof. H.-J. Lüthi Portfolio optimization Spot price Scenarios j Inflow WS Budapest 10.-13..9.2003, 11 Prof. H.-J. Lüthi Demand Notations in Period s Is xs Production / Pumping Ls Is Es Inflow Es Waterlevel Ls Spill-over xs WS Budapest 10.-13..9.2003, 12 Prof. H.-J. Lüthi Modeling of hydro plant i i i s1 s1 s1 0 E i E 0 Is Ls x s, i 1,...,v i E max i i E i E 0 I s Ls xs, i 1,...,v s1 s1 s1 E end E E 0 I s Ls xs s1 P min xi P max s1 s1 , i 1,...,v Don’t produce when storage empty Don’t pump when storage full Leave water for future production Technical constraint Li 0 ,i 1,...,v Note: E, I, and L are stochastic variables !!! WS Budapest 10.-13..9.2003, 13 Prof. H.-J. Lüthi WS Budapest 10.-13..9.2003, 14 Prof. H.-J. Lüthi Dynamic Dispatch • Dispatch responds to observations of uncertainties – Spot-price S – Aggregated Inflow up to time t: I – Demand • Corresponds to an exercise-frontier in American options WS Budapest 10.-13..9.2003, 15 Prof. H.-J. Lüthi Modeling exercise conditions • Let the decision variable determine exercise conditions instead of the actual dispatch in each period Exercise condition r x s i gi S,D,I i1 Decision variables The dispatch is allowed to react to new information WS Budapest 10.-13..9.2003, 16 Prof. H.-J. Lüthi Hydro dispatch strategy • Pure profit maximization dispatch is a step function • Risk averse case convex combination of step functions r x g S,D,I,t, i i i1 x i gi S,D,I,t i1 • The step functions gi and gi are given exogenously and the weighting factors i and i are decision variables • Can optimize the complex hydro storage plant with LP WS Budapest 10.-13..9.2003, 17 Prof. H.-J. Lüthi Portfolio optimization & hedging strategy Dispatch strategy No risk constraint (high C) WS Budapest 10.-13..9.2003, 18 Tight risk constraint (low C) Prof. H.-J. Lüthi Hedging strategy • Uncertain demand is risky • Cannot hedge with standardized contracts • Operational flexibility to hedge against volume risk What is the operational flexibility worth? WS Budapest 10.-13..9.2003, 19 Prof. H.-J. Lüthi Profit Distribution for CVaR = -23,500,000 Euro (Expected Profit: 24,083,091.74) 0.6 0.5 0.4 Probability 0.3 0.2 0.1 0 21 ,4 0 22 0,0 ,2 00 0 23 0,0 ,0 00 0 23 0,0 ,8 00 0 24 0,0 ,6 00 0 25 0,0 ,4 00 0 26 0,0 ,2 00 0 27 0,0 ,0 00 0 27 0,0 ,8 00 00 ,0 00 Enlarged Efficiency Fontier 24098000 24093000 24088000 Profit Distribution for CVaR = -21,600,000 Euro (Expected Profit: 24,095,411.84) 24083000 0.16 0.14 0.12 0.1 Probability 0.08 0.06 0.04 0.02 0 24078000 24073000 -23600000 -23100000 -22600000 -22100000 Risk (CVaR) [in Euro] WS Budapest 10.-13..9.2003, 20 Prof. H.-J. Lüthi -21600000 21 ,4 0 22 0,0 ,2 00 0 23 0,0 ,0 00 0 23 0,0 ,8 00 0 24 0,0 ,6 00 0 25 0,0 ,4 00 0 26 0,0 ,2 00 0 27 0,0 ,0 00 0 27 0,0 ,8 00 00 ,0 00 Profit (in Euro) Profit (in Euro) Profit (in Euro) Additional Flexibility WS Budapest 10.-13..9.2003, 21 Prof. H.-J. Lüthi Slide 1 Additional Flexibility Slide 2 Risk Expected Profit: Constant 24, 2 Mio 24,0 Mio Volume WS Budapest 10.-13..9.2003, 22 Prof. H.-J. Lüthi Achievements • Guidance on how to dispatch hydro storage plants under risk / return considerations. • Not just identify but actually quantify operational flexibility with regard to handle uncertainty. • Perceive uncertainty as a challenge to flexibility instead of a threat. • Identified an important value driver in hydro storage plants (and flexible plants in general). WS Budapest 10.-13..9.2003, 23 Prof. H.-J. Lüthi
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