Prof. H.-J. Lüthi WS Budapest 10.-13..9.2003, 1 Hedging strategy and operational flexibility in the...

Prof. H.-J. LüthiWS Budapest 10.-13..9.2003, 1

Hedging strategy and operational flexibility in the electricity market

Characteristics of the electricity market

• Non-storability

• Transmission constraints

• Very complex contracts

• Physical production


European Energy Exchange

Profit in 2002 (for FPD): 5'127 €/MWh

Profit in 2003 (for FPD): -15'434 €/MWh


Introduction

Focus of the Study

Risk management in the electricity market

Interaction between physical production and contracts

Operational flexibility as hedging tool


Hydro plant and Options

xs

Es

I sLs

In each period we have the option to produce

Payoff

Electricity price

K = marginal cost of production

K


• If we produce today the possibility to produce tomorrow will be affected

• In each period we have the option to produce if Es > 0

Time (hourly buckets)

Max capacity, 500MW

Min capacity, -50MW

A series of interdependent options

Storage almost emptyHigh spot prices

Low spot prices


Portfolio optimization

Production portfolio

Engineering thinking

Marginal costs

Fixed costs

Flexibility

Availability

Contract engineering & Portfolio optimization

Optimal dispatch strategy

Interaction

Inflow (I)

Fuel prices

Demand (D)

Spot price (S)

Contract portfolio

Financial thinking

Exercise flexibility

Interruptability

Strike

Volume uncertainty

Optimal contract portfolio



• Maximize expected profit– Given risk constraint (measured as CVaR)

• 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

Optimal (static) portfolio

€

maxx∈X

E -l(x,ω)[ ]

s.t. CVaR x( )≤C


Case study portfolio

Long positions Short positions

Hydro plants Swing options

Future contract

Spot contracts


Modeling the Stochastics

• Jumps

• Mean reversion

Risk measure?

• Yearly seasonality

• Daily variations

Modeling the Stochastics?

Inflow

0

500

1000

1500

2000

2500

3000

3500

4000

4500

O N D J F M A M J J A S

Month

Inflow (in m

3/s)

Spot Price Electricity (European Energy Exchange)

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

O N D J F M A M J J A S

Month

Spot Price (in Euro/MWh)



Spot price

Inflow

DemandScenarios j


Notations in Period s

xs

Es

I sLs

xs Production / Pumping

Is Inflow

Es Waterlevel

Ls Spill-over


Modeling of hydro plant

Li ≥0 ,i =1,...,v

€

0≤Ei =E0 + Is − Lss=1

i

∑ − xs, i=1,...,vs=1

i

∑s=1

i

∑

€

Emax≥Ei =E0 + I s− Lss=1

i

∑ − xss=1

i

∑s=1

i

∑ , i=1,...,v

€

Pmin ≤xi ≤Pmax, i=1,...,v

€

E end≤Eν =E0 + I s− Lss=1

ν

∑ − xss=1

ν

∑s=1

ν

∑

Don’t produce when storage empty

Don’t pump when storage full

Leave water for future production

Technical constraint

Note: E, I, and L are stochastic variables !!!


Dispatch Policy

0

10000

20000

30000

40000

50000

60000

70000

Month

Water Level

Real Dispatch

Optimized Dispatch


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


Modeling exercise conditions

• Let the decision variable determine exercise conditions instead of the actual dispatch in each period

The dispatch is allowed to react to new information

€

xs = γigi S,D,I( )i=1

r

∑

Decision variables

Exercise condition


• Pure profit maximization dispatch is a step function

• Risk averse case convex combination of step functions

• The step functions and are given exogenously and the weighting

factors and are decision variables

• Can optimize the complex hydro storage plant with LP

Hydro dispatch strategy

€

gi+

€

gi−

€

γi+

€

γi−


Portfolio optimization & hedging strategy

Dispatch strategy

Tight risk constraint (low C)No risk constraint (high C)


Hedging strategy

• Uncertain demand is risky

• Cannot hedge with standardized contracts

• Operational flexibility to hedge against volume risk

What is the operational flexibility worth?


Enlarged Efficiency Fontier

24073000

24078000

24083000

24088000

24093000

24098000

-23600000 -23100000 -22600000 -22100000 -21600000

Risk (CVaR) [in Euro]

Profit (in Euro)

00.10.20.30.40.50.6

Probability

21,400,00022,200,00023,000,00023,800,00024,600,00025,400,00026,200,00027,000,00027,800,000

Profit (in Euro)

Profit Distribution for CVaR = -23,500,000 Euro(Expected Profit: 24,083,091.74)

00.020.040.060.080.1

0.120.140.16

Probability

21,400,00022,200,00023,000,00023,800,00024,600,00025,400,00026,200,00027,000,00027,800,000

Profit (in Euro)

Profit Distribution for CVaR = -21,600,000 Euro(Expected Profit: 24,095,411.84)


Additional FlexibilitySlide

1


Additional Flexibility

Expected Profit: Constant

Slide 2

Volume

Risk

24,0 Mio

24, 2 Mio


• 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).

Achievements

Prof. H.-J. Lüthi WS Budapest 10.-13..9.2003, 1 Hedging strategy and operational flexibility in the...

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