A Risk Analysis - the AXPO Portfolio Gustaf Unger 2002-06-19

Hedging strategy and operational flexibility in
the electricity market
Characteristics of the electricity market
• Non-storability
• Transmission constraints
• Very complex contracts
• Physical production
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Prof. H.-J. Lüthi
European Energy Exchange
Profit in 2002 (for FPD): 5'127 €/MWh
Profit in 2003 (for FPD): -15'434 €/MWh
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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
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Prof. H.-J. Lüthi
Hydro plant and Options
Is
In each period we have the
option to produce
Ls
Es
Payoff
K
xs
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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
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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
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Prof. H.-J. Lüthi
Optimal (static) portfolio
• Maximize expected profit
– Given risk constraint (measured as CVaR)
max E -l(x,  )
xX
s.t. CVaRx   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
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Prof. H.-J. Lüthi
Case study portfolio
Long positions
Short positions
Hydro plants
Swing options
Future contract
Spot contracts
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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
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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
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Prof. H.-J. Lüthi
Portfolio optimization
Spot price
Scenarios j
Inflow
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Prof. H.-J. Lüthi
Demand
Notations in Period s
Is
xs Production / Pumping
Ls
Is
Es
Inflow
Es Waterlevel
Ls Spill-over
xs
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Prof. H.-J. Lüthi
Modeling of hydro plant
i
i
i
s1
s1
s1
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
s1

s1

s1

E end  E  E 0   I s   Ls   xs
s1
P
min
 xi  P
max
s1
s1
, 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 !!!
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Prof. H.-J. Lüthi
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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
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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 
i1
Decision variables
The dispatch is allowed to react to new information
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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
i1

x    i gi S,D,I,t

i1


• 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
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Prof. H.-J. Lüthi
Portfolio optimization & hedging strategy
Dispatch strategy
No risk constraint (high C)
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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?
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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]
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-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
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Prof. H.-J. Lüthi
Slide
1
Additional Flexibility
Slide 2
Risk
Expected Profit: Constant
24, 2 Mio
24,0 Mio
Volume
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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).
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Prof. H.-J. Lüthi