Operational Planning Constrained by
Financial Requirements
Guillermo Gutiérrez Gerald B. Sheblé
Iowa State University
Electricity Transmission in Deregulated Markets:
Challenges, Opportunities, and Necessary R&D Agenda
Carnegie Mellon University
December 15-16, 2004
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 1
Outline
•
•
•
•
•
•
•
Introduction
Capital Asset Pricing Method (CAPM)
Real Options Analysis
Model and Solution
Case Studies
Future work: Uncertainty modeling
Summary
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 2
Introduction
• GENCO’s objective is to maximize the profit in
future periods commensurate with the risk and return
expected.
• Bidding strategy, implemented by GENCOs in a
competitive market is essential in determining the
future cash flows.
• GENCOs need to find output decisions based on
expectations of competitors’ product consumptions,
forecasted demand, forecasted fuel prices, and
expected transmission capabilities
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 3
Capital Asset Pricing Method
β indicates how sensitive a security’s
returns are to changes in the return on
the market portfolio
Operational constraints of the generating
units, the interest rate, forecasted electricity
and fuel prices error deviation, etc, will
create a SML bandwidth
Expected Return
• CAPM is an important tool used to analyze the
relationship between risk and rate of return
Market Risk Premium
rf
1.0
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 4
Risk ( β )
Real Option Analysis
• The financial concepts applied to the electricity
market results in the spark spread option.
• The spark spread option is based on the difference
t
p
between the electricity price, E , and the price of a
t
p
particular fuel, F , used to generate it
• The spark spread payoff associated with a specific
heat rate, is defined as:
payoff = p Et − HpFt
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 5
Model and Solution
Maximize
PGt
S . to
∑ (P
T
t =1
t
G
( )) (1 + r )
p Et − C PGt
HPGt ≤ Dt
∀t = 1,..., T
PEt ≥ H ⋅ pFt
∀t = 1,..., T
PGt ≥ 0
∀t = 1,..., T
t
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 6
Model and Solution (Cont’)
Fuel
1
Energy
Fuel
1+r
…
n
1+r
Energy
N-periods production decision network flow
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 7
Case Studies
• A GENCO is designing the bidding strategy for the
next 4 periods.
• Fixed cost, variable production cost, and an
expected rate of return must be recovered
• Forecasted electricity spot prices for the
upcoming periods are assumed known.
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 8
Base case parameter values
Parameter Value
Period
Demand (MWh) Price ($/MWh)
1
500
20.0
2
600
24.3
3
550
26.5
P
MAX
(MW)
50
a ($)
b ($/MWh)
r (%)
rM (%)
120
β
1.2
Fuel ($)
21
G
1.0
8
f
4
580
28.0
12
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 9
Results
MWh
Period Power (MWh)
Prices, committed power, and revenues
$/MWh
Optimal forward power committed
30
70
25
60
1
0
2
50
20
3
50
15
4
50
50
40
30
20
10
0
1
2
3
4
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 10
Period
Results (Cont’)
Now, consider that the price in period 1 = $23.6 and in period 2 = $20.3.
MWh
Period Power (MWh)
Prices, committed power, and revenues
$/MWh
Optimal forward power committed
30
70
25
60
1
50
2
0
20
3
50
15
4
50
50
40
30
20
10
0
1
2
3
4
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 11
Period
Future Expected Profits
Period Case I ($) Case II ($)
1
- 115.248
2
129.678
3
191.604 191.604
4
216.188 216.188
NPV
10.526
-
10.78
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 12
Future work
• Uncertainty modeling
– Our approach, LP optimal
committed power for
multiple time periods can
be expanded by using the
decision tree.
– The introduction of
uncertainty for fuel and
electricity price for a given
period t can be graphically
represented as follows
Fuel price
t
t+r
Electricity price
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 13
Summary
• An intertemporal LP optimization program has
been proposed in this document.
• GENCOs operational planning is not only constrained
for its technical operational limits and fuel inventory,
but also for the financial requirements.
• By committing forward contracts in the earliest
deadline, the company will gain a flexibility option.
• Flexibility option will allow GENCo to modify
operations depending on how conditions develop as
time progresses
Guillermo Gutierrez-Alcaraz and Gerald B. Sheblé, Iowa State University 14