Hedging Strategy and Electricity Contract Engineering - IFOR

¢
zÿ V end
ì.
¢
¢
zÿ V end
ì.
¢
164 Power portfolio optimization
off-peak periods, and the hedging value of water. We hence define the value of
the operational flexibility as the difference between the marginal value of water
and the average spot price
Definition 6.10
The total value of the operational flexibility is given by
S h S h S
S.
ì zÿ V end
¢
ì zÿ V end
¢
In the case studies performed in Chapter 7, we will see that especially the
hedging value stemming from the optionality in the hydro storage plant can be
substantial.
In order to analyze the marginal value of water, we introduce the so-called
optimal value function zÛ bÝ .
Proposition 6.11
The optimal value function zÛ bÝ is piecewise linear and concave.
A proof is given in Appendix A on page 198.
is piecewise constant and increas-
Corollary 6.12
The marginal value of water, V end
ì.
ing in V end .
zÿ
ì zÿ V end
¢
Again a proof in given in Appendix A on page 199.
Observe that the value of the water stored in the dam can be expressed as the
integral of the marginal value of water over the available water, ranging from 0
to the actual available amount of water. Hence following from Corollary 6.12,
stating that the marginal value is decreasing in the available amount of water,
zÿ V end zÿ V
¢
end
is actually a lower bound for the value of the water in the dam.
ì ì.
6.6.9. Positioning of contracts and plants
The dual problem does however not only give us insight into the hedging value
of water. Instead of studying the value of additional water, we can study the