Hedging Strategy and Electricity Contract Engineering - IFOR

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6.6 Power portfolio optimization with CVaR 163
the time horizon studied. Hence, the optimal dual variable yú6 corresponding
to the sixth constraint and consequently the ’resource’ V end will give us the
value of one unit of additional water V ì. ì zÿ end
¢
V end
, i. e. the marginal value
of water. One could argue that for an almost empty dam the value of having
the possibility to leave one unit less of water to the periods after the zÿ horizon
will differ from having one additional unit of water at disposal already at
period one. When the constraints (6.56) and (6.57), stating that for all k and
j, 0 V kã j V max , are not binding then these values will however coincide.
In any case the dual variable yú6
will give the marginal value of water made
available in the end of the horizon.
The dimension of the dual variable yú6
is expected profit divided by amount of
water [CHF/MWh] and is hence comparable with the average price of produced
electricity S h . A marginal value of water that exceeds the value that this water,
on average, has on the market, given the current dispatch strategy S h is a result
of the hydro storage plant’s ability to manage risk. This ability allows us, for
example, to take on more aggressive positions in the contract portfolio, which
motivates a high marginal value of water. We hence quantify the hedging value
of water as the difference between the marginal value of water and the average
price of produced electricity
Definition 6.9
The hedging value of water is given by
zÿ V end
ì.
S h ,
zÿ
¢
V end
ì
which in the non-degenerate case will equal
yú6
S h .
From Proposition 6.5 we know that the hedging value will be negative if the
risk constraint and the water constraints (6.56) and (6.57) are non-binding.
This difference will however typically be close to zero. 5
In the risk averse case the value of the operational flexibility thus can be seen as
the sum of the ability to produce at high prices and arbitrage between peak and
5 This is verified in the case study in Chapter 7.