Hedging Strategy and Electricity Contract Engineering - IFOR

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152 Power portfolio optimization
Since the hydro storage plant is modeled as a series of hourly futures, the
optimal static dispatch can be seen as the optimal way to sell the available
water in the futures market. Interestingly, the optimal dispatch will not only
sell the stored water in peak hours in the best possible way, it will also
’arbitrage’ between futures in different periods.
The possibility to pump is actually a way to exchange electricity in one period
for electricity in a later period, i. e. to virtually ’store’ electricity. Since the
static dispatch strategy is solely a function of time, the value of the pumping
ability will be determined by the differences in futures prices between periods.
Or if hourly futures do not exists, the value of the pumping will be determined
by the daily and seasonal variations in the expected spot price. A risk free
portfolio can then however not be achieved. But by assuming that hourly
futures do exists, the optimal dispatch will try to ’arbitrage’ between futures in
different periods, through the hydro storage plant’s virtual storage. The price
difference needed to conduct pumping of course depends on the efficiency of
the è pump .
Let ! denote the value of the hydro storage plant with pumps in terms of the
expected profit given the optimal static strategy
!
1
J
J
lÛ xú Ü y j Ý?Ü
1 jâ
which thus is given by the solution to (6.35)-(6.44). Let ! similarly denote the
value in terms of the expected profit given the optimal static strategy xú , where
no pumping is allowed. The upper boundary on the pumping in constraint
(6.43) p min is hence set to zero. The value of the pump capacity can then be
written as ! ! .
To exemplify how this virtual storage is used, let the future prices in period 1
to 7 be as in Figure 6.5, where the price in period 0 for a future with delivery
in period k is denoted by F Û 0Ü kÝ . Now assume that the following holds
Û 0Ü 1Ý F
Û 0Ü 3Ý F
Û 0Ü 5Ý F
Û 0Ü 7Ý á F
(6.46)
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