Hedging Strategy and Electricity Contract Engineering - IFOR

124 Power portfolio optimization
p min x k p max k 1Ü Ü Ü K Ü (6.3)
á@á?á
where the amount of stored water in period k is given by
V k V 0
k
I i
k
L i
k
iâ 1
iâ 1
iâ 1
x i Ü k 1Ü
Ü K á
(6.4)
á?á@á
We can however not guarantee that a static dispatch strategy, which is only
allowed to be a function of time will fulfill the probabilistic constraint (6.2). It
is actually very likely that it will be violated for any such strategy if the inflow
is random. We note this immediate drawback of the static dispatch strategy and
relax (6.2) to
0 V k V max k 1Ü Ü Ü K Ü (6.5)
á?á@á
where V k denotes the average amount of water, which is naturally given by
V k V 0
k
I i
k
L i
k
iâ 1
iâ 1
iâ 1
x i Ü k 1Ü
Ü K á
(6.6)
á?á@á
Observe that E x k x k , since x is not a random variable. As a matter of fact
the decision variables associated with dispatching the hydro storage plant is in
this static approach given by x p x Û 1 Ü Ü x K Ý . Further, note that the average
spill over L
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k will be non-zero, only when the average inflow I k is greater than
the maximum possible production p max in combination with a full dam, when
applied in a expected profit maximization. If we are not modeling the plant
over its whole life time, which can be over 50 years, we need to avoid a myopic
strategy, that could leave an empty dam for the periods following after the
horizon. Hence we impose a lower limit V end on the average amount of water
left for subsequent periods V K
V K V end (6.7)
á
Note, as seen in (6.6) our modeling of the plant (6.3), (6.5) and (6.7) is now
actually deterministic.