Hedging Strategy and Electricity Contract Engineering - IFOR

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156 Power portfolio optimization
0 V kã j V 0 Ü iã iã iã
iâ iâ iâ
JÜ 1Ü Ü 1Ü Ü Ü
á?á@á
á@á?á
V kã j V 0 iã Ü iã iã
iâ iâ iâ
I j L j x j (6.48)
k
k
k
1
1
1
k K j
I j L j x j V max (6.49)
k
k
k
1
1
1
k
L kã j 0Ü k 1Ü
1Ü
Ü K Ü j 1Ü
Ü JÜ
á?á@á
á@á?á
Ü K Ü j 1Ü
Ü J á
Further as in Chapter 6.5 we impose a constraint on the average end-water level
to avoid a myopic solution of an empty water dam at the end of the horizon
á@á?á
á@á?á
V K J ì
1
J
V 0
K
I iã j
K
L iã j
K
x iã j
(6.50)
jâ 1
iâ 1
iâ 1
iâ 1
j
Ü xëKã j and x ì 1ã j Ü Ü x
á?á@á
ìKã j
denote generating and pumping respectively
xë1ã
in each period in scenario j [MWh], which as before are given
á@á?á
Ü by
xëkã j
r
Ü J (6.51)
iâ 1
ë Û õ kã Ü Ü kã jÝaÜ kã 1Ü
i
gëi
S j D j I a k
Ü K Ü j 1Ü
á@á?á
á@á?á
x ìkã j
iâ 1
iì
i
S kã j Ü D kã j Ü I a kã j k ÝaÜ 1Ü gì Û
á@á?á
Ü K Ü j 1Ü
Ü J á
(6.52)
The exercise gì
functions gëi
and
i
are given by the step functions (6.31)
and (6.32). The weighting factors, i. e. the decision variables building
up the dispatch from the individual exercise functions are denoted by
Ü õ Ü õ
ë1 r Ü õ
1
. As in the static case, the hydro storage plant
has yet another component of decision variables, namely the spill over losses,
á@áaá
Ü Ü á@á?á
L kã j.
á@á?á