Hedging Strategy and Electricity Contract Engineering - IFOR

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158 Power portfolio optimization
x c 2K
÷ ã ÙˆÚ ný
subject to
max
ÙˆÚ
r ø ¤ ã zÙˆÚ
J ãÑÙmÚOã LÙˆÚ K, J
J
J ì
1
J
jâ 1
lÛ x c Ü õ Ü y j Ý (6.53)
1
1 Ý
z j C (6.54)
jâ
Û J
1
z j x c lÛ Ü õ Ü y j z Ý ŒÜ j j J Ü 1Ü
(6.55)
0Ü
0 V kã j V 0
k
k
1Ü
á?á@á
kã V j V 0
k
k
I iã j
1 iâ
Ü K 1Ü j
I iã j
1Ü
á?á@á
0Ü kã 1Ü
L j k
V K V 0
1
J
r
iâ 1
ië
1Ü õ
á?á@á
k
1 iâ
J Ü
1 iâ 1
iâ
Ü K 1Ü Ü j J
K
iâ 1
á?á@á
I iã j
k
L iã j
á?á@á
Ü K 1Ü j
K
iâ 1
i
0Ü i 1Ü
ë
L iã j
k
iâ 1
á@á?á
L iã j
K
k
iâ 1
xëiã j
á?á@á
xëiã j
ì iã x Ü
j
(6.56)
ì iã x
j
V max (6.57) Ü
Ü J (6.58)
iâ 1
xëiã j
ì iã x
j
V end (6.59)
Ü r (6.60)
áaá@á
x c
iâ 1
iì
X c á
1Ü õ
i
0Ü i 1Ü
ì
áaá@á
(6.62)
Ükô (6.61)
As in the static case, (6.54) and (6.55) governs that the risk is kept below an
acceptable level, (6.56) prevents us from producing when no water is available,
(6.57) assures that we do not pump up water above the maximal accepted level
and together with (6.58) that excessive water inflow is lost through spill over.
Sustainability is again governed by (6.59). Constraint (6.60) and (6.61) put
technical limits on the dispatch and again the general constraint (6.62) can
enforce any linear contract portfolio constraint.
To penalize the scenarios where the end-water level is below the threshold V end