Hedging Strategy and Electricity Contract Engineering - IFOR
Hedging Strategy and Electricity Contract Engineering - IFOR
Hedging Strategy and Electricity Contract Engineering - IFOR
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ìj<br />
Û 1 bë<br />
j Ý?Ü j 1Ü á?á@á<br />
ö<br />
ö<br />
õ<br />
ìj<br />
1Ü õ<br />
ìj<br />
0Ü j 1Ü<br />
ö<br />
á<br />
6.5 Analysis of optimal dispatch strategy 137<br />
ÜÑôkÜ<br />
where j denotes an index from the set of pumping thresholds<br />
r<br />
opposed to an index from the set of production thresholds Sëi iâ 1 .<br />
Sìj<br />
ö<br />
1 as jâ<br />
Using these expressions in (6.25) results in<br />
÷uø<br />
max<br />
ÙmÚ<br />
r ã<br />
÷ ý ÙˆÚ¥¤<br />
s á<br />
t á<br />
r<br />
iâ 1<br />
ë õ<br />
i<br />
aëi<br />
¦<br />
è<br />
õ<br />
ìj<br />
aëj<br />
E S (6.26)<br />
1 jâ<br />
r<br />
r<br />
iâ 1<br />
iâ 1<br />
ë õ<br />
i<br />
¦ bëi<br />
ë õ<br />
i<br />
õ<br />
ìj<br />
bë<br />
j<br />
Wú ¦<br />
1 jâ<br />
õ ë<br />
i<br />
0Ü i 1Ü<br />
1Ü<br />
Ü r<br />
á@á?á<br />
Ükô<br />
á@á?á<br />
jâ 1<br />
§ ¨ Again a is concave <strong>and</strong> monotone increasing in b as shown by Theorem 6.1<br />
<strong>and</strong> hence we can conclude<br />
Corollary 6.6<br />
In the solution of (6.26)<br />
(i) Wú If bë1 then ë1<br />
1 <strong>and</strong> õ ì<br />
1<br />
1 is optimal<br />
õ<br />
(ii) If Wú ¦ é bër ¦ bë ö<br />
then the problem is infeasible<br />
(iii) Else at most two adjacent production weights õ i 1 <strong>and</strong> ë<br />
i<br />
<strong>and</strong> at most<br />
ë õ ì<br />
two adjacent pumping weights ìj 1 <strong>and</strong> ìj<br />
will be non-zero.<br />
õ õ ì<br />
A proof is given in Appendix A on page 196. To actually derive the solution we<br />
however need to study the dual problem. Consider the dual to the productionpumping<br />
problem (6.26)
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