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▼♦❞❡❧✐♥❣ ❛♥❞ ❋♦r❡❝❛st✐♥❣ ❊❧❡❝tr✐❝✐t② ❙♣♦t Pr✐❝❡s✿ ❆ ❋✉♥❝t✐♦♥❛❧ ❉❛t❛ P❡rs♣❡❝t✐✈❡ ❉♦♠✐♥✐❦ ▲✐❡❜❧ ❯♥✐✈❡rs✐t② ♦❢ ❈♦❧♦❣♥❡ ✴ ❇♦♥♥ ✼è♠❡s ❏♦✉r♥é❡s ❞❡ ❙t❛t✐st✐q✉❡ ❋♦♥❝t✐♦♥♥❡❧❧❡ ❡t ❖♣ér❛t✐♦♥♥❡❧❧❡ ▼♦♥t♣❡❧❧✐❡r ✷✵✶✷

❉❛t❛ ✫ ■❞❡❛ ❚✐♠❡✲❙❡r✐❡s ♦❢ ❊❧❡❝tr✐❝✐t② ❙♣♦t Pr✐❝❡s 200 150 EUR/MWh 100 50 0 0 2000 4000 6000 8000 10000 12000 14000 Workingdays (Jan.2006−Jun.2008)

❉❛t❛ ✫ ■❞❡❛ ❚✐♠❡✲❙❡r✐❡s ♦❢ ❊❧❡❝tr✐❝✐t② ❙♣♦t Pr✐❝❡s Workingdays: Mo. 3. − Fr. 7. Mar. 2008 80 60 EUR/MWh 40 20 0 20 40 60 80 100 120 Hours

❉❛t❛ ✫ ■❞❡❛ ❚✐♠❡✲❙❡r✐❡s ♦❢ Pr✐❝❡✲❉❡♠❛♥❞ ❋✉♥❝t✐♦♥s ( ❳ t ) Mo. 3. Mar. 2008 Tu. 4. Mar. 2008 We. 5. Mar. 2008 ● ● 80 80 80 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 60 60 60 ● ● ● ● ● ● ● EUR/MWh ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 40 40 40 ● ● ● ● ● ● ● ● ● 20 20 20 ● ● ● 40000 50000 60000 40000 50000 60000 40000 50000 60000 MW MW MW

❉❛t❛ ✫ ■❞❡❛ ❊❝♦♥♦♠✐❝ ❏✉st✐✜❝❛t✐♦♥✿ ▼❡r✐t✲❖r❞❡r ▼♦❞❡❧

❉❛t❛ ✫ ■❞❡❛ ❚✐♠❡✲❙❡r✐❡s ♦❢ Pr✐❝❡✲❉❡♠❛♥❞ ❋✉♥❝t✐♦♥s ( ❳ t ) 200 100 150 80 EUR/MWh EUR/MWh 100 60 50 40 20 0 40000 50000 60000 70000 0 100 200 300 400 500 600 MW Workingdays (Jan.2006−Jun.2008)

❉❛t❛ ✫ ■❞❡❛ ❖✉t❧✐♥❡ ✶✳ ❉❛t❛ ✫ ■❞❡❛ ✷✳ ❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮ ✸✳ ✷✲❙t❡♣ ❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ✹✳ ❆♣♣❧✐❝❛t✐♦♥ ✹✳✶ ❋♦r❡❝❛st✐♥❣

❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮ ▼♦❞❡❧ ✫ ❆ss✉♠♣t✐♦♥s ② t❤ = ❳ t ( ✉ t❤ ) + ε t❤ 90 ● ● ● ● ● ● ● ● 80 ● ● 70 ● ● ● ● ● EUR/MWh ● 60 ● ● 50 ● ● 40 ● ● ● 30 ● 45000 50000 55000 60000 65000 MW

❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮ ▼♦❞❡❧ ✫ ❆ss✉♠♣t✐♦♥s ✲ ❋♦r♠❛❧❧② ② t❤ = ❳ t ( ✉ t❤ ) + ε t❤ ❆ss✉♠♣t✐♦♥s✿ ◮ ② t❤ ∈ R ❛♥❞ ❳ t ∈ H ❑ ✱ ∀ t ∈ { ✶ , . . . , ❚ } , ∀ ❤ ∈ { ✶ , . . . , ◆ t } ◮ H ❑ ⊂ ▲ ✷ [ ❆ , ❇ ] ✇✐t❤ ❞✐♠ ( H ❑ ) = ❑ ◮ ( ε t❤ ) ❤ = ✶ ,..., ◆ t ✿ ❲❤✐t❡✲♥♦✐s❡ ♣r♦❝❡ss

❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮ ▼♦❞❡❧ ✫ ❆ss✉♠♣t✐♦♥s ❑ � ❳ t ( ✉ ) = β t❦ ❢ ❦ ( ✉ ) ❦ = ✶ ^ ^ β t1 and β t2 200 25000 100 150 20000 EUR/MWh 15000 EUR/MWh 100 50 10000 50 0 5000 0 0 40000 50000 60000 70000 0 100 200 300 400 500 600 30000 40000 50000 60000 70000 MW Working−Days (1. Jan. 2006 − 30. Jun. 2008) MW

❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮ ▼♦❞❡❧ ✫ ❆ss✉♠♣t✐♦♥s ✲ ❋♦r♠❛❧❧② ◮ ❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧✿ ❑ � ❳ t = β t❦ ❢ ❦ ❢♦r ❛❧❧ t ∈ { ✶ , . . . , ❚ } ❦ = ✶ ❢ ❦ ∈ ▲ ✷ [ ❆ , ❇ ] H ❑ = s♣❛♥ ( ❢ ✶ , . . . , ❢ ❑ ) ✇✐t❤ ⊲ ❖rt❤♦♥♦r♠❛❧ ❇❛s✐s✲❙②st❡♠✿ { ❢ ✶ , . . . , ❢ ❑ } � ❇ ⊲ Pr♦❥❡❝t✐♦♥ P❛r❛♠❡t❡rs✿ β t❦ = ❆ ❳ t ( ✉ ) ❢ ❦ ( ✉ ) ❞✉

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ✶ st ❙t❡♣✿ Pr✐❝❡✲❉❡♠❛♥❞ ❋✉♥❝t✐♦♥s ❳ t ❊❛❝❤ ❢✉♥❝t✐♦♥ ❳ t ✐s ❡st✐♠❛t❡❞ ❜② ♠✐♥✐♠✐③✐♥❣ � ❜ t ◆ t � ( ② t❤ − X ( ✉ t❤ )) ✷ + ❜ ( ❉ ✷ X ( ✉ )) ✷ ❞✉ � ❳ t = ❛r❣♠✐♥ X ❛ t ❤ = ✶ ♦✈❡r ❛❧❧ ✷✲t✐♠❡s ❝♦♥t✐♥✉♦✉s❧② ❞✐✛❡r❡♥t✐❛❜❧❡ ❢✉♥❝t✐♦♥s X ✳ 90 ● ● ● ● ● ● ● ● ◮ ❉ ✷ X ❞❡♥♦t❡s t❤❡ ✷✲♥❞ 80 ● ● 70 ● ● ❞❡r✐✈❛t✐✈❡ ♦❢ X ● ● ● EUR/MWh ● 60 ● ● ◮ ❯♥❞❡rs♠♦♦t❤✐♥❣✿ 50 ● ● ❜ < ❜ ♦♣t 40 ● 30 ● ● ● 45000 50000 55000 60000 65000 MW

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ❇❛s✐s ❙②st❡♠ { ❢ ✶ , . . . , ❢ ❑ } ●✐✈❡♥ ♦✉r ❛ss✉♠♣t✐♦♥s ♦♥ ( ❳ t ) ✇❡ ❤❛✈❡ ❚ ❑ ❚ ❑ � � � � β t❦ ❢ ❦ || ✷ γ t❦ ❣ ❦ || ✷ || ❳ t − = γ t ✶ ,...,γ t❑ ∈ R || ❳ t − ♠✐♥ ♠✐♥ ✷ ✷ ❇ ❑ t = ✶ ❦ = ✶ t = ✶ ❦ = ✶ ♦✈❡r ❛❧❧ ❑ ✲❞✐♠✳ ♦rt❤♦♥♦r♠❛❧ ❜❛s✐s s②st❡♠s ❇ ❑ = { ❣ ✶ , . . . , ❣ ❑ }

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ❇❛s✐s ❙②st❡♠ { ❢ ✶ , . . . , ❢ ❑ } ❙t❛♥❞❛r❞✐③❡❞ Pr✐❝❡✲❉❡♠❛♥❞ ❋❝t✬s✿ ❚ ❑ ❚ ❑ � � � � || ❳ ∗ β ∗ t❦ ❢ ❦ || ✷ γ t ✶ ,...,γ t❑ ∈ R || ❳ ∗ γ t❦ ❣ ❦ || ✷ t − = ♠✐♥ ♠✐♥ t − ✷ ✷ ❇ ❑ t = ✶ ❦ = ✶ t = ✶ ❦ = ✶ ✇✐t❤ ❳ ∗ t = ( ❳ t / || ❳ t || ✷ ) ✳

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ❆♥❛❧②t✐❝ ❙♦❧✉t✐♦♥ ❚❤❡ ❡♠♣✐r✐❝❛❧ ❡✐❣❡♥❢✉♥❝t✐♦♥s ❡ ❚ , ✶ , . . . , ❡ ❚ , ❑ ✱ t❤❛t ❜❡❧♦♥❣ t♦ t❤❡ ❑ ❣r❡❛t❡st ❡✐❣❡♥✈❛❧✉❡s λ ❚ , ✶ > λ ❚ , ✷ > · · · > λ ❚ , ❑ > ✵ ♦❢ t❤❡ ❡♠♣✐r✐❝❛❧ ❝♦✈❛r✐❛♥❝❡ ♦♣❡r❛t♦r Γ ❚ ✱ ❛r❡ t❤❡ ❜❡st ❜❛s✐s ❢❛❝t♦rs ✐♥ t❤❡ s❡♥s❡ t❤❛t t❤❡② ♠✐♥✐♠✐③❡ ❢♦r ❛♥② ❑ ≤ ❚ � ❚ � ❑ � ❚ � ❑ t❦ ❢ ❦ || ✷ γ t❦ ❣ ❦ || ✷ || ❳ ∗ β ∗ γ t ✶ ,...,γ t❑ ∈ R || ❳ ∗ t − = ♠✐♥ ♠✐♥ t − ✷ ✷ ❇ ❑ t = ✶ ❦ = ✶ t = ✶ ❦ = ✶ ❲❤❡r❡✿ � ❇ ❢♦r ❛❧❧ ① ∈ ▲ ✷ [ ❆ , ❇ ] ◮ (Γ ❚ ① )( ✉ ) = ❆ γ ❚ ( ✉ , ✈ ) ① ( ✈ ) ❞✈ ◮ γ ❚ ( ✉ , ✈ ) = ❚ − ✶ � ❚ t ❳ t ( ✉ ) ❳ t ( ✈ ) ❢♦r ❛❧❧ ✉ , ✈ ∈ [ ❆ , ❇ ]

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ❘❛♥❞♦♠ ❉♦♠❛✐♥s [ ❛ t , ❜ t ] ⊆ [ ❆ , ❇ ] ◗✉❡st✐♦♥✿ ✲ ❈♦♠♣✉t❛t✐♦♥ ♦❢ 200 γ ❚ ( ✉ , ✈ ) = � ❚ − ✶ � ❚ t � t ( ✉ ) � ❳ ∗ ❳ ∗ t ( ✈ ) ❄ 150 EUR/MWh 100 ❙♦❧✉t✐♦♥✿ 50 ✲ � γ ❚ ( ✉ , ✈ ) ❜② ❧♦❝❛❧ ❧✐♥❡❛r s✉r❢❛❝❡ s♠♦♦t❤✐♥❣ 0 40000 50000 60000 70000 ✭❙❡❡ ❡✳❣✳ ❨❛♦✱ ❡t MW ❛❧✳ ✷✵✵✺✱ ❏❆❙❆✮

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ❈♦✈❛r✐❛♥❝❡✲❋✉♥❝t✐♦♥ 0.04 0.02 60000 MW 40000 60000 40000 M W

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ❯♥❞❡rs♠♦♦t❤✐♥❣ ❛♥❞ ❙❡❧❡❝t✐♦♥ ♦❢ ❉✐♠✳ ❑ ◮ ❈❱✲❯♥❞❡rs♠♦♦t❤✐♥❣✿ � � ❚ ◆ t ❑ � � � γ t❦ � ❈❱ ( ❜ , ❑ ) = ② t❤ − � ❢ ❦ , − t ( ✉ t❤ ) t = ✶ ✐ = ✶ ❦ = ✶ ◮ ❙❡❧❡❝t✐♦♥ ♦❢ ❉✐♠✳ ❑ ✿ ❆■❈✲t②♣❡ ❝r✐t❡r✐♦♥ ✭❙❡❡ ❡✳❣✳ ❨❛♦✱ ❡t ❛❧✳ ✷✵✵✺✱ ❏❆❙❆✮

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡ ✷ ♥❞ ❊st✐♠❛t✐♦♥ ❙t❡♣✿ ❘❡✲❊st✐♠❛t❡ ❳ t � ❑ � � β t❦ � � ❳ t := ❢ ❦ ❦ = ✶ ^ ^ β t1 and β t2 200 25000 100 150 20000 EUR/MWh 15000 EUR/MWh 100 50 10000 50 0 5000 0 0 40000 50000 60000 70000 0 100 200 300 400 500 600 30000 40000 50000 60000 70000 MW Working−Days (1. Jan. 2006 − 30. Jun. 2008) MW ◮ Pr♦❥❡❝t✐♦♥ P❛r❛♠❡t❡rs � β t❦ ✿ ❱✐❛ ❖▲❙ ♦❢ ② t❤ ♦♥ � ❢ ✶ ❛♥❞ � ❢ ✷

❆♣♣❧✐❝❛t✐♦♥ ❉❛t❛ ◮ ❍♦✉r❧② ❡❧❡❝tr✐❝✐t② s♣♦t ♣r✐❝❡s ✭❊❊❳✮ ◮ ❍♦✉r❧② ❡❧❡❝tr✐❝✐t② ❞❡♠❛♥❞ ✭❊◆❚❙❖❊✮ ❈♦rr❡❝t❡❞ ❜② ❲✐♥❞✐♥❢❡❡❞s ✭✺✵ ❍❡rt③✱ ❆♠♣r✐♦♥✱ ❊♥❇❲✲❚◆●✱ ❛♥❞ ❚❡♥♥❡❚✮ ◮ ❚✐♠❡ s♣❛♥✿ ❋r♦♠ ❏❛♥✲✷✵✵✻ t♦ ❏✉♥✲✷✵✵✽