rst trt - - PowerPoint PPT Presentation

▶
r st tr t t
SMART_READER_LITE
LIVE PREVIEW

rst trt - - PowerPoint PPT Presentation

Feb 06, 2023 257 likes •568 views

rst trt t Prs t t Prst

slide-1
SLIDE 1

▼♦❞❡❧✐♥❣ ❛♥❞ ❋♦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 ✷✵✶✷

slide-2
SLIDE 2

❉❛t❛ ✫ ■❞❡❛

❚✐♠❡✲❙❡r✐❡s ♦❢ ❊❧❡❝tr✐❝✐t② ❙♣♦t Pr✐❝❡s

Workingdays (Jan.2006−Jun.2008) EUR/MWh 2000 4000 6000 8000 10000 12000 14000 50 100 150 200

slide-3
SLIDE 3

❉❛t❛ ✫ ■❞❡❛

❚✐♠❡✲❙❡r✐❡s ♦❢ ❊❧❡❝tr✐❝✐t② ❙♣♦t Pr✐❝❡s

20 40 60 80 100 120 20 40 60 80

Workingdays: Mo. 3. − Fr. 7. Mar. 2008

Hours EUR/MWh

slide-4
SLIDE 4

❉❛t❛ ✫ ■❞❡❛

❚✐♠❡✲❙❡r✐❡s ♦❢ Pr✐❝❡✲❉❡♠❛♥❞ ❋✉♥❝t✐♦♥s (❳t)

  • ●

40000 50000 60000 20 40 60 80

  • Mo. 3. Mar. 2008

MW EUR/MWh

  • ●
  • 40000

50000 60000 20 40 60 80

  • Tu. 4. Mar. 2008

MW

  • 40000

50000 60000 20 40 60 80

  • We. 5. Mar. 2008

MW

slide-5
SLIDE 5

❉❛t❛ ✫ ■❞❡❛

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

slide-6
SLIDE 6

❉❛t❛ ✫ ■❞❡❛

❚✐♠❡✲❙❡r✐❡s ♦❢ Pr✐❝❡✲❉❡♠❛♥❞ ❋✉♥❝t✐♦♥s (❳t)

40000 50000 60000 70000 50 100 150 200 MW EUR/MWh 100 200 300 400 500 600 20 40 60 80 100 Workingdays (Jan.2006−Jun.2008) EUR/MWh

slide-7
SLIDE 7

❉❛t❛ ✫ ■❞❡❛

❖✉t❧✐♥❡

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

✹✳✶ ❋♦r❡❝❛st✐♥❣

slide-8
SLIDE 8

❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮

▼♦❞❡❧ ✫ ❆ss✉♠♣t✐♦♥s

②t❤ = ❳t(✉t❤) + εt❤

MW EUR/MWh

45000 50000 55000 60000 65000 30 40 50 60 70 80 90

slide-9
SLIDE 9

❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮

▼♦❞❡❧ ✫ ❆ss✉♠♣t✐♦♥s ✲ ❋♦r♠❛❧❧②

②t❤ = ❳t(✉t❤) + εt❤

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

slide-10
SLIDE 10

❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮

▼♦❞❡❧ ✫ ❆ss✉♠♣t✐♦♥s

❳t(✉) =

❑

  • ❦=✶

βt❦ ❢❦(✉)

40000 50000 60000 70000 50 100 150 200 MW EUR/MWh

β ^

t1 and β

^

t2 Working−Days (1. Jan. 2006 − 30. Jun. 2008) 100 200 300 400 500 600 5000 10000 15000 20000 25000 30000 40000 50000 60000 70000 50 100 MW EUR/MWh
slide-11
SLIDE 11

❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧ ✭❋❋▼✮

▼♦❞❡❧ ✫ ❆ss✉♠♣t✐♦♥s ✲ ❋♦r♠❛❧❧②

◮ ❋✉♥❝t✐♦♥❛❧ ❋❛❝t♦r ▼♦❞❡❧✿ ❳t =

❑

  • ❦=✶

βt❦❢❦ ❢♦r ❛❧❧ t ∈ {✶, . . . , ❚} H❑ = s♣❛♥(❢✶, . . . , ❢❑) ✇✐t❤ ❢❦ ∈ ▲✷[❆, ❇]

⊲ ❖rt❤♦♥♦r♠❛❧ ❇❛s✐s✲❙②st❡♠✿ {❢✶, . . . , ❢❑} ⊲ Pr♦❥❡❝t✐♦♥ P❛r❛♠❡t❡rs✿ βt❦ = ❇

❆ ❳t(✉) ❢❦(✉) ❞✉

slide-12
SLIDE 12

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡

✶st ❙t❡♣✿ Pr✐❝❡✲❉❡♠❛♥❞ ❋✉♥❝t✐♦♥s ❳t

❊❛❝❤ ❢✉♥❝t✐♦♥ ❳t ✐s ❡st✐♠❛t❡❞ ❜② ♠✐♥✐♠✐③✐♥❣

  • ❳t

= ❛r❣♠✐♥

X ◆t

  • ❤=✶

(②t❤ − X(✉t❤))✷ + ❜ ❜t

❛t

(❉✷X(✉))✷ ❞✉ ♦✈❡r ❛❧❧ ✷✲t✐♠❡s ❝♦♥t✐♥✉♦✉s❧② ❞✐✛❡r❡♥t✐❛❜❧❡ ❢✉♥❝t✐♦♥s X✳ ◮ ❉✷X ❞❡♥♦t❡s t❤❡ ✷✲♥❞ ❞❡r✐✈❛t✐✈❡ ♦❢ X ◮ ❯♥❞❡rs♠♦♦t❤✐♥❣✿ ❜ < ❜♦♣t

MW EUR/MWh

45000 50000 55000 60000 65000 30 40 50 60 70 80 90

slide-13
SLIDE 13

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡

❇❛s✐s ❙②st❡♠ {❢✶, . . . , ❢❑}

  • ✐✈❡♥ ♦✉r ❛ss✉♠♣t✐♦♥s ♦♥ (❳t) ✇❡ ❤❛✈❡

❚

  • t=✶

||❳t −

❑

  • ❦=✶

βt❦❢❦||✷

✷

= ♠✐♥

❇❑ ❚

  • t=✶

♠✐♥

γt✶,...,γt❑∈R||❳t − ❑

  • ❦=✶

γt❦❣❦||✷

✷

♦✈❡r ❛❧❧ ❑✲❞✐♠✳ ♦rt❤♦♥♦r♠❛❧ ❜❛s✐s s②st❡♠s ❇❑ = {❣✶, . . . , ❣❑}

slide-14
SLIDE 14

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡

❇❛s✐s ❙②st❡♠ {❢✶, . . . , ❢❑}

❙t❛♥❞❛r❞✐③❡❞ Pr✐❝❡✲❉❡♠❛♥❞ ❋❝t✬s✿

❚

  • t=✶

||❳ ∗

t − ❑

  • ❦=✶

β∗

t❦❢❦||✷ ✷

= ♠✐♥

❇❑ ❚

  • t=✶

♠✐♥

γt✶,...,γt❑∈R||❳ ∗ t − ❑

  • ❦=✶

γt❦❣❦||✷

✷

✇✐t❤ ❳ ∗

t = (❳t/||❳t||✷)✳

slide-15
SLIDE 15

❊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=✶

||❳ ∗

t − ❑

  • ❦=✶

β∗

t❦❢❦||✷ ✷

= ♠✐♥

❇❑ ❚

  • t=✶

♠✐♥

γt✶,...,γt❑ ∈R||❳ ∗ t − ❑

  • ❦=✶

γt❦❣❦||✷

✷

❲❤❡r❡✿ ◮ (Γ❚①)(✉) = ❇

❆ γ❚(✉, ✈)①(✈)❞✈

❢♦r ❛❧❧ ① ∈ ▲✷[❆, ❇] ◮ γ❚(✉, ✈) = ❚ −✶ ❚

t ❳t(✉)❳t(✈)

❢♦r ❛❧❧ ✉, ✈ ∈ [❆, ❇]

slide-16
SLIDE 16

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡

❘❛♥❞♦♠ ❉♦♠❛✐♥s [❛t, ❜t] ⊆ [❆, ❇]

40000 50000 60000 70000 50 100 150 200 MW EUR/MWh

◗✉❡st✐♦♥✿ ✲ ❈♦♠♣✉t❛t✐♦♥ ♦❢

  • γ❚(✉, ✈) =

❚ −✶ ❚

t

❳ ∗

t (✉)

❳ ∗

t (✈)❄

❙♦❧✉t✐♦♥✿ ✲ γ❚(✉, ✈) ❜② ❧♦❝❛❧ ❧✐♥❡❛r s✉r❢❛❝❡ s♠♦♦t❤✐♥❣ ✭❙❡❡ ❡✳❣✳ ❨❛♦✱ ❡t ❛❧✳ ✷✵✵✺✱ ❏❆❙❆✮

slide-17
SLIDE 17

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡

❈♦✈❛r✐❛♥❝❡✲❋✉♥❝t✐♦♥

M W 40000 60000 MW 40000 60000 0.02 0.04

slide-18
SLIDE 18

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡

❯♥❞❡rs♠♦♦t❤✐♥❣ ❛♥❞ ❙❡❧❡❝t✐♦♥ ♦❢ ❉✐♠✳ ❑

◮ ❈❱✲❯♥❞❡rs♠♦♦t❤✐♥❣✿ ❈❱ (❜, ❑) =

❚

  • t=✶

◆t

  • ✐=✶
  • ②t❤ −

❑

  • ❦=✶
  • γt❦

❢❦,−t(✉t❤)

  • ◮ ❙❡❧❡❝t✐♦♥ ♦❢ ❉✐♠✳ ❑✿

❆■❈✲t②♣❡ ❝r✐t❡r✐♦♥ ✭❙❡❡ ❡✳❣✳ ❨❛♦✱ ❡t ❛❧✳ ✷✵✵✺✱ ❏❆❙❆✮

slide-19
SLIDE 19

❊st✐♠❛t✐♦♥✲Pr♦❝❡❞✉r❡

✷♥❞ ❊st✐♠❛t✐♦♥ ❙t❡♣✿ ❘❡✲❊st✐♠❛t❡ ❳t

  • ❳t

:=

  • ❑
  • ❦=✶
  • βt❦

❢❦

40000 50000 60000 70000 50 100 150 200 MW EUR/MWh

β ^

t1 and β

^

t2 Working−Days (1. Jan. 2006 − 30. Jun. 2008) 100 200 300 400 500 600 5000 10000 15000 20000 25000 30000 40000 50000 60000 70000 50 100 MW EUR/MWh

◮ Pr♦❥❡❝t✐♦♥ P❛r❛♠❡t❡rs βt❦✿ ❱✐❛ ❖▲❙ ♦❢ ②t❤ ♦♥ ❢✶ ❛♥❞ ❢✷

slide-20
SLIDE 20

❆♣♣❧✐❝❛t✐♦♥

❉❛t❛

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

slide-21
SLIDE 21

❆♣♣❧✐❝❛t✐♦♥

❈❱✲❯♥❞❡rs♠t❤✳✲P❛r❛♠✳ ❑ ❆■❈ ✺❡ + ✵✾ (< ✸✺❡ + ✾) ✶ ✼✼✼✻✻✳✶✷ ✼❡ + ✵✾ (< ✸✺❡ + ✾) ✷ ✼✼✶✻✾✳✼✺ ✶✵❡ + ✵✾ (< ✸✺❡ + ✾) ✸ ✼✼✷✷✷✳✻✹

◮ ❋✐rst t✇♦ ❊✐❣❡♥❢✉♥❝t✐♦♥s✿ ❢✶ ❛♥❞ ❢✷ ❡①♣❧❛✐♥✿ ✺✼.✽✻% ❛♥❞ ✹✷.✵✽% ♦❢ t❤❡ t♦t❛❧ s❛♠♣❧❡ ✈❛r✐❛♥❝❡✳

30000 40000 50000 60000 70000 50 100 MW EUR/MWh
slide-22
SLIDE 22

❆♣♣❧✐❝❛t✐♦♥

❱❛❧✐❞❛t✐♦♥✿ ❚✐♠❡ ❈♦♥st❛♥t ❋❛❝t♦rs

  • ❡(✻✲✶)

✶

  • ❡(✻✲✶)

✷

  • ❡(✻✲✷)

✶

  • ❡(✻✲✷)

✷

  • ❡(✼✲✶)

✶

  • ❡(✼✲✶)

✷

  • ❡(✼✲✷)

✶

  • ❡(✼✲✷)

✷

  • ❡(✽✲✶)

✶

  • ❡(✽✲✶)

✷

{ ❡(✻✲✶)

✶

, ❡(✻✲✶)

✷

} ✖ ✖ ✵✳✾✾ ✵✳✾✹ ✶✳✵✵ ✵✳✾✼ ✶✳✵✵ ✵✳✽✾ ✶✳✵✵ ✵✳✾✾ { ❡(✻✲✷)

✶

, ❡(✻✲✷)

✷

} ✵✳✾✾ ✵✳✾✹ ✖ ✖ ✵✳✾✾ ✵✳✽✸ ✶✳✵✵ ✵✳✾✽ ✶✳✵✵ ✵✳✾✹ { ❡(✼✲✶)

✶

, ❡(✼✲✶)

✷

} ✶✳✵✵ ✵✳✾✼ ✵✳✾✾ ✵✳✽✸ ✖ ✖ ✶✳✵✵ ✵✳✼✼ ✶✳✵✵ ✵✳✾✻ { ❡(✼✲✷)

✶

, ❡(✼✲✷)

✷

} ✶✳✵✵ ✵✳✽✾ ✶✳✵✵ ✵✳✾✽ ✶✳✵✵ ✵✳✼✼ ✖ ✖ ✶✳✵✵ ✵✳✽✾ { ❡(✽✲✶)

✶

, ❡(✽✲✶)

✷

} ✶✳✵✵ ✵✳✾✾ ✵✳✾✾ ✵✳✾✹ ✶✳✵✵ ✵✳✾✻ ✶✳✵✵ ✵✳✽✾ ✖ ✖ { ❡✶, ❡✷} ✶✳✵✵ ✵✳✾✾ ✶✳✵✵ ✵✳✾✻ ✶✳✵✵ ✵✳✾✺ ✶✳✵✵ ✵✳✾✵ ✶✳✵✵ ✶✳✵✵

  • ❢❦(✉)−❢❦(✉) =
  • ❧=❦
  • ✶

❚(λ❦ − λ❧)

❚

  • t=✶

β❧tβ❦t

  • ❢❧(t)+❘❦(t)

✇✐t❤ ||❘❦|| = OP(❚ −✶) ✭✶✮ ❇❡♥❦♦✱ ▼✳✱ ❍är❞❧❡✱ ❲✳✱ ❛♥❞ ❑♥❡✐♣✱ ❆✳ ✭✷✵✵✾✮ ❆❖❙

slide-23
SLIDE 23

❆♣♣❧✐❝❛t✐♦♥

Pr♦❥❡❝t✐♦♥ P❛r❛♠❡t❡rs ( βt✶) ❛♥❞ ( βt✷)

β ^t1 and β ^t2

Working−Days (1. Jan. 2006 − 30. Jun. 2008) 100 200 300 400 500 600 5000 10000 15000 20000 25000

slide-24
SLIDE 24

❆♣♣❧✐❝❛t✐♦♥ ❋♦r❡❝❛st✐♥❣

▲✐♥❡❛r ❋♦r❡❝❛sts✿ ℓ✲❉❛②s ❆❤❡❛❞

◮ ▲❡❛r♥✐♥❣ s❛♠♣❧❡✿ t ∈ {✶, . . . , ❚ ▲} ❱❛❧✐❞❛t✐♦♥ s❛♠♣❧❡✿ t ∈ {❚ ▲ + ✶, . . . , ❚} ❚ ▲ = ✺✵✵ ❛♥❞ ❚ = ✺✼✾ ②❚ ▲,❤(ℓ) =

✷

  • ❦=✶
  • β❚ ▲,❦(ℓ)

❢❦

  • ✉❚ ▲,❤(ℓ)
  • ⊲ ❙❆❘■▼❆(✹, ✶, ✵) × (✵, ✵, ✷)✺✲♠♦❞❡❧s ❢♦r

β❚ ▲,❦(ℓ) ⊲ ✏❲♦rst ❋♦r❡❝❛st✑✿ ✉❚ ▲,❤(ℓ) :=▲❛st ❖❜s❡r✈❛t✐♦♥ ⊲ ✏❇❡st ❋♦r❡❝❛st ✑✿ ✉❚ ▲,❤(ℓ) :=❆❝t✉❛❧ ❖❜s❡r✈❛t✐♦♥

slide-25
SLIDE 25

❆♣♣❧✐❝❛t✐♦♥ ❋♦r❡❝❛st✐♥❣

❇❡♥❝❤♠❛r❦♠♦❞❡❧ ■

❈❧❛ss✐❝❛❧ ❆❘✭✶✮✿

❳t = ❞ + α ❳t−✶ + ωt ✇❤❡r❡✿ ◮ ❳t := ❧♦❣(② P

t ) − ❣ P t

❢♦r ♣❡❛❦❧♦❛❞ ♣r✐❝❡s ◮ ❳t := ❧♦❣(② ❇

t ) − ❣ ❇ t

❢♦r ❜❛s❡❧♦❛❞ ♣r✐❝❡s

slide-26
SLIDE 26

❆♣♣❧✐❝❛t✐♦♥ ❋♦r❡❝❛st✐♥❣

❇❡♥❝❤♠❛r❦♠♦❞❡❧ ■■ ▼❛r❦♦✈ ❘❡❣✐♠❡ ❙✇✐t❝❤✿ ❳▼,t = ❞ + α ❳▼,t−✶ + ω▼,t ❳❙,t = µ❙ + ω❙,t

❲✐t❤ ❝♦♥❞✐t✐♦♥❛❧ tr❛♥s✐t✐♦♥ ♣r♦❜❛❜✐❧✐t✐❡s P[❙t = ▼|❙t−✶ = ▼] P[❙t = ▼|❙t−✶ = ❙] P[❙t = ❙ |❙t−✶ = ▼] P[❙t = ❙ |❙t−✶ = ❙]

  • =
  • q

✶ − ♣ ✶ − ♣ ♣

slide-27
SLIDE 27

❆♣♣❧✐❝❛t✐♦♥ ❋♦r❡❝❛st✐♥❣

❘▼❙❊✲❈♦♠♣❛r✐s✐♦♥ ✭✶✴✷✮

Peakload Prices

Days Ahead RMSE 5 10 15 20 0.1 0.2 0.3 0.4 0.5 0.6 Models FFM Model I Model II

slide-28
SLIDE 28

❆♣♣❧✐❝❛t✐♦♥ ❋♦r❡❝❛st✐♥❣

❘▼❙❊✲❈♦♠♣❛r✐s✐♦♥ ✭✷✴✷✮

Baseload Prices

Days Ahead RMSE 5 10 15 20 0.1 0.2 0.3 0.4 0.5 0.6 Models FFM Model I Model II

slide-29
SLIDE 29

❚❤❡ ❊♥❞

❚❤❛♥❦ ②♦✉r ❢♦r ②♦✉r ❛tt❡♥t✐♦♥✦