Bidding in sequential electricity markets: The Nordic case

Transcription

1 Bidding in sequenial elecriciy markes: The Nordic case Trine Krogh Boomsma Deparmen of Mahemaical Sciences, Universiy of Copenhagen Join work wih Sein-Erik Fleen and Nina Juul Par of he ENSYMORA projec suppored by he Danish Council for Sraegic Research ICSP, Bergamo, July 8-12, 2013 Deparmen of Mahemaical Sciences Slide 1/20

2 Agenda The Nordic power markes spo marke balancing marke A muli-sage sochasic programming model for bidding ino sequenial markes marke exchange operaion Generaion of marke price scenarios auo-correlaions cross-correlaions The gain from coordinaed bidding is i profiable o hold back capaciy in he spo marke for he balancing marke? wha is he gain from doing his? Slide 2/20

3 The Nordic shor-erm power markes The spo marke (Elspo) Organized by Nord Pool Members 350, Volume 2011: TWh Physical exchange of producion and consumpion Day-ahead marke: Offering and clearing is a day ahead of operaion The balancing marke (Regulerkrafmarkede) Organized by he TSO(s) Members DK: 6, Supply DK 2011: 0.75 TWh, Demand DK 2011: 3 TWh(!) Ensuring securiy of supply Inra-day marke: Offering is an hour ahead of operaion, clearing is real-ime Balance selemen TSO is responsible Physical balancing of producion and consumpion Imbalances are seled following he operaion day Slide 3/20

4 The Nordic shor-erm power markes spo marke offer submission deadline balancing marke offer submission deadline spo marke clearing balancing marke offer submission deadline balancing marke clearing }{{} balancing marke clearing }{{} 0:00 12:00 13:00 0:00 1:00 2:00 22:00 23:00 24:00 } {{ }} {{ } day-ahead of operaion day of operaion Slide 4/20

5 Spo marke bidding Bidding: Supply and demand curves are submied for 24 hours of he following operaion day Marke clearing (daily): Equilibrium beween aggregaed supply and demand curves is deermined, and marke paricipans are dispached accordingly Sales (purchase) bids are acceped if he bid (ask) price is below (above) he marke price Sep-wise bidding curve: Piece-wise linear bidding curve: y = x i, if p i ρ < p i+1 y = p i+1 ρ p i+1 p i x i + p i ρ p i p i+1 x i+1, if p i ρ < p i+1 The bidding problem is non-linear. Therefore, assume ha bid prices are fixed exogenously (parameers) and only volumes are endogenous (variables) Assume ha he marke paricipan is a price-aker. Then, one can deermine he dispach of bids a priori Slide 5/20

6 Spo marke bidding Sep-wise bidding curve: Piece-wise linear bidding curve: price price p4 p4 p3 p3 p2 p2 p1 volume p1 volume x1 x2 x3 x4 x1 x2 x3 y x4 Slide 6/20

7 Balancing marke bidding and selemen Bidding: Up-regulaion and down-regulaion bids are submied for he following hour of operaion Marke clearing (real-ime): In case of a negaive (posiive) sysem imbalance, i.e. consumpion exceeds producion, up-regulaion (down-regulaion) bids are dispached Up-regulaion (down-regulaion) bids are acceped if he bid (ask) price is below (above) he marke price and he sysem imbalance is negaive (posiive) Sep-wise bidding curve: y = { x i, p i ρ µ < p i+1 0, ρ > µ Under he price-aker assumpion, one can deermine he sign of he sysem imbalance a priori, and hence he dispach of bids One-price balancing selemen: Negaive (posiive) imbalances are charged (paid) he balancing marke price, µ Two-price balancing selemen: Negaive (posiive) imbalances are charged (paid) he spo price in case of a posiive (negaive) sysem imbalance, and oherwise he balancing price, i.e. max{ρ, µ} (min{ρ, µ}) Slide 7/20

8 Three-sage sochasic programming Assume a probabiliy space (Ω,F,P) wih he filer {F 1,F 2,F 3 } Decision process and informaion flow: 1. sage Day-ahead bidding (F 1 = {Ø,Ω}) 2. sage Day-ahead prices and dispach realized (F 2 = σ(ρ : = 1,...,24)), inra-day bidding 3. sage Inra-day prices and dispach realized (F 3 = σ(ρ,µ : = 1,...,24)), operaion, balance selemen 0:00 1:00 2:00 22:00 23:00 24:00 0:00 1:00 2:00 22:00 23:00 24:00 0:00 1:00 2:00 22:00 23:00 24:00 } {{ } } {{ } } {{ } 1. sage 2. sage 3. sage Slide 8/20

9 The sochasic programming problem: Bidding Le γ 1,+ = γ 1, = µ, γ 2,+ = min{µ,ρ },γ 2, = max{µ,ρ }. Then, { [ ] z j = max E Q 2 (x spo ) F 2 { T Q 2 (x spo ) = max ρ (y spo,+ =1 y spo,+ { T Q 3 (x reg,y spo ) = max µ (y reg,+ =1 y reg,+ = : x spo X 1 } [ y spo, )+E ] Q 3 (x reg,y spo ) F 3 : = x spo,+ i, p + i ρ < p+ i+1, i,, xreg X 2 } { z z + = y spo,+ y reg, ) T =1 x reg,+ i, p + i ρ µ < p+ i+1 0, µ n < ρn y spo,+ ( γ j, z γ j,+ z + ) O(q) : +y reg,+ i, } y reg, q, Furher consrains: Demand-side consrains, increasing (decreasing) supply (demand) curves, minimum and maximum bid sizes (LP/IP) Slide 9/20

10 Relaxing he price-aker assumpion Assume linear price response funcions µ = ˆµ α(y spo,+ ρ = ˆρ α(y spo,+ y spo, ) β(y reg,+ For 4β > α > 0, he problem becomes a QP. y spo, ), y reg, ), Slide 10/20

11 The sochasic programming problem: Operaion Thermal generaion: { T O(q 1,...,q T ) = min Hydro-power producion: =1 j=1 J J a j g j j=1 g j = q, g min j } g j gj max, j, { J J O(q 1,...,q T ) = max V j l jt η j v j = q, l j+1 = l j +ν j +v j 1 v j, j=1 l min j j=1 l j lj max, vj min } v j vj max, j, Slide 11/20

12 Scenario generaion Sage-wise scenario generaion and scenario reducion: Fi an auoregressive model o spo prices Fi an auoregressive model o balancing prices ha includes exogenous spo prices Sample a fan of spo price scenario pahs for he following 24 hours Reduce he number of spo price pahs (second-sage scenarios) by clusering Condiional on a given spo price pah (cluser), sample a number of balancing price pahs for he following 24 hours Reduce he number of balancing price pahs (hird-sage scenarios) by clusering Slide 12/20

13 Scenario generaion: Resuls Spo prices (Dec ): Euro/MWh Hour Scenario generaion (20 samples) Euro/MWh Hour Scenario reducion (5 samples) Balancing prices (Dec ): Euro/MWh Hour Scenario generaion (20 20 samples) Euro/MWh Hour Scenario reducion (5 5 samples) Slide 13/20

14 Scenario generaion: Resuls Auocorrelaions, spo prices Auocorrelaions, balancing prices Hour Hour Cross-correlaions, spo and regulaing prices Hour and samples before (solid line) and afer scenario reducion (dashed line) Slide 14/20

15 Separaion of he bidding process Spo marke bidding (hree-sage): { [ ] } z spo,j = max E Q 2 (x spo ) F 2 : x spo X 1 { T Q 2 (x spo ) = max ρ (y spo,+ =1 [ y spo, )+E =1 { T Q 3 (y spo ( ) = max γ j, z γ j,+ z + ) O(q) : z z + = y spo,+ y spo,+ ] Q 3 (y spo ) F 3 } q, } : y spo Y 2 (x spo ) Balancing marke bidding (wo-sage): { [ ] } z reg,j (y spo ) = max E Q(x reg,y spo ) F 3 : x reg X 2 { T T Q(x reg,y spo ) = max µ (y reg,+ y reg, ( ) γ j, z γ j,+ z + ) O(q) : =1 =1 y reg Y 3 (x reg ), z z + = y spo,+ y spo,+ +y reg,+ } y reg, q, Slide 15/20

16 The gain from coordinaion: Bounds Under balancing price-sysem j, he opimal profi in he spo marke bidding problem provides a lower bound, i.e. [ T z spo,j E ρ (y spo,j,+ =1 ] y spo,j, )+z reg,j (y spo ) F 2 z j, j = 1,2 Assume a price-aker. The opimal profi in he spo marke bidding problem under a one-price balancing sysem provides an upper bound, i.e. z j z spo,1, j = 1,2 Assume a price-aker. In paricular, under a one-price balancing sysem, he opimal profi in he spo marke bidding problem equals ha of he coordinaion problem Slide 16/20

17 Separae versus coordinaed bidding: Preliminary resuls Euro/MWh Volume/MWh Euro/MWh Volume/MWh Spo supply curves Dec :00 and 16:00, using separae (dashed line) and coordinaed (solid line) bidding Slide 17/20

18 Separae versus coordinaed bidding: Preliminary resuls One-price Two-price Spo price Bal. price Profi Profi Profi Profi Gain Gain (UB-LB 1 )/LB 1 Bal. spo sep. cor. pc. vol. Euro/MWh Euro/MWh Euro Euro Euro Euro Euro % % % Jan (17.40) (27.55) Feb (16.58) (26.34) Mar (18.09) (27.19) Apr (16.58) (26.04) May (19.77) (27.99) Jun (19.48) (28.65) Jul (19.40) (27.53) Aug (17.06) (25.79) Sep (13.36) (24.73) Oc (17.59) (26.62) Nov (12.80) (23.97) Dec (19.96) (28.97) No price-response, 2010 Slide 18/20

19 Separae versus coordinaed bidding: Preliminary resuls Large volumes are raded in he balancing marke ( 56%,28%) even if average balance price < average spo price: No everyhing is raded in he balancing marke even if average balancing price > average spo price (risk-adjused balancing prices Dec 2010: up: Euro/MWh, down: Euro/MWh) Hence, he risk of no being dispached can o some exend explain a hesiaion o hold back capaciy for he balancing marke value of deferring decisions >> coss of risk of no being dispached Low gain from coordinaed bidding ( 1.5%, 1.0%) Raher han he addiional risk he low gain can jusify a hesiaion o hold back capaciy for he balancing marke Transacion coss? marke rules? The larger he deviaion beween spo and balancing prices, he larger he gain from coordinaed bidding (gain Dec 2010: 150% dev: 2.65%, 200% dev: 3.95%) Increasingly relevan wih an increased share of renewables? Slide 19/20

20 The end Thank you for lisening! Slide 20/20