Short-Term Trading for a Wind Power Producer

Transcription

1 Shor-Term Trading for a Wind Power Producer Juan M. Morales Anonio J. Conejo Juan Pérez Univ. Casilla La Mancha Spain Sepember

2 Wha 1. Aim 2. Moivaion 3. Problem descripion 4. Mahemaical formulaion 5. Sochasic programming approach 6. Numerical simulaions 7. Conclusions 2

3 Aim esigning a sochasic programming model o build offers for wind producers o rade in differen shor-erm markes wihin a fully-fledged elecriciy marke. 3

4 Wind producer problem Wind power echnology mauring and reaching break-even coss Subsides decreasing or even being suspended Ineres in paricipaing in elecriciy markes o maximize profi 4

5 Wind producer problem Compeiiveness damaged by uncerain wind availabiliy Imbalances covered by expensive energy sources hrough a balancing mechanism Imbalance cos! 5

6 Wind producer problem The wind producer offer sraegy should: 1. Be profi effecive 2. Limi profi variabiliy 3. Minimize need for balancing energy 6

7 Marke framework Three independen and successive markes: 1. ay-ahead marke 2. Adjusmen marke 3. Balancing marke No marke power capabiliy by he wind producer in any of he markes. 7

8 Marke framework 10 am ay-ahead Marke ay d, hours: pm Adjusmen Marke ay d, hours: 1-24 Balancing Marke before each hour... ay d-1 ay d Wind uncerainy Price uncerainy 8

9 Marke framework 10 am ay-ahead Marke ay d, hours: pm Adjusmen Marke ay d, hours: 1-24 Balancing Marke before each hour... ay d-1 ay d Price uncerainy Cerainy gain Wind uncerainy Knowledge gained on wind power sochasic behavior 9

10 Imbalance prices A price for posiive deviaion: A price for negaive deviaion: λ λ Seled in a balancing marke organized for each ime period (hour) Cos of he energy required o counerac he sysem imbalance 10

11 Imbalance prices We define: r = λ λ, 0 r 1 r = λ λ, r 1 11

12 Uncerainy sources Price uncerainy in (i) day-ahead, (ii) adjusmen, and (iii) balancing markes Wind generaion availabiliy makes he wind producer problem unique and is responsible for is profiabiliy loss 12

13 Uncerainy characerizaion Seasonal ARIMA models o characerize prices Variable Time series model log(λ λ -λ A ) ARIMA(2,0,1)(1,1,1) 24 ARIMA(1,0,11)(1,0,1) 24 r r 1 ARIMA(2,0,1)(1,0,1) 24 13

14 Uncerainy characerizaion 120 N scenarios for λ 30 N A scenarios for λ A -λ /MWh /MWh Period (h) N I scenarios for r r Period (h) /MWh Period (h) 14

15 Uncerainy characerizaion ARMA model (filered wih he marginal disribuion) o characerize wind speed uncerainy Wind speed scenarios Power curve Wind urbine power scenarios Aggregaing Wind plan power scenarios Hypohesis: The same wind characerisics all over he plan a each insan 15

16 Uncerainy characerizaion The generaion of wind power scenarios should consider he cerainy gain phenomenon Nw 1 scenarios beween day-ahead and adjusmen marke Nw 2 scenarios afer he adjusmen marke 16

17 Uncerainy characerizaion N w1 x N w2 = 2 x 50 MW Average wind power values observed from he day-ahead marke (and from he adjusmen marke if he cerainy gain is no considered) Period (h) 17

18 Uncerainy characerizaion N w1 x N w2 = 2 x Average wind power values observed from he adjusmen marke if he cerainy gain effec is modeled MW Period (h) 18

19 19 Sochasic programming approach ) ay - ahead marke ( P r r P,,,,, Uncerainy : λ A λ T T N N P r r, 1,,,,, Uncerainy : 1 A = λ r r,, Uncerainy : ) marke ( Adjusmen A P ) marke ( Balancing I 1, 1,, ;, T N P = λ T T N N P, 1,, ;, 1 A = λ Three sages, each one represening a marke

20 Problem formulaion Maximize Expeced profi β CVaR Subjec o consrains associaed wih: Linearizaion of imbalance income Non-anicipaiviy of informaion CVaR The radeoff beween expeced profi and risk is enforced hrough he weighing facor β ϵ [0, ) 20

21 Risk managemen Probabiliy 1 - α CVaR VaR 21

22 Expeced profi E{profi} = E{ Revenue from rading in he day-ahead marke Revenue from rading in he adjusmen marke Imbalance income } = N N Ω T ω= 1 = 1 π ω [ ] A A I λ P d λ P d I ω ω ω ω ω 22

23 Expeced profi E{profi} = E{ Revenue from rading in he day-ahead marke Revenue from rading in he adjusmen marke Imbalance income } = N N [ ] A A I = πω λ ωpωd λ ωpωd Iω Ω T ω= 1 = 1 23

24 Expeced profi E{profi} = E{ Revenue from rading in he day-ahead marke Revenue from rading in he adjusmen marke Imbalance income } = N N [ ] A A I = πω λ ωpωd λ ωpωd Iω Ω T ω= 1 = 1 24

25 Expeced profi E{profi} = E{ Revenue from rading in he day-ahead marke Revenue from rading in he adjusmen marke Imbalance income } = N N [ ] A A I = πω λ ωpωd λ ωpωd Iω Ω T ω= 1 = 1 25

26 Non-anicipaiviy consrains P ω = P ω,, ω,ω' 26

27 Non-anicipaiviy consrains Relaxed o obain offer curves! P ω = P, ω, ω,ω' : λ ω = λ ω Power raded in day-ahead marke can be differen for differen price realizaions! Pairs (P,λ ) ω ω making up anoffer curve 27

28 Non-anicipaiviy consrains P A ω = P A ω,, ω,ω': (λ and (P = ω ω = P ω λ ω ), = 1, 2,, N T 1 ) Relaxed o model he cerainy gain effec! Power raded in he adjusmen marke can be differen depending on he wind realizaion beween he closure of he day-ahead and adjusmen markes! 28

29 Numerical simulaions Price daa from he elecriciy marke of he Iberian Peninsula Wind speed daa from a locaion in Kansas (U.S.) 1 day 29

30 Some resuls No adjusmen marke Reducing he energy raded in he day-ahead marke in he hope of selling in he balancing marke a a compeiive price MWh MWh MWh Expeced oal deviaion Expeced posiive deviaion Expeced negaive deviaion Risk aversion (β) β Power raded in he day-ahead marke (MW) Risk aversion β Ε{P E{Δ } E{Δ } } 30

31 Some resuls Single sacks of energy for β = 0 Period T8 T12 T13 T14 T15 T23 Bid (MW)

32 Some resuls urning ino curves for β 0 β = To reduce he energy raded in he dayahead marke in he hope of selling in he balancing marke a a compeiive price 60 /MWh T8 T12 T13 T14 T15 T MWh 32

33 Analysis of cerainy gain effec Adjusmen marke included! 950 Expeced oal deviaion 25 Reducion in expeced oal deviaion per hour β = MWh 800 MW Wihou cerainy gain Wih cerainy gain Risk aversion (β) Hour A significan reducion for he firs few hours 33

34 Analysis of cerainy gain effec The key figure: EFFICIENT FRONTIER 7.4 x 104 Expeced profi ( ) β = 0 β = 0.1 β = 0 β = 0.1 β = 0.2 β = 0.2 β = 0.3 β = 0.3 β = 0.4 β = 0.4 β = 0.5 Considering cerainy gain No considering cerainy gain β = CVaR ( ) x

35 Analysis of cerainy gain effec The key figure Expeced profi ( ) 7.4 x E{profi} β = 0 β = 0.1 CVaR β = 0.2 β = 0.3 β = 0.4 β = 0.5 ΔCVaR ΔE{profi} ΔE{profi} E{profi} ΔCVaR CVaR (β= 0 0.5) (β= 0 0.5) (β= 0) (β= 0 0.5) (β= 0 0.5) (β= 0) = = 1.66 % 100 = % CVaR ( ) x

36 Value of he Sochasic soluion (VSS) Economic gain expeced from applying he sochasic soluion insead of a predicionbased one Risk-neural case (β = 0) 36

37 Value of he Sochasic soluion (VSS) No adjusmen marke VSS = 2.3% Adjusmen marke, no cerainy gain effec VSS = 2.9% (Increase: 0.6%) Adjusmen marke, cerainy gain effec VSS = 3.3% (Increase: 0.4%) 37

38 Conclusions Sochasic vs deerminisic Significan economic improvemens expeced from a sochasic modeling approach Risk managemen is possible A high decrease in he risk of profi variabiliy for a comparaively low reducion in expeced profi Adjusmen markes are imporan These markes allow designing offering sraegies wih a reduced uncerainy level, which resuls in a higher profi and a smaller risk 38

39 Fuure work Offers for a wind porfolio: scenarios spaially correlaed Wind producion scenarios? Financial insrumens? 39

40 Thanks for your aenion! GSEE: hp:// 40

41 Balancing mechanism A balancing mechanism is required o cope wih unexpeced producion/consumpion deviaions Posiive (negaive) deviaion: higher (lower) producion or lower (higher) consumpion han scheduled 41

42 Mechanism for imbalance prices Price Aggregaed power supply curve λ UP λ λ N - Energy 42

43 Mechanism for imbalance prices If he sysem imbalance > 0 (excess of generaion): λ λ = = min(λ λ,λ N ) λ λ N : ay-ahead marke price : Price for he downward energy required o resore sysem balance 43

44 Mechanism for imbalance prices Price Aggregaed power supply curve λ UP λ λ N - Energy 44

45 Mechanism for imbalance prices If he sysem imbalance < 0 (defici of generaion): λ λ = = λ max(λ, λ UP ) λ UP : price for he upward energy required o resore sysem balance I holds: λ λ and λ λ 45

46 Imbalance cos An opporuniy cos Loss of profi resuling from no having raded he deviaed energy in he day-ahead marke If we define: λ λ r =, r 1 λ r =, r 1 λ 46

47 Imbalance cos Then, he imbalance cos is given by: I = λ λ (1 (r r )Δ 1)Δ,, Δ Δ < 0 0 :Toal energy deviaion 47

48 r Period (h) superimposing r Period (h) 0.6 r r Period (h) Easier o model! 48

49 Sochasic programming approach Three-sage sochasic programming model: Firs-sage variables: Energy sold in he dayahead marke Second-sage variables: Energy raded in he adjusmen marke Third-sage variables: deviaions and heir associaed cos 49

50 50 Linearizaion of imbalance income < = 0 Δ, Δ r λ 0 Δ, Δ r λ I ω ω ω ω ω ω ω ω I ω Linearizaion max ω ω ω ω ω ω A ω ω ω ω ω ω ω ω ω I ω d P Δ 0 d P Δ 0 Δ Δ Δ ) P P (P d Δ ) Δ r Δ (r λ I = = = Toal deviaion decomposed ino posiive and negaive deviaions

51 51 Risk measure (CVaR) ω 0 η ω 0 η ξ )] Δ r Δ (r λ d P λ d P [λ η π α 1 1 ξ CVaR ω ω ω ω ω ω ω A ω A ω ω N 1 ω Ω ω ω ω T = =

52 Risk hedging No risk hedging insrumens! Risk hedging sraegies are possible 52

53 53 Oher consrains Non-decreasing condiion ) (λ 1 ) (λ ω,ω':, 0, P P ω ω ω ω = O O Bounds ω,, P P P 0 ω,, P P 0 max A ω ω max ω

54 Expeced Value of Perfec Informaion (EVPI) How much he wind producer loses for no having perfec informaion on a given sochasic process (risk-neural case, β = 0) Perfec informaion on λ P (r, r ) EVPI (%)

55 Analysis of cerainy gain effec MWh Resuling energy schedule Wihou cerainy gain Wih cerainy gain MWh MWh Energy raded in he adjusmen marke Energy raded in he day-ahead marke Risk aversion (β) Transfer of rading from he day-ahead marke o he adjusmen marke (beer wind-behavior knowledge) 55

56 Analysis of cerainy gain effec The key figure: EFFICIENT FRONTIER Expeced Profi ( ) 7.4 x 104 β = β = 0 β = 0.1 β = 0.1 β = 0.2 β = 0.2 β = 0.3 β = 0.3 β = 0.5 β = 0.5 Reflecing cerainy gain Wihou reflecing cerainy gain β = 1 β = 1 β = 2 β = 5 β = 50 β = 2 β = 5 β = 10 β = CVaR ( ) x