Control and System Design for Energy Market Responsiveness

Transcription

1 Control and System Desgn for Energy Market Responsveness Donald J. Chmelewsk Department of Chemcal & Bologcal Engneerng EDOR s due to dfferent controller tunngs BOP wth less proft BOP wth more proft * * OSSOP

2 Outlne Motvatng Example Pseudo-Constraned Control Proft Control Market Responsve Control

3 Motvatng Example (Non-sothermal Reactor) F C A, F dca V = F( CAn CA) + VrA dt d V = F( n ) + ( V H / ρc dt r = k( ) A C A p ) r A Increase F Increased producton rate

4 Motvatng Example (Non-sothermal Reactor) F C A, F dca V = F( CAn CA) + VrA dt d V = F( n ) + ( V H / ρc dt r = k( ) A C A p ) r A Increase F Increased producton rate Decrease F Increase Increase reacton rate Increase producton

5 Lmted Operatng Regon Process Lmtatons: ( t) () - Catalyst protecton or onset of sde reactons F( t) F () - Pump lmt or lmt on downstream unt

6 Lmted Operatng Regon Process Lmtatons: ( t) () - Catalyst protecton or onset of sde reactons F( t) F () - Pump lmt or lmt on Possble Controller: ( sp F = K ( ) + c downstream unt ) F ( sp )

7 Performance n me Seres F (sp) (t) () C A, F F(t) tme F () F (sp) tme

8 Performance n Phase Plane (t) * F(t)

9 Expected Dynamc Operatng Regon (EDOR) (t) * F(t)

10 Expected Dynamc Operatng Regon (EDOR) (t) * F(t)

11 Steady-State Relaton Controller: ( sp F = K ( ) + c ) F ( sp ) Steady-State Relaton: ( sp ) ( sp F = f ( ) )

12 Expected Dynamc Operatng Regon (EDOR) (t) * F(t)

13 Steady-State Operatng Lne (t) * F(t)

14 Optmal Operatng Pont (t) Decrease F Increase * Increase converson Increase producton F(t)

15 Optmal Operatng Pont: (t) Another Possblty * Increase F Increased producton rate F(t)

16 Optmal Operatng Pont: Another Possblty (t) Increase F Increased producton rate * F(t)

17 Requres Dfferent Controller unng (t) * F(t)

18 Less Aggressve unng (t) (sp) (t) () tme * F (t ) F (sp) F(t) () F tme

19 Need for Automated unng (t) * * F(t)

20 Outlne Motvatng Example Pseudo-Constraned Control Proft Control Market Responsve Control

21 Process Model: x& z = = w (t) A x Covarance Analyss (Open-Loop Case) + G w w (t) z(t) Plant Dx Gaussan whte nose wth covarance Steady State Covarance: A Σ Σ x + Σ x A + G ΣwG = z = DΣ x D Σ w

22 Expected Dynamc Operatng Regon (EDOR) z 1 EDOR defned by: σ 11 * 2 2 Σ σ σ = z σ 2 σ σ 22 z 2

23 Closed-Loop Covarance Analyss (Full State Informaton Case) Process Model: x& = Ax + Bu + G w z = Dx x + Controller: D u u ( t) = Lx( t) Steady-State Covarance: u w(t) u(t) Plant L z(t) x(t) ( A + BL) Σ + Σ ( A + BL) + G Σ G = Σ z = ( D + D L) Σ ( D + D L) x x u x x x u w

24 Closed-Loop EDOR z 1 EDOR s from dfferent controllers * u = L1 x u = L2 x z 2

25 Constraned Closed-Loop EDOR z1 Constrants σ ( z < z ) * z 2

26 such that: Pseudo-Constraned Control > Σ L d x ξ ξ mn,, ) ( ) ( = Σ Σ Σ + w x x G G BL A BL A u x x u x z L D D L D D ) ( ) ( + Σ + = Σ z z n z K 1 2 = < Σ = φ φ ξ

27 Pseudo-Constraned Control Σ mn >, L, ξ such that: x d ξ ( A + BL) Σ + Σ ( A + BL) + G Σ G = Σ z x x u x = ( D + D L) Σ ( D + D L) ξ = φ Σ φ z < z 2 x x u = 1Kn z w φ = [ K 1 K ] th column

28 Constraned Controller Exstence (Convex Condton) here exst L such that: ( A + BL) Σ + Σ ( A + BL) + G Σ G = φ x x w 2 ( D x + Du L) Σ x( Dx + Du L) φ < z If and only f there exst X> and Y such that: ( AX + BY ) + ( AX + BY ) + G Σ G < ( D x X ξ z 2 + D Y ) u φ φ ( D x w X + D ) uy > X And controller u = Lx s constructed as: L = YX 1

29 Pseudo-Constraned Control mn,ξ X >, Y such that: d ξ ( AX + BY ) + ( AX + BY ) + G Σ G < ( D x X ξ z 2 + D Y ) u φ φ ( D x w X + D ) uy > X =1Kn z

30 MPC Equvalence heorem 1 (Chmelewsk & Manthanwar, 24): All controllers generated by Pseudo- Constraned Control (PCC) are concdent wth a controller generated by some Unconstraned Model Predctve Controller.

31 Inverse Optmalty heorem 2 (Chmelewsk & Manthanwar, 24): If there exsts P > and R > such that A P + PA + L Q RL A ( PB M ) 1 L = R + P PA ( L R + PB) ( L R + PB) then M = ( L R + PB) and Q = L RL A P + PA are such that Q M M R > R 1 ( PB + M ) R ( PB + M ) = > and P and L satsfy

32 Pseudo-Constraned Control z 1 * σ z = ξ < z PCC fnds controllers that satsfy statstcal constrants z 2

33 Outlne Model Predctve Controller unng Pseudo-Constraned Control Proft Control Market Responsve Control

34 Constraned Operatng Regon CV s Constrants MV s

35 Real-me Optmzaton Orgnal Nonlnear Process Model: s & = f ( s, m, p) q = h( s, m, p) (s,m,p,q) ~ (state, mv, dst, performance) ~ (x,u,w,z)

36 Real-me Optmzaton Orgnal Nonlnear Process Model: s & = f ( s, m, p) q = h( s, m, p) (s,m,p,q) ~ (state, mv, dst, performance) ~ (x,u,w,z) Real-me Optmzaton (mnmze proft loss): mn s, m, q { g( q) } s.t. = f ( s, m, p) q = h( s, m, p) q φ q q mn RO soluton denoted as (s ossop,m ossop,p ossop,q ossop )

37 Real-me Optmzaton CV s Optmal Steady-State Operatng Pont (OSSOP) * MV s

38 Backed-off Operatng Pont (BOP) CV s Backed-off Operatng Pont (BOP) EDOR * * * MV s Optmal Steady-State Operatng Pont (OSSOP)

39 mn Steady-State BOP Selecton (Bahr, Bandon & Romagnol, 1996) Solve the followng Sem-nfnte Programmng Problem { g( q) } s.t. s.t. s, m, q mn p [ p, p ] Extensons: - Dynamc verson n Bahr, et al, (1995) { q = f q ( s, m, = h( s, m, q q - Lnearzed verson n Contreras-Dordelly & Marln (2) q < } p) p)

40 Stochastc BOP Selecton (Loeblen & Perkns, 1999)

41 Assume controller L s gven and calculate ξ : ( A + BL) Σ + Σ ( A + BL) + G Σ G = Σ = ( D + D L) Σ ( D + D L) z Stochastc BOP Selecton (Loeblen & Perkns, 1999) x ξ = φ Σ φ z x u x x x =1Kn z u + D w w Σ w D w

42 Assume controller L s gven and calculate ξ : ( A + BL) Σ + Σ ( A + BL) + G Σ G = Σ = ( D + D L) Σ ( D + D L) z Stochastc BOP Selecton (Loeblen & Perkns, 1999) x ξ = φ Σ φ z x u x x x =1Kn Solve the followng Lnear Program: z u + D w w Σ w D w mn s', m', q' { g q' } q s.t. = As' + Bm' q ξ ' = φ ( D s' + D m') 1/ 2 < q' x q' u q mn ξ 1/ 2 q' < q' q q' mn

43 Fxed Controller BOP Selecton Loeblen and Perkns (1999): x * EDOR * * u OSSOP Controller s fxed EDOR has fxed sze and shape

44 Varable Controller BOP Selecton Peng et al. (25): x EDOR Varable Controller * OSSOP * * u EDOR has varable sze and shape

45 Proft Control (Smultaneous BOP and Controller Selecton) EDOR s due to dfferent controller tunngs BOP wth less proft BOP wth more proft * * Max Proft

46 Assume controller L s gven and calculate ξ : ( A + BL) Σ + Σ ( A + BL) + G Σ G = Σ = ( D + D L) Σ ( D + D L) z Stochastc BOP Selecton (Loeblen & Perkns, 1999) x ξ = φ Σ φ z x u x x x =1Kn Solve the followng Lnear Program: z u + D w w Σ w D w mn s', m', q' { g q' } q s.t. = As' + Bm' q ξ ' = φ ( D s' + D m') 1/ 2 < q' x q' u q mn ξ 1/ 2 q' < q' q q' mn

47 Proft Control (Smultaneous BOP and Controller Selecton) mn s ', ', ' ξ, m X, q Y q ξ 1/ 2 { g q' } ' = φ ( D s' + D m') q ξ φd ( Dx X + x < q ' q ' ξ w Σ w D D Y ) u s.t. w u φ φ q φ ( D = mn 1/ 2 x As' + Bm' q' < q ' q ' q mn ( AX + BY ) + ( AX + BY ) + G Σ G < w X + D ) uy > X Peng et al. (25)

48 mn s ', ', ' ξ, m X, q Y q ξ Computatonal Aspects of 1/ 2 { g q' } ' = φ ( D s' + D m') q ξ φd ( Dx X + x < q ' q ' ξ w Σ w D Y ) u Proft Control D s.t. w u φ φ q φ ( D = mn 1/ 2 x As' + Bm' q' < q ' q ' q mn ( AX + BY ) + ( AX + BL) + G Σ G < w X + D ) uy > X Peng et al. (25)

49 Reverse-Convex Constrants 1 ξ ξ 1 ξ (z ss, +d mn, ) 2 2 (z ss, +d, ) 2 mn 2 1 < ( q' 1 q' 1 ) 1 < ( q' 1 q' 1 ) ξ z ss, q' 1 Feasble Regon

50 Global Soluton Based on Branch and Bound algorthm Regon 2 Regon 3 Regon 4 ξ ξ 1 Regon 1 Regon q' 1 z ss,

51 Proft Control Applcatons Mechancal Systems Chemcal and Reacton Systems Hybrd Vehcle Desgn Inventory Control Electrc Power System Desgn Buldng HVAC Water Resource Management

52 Proft Control Applcatons Mechancal Systems Chemcal and Reacton Systems Hybrd Vehcle Desgn Inventory Control Electrc Power System Desgn Buldng HVAC Water Resource Management

53 Fludzed Catalytc Cracker Regenerator and Separator (dynamc): Rser (pseudo steady state): (adapted from Loeblen & Perkns, 1999)

54 FCC Constrants and Economcs Process Constrants: Proft Functon: F gs F gl and F ugo are product flows (gasolne, lght gas and unconverted ol). (adapted from Loeblen & Perkns, 1999)

55 Proft Control vs. Fxed Controller Back-off Regenerator emp (K) Fxed Controller Free Controller Cyclone emperature (K) Coke Fracton n Separator Separator emperature (K) 4 32 Catalyst Flow (kg/s) Fracton of Coke n Regenerator x 1-3 Inlet Ar (kg/s) Oxygen Mass Fracton x 1-4

56 FCC Proft Gross Proft ($/day) Dff from OSSOP ($/day) OSSOP $36,95 $. Fxed Control $34,631 - $2,274 Proft Control $35,416 - $1,489 Improves proft by 2%

57 Inventory Control Actual Inventory: stock-on-hand capable of meetng demand mmedately Inventory Poston: sum of the actual nventory and all orders placed Slver et al.(1998)

58 Recursve Model I + + = I q k + 1 k k θ d k I k : actual nventory at the end of 14 nterval k 12 d k : total demand durng nterval k 1 q k-θ : amount ordered at the end 8 of nterval k-θ and arrvng at the 6 end of nterval k 4 θ = L/R me (Days) * ponts ndcate sequence I k 16 Actual Inventory

59 State Space Model Example 4 Convert the recursve model to state-space form, assumng θ = 3. k k k k Gw Bu Ax x + + = +1 k u k x k u D x D z + = ~ ~ ~ ~ [ ] [ ] () (1) (2) 3) ( ~ ~ ~ ~ ~ k k k k k k k q u q q q I x = = [ ] ~() ~ ] ~ [ k k k k k q I z d w = = = = = 1, 1, G B A = = 1, 1 D x D u

60 PCC Approach to Inventory Control Pseudo-Constraned Control = Σ p L g x 1,, mn ζ ζ + Σ ) ( ) ( > + + Σ X BY AX BY AX G G X w ) ( ) ( ' > + + X Y D X D Y D X D u x u x φ φ ζ p z,..., 1, 2 = < ζ

61 PCC Approach to Inventory Control Example : Σ x mn, L, ζ 34 p = 1 g ζ ζ 1 ζ 2 = varance of nventory = varance of starts Case A: g 1 = 1, g 2 = Case B: g 1 = 1, g 2 = 5 Case C: g 1 = 1, g 2 = 1 Std. Dev. Inventory C B Std. Dev. Starts A Inventory Starts C B A

62 Connecton to (R,S) Approach 34 Case A gves a controller dentcal to the (R,S) approach p mn gζ Σ x, L, ζ = 1 Case A: g 1 = 1, g 2 = Case B: g 1 = 1, g 2 = 5 Case C: g 1 = 1, g 2 = 1 Std. Dev. Inventory C B Std. Dev. Starts A Inventory Starts C B A

63 Mult-Echelon System

64 Closed-loop Smulaton: Inventory at Retal 1

65 Closed-loop Smulaton: Inventory at Warehouse 1

66 Electrc Power Management Power Produced Equals Power Consumed

67 Power Management wth Renewable Power Power Produced Power Consumed

68 Power Management Wth Renewable Power Dspatchable Renewable Load MW MW

69 Motvaton Structure Utlty Perspectve Merchant Perspectve Drven by Consumers Relablty Requrements Focused on Captal Costs Drven by Opportunty Attenton to Market Prces Focused on Revenue

70 Electrc Power System Desgn Gas urbne Consumer Demand PC Boler Renewable ransmsson Grd Energy Storage

71 System Dsturbances Consumer Demand P ow er Load (G W ) Forcasted Data Smulated Data Renewable Power Generated P r (MW) Days

72 Electrc Power System Model PC Boler P & C = r C Gas urbne P & = r Pumped Hydro E & S = P S Power Lmts P P P P P mn C C C mn C C =.8 P = 12 Rate Lmts r r r r C mn C C C C =.5 P C Power Lmts P P P P P mn mn =.2 P = 1 Rate Lmts r r r mn r = 6 P Energy Lmts E S E S Power Lmts P P P mn S S S

73 Manpulated Varables PC Boler P & C = r C Gas urbne P & = r Pumped Hydro E & S = P S Power Lmts P P P P P mn C C C mn C C =.8 P = 12 Rate Lmts r r r r C mn C C C C =.5 P C Power Lmts P P P P P mn mn =.2 P = 1 Rate Lmts r r r mn r = 6 P Energy Lmts E S E S Power Lmts P P P mn S S S

74 Equpment Costs PC Boler P & C = r C Gas urbne P & = r Pumped Hydro E & S = P S Power Lmts P P P P P mn C C C mn C C =.8 P = 12 Rate Lmts r r r r C mn C C C C =.5 P C Power Lmts P P P P P mn mn =.2 P = 1 Rate Lmts r r r mn r = 6 P Energy Lmts E S E S Power Lmts P P P mn S S S

75 Case Study Average of Power Generators 32% Gas urbne 48% PC Boler 2% Renewable Pumped Hydro Equpment Costs Energy Storage: $55 /kwh Power Ratng: $13/kW

76 Case Study Results Rate (MW/hr) 5-5 Gas urbne Power (MW) 1 Rate (MW/hr) Storage Coal Power (MW) Power (MW) Energy (MWh)

77 Other Cases Case Coal Power Gas urbne Renewable Storage Sze Storage Power 1 48% 32% 2% 12.9 GWh 948 MW 2 18% 32% 5% 26.8 GWh 1398 MW 3 75% 5% 2% 61.1 GWh 1188 MW

78 Outlne Model Predctve Controller unng Pseudo-Constraned Control Proft Control Market Responsve Control

79 Motvaton Structure Utlty Perspectve Merchant Perspectve Drven by Consumers Relablty Requrements Focused on Captal Costs Drven by Opportunty Attenton to Market Prces Focused on Revenue

80 Electrcty Spot Prce Merchant Perspectve Cent ts per kw hr RP Electrcty Forecasted Data me (days) Drven by Opportunty Attenton to Market Prces Focused on Revenue

81 Integrated Gasfcaton Combned Cycle (IGCC)

82 Dspatchable IGCC Synthess Gas Storage Compressed Ar Storage

83 Cryogenc Ar Separaton Unt (CASU) Compressor Work Compressed Ar N 2 Rch Vapor Lqud N 2 Ar Pretreatment GOX GN2 Low Pressure Column Ar Heat Exchanger GOX Expander Expander Hgh Pressure Column Crude Lqud Oxygen

84 Why Not O2 Storage? Work Compressor Compressed Ar N 2 Rch Vapor Lqud N 2 Ar Pretreatment GOX GN2 Low Pressure Column Ar Heat Exchanger GOX Expander Expander Hgh Pressure Column Crude Lqud Oxygen

85 Why Not O2 Storage? Compressor Work N 2 Rch Vapor Ar Pretreatment Compressed Ar Ar GOX GN2 Low Pressure Column Lqud N 2 Cryogenc dstllaton has very large response tme Heat Exchanger GOX Hgh Pressure Column Expander Expander ypcally the slowest unt of the whole IGCC process Crude Lqud Oxygen

86 Why Compressed Ar Storage? 95% of CASU power s used by the Man Ar Compressor. r atment A Pretrea Heat Exchanger Man Ar Compressor can respond quckly. Dstllaton Unt can stll be run at constant throughput.

87 Dspatchablty from IGCC C G F 6, P to CASU C 4 η 4 F 5, P e F 4, P e F, P C η F 2, P s F, P s C N to grd Compressed Ar Storage P s, s, V s

88 Electrcty Spot Prce Merchant Perspectve Cent ts per kw hr RP Electrcty Forecasted Data me (days) Drven by Opportunty Attenton to Market Prces Focused on Revenue

89 Response to Market Changes EDOR s due to dfferent controller tunngs BOP wth less proft BOP wth more proft * * OSSOP

90 Electrc Prce Model

91 Electrc Prce Model

92 Electrc Prce Model Cents per kw hr RP Electrcty Forecasted Data me (days)

93 Model Predctve Control v p ( t) where p e pe( t)* v p ( t) dt ( t) ~ the predcted prce (or value) v p (t) ~ the producton rate

94 Model Predctve Control pe( t)* v p ( t) dt v p ( t) where pe( t) ~ the predcted prce (or value) v p ( t) ~ the producton rate and S( t) ~ amount n storage Constrants nclude : v p ( t) v p and S( t) S

95 where p and Operatonal Objectve (Max Average Proft) Ce ~ the predcted prce (or value) pe( t)* v p ( t) dt E[ pe * v p ] = v p ( t) v e ( t) S( t) Constrants nclude : p ( t) v p ( t) ~ the producton rate ~ amount n storage v p and S( t) S

96 System Desgn v p ( t) pe( t)* v p ( t) dt E * [ p ] e v p Ce ( v p ( t) v p and How does v and S mpact C p e S( t) S )?

97 System Desgn v p ( t) pe( t)* v p ( t) dt E * [ p ] e v p Ce How does ( v p ( t) v p and v and S mpact C p e S( t) S )? MPC cannot answer ths queston!

98 Expected Proft

99 Re-Scalng of Prce ( p' e α pe)

100 Correlatng Prce and Producton If E [ ] 2 ( ' ) < ε p e v p and p' e α p e then v p ( t) α p e ( t)

101 Correlatng Prce and Producton ) ( ) ( then t p t v e p α [ ] ) ' ( If 2 < ε p e v p E e e p p α ' and 2 2 ] [ ] [ 2 ] [ Also, p p e e v E v p E p E α α ] [ ] [ ] [ p p e e v E v p E p E = = α α e p e e C v p E p E = ] [ ] [ 2 α

102 Maxmum Proft C e = c L, α { α} R 2 R p e ( c = E[ ]) E [ ] 2 ( ' ) < ε p e v p [ ] 2 2 v p v ) E < ( p [ ] 2 2 S (S ) E <

103 Maxmum Levelzed Proft L, α, v p, S E { c c v c S } α R L,1 [ ] 2 ( ' ) < ε p e v p p [ ] 2 2 v p v ) E < ( p [ ] 2 2 S (S ) E < L,2

104 L, α, v Maxmum Levelzed Proft p, S E { c c v c S } α R L,1 [ ] 2 ( ' ) < ε p e v p p [ ] 2 2 v p (vv ) E < ( p [ ] 2 2 S (S ) E < L,2 Non-Convex Problem (but global soluton from branch and bound)

105 Captal Costs c Compressor CASU Storage cost: Water Reservor $.54/m 3 of workng volume. Compressed Ar Inventory Compressor cost: $16/kW

106 Dspatchablty from IGCC C G F 6, P to CASU C 4 η 4 F 5, P e F 4, P e F, P C η F 2, P s F, P s C N to grd Compressed Ar Storage P s, s, V s

107 Dspatchable Operaton MW MW a CASU Man Compressor Stroage Man Compressor 8 b Mm 3 $/MWh.4.2 c Volume of Storage Prce of Electrcty 2 d

108 Changes n Revenue b on $/day Revenue, mll wth storage no storage tme, day

109 Levelzed Annual Revenue Compressor Costs Storage Costs Levelzed Revenue Wthout Storage $96M - $368M/yr Wth Storage $192M $.2M $377M/yr 2.5% mprovement n levelzed revenue

110 Dspatchable IGCC Synthess Gas Storage Compressed Ar Storage

111 hermal Energy Storage (ES) Heat Leakage outsde Volume of Ar (the Room) room Heat from Room Heat to Cooler Heat to ES Unt Coolng Unt ES Unt Energy Usage In HVAC systems ES s used for Load Levelng and to shft usage to Off-Peak Hours

112 hermal Energy Storage (Comparson of Storage Cases) 25 2 Heat from Room Heat to Cooler Heat to ES Unt kw hr / day me (days) Heat from Room Heat to Cooler Heat to ES Unt 3 2 Heat from Room Heat to Cooler Heat to ES Unt kw hr / day 1 5 kw hr / day me (days) me (days)

113 hermal Energy Storage (Cost Comparsons) Electrcty Costs ($ / day) One on ES Unt Fve ons ES Unt en ons ES Unt Electrcty Prce $ / kw hr me (days) Average Coolng Costs: One ton: $8 per day Fve tons: $7 per day (14% savngs) en tons: $6 per day (25% savngs)

114 Acknowledgements Current Students: Syed K. Amed, Ben Omell and Davd Mendoza-Serrano Former Students: Amt Manthanwar (MS), Mchael Peng (PhD), Mng-We Yang (PhD) and Wa-Kt Ong (UG) Collaborators Professor Durango-Cohen (Stuart Busness School, II) Professor Abbason (Chem Eng, II) Professor Muehleson (Arch Eng, II) Professor Moschandreas (Env Eng, II) Fundng: Natonal Scence Foundaton (CBE 96796) II Graduate College and Armour College og Engneerng II Chemcal & Bologcal Engneerng Department

115 Conclusons Relatonshp between controller performance and plant proft quantfed. Enables proft guded controller and closed-loop system desgn. Applcable to a broad set of problems from a varety of dscplnes. Lnear controller can be used for market responsveness. Non-convex, but global soluton methods used.