New Perspectives in Control System Design: Pseudo-Constrained to Market Responsive Control

Transcription

1 New Perspectves n Control System Desgn: Pseudo-Constraned to Market Responsve Control Donald J. Chmelewsk Department of Chemcal & Bologcal Engneerng x PRODUCS SEPARAR * EDOR s due to dfferent controller tunngs BOP wth less proft FLUE-GAS SRP-SM RISER REGEN-R u BOP wth more proft * * OSSOP AIR REG-CAY SEAM FEED-OIL

2 Outlne Motvatng Example Pseudo-Constraned Control Proft Control Market Responsve Control Department of Chemcal and Bologcal Engneerng

3 Motvatng Example (Non-sothermal Reactor) F C A, F V V r A dca F( CAn CA) VrA dt d F( n ) ( VH / C dt k( ) C A p ) r A Increase F Increased producton rate Department of Chemcal and Bologcal Engneerng

4 Motvatng Example (Non-sothermal Reactor) F C A, F V V r A dca F( CAn CA) VrA dt d F( n ) ( VH / C dt k( ) C A p ) r A Increase F Decrease F Increased producton rate Increase Increase reacton rate Increase producton Department of Chemcal and Bologcal Engneerng

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

6 Lmted Operatng Regon Process Lmtatons: ( t) F( t) F F K c (max) ( (max) Possble Controller: ( sp) - Catalyst protecton or onset of sde reactons - Pump lmt or lmt on downstream unt ) F ( sp) Department of Chemcal and Bologcal Engneerng

7 Performance n me Seres F (sp) (t) (max) C A, F F(t) tme F (max) F (sp) tme Department of Chemcal and Bologcal Engneerng

8 Performance n Phase Plane (t) * F(t) Department of Chemcal and Bologcal Engneerng

9 Dynamc Operatng Regon (t) * F(t) Department of Chemcal and Bologcal Engneerng

10 Expected Dynamc Operatng Regon (t) * F(t) Department of Chemcal and Bologcal Engneerng

11 Steady-State Relaton Controller: F K c ( ( sp) ) F ( sp) Steady-State Relaton: F ( sp) ( sp) f ( ) Department of Chemcal and Bologcal Engneerng

12 Dynamc Operatng Regon (t) * F(t) Department of Chemcal and Bologcal Engneerng

13 Steady-State Operatng Lne (t) * F(t) Department of Chemcal and Bologcal Engneerng

14 Optmal Operatng Pont (t) * Decrease F Increase Increase converson Increase producton F(t) Department of Chemcal and Bologcal Engneerng

15 Optmal Operatng Pont: (t) Another Possblty * Increase F Increased producton rate F(t) Department of Chemcal and Bologcal Engneerng

16 Optmal Operatng Pont: Another Possblty (t) Increase F Increased producton rate * F(t) Department of Chemcal and Bologcal Engneerng

17 Requres Dfferent Controller unng (t) * F(t) Department of Chemcal and Bologcal Engneerng

18 Less Aggressve unng (t) (sp) (t) (max) * F(t) F (sp) F(t) tme F (max) tme Department of Chemcal and Bologcal Engneerng

19 Need for Automated unng (t) * * F(t) Department of Chemcal and Bologcal Engneerng

20 Outlne Motvatng Example Pseudo-Constraned Control Proft Control Market Responsve Control Department of Chemcal and Bologcal Engneerng

21 Mass-Sprng-Damper Example r s the mass poston Mass r r max v f s the velocty s thenput force (MV)and f w r mn w s the dsturbance force Department of Chemcal and Bologcal Engneerng

22 Mass-Sprng-Damper Example r s the mass poston Mass r r max v f s the velocty s thenput force (MV)and f w r mn w s the dsturbance force System Model: r v r v 1 f 1 w Department of Chemcal and Bologcal Engneerng

23 Mass-Sprng-Damper Example r s the mass poston Mass r r max v f s the velocty s thenput force (MV)and f w r mn w s the dsturbance force System Model: r 1 v 2 3 r v 1 f 1 w System Constrants: 1 r 1 and f 16 Department of Chemcal and Bologcal Engneerng

24 Department of Chemcal and Bologcal Engneerng Mass-Sprng-Damper Example 16 and 1 1 f r System Model: w f v r v r System Constrants: z n z t z z 1 ) ( w D D u D x z Gw Bu Ax x w u x w f v r z z

25 Process Model: Covarance Analyss (Open-Loop Case) Steady State Covarance: A x z x x A G wg z w(t) A x D x G w D w (t) z(t) Plant Dx Gaussan whte nose wth covarance w Department of Chemcal and Bologcal Engneerng

26 Expected Dynamc Operatng Regon (EDOR) z 1 EDOR defned by: 11 * z z 2 Department of Chemcal and Bologcal Engneerng

27 Closed-Loop Covarance Analyss (Full State Informaton Case) Process Model: x Ax Bu G w z u( t) Lx( t) ( A BL) ( A BL) G G ( D D L) ( D D L) z D x x Controller: x D u x u u D x x w Steady-State Covarance: w x u w(t) u(t) w D w w D Plant w L z(t) x(t) Department of Chemcal and Bologcal Engneerng

28 Closed-Loop EDOR z 1 EDOR s from dfferent controllers * u L x 1 u L2 x z 2 Department of Chemcal and Bologcal Engneerng

29 Constraned Closed-Loop EDOR z 1 Constrants ( z z ) * z 2 Department of Chemcal and Bologcal Engneerng

30 Constraned Closed-Loop EDOR z 1 Constrants ( z z ) * z 2 Department of Chemcal and Bologcal Engneerng

31 Department of Chemcal and Bologcal Engneerng Does there exst L such that: 1 column th Constraned Controller Exstence w w w u x x u x z D D D L D D L D ) ( ) ( ) ( ) ( w x x G G BL A BL A z z n z 1 2

32 Department of Chemcal and Bologcal Engneerng If and only f there exst X> and Y such that: 1 Constraned Controller Exstence (Convex Condton) ) ( ) ( X D Y X D D Y X D D D u x u x w w w ) ( ) ( w G G BY AX BY AX z n z L YX And controller s constructed as: u Lx

33 Regon of Controller Exstence 1 Achevable Performance Levels Unachevable 2 Department of Chemcal and Bologcal Engneerng

34 Department of Chemcal and Bologcal Engneerng such that: Pseudo-Constraned Control Y X d mn,, ) ( ) ( X D Y X D D Y X D D D u x u x w w w ) ( ) ( w G G BY AX BY AX z n z 1 2

35 Pareto Fronter Interpretaton 1 All Pseudo-Constraned Controllers are on the Pareto Fronter Unachevable Regon Achevable Regon 2 Department of Chemcal and Bologcal Engneerng

36 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. Department of Chemcal and Bologcal Engneerng

37 Inverse Optmalty heorem 2 (Chmelewsk & Manthanwar, 24): If there exsts P > and R > such that A P PA Q L R 1 L PB M RL A L 1 PB M R PB M R PB P PA L R PB then M ( L R PB) and Q L RL A P PA are such that Q M M R R and P and L satsfy Department of Chemcal and Bologcal Engneerng

38 Outlne Model Predctve Controller unng Pseudo-Constraned Control Proft Control Market Responsve Control Department of Chemcal and Bologcal Engneerng

39 Constraned Operatng Regon CV s Steady-State Operatng Pont Constrants EDOR * MV s Department of Chemcal and Bologcal Engneerng

40 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) Department of Chemcal and Bologcal Engneerng

41 Department of Chemcal and Bologcal Engneerng Real-me Optmzaton ),, ( ),, ( p m s h q p m s f s Orgnal Nonlnear Process Model: max mn,, ),, ( ),, ( s.t. ) ( mn m q s q q q p m s h q p m s f q g Real-me Optmzaton (mnmze proft loss): (s,m,p,q) ~ (state, mv, dst, performance) ~ (x,u,w,z) RO soluton denoted as (s ossop,m ossop,p ossop,q ossop )

42 Real-me Optmzaton Steady-State Operatng Pont CV s Constrants EDOR * Optmal Steady-State Operatng Pont (OSSOP) * MV s Department of Chemcal and Bologcal Engneerng

43 Backed-off Operatng Pont (BOP) CV s Backed-off Operatng Pont (BOP) EDOR * * * MV s Optmal Steady-State Operatng Pont (OSSOP) Department of Chemcal and Bologcal Engneerng

44 Stochastc BOP Selecton (Loeblen & Perkns, 1999) Department of Chemcal and Bologcal Engneerng

45 Department of Chemcal and Bologcal Engneerng Assume controller L s gven and calculate : w w w u x x u x z D D D L D D L D ) ( ) ( ) ( ) ( w x x G G BL A BL A z z n 1 Stochastc BOP Selecton (Loeblen & Perkns, 1999)

46 Assume controller L s gven and calculate : ( A BL) ( A BL) G G ( D D L) ( D D L) z Stochastc BOP Selecton (Loeblen & Perkns, 1999) x z x u x x x 1n u D Solve the followng Lnear Program: z w w w D w mn s', m', q' g q q' s.t. As' Bm' q ' ( D s' D m') 1/ 2 q' x max q' u q mn 1/ 2 q' q' q q' max mn Department of Chemcal and Bologcal Engneerng

47 Fxed Controller BOP Selecton Loeblen and Perkns (1999): x * EDOR * * u OSSOP Controller s fxed EDOR has fxed sze and shape Department of Chemcal and Bologcal Engneerng

48 Varable Controller BOP Selecton Peng et al. (25): x EDOR Varable Controller * OSSOP * * u EDOR has varable sze and shape Department of Chemcal and Bologcal Engneerng

49 Proft Control (Smultaneous BOP and Controller Selecton) EDOR s due to dfferent controller tunngs BOP wth less proft BOP wth more proft * * Max Proft Peng et al. (25) Department of Chemcal and Bologcal Engneerng

50 Assume controller L s gven and calculate : ( A BL) ( A BL) G G ( D D L) ( D D L) z Stochastc BOP Selecton (Loeblen & Perkns, 1999) x z x u x x x 1n u D Solve the followng Lnear Program: z w w w D w mn s', m', q' g q q' s.t. As' Bm' q ' ( D s' D m') 1/ 2 q' x max q' u q mn 1/ 2 q' q' q q' max mn Department of Chemcal and Bologcal Engneerng

51 Department of Chemcal and Bologcal Engneerng mn 2 1/ max 2 1/ max mn,, ' ', ', ' ' ' ' ' ') ' ( ' ' ' s.t. ' mn u x q Y X q m s q q q q q q q D m D s q Bm As q g ) ( ) ( X D Y X D D Y X D D D u x u x w w w ) ( ) ( w G G BY AX BY AX Proft Control (Smultaneous BOP and Controller Selecton) Peng et al. (25)

52 Department of Chemcal and Bologcal Engneerng mn 2 1/ max 2 1/ max mn,, ' ', ', ' ' ' ' ' ') ' ( ' ' ' s.t. ' mn u x q Y X q m s q q q q q q q D m D s q Bm As q g ) ( ) ( X D Y X D D Y X D D D u x u x w w w ) ( ) ( w G G BL AX BY AX Peng et al. (25) Computatonal Aspects of Proft Control

53 Reverse-Convex Constrants 1 1 (z ss, +d max mn, ) 2 2 (z ss, +d max, ) 2 mn 2 1 ( q' 1 q' 1 ) 1 ( q' 1q' 1 ) z ss, q' 1 Feasble Regon Department of Chemcal and Bologcal Engneerng

54 Global Soluton Based on Branch and Bound algorthm Regon 2 Regon 3 Regon Regon 1 Regon q' 1 z ss, Department of Chemcal and Bologcal Engneerng

55 Proft Control Applcatons Mechancal Systems Chemcal and Reacton Systems Hybrd Vehcle Desgn Inventory Control Electrc Power System Desgn Buldng HVAC Water Resource Management Department of Chemcal and Bologcal Engneerng

56 Proft Control Applcatons Mechancal Systems Chemcal and Reacton Systems Hybrd Vehcle Desgn Inventory Control Electrc Power System Desgn Buldng HVAC Water Resource Management Department of Chemcal and Bologcal Engneerng

57 Fludzed Catalytc Cracker Regenerator and Separator (dynamc): Rser (pseudo steady state): Department of Chemcal and Bologcal Engneerng (adapted from Loeblen & Perkns, 1999)

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

59 Catalyst Flow (kg/s) Inlet Ar (kg/s) Regenerator emp (K) Cyclone emperature (K) Proft Control vs. Fxed Controller Back-off Fxed Controller Free Controller Coke Fracton n Separator Separator emperature (K) Fracton of Coke n Regenerator x Oxygen Mass Fracton x 1-4 Department of Chemcal and Bologcal Engneerng

60 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% Department of Chemcal and Bologcal Engneerng

61 Hybrd Vehcle Desgn Power Bus arm fc bat scap R arm Fuel Cell E fc R bat E bat R scap E scap E arm L arm w arm Department of Chemcal and Bologcal Engneerng

62 DC-DC Converters Power Bus arm fc afc bat abat scap ascap R arm Fuel Cell E fc DC-DC Converter R bat E bat DC-DC Converter R scap E scap DC-DC Converter E arm L arm w arm k fc k bat k scap Department of Chemcal and Bologcal Engneerng

63 Servo-Loops wth PI Controllers PI (sp) P fc + - PI (sp) P bat + - PI (sp) P scap + - k fc P fc k bat P bat k scap P scap Vehcle Power System Department of Chemcal and Bologcal Engneerng

64 Supervsory Control Hgh Level Controller (sp) P mot PI (sp) P fc + - PI (sp) P bat + - PI (sp) P scap + - k fc P fc k bat P bat k scap P scap Vehcle Power System Department of Chemcal and Bologcal Engneerng

65 Power to Motor (kw) Speed (mph) Drve Cycle Data and Modelng tme (sec) tme (sec) Department of Chemcal and Bologcal Engneerng

66 Hgh Level Battery Model E bat P bat P (loss) bat Department of Chemcal and Bologcal Engneerng

67 Hgh Level Battery Model E bat P bat P (loss) bat E mn bat E mn E bat bat E max bat E max bat eˆ bat m bat Department of Chemcal and Bologcal Engneerng

68 Hgh Level Battery Model E bat P bat P (loss) bat E mn bat E mn E bat bat E max bat E max bat eˆ bat m bat P P P mn bat mn bat P mn bat P max bat bat rate d Cˆ, bat eˆ batmbat ˆ rate, c bat eˆ batmbat C Department of Chemcal and Bologcal Engneerng

69 Power and Energy Constrants of the Battery E bat P C E max rate,c max bat bat bat E eˆ m max bat bat bat E mn bat P bat Department of Chemcal and Bologcal Engneerng P C E mn rate,d max bat bat bat

70 Constrants a Functon of the Mass E bat P C E max rate,c max bat bat bat E eˆ m max bat bat bat P bat Department of Chemcal and Bologcal Engneerng

71 Aspect Rato a Functon of C-Rate E bat P C E max rate,c max bat bat bat E eˆ m max bat bat bat P bat Department of Chemcal and Bologcal Engneerng

72 Hgh Level Battery Model E bat P bat P (loss) bat E mn bat E mn E bat bat E max bat E max bat eˆ bat m bat P ( loss) bat lˆ P bat 2 bat m bat P P P mn bat mn bat P mn bat P max bat bat rate d Cˆ, bat eˆ batmbat ˆ rate, c bat eˆ batmbat C Department of Chemcal and Bologcal Engneerng

73 Operatng Regon wth Power Losses E bat P bat Department of Chemcal and Bologcal Engneerng

74 Hgh Level Super Cap Model E sc P sc P (loss) sc E mn sc E mn E sc sc E max sc E max sc eˆ sc m sc P ( loss) sc 2 Psc lˆ m sc sc P P P mn sc mn sc mn sc P P max sc sc rate d Cˆ, sc eˆ scmsc ˆ rate, c sc eˆ scmsc C Department of Chemcal and Bologcal Engneerng

75 Fuel Cell Model Anode Sold Materal Current Collector In Cathode (H 2, H 2 O) H Ar n 2 O 2 H + H + H 2 O H + H + H + N 2 Anode Exhaust H + H + H + H 2 O Cathode Exhaust MEA Department of Chemcal and Bologcal Engneerng

76 Hgh Level Fuel Cell Model P P fc fc P mn fc P P mn fc P max pˆ fc fc fc m P fc max fc P P P mn fc mn fc max fc P fc C C P rate, d bat rate, c bat pˆ max fc pˆ fc fc m m fc fc Department of Chemcal and Bologcal Engneerng

77 Power Losses Increases Average Fuel Cell Power P fc E bat ` Δ P fc P bat Department of Chemcal and Bologcal Engneerng

78 Desgn Problem Formulaton mn{ cˆ m cˆ m cˆ m } st.. fc fc bat bat sc sc P P P P fc o bat sc m m m m m v o fc bat sc Pbat bat Pbat bat lbatmbat Pbat lbatm bat P P sc sc sc l m sc sc sc sc sc sc P l m AX BY AX BY Go mvg 1 1 Go mvg1 w x u x u D X D X D Y X D Y P E E 2 max fc max bat max sc P P P max fc max bat max sc P fc E E bat sc P 1 2 E 3 4 P 5 6 fc E bat sc P P P P bat sc fc bat P sc P fc mn fc E E mn bat mn sc P P P mn bat mn sc mn fc Department of Chemcal and Bologcal Engneerng

79 Case Study Data echnology Lthum Battery Super- Capactor PEM Fuel Cell Cost $59/kg $93/kg $3/kg C-Rate.5 hr hr -1 1 hr -1 Power Densty 1 W/kg 11, W/kg 1 W/kg Appetecch & Prosn (25) Portet, aberna, Smon, Flahaut, & Laberty-Robert (25) Murphy, Csar & Clarke (1998) Department of Chemcal and Bologcal Engneerng

80 Case Study Soluton echnology Lthum Battery Super- Capactor PEM Fuel Cell Mass 3 kg 2.8 kg 3.5 kg Nomnal Power.1 kw 1.5 kw 1.8 kw otal Captal Cost Cost $177 $26 $15 $3,8 Department of Chemcal and Bologcal Engneerng

81 P fc (kw) Optmal Fuel Cell Sze and Operatng Regon 3.5 Fuel Cell 2.1 Fuel Cell Power(kW) P fc (kw/s) x tme(hr) Department of Chemcal and Bologcal Engneerng

82 E sc (kj) Optmal Super Cap Sze and Operatng Regon 7 Super Capactor 15 SuperCap Power, kw P sc (kw) tme(hr) Department of Chemcal and Bologcal Engneerng

83 E bat (kj) Optmal Battery Sze and Operatng Regon 1 8 Battery Battery Power, kw P bat (kw) tme(hr) Department of Chemcal and Bologcal Engneerng

84 Buldng HVAC Heat Leakage ( outsde measured) Volume of Ar (the Room) Sold Materal sold room, C room Contamnant Source: S c F rcy, room, C room F rcy, cool, C room F fresh, room, C room F fresh, cool, C fresh Ar Processng Unt ( cool = 2 o C) Energy Usage F fresh, room, C room F fresh, outsde, C fresh (C fresh = ) Control Varables: room and C room Manpulated Varables: F rcy and F fresh Dsturbances: outsde and S c Department of Chemcal and Bologcal Engneerng

85 F fresh (m 3 /s) F ryc (m 3 /s) HVAC Control C (ppm) room ( o C) room Energy Usage of radtonal Controller: 3.16 kw Energy Usage of Energy Effcent Controller: 2.55 kw (a reducton of almost 2%). Department of Chemcal and Bologcal Engneerng

86 Outlne Model Predctve Controller unng Pseudo-Constraned Control Back-off and Proft Control Market Responsve Control Department of Chemcal and Bologcal Engneerng

87 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 Department of Chemcal and Bologcal Engneerng

88 Cents per k hr emperature ( C) Energy Prces and Weather 4 Electrcty Prce Outsde emperature me (days) Cyclcal pattern wth a phase shft of about 3 hours. Department of Chemcal and Bologcal Engneerng

89 Cents per k hr emperature ( C) Operaton of the 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 4 Electrcty Prce Outsde emperature me (days) Department of Chemcal and Bologcal Engneerng

90 Response to Market Changes EDOR s due to dfferent controller tunngs BOP wth less proft BOP wth more proft * * OSSOP Peng et al. (25) Department of Chemcal and Bologcal Engneerng

91 Electrc Prce Model Whte Nose Input Shapng Flter Sequence wth Electrcty Prce Characterstcs Department of Chemcal and Bologcal Engneerng

92 Electrc Prce Model Whte Nose Input Shapng Flter Sequence wth Electrcty Prce Characterstcs Measured Electrcty Prce State Estmator and/or Predctor Predcton of Electrcty Prce Department of Chemcal and Bologcal Engneerng

93 Model Predctve Control mn pe( t)* vu ( t) dt v u ( t) where pe( t) ~ the predcted prce (or value) vu ( t) ~ the velocty of usage and S(t) ~ amount n storage Constrants nclude : v u ( t) v max u and S( t) S max Department of Chemcal and Bologcal Engneerng

94 Model Predctve Control mn pe( t)* vu ( t) dt E[ pe * vu ] Ce v u ( t) where pe( t) ~ the predcted prce (or value) vu ( t) ~ the velocty of usage and S(t) ~ amount n storage Constrants nclude : v u ( t) v max u and S( t) S max Department of Chemcal and Bologcal Engneerng

95 System Desgn mn vu ( t) pe( t)* vu ( t) dt E * p e vu Ce ( v u ( t) max v max u and max How does v and S mpact C u e S( t) S max )? Department of Chemcal and Bologcal Engneerng

96 System Desgn mn vu ( t) pe( t)* vu ( t) dt E * p e vu Ce ( v u ( t) max v max u and max How does v and S mpact C u e S( t) S max )? MPCcannot answer ths queston! Department of Chemcal and Bologcal Engneerng

97 Expected Cost of Electrcty Whte Nose Input Shapng Flter p e (t) E[p e* v u ] Manpulated Varables (Controller s u=lx) Process Model v u (t) Department of Chemcal and Bologcal Engneerng

98 Re-Scalng of Prce a w(t) Shapng Flter p' e (t) ( p' e a pe) E[p' e* v u ] Manpulated Varables Process Model v u (t) (Controller s u=lx) Department of Chemcal and Bologcal Engneerng

99 Correlatng Prce and Usage If E 2 ( ' ) p e v u and p' e a p e then v u ( t) a p e ( t) Department of Chemcal and Bologcal Engneerng

100 Department of Chemcal and Bologcal Engneerng Correlatng Prce and Usage ) ( ) ( then t p t v e u a ) ' ( If 2 p e v u E e e p p a ' and ] [ ] [ 2 ] [ u u e e v E v p E p E a a ] [ ] [ ] [ u u e e v E v p E p E a a e u e e C v p E p E ] [ ] [ 2 a

101 Mnmum Cost of Electrcty L, a C e mn c R a 2 R p e ( c E[ ]) E E E 2 ( ' ) p e v u 2 max 2 v u v ) ( u 2 max 2 S (S ) Department of Chemcal and Bologcal Engneerng

102 kw hr / day hermal Energy Storage (Small Storage Unt) 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 25 2 Heat from Room Heat to Cooler Heat to ES Unt me (days) Department of Chemcal and Bologcal Engneerng

103 kw hr / day hermal Energy Storage (Medum Storage Unt) 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 Heat from Room Heat to Cooler Heat to ES Unt me (days) Department of Chemcal and Bologcal Engneerng

104 kw hr / day hermal Energy Storage (Large Storage Unt) 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 3 2 Heat from Room Heat to Cooler Heat to ES Unt me (days) Department of Chemcal and Bologcal Engneerng

105 kw hr / day kw hr / day kw hr / day hermal Energy Storage (Comparson of Storage Cases) 25 2 Heat from Room Heat to Cooler Heat to ES Unt me (days) Heat from Room Heat to Cooler Heat to ES Unt 3 2 Heat from Room Heat to Cooler Heat to ES Unt me (days) me (days) Department of Chemcal and Bologcal Engneerng

106 $ / kw hr Electrcty Costs ($ / day) hermal Energy Storage (Cost Comparsons) 3 2 One on ES Unt Fve ons ES Unt en ons ES Unt 1 Electrcty Prce me (days) Average Coolng Costs: One ton: $8 per day Fve tons: $7 per day (14% savngs) en tons: $6 per day (25% savngs) Department of Chemcal and Bologcal Engneerng

107 Mnmum Levelzed Cost L, a, v mn max u, S max c R a c L,1 v max u c L,2 S max E E E 2 ( ' ) p e v u 2 max 2 v u v ) ( u 2 max 2 S (S ) Department of Chemcal and Bologcal Engneerng

108 Mnmum Levelzed Cost L, a, v mn max u, S max E c R a c L,1 v max u 2 ( ' ) p e v u c L,2 S max E E 2 max 2 v u v ) ( u 2 max 2 S (S ) Non-Convex Problem (but global soluton from branch and bound) Department of Chemcal and Bologcal Engneerng

109 Integrated Gasfcaton Combned Cycle (IGCC) Department of Chemcal and Bologcal Engneerng

110 Acknowledgements Current Students: Ben Omell Mng-We Yang Former Students and Collaborators: Amt Manthanwar Davd Mendoza-Serrano Syed Amed Dr. Ju-Kun Peng (ANL) Professor Ralph Muehleson (CAEE, II) Professor Demetros Moschandreas (CAEE, II) Fundng: Natonal Scence Foundaton (CBE 96796) Graduate and Armour Colleges, II Chemcal & Bologcal Engneerng Department, II Department of Chemcal and Bologcal Engneerng

111 Conclusons Relatonshp between control system performance and plant proft quantfed. Enables proft guded control system desgn. Broad set of applcatons from a varety of dscplnes. Lnear controller can be desgned for market responsveness. Non-convex, but global methods can be used to sze and/or select equpment. Department of Chemcal and Bologcal Engneerng