Donald J. Chmielewski
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1 (K P c ma (We Optmal Desgn of Smart Grd Coordnated Systems Donald J. Chmelews Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology (K Illnos Insttute of echnology mn E (W hr s Department of Chemcal and Bologcal Engneerng Steady-State Operatng Lne Dfferent Controller unng Values Epected Dynamc Operatng Regons Optmal Steady-State Operatng Pont Mnmally Baed-off Operatng Pont
2 Chcago Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 2
3 II and Chcago Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 3
4 Presentaton Outlne Revew of Economc Model Predctve Control (EMPC Challenges Assocated wth the Desgn of Smart Grd Systems ELOC and Constraned ELOC Computatonally Effcent Desgn of Smart Grd Systems Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 4
5 Acnowledgements Former Students: Benjamn Omell (PhD 2013 Davd Mendoa-Serrano (PhD 2013 Mng-We Yang (PhD 2010 Ju-Kun Peng (PhD 2004 Amt Manthanwar (MS 2003 Current Students: Oluwasanm Adeodu Jn Zhang Fundng: Natonal Scence Foundaton (CBE Wanger Insttute for Sustanable Engneerng Research (II Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 5
6 Department of Chemcal and Bologcal Engneerng Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology Illnos Insttute of echnology Revew of MPC Revew of MPC N f N m s s s N q q q p m s h q p m s f s s t s l p m s l ma mn ( (.. ( ( mn At tme the current tme solve: hen the manpulated varable s set as: * m m 6
7 radtonal vs. Economc MPC In tradtonal MPC the objectve s regulaton: mn u N 1 ( Q u Ru N P N In EMPC the objectve s mame average proft (ntegral of nstantaneous proft: N 1 ma g s m ( IP ( s m p Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 7
8 Economc MPC Lterature Conceptual Development and Stablty Issues: Rawlngs and Amrt (2009; Dehl et al. (2011; Huang and Begler (2011; Hedarnejad et al. (2012 Process Schedulng: Karwana and Keblsb (2007; Baumrucer and Begler (2010; Lma et al. (2011; Kostna et al. (2011 Buldng HVAC Systems: Braun (1992; Morrs et al. (1994; Kntner-Meyer and Emery (1995; Hene et al. (2003; Braun (2007; Oldewurtel et al. (2010 Ma et al. (2012; Mendoa and Chmelews (2012 Power Schedulng: Zavala et al. (2009; Xe and Ilć (2009 Hovgaard et al. (2011 Omell and Chmelews (2013 Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 8
9 Economc MPC Eample A non-sothermal CSR: C A0 0 n dc dt dc dt d dt A B n ( CA V n C V n ( V 390K Dsturbance: 0 0 B Manpulaton: C 0 A e H C E R r p 0 e C E A 0 e R E C A R ss ss CA0 CA C A K C A C A C B n Instantaneous Proft: g ( IP ( C B 10n C B Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 9
10 Department of Chemcal and Bologcal Engneerng Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology Illnos Insttute of echnology Economc Economc MPC Eample MPC Eample (.. 10 ma N s s N K K C C s C s f s s t C B A Ao N B s n * Model converted to dscrete-tme usng Euler s eplct method. 10
11 (K (K 0 (K C A0 (mole/m 3 Economc MPC Smulaton tme (mnutes tme (mnutes tme (mnutes (K Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 11
12 Economc MPC Eample A non-sothermal CSR: C A0 0 n C A C B n Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 12
13 Economc MPC Eample A non-sothermal CSR wth preheater: f = 303K C A0 0 n Manpulaton: Q 303K 0 385K C A C B n Instantaneous Proft: g ( IP 10C 0.005( n5 0.4 ( CB 0 n B 0 C B Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 13
14 (K (K 0 (K 0 (K C A0 (mole/m 3 Economc MPC Smulaton tme (mnutes tme (mnutes tme (mnutes tme (mnutes tme (mnutes Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 14
15 C B (mole/m 3 C A (mole/m 3 C A (mole/m 3 C A0 (mole/m 3 Economc MPC Smulaton tme (mnutes g ( IP ( C 1 B 0 n 10C B 0.005( tme (mnutes tme (mnutes C B (mole/m 3 Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 15
16 (K C B (mole/m 3 0 (K C A (mole/m 3 C A0 (mole/m 3 Economc MPC Smulaton Change horon from N = 8 to N = tme (mnutes tme (mnutes tme (mnutes tme (mnutes tme (mnutes Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 16
17 Stablty of EMPC 1 If N=8 and objectve n 10C B then SABLE 2 If N=8 and objectve n 10 C 0.005( B then UNSABLE 3 If N=10 and objectve n 10 C 0.005( B then SABLE 4 If N=10 and objectve n 10 C 0.025( B then UNSABLE 5 If N=25 and objectve n 10 C 0.025( B then SABLE Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 17
18 Why the Instablty? f = 303K C A0 0 n n ( 0 C B Q 303 C A C B n Answer: Myopc Behavor EMPC tres to lower costs by lowerng o In the short run C B and Proft wll reman hgh In the long run C B and Proft wll drop-off If N s small then EMPC wll not now about the drop-off Short term gans lead to long term losses Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 18
19 Presentaton Outlne Revew of EMPC Challenges Assocated wth the Desgn of Smart Grd Systems ELOC and Constraned ELOC Computatonally Effcent Desgn of Smart Grd Systems Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 19
20 Smart Grd Opportuntes Generators wth Dspatch ransmsson Consumer Demand Renewable Sources Energy Storage Smart Homes Commercal Buldngs Smart Manufacturng Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng
21 Electrcty Prce ($/MWhr Motvaton for Smart Grd Coordnaton 150 Hstorc electrcty prces (Chcago 2008 [PJM 2013] Day of the Year Desgn systems to eplot these tme-varyng electrcty prces. Applcatons range from: Buldng HVAC Electrc Vehcle Chargng Dstrbuted Generaton and Storage Industral Demand Response Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 21
22 Buldng HVAC Eample Heat from Envronment Buldng Heat from Buldng Chller Power Consumpton Houston X (July 2012 Sold Outsde emperature Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng Dotted Electrcty Prce 22
23 Heat Flow (KW e Buldng HVAC Eample Heat from Envronment Buldng Heat from Buldng Chller Coolng Load (Qc Heat to Chller Heat to ES hermal Energy Storage Qc Qr Chller Power Consumpton hermal Energy Storage me (days Heat to Chller Heat from Room Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 23
24 Heat Flow (KW e Heat Flow (KW e Heat Flow (KW e HVAC Equpment Sng Problem Heat from Envronment Buldng Heat from Buldng Heat to Chller Heat to ES hermal Energy Storage Chller Power Consumpton Heat from Envronment Buldng Heat from Buldng Heat to Chller Heat to ES hermal Energy Storage Chller Power Consumpton Chller Coolng Load (Qc Qc Qr Chller Coolng Load (Qc Qc Qr me (days Heat to Chller Illnos Insttute of echnology 6000 Heat from 4000 Room me (days Department of Chemcal and Bologcal Engneerng Heat to Chller Heat from Room
25 State Buldng Eample Walls o o Room Room Room Room Wndows o 21 3 N 1 mn C Pc e P c Outsde Envronment ( 3 Room Room Outsde Envronment ( 3 o K 11 A1 ( 11 o K 21A2 ( 21 o C o p0 V o Q c Q s 11 K 11 ( o 11 C 1 K p1 12 ( K12( C 1 11 p K E s Q s 22 ( 3 21 C 2 K p ( o 21 Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 25
26 EMPC Smulaton Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng Sold EMPC wth ES Dotted EMPC wthout ES 26
27 EMPC Smulaton wth Smaller Storage Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng Sold EMPC wth ES Dotted EMPC wthout ES 27
28 Smart Grd Equpment Desgn Problem Desgn problem s a Stochastc Program mn Equp Se PV f OpCost OpCost CapCost mn 1 N 0OpVar EqpSe 1 If no energy storage then two-stage problem If energy storage s allow then a multstage problem N InstOpCost ( OpVar Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 28
29 Possble Soluton Method Smulaton Perod: 28 days Operatng Cost (no ES: $759 Operatng Cost Reducton wth 1.5MWhr: 31.4% Smulaton me: 1.4 hrs EMPC Horon Se: 24 hrs Operatng Cost Reducton wth 1.5MWhr: 13.8% Smulaton me: 6.7 sec EMPC Horon Se: 3 hr Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 29
30 Inventory Creep Smulaton Perod: 28 days Operatng Cost (no ES: $759 Operatng Cost Reducton wth 1.5MWhr: 31.4% Smulaton me: 1.4 hrs EMPC Horon Se: 24 hrs Sold EMPC wth 24hr horon Operatng Cost Reducton wth 1.5MWhr: 13.8% Smulaton me: 6.7 sec EMPC Horon Se: 3 hr Dotted EMPC wth 3hr horon Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 30
31 Use of Surrogate Controllers ELOC Constraned ELOC Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 31
32 Presentaton Outlne Revew of EMPC Challenges Assocated wth the Desgn of Smart Grd Systems ELOC and Constraned ELOC Computatonally Effcent Desgn of Smart Grd Systems Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 32
33 Economc Lnear Optmal Control (ELOC u L ELOC Steady-State Operatng Lne Epected Dynamc Operatng Regons Mnmally Baed-off Operatng Pont Dfferent Controller unng Values Optmal Steady-State Operatng Pont Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 33
34 Department of Chemcal and Bologcal Engneerng Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology Illnos Insttute of echnology Economc Lnear Optmal Control Economc Lnear Optmal Control 34 mn ma.cos ( ( ( ( ( (.. ( mn j j j j j j u u w t op L q m s q q q q D L D D L D G G BL A BL A m s h q p m s f s s t q g Global Solutons can be effcently determned usng GBD
35 CSR Eample CB(mol/m (K (K CA(mol/m Statstcal constrants are clearly enforced. What about pont-wse-n-tme constrants? Constraned ELOC Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 35
36 Lnear Quadratc Regulator mn u N 1 1 ( Q A u Bu Ru N P N s. t. u L LQR Predctve Form of ELOC mn u N 1 1 ( Q A ELOC Bu u R ELOC u N P ELOC u L N ELOC s. t. Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng * see Chmelews & Manthanwar (2004 for detals 36
37 Constraned Predctve Form ELOC of ELOC N 1 mn ( QELOC u RELOC u N PELOC N s.t. u 1 A Bu D Du u mn ma (K (K CB(mol/m Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng CA(mol/m
38 Constraned ELOC (K (K 385 Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng Reactor emperature (K (K (K Manpulated Varable n(k
39 (K 0 (K Constraned ELOC EMPC Constraned ELOC Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 39
40 0 (K Constraned ELOC and Horon Se EMPC Constraned ELOC N=1 Constraned ELOC N= Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 40
41 Department of Chemcal and Bologcal Engneerng Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology Illnos Insttute of echnology Constraned ELOC Constraned ELOC and Nonlnear Plants and Nonlnear Plants N ELOC N N ELOC ELOC u Bu A s t P u R u Q ( mn 41 ma mn D u D u ma mn 1 ( ( u h u f
42 ELOC n Buldng HVAC Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 42
43 Constraned ELOC n Buldng HVAC Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 43
44 Horon Se Insenstvty Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 44
45 Computatonal Effcency Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 45
46 Presentaton Outlne Revew of EMPC Challenges Assocated wth the Desgn of Smart Grd Systems ELOC and Constraned ELOC Computatonally Effcent Desgn of Smart Grd Systems Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 46
47 Where Are We? EMPC Provdes economcally optmed performance Need for large horons maes t slow ELOC and Constraned ELOC Both are good surrogates for EMPC Both are computatonally fast Objectve: Use ELOC to enable computatonal tractablty of Equpment Desgn problem Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 47
48 Use of Surrogate Controllers ELOC Constraned ELOC Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 48
49 Possble Search Scheme Global Search wth ELOC mnme NPV over here-and-now varables and ELOC parameters Statstcal Constrant Enforcement Gradent Search wth Constraned ELOC Provde: Constraned ELOC Smulatons Pont-wse-n-tme Constrant Enforcement here-and-now values Return: mnmum average operatng costs Gradent Search mnme NPV over here-and-now varables Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 49
50 Department of Chemcal and Bologcal Engneerng Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology Illnos Insttute of echnology Economc Lnear Optmal Control Economc Lnear Optmal Control ELOC Based Desgn ELOC Based Desgn 50 mn ma.cos ( ( ( ( ( (.. ( mn j j j j j j u u w t op L q m s q q q q D L D D L D G G BL A BL A m s h q p m s f s s t q g ( ( mn mn ma.cos.cos mn ma j j t cap t op q q L q m s q q g q g j j Global Solutons can be determned effcently usng GBD
51 HVAC Equpment Sng Problem Heat from Envronment Buldng Heat from Buldng Heat to Chller Heat to ES Chller Power Consumpton hermal Energy Storage Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 51
52 ELOC Based Desgn Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 52
53 Proposed Search Scheme Global Search wth ELOC mnme NPV over here-and-now varables and ELOC parameters Statstcal Constrant Enforcement Gradent Search wth Constraned ELOC Provde: Constraned ELOC Smulatons Pont-wse-n-tme Constrant Enforcement here-and-now values Return: mnmum average operatng costs Gradent Search mnme NPV over here-and-now varables Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 53
54 ma P (We c Gradent Search wth Constraned ELOC mn E (W s hr Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 54
55 Department of Chemcal and Bologcal Engneerng Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology Illnos Insttute of echnology Constraned Constraned ELOC ELOC 55 ma mn D u D u N ELOC N N ELOC ELOC u Bu A s t P u R u Q ( mn s s ma mn s c P u R u Q s N ELOC N N ELOC ELOC u 1 ( mn Constraned Constraned ELOC wth Soft Constrants ELOC wth Soft Constrants
56 Penalty for Infeasble Operaton Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 56
57 Conclusons EMPC Provdes economcally optmed performance Need for large horons maes t slow ELOC and Constraned ELOC Both are good surrogates for EMPC Both are computatonally fast Equpment Desgn for Smart Grd Systems ELOC enables computatonal tractablty Penalty method developed to address nfeasbltes Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 57
58 Desgn of Dspatchable Energy Storage ma 0 ES1 ES1 ma 0 ES 2 ES 2 CapCost j ma $ * ESj ELOC Soluton: ma ma ES1 ES 2 239MWhr Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 58
59 Power Flow P 42 (MW Power Flow P 41 (MW Coal Plant P G6 (MW Power Flow P 21 (MW ELOC Operatng Regon wth ELOC Optmal Storage Sng Gas urbne P G1 (MW Power Flow P 23 (MW Power Flow P 62 (MW Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng Power Flow P 46 (MW 59
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