Donald J. Chmielewski and David Mendoza-Serrano Department of Chemical and Biological Engineering Illinois Institute of Technology

Size: px

Start display at page:

Download "Donald J. Chmielewski and David Mendoza-Serrano Department of Chemical and Biological Engineering Illinois Institute of Technology"

Hannah Simon
5 years ago
Views:

1 Multstage Stochastc Programmng for the Desgn of Smart Grd Coordnated Buldng HVAC Systems Donald J. Chmelews and Davd Mendoa-Serrano Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng

2 Power Requred from Dspatchable Generators (MW) Motvaton Smart Grd Electrc Power Networ: Estng Components Dspatch Capable Generaton Power Grd Demand (Consumers) Epected Future Components Renewable Generaton Energy Storage Responsve Demand Baselne Baselne wth Renewable Power Baselne wth Renewable Power Impact of S torage and DR tme (days) Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng tme (days) 2

3 Desgn of Buldng HVAC Systems Heat from Envronment Buldng Heat from Buldng Chller Power Consumpton Heat from Envronment Buldng Heat from Buldng Heat to Chller Heat to ES Chller Power Consumpton hermal Energy Storage Analyss requres detals of operatng polcy Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng Multstage Stochastc Programmng (MSP) framewor 3

4 Presentaton Outlne Motvaton for Multstage Stochastc Programmng (MSP) Revew of MSP Proposed Soluton Method for MSP Future Drectons Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 4

5 Revew of Stochastc Programmng wo-stage Stochastc Program: mn c Q( ) s.t A b where Q( ) E mn ( ) s.t ( ) q y Wy h y are here-and-now (equpment) varables y are wat-and-see (operatng) varables are random (stochastc) varables c and q() are captal and operatng costs h() s the dsturbance y m, m = 1 M m, m = 1 M Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 5

6 Revew of Stochastc Programmng Scenaro Based Appromaton: M A b mn c pmqm ym s.t, ym m 1 Wym hm m Fnte support of scenaros: m, m = 1 M Each wth outcomes: q m = q( m ) and h m = h( m ) Each wth a probablty: p m = p( m ) Correspondng wat-and-see varables: y m, m = 1 M 1... M Decomposton Methods Iterate over: c M m1 mn y m p m q m y m s.t Wy m h m Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 6

7 Multstage Stochastc Programmng Varables ndeed n tme: y(1), y(2), y(3),, y(n) and (1), (2), (3),, (N) If horon N = 3, then scenaro appromaton s: mn s.t c M m1 A b W y 0 W y 0 p m mnl mnl q m y mnl W y 0 (1) W y (2) W y (1) 1 1 mnl mnl mnl M m1 n1 (1) h (2) h (3) h m 1... M, n 1... M, l 1... M where p mnl = p( m (1), n (2), l (3)) s the jont probablty of scenaro mnl Non-antcpatory constrant requres past decsons cannot be changed: M p mnl mnl mnl mn q (1) (3) n (2) y mnl (2) y m11 (1) = y m12 (1) = = y m33 (1) and y mn1 (2) = y mn2 (2) = y mn3 (2) M M M m1 n1 l1 p mnl q l y mnl (3) Nested Decomposton Soluton Methods Requred Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng Other Soluton Methods Requred 7

8 MSP Operatng Polcy Soluton Methods * Cost Functon Appromatons - Uses reserve constrants n place of non-antcpatory constrants - Sub-optmal due conservatsm of reserve constrants Scenaro Appromatons - Computatonally ntensve (as dscussed prevously) - Easly etends to equpment desgn Polcy and Value Functon Appromatons - Same as Appromate Dynamc Programmng (curse of dmensonalty) - A bt dffcult to etend to equpment desgn Loo-Ahead Polces - Same as Economc MPC. Closed-loop mplementaton s non-antcpatory - Etenson to equpment desgn requres Monte Carlo search * Powell AI Magane 2014 Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 8

9 EMPC for Buldng HVAC Heat from Envronment Buldng Heat from Buldng Heat to Chller Heat to ES Chller Power Consumpton hermal Energy Storage Houston, X (July, 2012) N mn Pc ( t) t 1 0 C e ( t) P c ( t) Sold Outsde emperature Dotted Electrcty Prce 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) Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 9

10 Energy n Storage (W h) Heat to Chller (W ) EMPC Smulaton EMPC tme (days) EMPC tme (days) Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 10

11 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 11

12 Presentaton Outlne Motvaton for Multstage Stochastc Programmng (MSP) Revew of MSP Proposed Soluton Method for MSP Future Drectons Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 12

13 A Soluton Method Captal Cost = c c 0 where 1 ma 0. 6 E S 0,1 NPV(Equp Se) s non-conve Search over NPV mn { Captal Cost + Operatng Costs } Equpment Se Monte Carlo Smulaton usng EMPC Average Operatng Cost Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 13

14 Net Present Value Local Mnma n NPV Equpment Varables Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 14

15 Net Present Value NPV usng a Surrogate Polcy Equpment Varables Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 15

16 Net Present Value Intal Pont for Monte Carlo Search Equpment Varables Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 16

17 Novel wo-step Soluton Procedure Global Search over appromate NPV Intal Search Pont Search over NPV mn { Captal Cost + Operatng Costs } Economc Lnear Optmal Control (ELOC) as surrogate polcy Equpment Se Monte Carlo Smulaton usng EMPC Average Operatng Cost Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 17

18 Economc Lnear Optmal Control (ELOC) u L ELOC Steady-State Operatng Lne Epected Dynamc Operatng Regons Mnmally Baced-off Operatng Pont Dfferent Controller unng Values Optmal Steady-State Operatng Pont Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 18

19 Economc Standard ELOC Lnear Problem Optmal Control mn s, m, q,,, X, Y g op.cost ( q) s. t. s sqrt( dag( X GwG ( AX BY ) ( D As Bm q X ma q D Y ) u Gp 2 )) ( AX ( D q q q mn BY ) X X D s D m 0 DuY ) X u 0 Branch and Bound wth SDP solver Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 19

20 Energy n Storage (W h) Heat to Chller (W ) ELOC Smulaton EMPC ELOC tme (days) EMPC ELOC tme (days) Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 20

21 Economc ELOC Based Lnear Desgn Optmal (Global Control Soluton) mn s, sm, m, q, q,,,, X, YX,, Y ma mn q, q s. t. g op.cos op.cos t t s g ( D ( q) ( q ) g As Bm q ma sqrt( dag( X GwG ( AX BY ) X q D Y ) u cap.cost Gp 2 )) ( q mn ( AX ( D, q q q q mn BY ) X X ma ) D s D m 0 DuY ) X u 0 Generaled Benders Decomposton Master Problem (BARON) Prmal Problem (SDP solver) Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 21

22 Eample of ELOC Based Desgn Heat from Envronment Buldng Heat from Buldng Heat to Chller Heat to ES hermal Energy Storage Chller Power Consumpton c c ma 0. 6 where 0,1 E S Captal Cost = 0 1 Chller Cost = ($500/We) P ma c Case 1: ES Cost = (14.2 $/W h) E s ma Case 2: ES Cost = (2.8 $/W h) E s ma Case 3: ES Cost = (28.4 $/W h) E S ma Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 22

23 Eample of ELOC Based Desgn Case 1: ES Cost = (14.2 $/W h) E s ma Chller Cost = ($500/We) P c ma Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 23

24 Eample of ELOC Based Desgn Case 2: ES Cost = (2.8 $/W h) E s ma Case 3: ES Cost = (28.4 $/W h) E s ma Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng Chller Cost = ($500/We) P ma c 24

25 Proposed Soluton Method Global Search over appromate NPV Intal Search Pont Search over NPV mn { Captal Cost + Operatng Costs } Economc Lnear Optmal Control (ELOC) as surrogate polcy Equpment Se Monte Carlo Smulaton usng Constraned EMPC ELOC Average Operatng Cost Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 25

26 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 26

27 Constraned Predctve Form ELOC of ELOC mn, u N 1 1 mn ( D A Q ELOC D u ma Bu u u R ELOC u ) N P ELOC N s. t. Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 27

28 Energy n Storage (W h) Heat to Chller (W ) Constraned ELOC Smulaton EMPC Horon 24 hours Constraned ELOC Horon 3 hours EMPC Constraned ELOC tme (days) EMPC Constraned ELOC tme (days) Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 28

29 Proposed Soluton Method Global Search over appromate NPV Intal Search Pont Search over NPV mn { Captal Cost + Operatng Costs } Economc Lnear Optmal Control (ELOC) as surrogate polcy Equpment Se Monte Carlo Smulaton usng Constraned EMPC ELOC Average Operatng Cost Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 29

30 ma P (We c ) Gradent Search wth Constraned ELOC mn E (W s hr) Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 30

31 Department of Chemcal and Bologcal Engneerng Department of Chemcal and Bologcal Engneerng Illnos Insttute of echnology Illnos Insttute of echnology Constraned Constraned ELOC ELOC 31 ma mn D u D u N ELOC N N ELOC ELOC u Bu A s t P u R u Q 1 1,.. ) ( mn ma mn N ELOC N N ELOC ELOC u c P u R u Q 1, ) ( mn Constraned Constraned ELOC wth Soft Constrants ELOC wth Soft Constrants

32 Penalty for Infeasble Operaton Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 32

33 Electrcty Cost ($/MWh) Future Drectons Epand Eample: Non-conve captal cost for equpment se Integer varables for technology selecton Med Integer ELOC: HVAC operaton has many dscrete decsons Recently developed method of other applcatons Electrcty Prce Uncertanty: Day of the Year Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 33

34 Acnowledgements Former Students: Benjamn Omell (PhD, 2013) Mng-We Yang (PhD, 2010) Ju-Kun (Mchael) 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 34

35 Conclusons Identfed Multstage Stochastc Programmng as the approprate framewor for the desgn of smart grd coordnated systems Scenaro based soluton procedure seems ntractable EMPC seems reasonable as an operatng polcy Proposed a novel two-step soluton procedure Global search usng ELOC as a surrogate polcy Followed by gradent search usng Constraned ELOC as surrogate polcy Penalty method developed to address nfeasbltes Illnos Insttute of echnology Department of Chemcal and Bologcal Engneerng 35

Donald J. Chmielewski

Donald J. Chmielewski (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 391.5 391 390.5 390 389.5 389 388.5 388 387.5 383