Demand Response of Building HVAC Systems Using Infinite-Horizon Economic MPC
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1 Demand Response of Bilding HVAC Sysems Using Infinie-Horion Economic MPC David I. Mendoa-Serrano and Donald J. Chmielewski AIChE Annal Meeing Ocober 212, Pisbrg, PA
2 Presenaion Oline 2 Backgrond Bilding HVAC and hermal Energy Sorage (ES Economic Model Predicive Conrol (EMPC Applicaion of EMPC o Bilding HVAC wih ES Economic Benefis Some Isses wih EMPC Economic Linear Opimal Conrol ( Infinie Horion EMPC (IH-EMPC
3 emperare (F HVAC Power Consmpion 3 Cooling is mainly reqired dring he hoes imes of a day ime (days Oside emperare. Ags 3-6, 21. Pisbrg, PA.
4 radiional HVAC Sysem 4 Hea from Environmen Bilding Hea from Bilding Chiller Power Consmpion Hea is removed from he bilding by a chiller Chiller consmes elecric power Assme real-ime prices for elecriciy
5 HVAC and he Smar Grid Generaors ransmission Consmer Demand Generaor Dispach Renewable Smar Homes Smar Manfacring wih Sorage Commercial Bildings
6 Elecriciy Price ($/MWhr emperare (F Correlaion Beween Cooling Load and Energy Prices ime (hors ime (days Ags 3-6, 21. Pisbrg, PA.
7 hermal Energy Sorage (ES 7 ES helps ime shif elecriciy consmpion o periods of low elecriciy prices.
8 Model Predicive Conrol (MPC 8 min g,,,, w w d s.. f (,, w h(,, w min ( ma
9 radiional MPC 9 Qadraic Obecive g,, w Q R min g,, w d,, w s.. f (,, w h(,, w min ma (
10 Economic MPC 1 g,, w Economic Obecive Insananeos Ependire min g,, w d,, w s.. f (,, w h(,, w min ma (
11 Lierare on EMPC 11 Concepal Developmen and Sabiliy Isses: Rawlings and Amri (29; Diehl, e al. (211; Hang and Biegler (211; Heidarinead, e al. (212 Process Schedling: Karwana and Keblisb (27; Bamrcker and Biegler (21; Lima e al. (211; Kosina e al. (211 Power Sysems: Zavala e al. (29; Xie and Ilić (29, Hovgaard, e al. (211, Omell and Chmielewski (211 HVAC Sysems: Bran (1992; Morris e al. (1994; Kinner-Meyer and Emery (1995; Hene e al. (23; Bran (27; Oldewrel e al. (21, Ma e al. (212; Mendoa and Chmielewski (212
12 Presenaion Oline 12 Backgrond Bilding HVAC and hermal Energy Sorage (ES Economic Model Predicive Conrol (EMPC Applicaion of EMPC o Bilding HVAC wih ES Economic Benefis Some Isses wih EMPC Economic Linear Opimal Conrol ( Infinie Horion EMPC (IH-EMPC
13 Elecriciy Price ($/MWhr Economic MPC for HVAC 13 g,, w Economic Obecive P C C e ime (days Hea from Environmen Bilding Hea from Bilding Hea o Chiller Hea o ES Chiller Power Consmpion hermal Energy Sorage
14 An Eample Bilding 14 Walls Room Room Windows o o Room Room o 21 3 Oside Environmen ( 3 Room Room Oside Environmen ( 3
15 Energy in Sorage (MWhr Hea from Room (kw Hea o Chiller (kw emperare in Room (C Elecriciy Price ($/MWhr Oside emperare (C EMPC Simlaion ime (hors ime (hors ime (hors EMPC Predicion Horion is 12 hors Simlaion ime is 21,54 secs for a 6 simlaion days ime (hors ime (hors ime (hors
16 Oside emperare (C Energy in Sorage (MWhr Hea o Chiller (kw Impac of Horion Sie on EMPC ime (hors Simlaion imes: = 1 hr: 2.6 sec Operaing Coss: = 1 hr: $ ime (hors ime (hors
17 Oside emperare (C Energy in Sorage (MWhr Hea o Chiller (kw Impac of Horion Sie on EMPC ime (hors hr horion 12 hrs horion ime (hors Simlaion imes: = 12 hr: 21,54 sec = 1 hr: 2.6 sec Operaing Coss: = 12 hr: $746 = 1 hr: $ ime (hors
18 Infinie-Horion MPC 18 min s.,. g(,, w d min A D B ( D Gw ma
19 Infinie-Horion MPC wih Finie Consrains 19 min s.,. g(,, w d A B Gw D D min ( ma
20 2..,, (,, ( min, s d w g d w g D D Gw B A ma min ( Infinie-Horion MPC wih Finie Consrains
21 Finie-Horion MPC wih erminal Cos 21.. ( (,, ( min, s d w g..,, ( min ( (, s d w g where: Gw B A D D Gw B A ma min (
22 Unconsrained Vale Fncion 22 ( ( s.. A min, g(,, B Gw w d if: g(,, w Insananeos Ependire hen: does no eis
23 Unconsrained Vale Fncion 23 ( ( s.. A min, g(,, B Gw w d
24 Saisically Consrained Vale Fncion 24 ( ( s.. E A D min, D B Gw g(,, w d 2 min ma 2min, 2
25 Presenaion Oline 25 Backgrond Bilding HVAC and hermal Energy Sorage (ES Economic Model Predicive Conrol (EMPC Applicaion of EMPC o Bilding HVAC wih ES Economic Benefis Some Isses wih EMPC Economic Linear Opimal Conrol ( Infinie Horion EMPC (IH-EMPC
26 Economic Linear Opimal Conrol ( Developmen Sochasic Disrbance Model 26 Consrain Sochasic Conrol Analyical Epression for Revene Synhesis
27 Sochasic Disrbance Model 27 w SF1 3 a 1 SF2 C e a 2 SF3 B e A B Gw G ( G a G a G
28 Economic Linear Opimal Conrol ( Developmen Sochasic Disrbance Modeling 28 Consrain Sochasic Conrol Analyical Epression for Revene Synhesis
29 Sysem Model Hea from Environmen Bilding Hea from Bilding Hea o Chiller Hea o ES hermal Energy Sorage Chiller Power Consmpion A B Gw min D D ma Walls Room Room Windows w SF1 o o Room Room o 21 3 a 1 SF2 Oside Environmen ( 3 Room Room Oside Environmen ( 3 a 2 SF3
30 Consrained Sochasic Conrol A B Gw D L D Find L sch ha ( A BL ( A BL GS w G ( D D L ( D D L 2 ma and 2 min, 1... n
31 Consrained Sochasic Conrol 1 Consrains: 2 i i * 2 2 and 2, 1... n ma min
32 Economic Linear Opimal Conrol ( Developmen Sochasic Disrbance Modeling 32 Consrain Sochasic Conrol Analyical Epression for Revene Synhesis
33 Ependires R C e P c R 1 lim E[ C P e c ] C e P d c
34 Economic Linear Opimal Conrol ( R E [ C P ] e c Enforce he condiion: where: ~ Pc Pc Pc C ~ ~ ~ and E[ C ] C C e B e e e e ~ P c ~ a C 1 e a 2 ~ B e
35 Economic Linear Opimal Conrol ( R E [ C P ] e c Enforce he condiion: where: ~ Pc Pc Pc C ~ ~ ~ and E[ C ] C C e B e e e e ~ P c ~ a C 1 e a 2 ~ B e hen: R ~ ~ E[ Ce Pc ] CePc ~ E[ a C P a Ce ] Ce C e P c e c
36 Economic Linear Opimal Conrol ( Developmen Sochasic Disrbance Modeling 36 Consrain Sochasic Conrol Analyical Epression for Revene Synhesis
37 Economic Linear Opimal Conrol ( L,,,, a, a min 1 2 a 1 Ce C P e c
38 c e Ce L C P 1,,,,, 2 1 min a a a Economic Linear Opimal Conrol ( w n D L D D L D G G G G G GS BL A BL A s 1..., 2 and 2 ( ( ( (.. min ma a a
39 Synhesis w n D L D D L D G G G G G GS BL A BL A s 1..., 2 and 2 ( ( ( (.. min ma a a c e Ce L C P 1,,,,, 2 1 min a a a his problem can hen be convered o a Conve Opimiaion Problem L 39
40 Energy Sorage (MWhr Hea o Chiller (KW Comparison of EMPC and EMPC ime (hors 1 EMPC ime (hors
41 Presenaion Oline 41 Backgrond Bilding HVAC and hermal Energy Sorage (ES Economic Model Predicive Conrol (EMPC Applicaion of EMPC o Bilding HVAC wih ES Economic Benefis Some Isses wih EMPC Economic Linear Opimal Conrol ( Infinie Horion EMPC (IH-EMPC
42 42 L LQR.. min (, s d R M M Q Linear Qadraic Opimal Conrol Gw B A ( P LQR
43 Infinie-Horion Economic MPC 43 ( s.. min, A Q M B Gw M R d ( P L
44 Linear Qadraic Reglaor (LQR => Inverse Opimaliy * 44 L L R L L R A P P B P A L R R P B where:, P R Q L R L A P P A M ( L R P B * Chmielewski & Manhanwar (24
45 45.. ( ( min, s P d R M M Q D D Gw B A ma min ( Infinie-Horion Economic MPC
46 Energy in Sorage (MWhr Hea o Chiller (KW Comparison of and IH-EMPC 46 6 IH-EMPC ime (hors IH-EMPC ime (hors Predicion horions is 1 hor for IH-EMPC
47 Energy in Sorage (MWhr Hea o Chiller (KW Comparison of EMPC and IH-EMPC ime (hors ime (hors Predicion horions are: 12 hors EMPC and 1 hor for IH-EMPC EMPC Inf-horion EMPC
48 Comparison of EMPC and IH-EMPC 48 Simlaion imes: EMPC = 12 hr: 21,54 sec EMPC = 1 hr: 2.6 sec IH-EMPC = 1 hr: 2.8 sec % redcion in compaional effor
49 Comparison of EMPC and IH-EMPC 49 Simlaion imes: EMPC = 12 hr: 21,54 sec EMPC = 1 hr: 2.6 sec IH-EMPC = 1 hr: 2.8 sec Operaing Coss: EMPC = 12 hr: EMPC = 1 hr: IH-EMPC = 1 hr: $746 $845 $ % redcion in compaional effor 3.75% increase in operaing coss
50 Conclsions 5 EMPC provides desired economic performance EMPC has challenges: Bang-bang acaion and chaering Large compaional effor Invenory creep for small horions Infinie Horion EMPC shown o: Redce bang-bang and chaering Small compaional effor for small horions Virally no invenory creep for small horions
51 Acknowledgemens 51 Crren and Former Sdens: Benamin Omell (similar work wih IGCC Olwasanmi Adeod (similar work wih power ransmission Ming Yang, PhD (aiwan Elecric Ami Manhanwar (Imperial College Personal Commnicaions: Ignacio E. Grossman (CMU and Ricardo M. Lima (CMU Fnding: Naional Science Fondaion (CBE Wanger Insie for Ssainable Engineering Research (II
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