Cost and Efficiency Optimal HVAC System Operation and Design

Transcription

1 Cost and Efficiency Optimal HVAC System Operation and Design D. Chmielewski, D. Mendoza-Serrano, and B. Omell Department of Chemical & Biological Engineering Heat Leakage (T outside measured) Volume of Air (the Room) Solid Material T solid T room, C room Contaminant Source: S c F rcy, T room, C room F rcy, T cool, C room F fresh, T room, C room F fresh, T cool, C fresh Air Processing Unit (T cool = 20 o C) Energy Usage F fresh, T room, C room F fresh, T outside, C fresh (C fresh = 0) Control Variables: T room and C room Manipulated Variables: F rcy and F fresh Disturbances: T outside and S c EDOR s due to different controller tunings BOP with less profit BOP with more profit * * OSSOP

2 Outline Introduction (Economic Based Tuning) HVAC / Indoor Air Quality HVAC / Thermal Energy Storage Minimum Levelized Costs

3 Motivating Example (Non-isothermal Reactor) F C A, T F dca V = F( CAin CA) + VrA dt dt V = F( Tin T ) + ( VΔH / ρc dt r = k( T ) A C A p ) r A

4 Limited Operating Region Process Limitations: T ( t) T (max) - Catalyst protection or onset of side reactions F( t) F (max) - Pump limit or limit on downstream unit

5 Limited Operating Region Process Limitations: T ( t) T (max) - Catalyst protection or onset of side reactions F( t) F (max) - Pump limit or limit on Possible Controller: ( sp F = K ( T T ) + c downstream unit ) F ( sp )

6 Performance in Time Series F T (sp) T(t) T (max) C A, T F F(t) time F (max) F (sp) time

7 Performance in Phase Plane T(t) * F(t)

8 Dynamic Operating Region T(t) * F(t)

9 Dynamic Operating Region T(t) * F(t)

10 Steady-State Relation Controller: ( sp F = K ( T T ) + c ) F ( sp ) Steady-State Relation: ( sp ) ( sp F = f ( T ) )

11 Steady-State Operating Line T(t) * F(t)

12 Optimal Operating Point T(t) Decrease F Increase T * Increase conversion Increase production F(t)

13 Optimal Operating Point: T(t) Another Possibility * Increase F Increased production rate F(t)

14 Optimal Operating Point: Another Possibility T (t) Increase F Increased production rate * F(t)

15 Requires Different Tuning of the Controller T(t) * F(t)

16 Performance in Time Series F T (sp) T(t) T (max) time C A, T F F (sp) F(t) F (max) time

17 Profit Control (Simultaneous BOP and Controller Selection) EDOR s due to different controller tunings BOP with less profit BOP with more profit * * OSSOP (max profit) Peng et al. (2005)

18 Outline Introduction (Economic Based Tuning) HVAC / Indoor Air Quality HVAC / Thermal Energy Storage Minimum Levelized Costs

19 Indoor Air Quality (IAQ) People spend 90% of time indoors, where pollutant levels are often higher than outdoors. The EPA ranked indoor air pollution among the top five environmental risks to public health. The infirm, elderly, and young spend more time indoors, being exposed to higher levels of air pollution. Exposure to air pollutants can lead to decreases in productivity.

20 HVAC for IAQ Demand-Controlled Ventilation (DCV) for Indoor Air Quality (IAQ)

21 Modeling IAQ Temperature ( C) 40 Outside Temperature Contaminant Generation Time (days) 0.25 Concentration (ppm/s)

22 System Modeling T& room = ( F rcy V + F room fresh ) ( T room cool T room ) UAroom UAsolid + ( Tout Troom) + ( Tsolid Troom) V ρcp V ρcp room T& solid = V solid UAsolid ( ρcp) solid ( T room T solid ) & F fresh C room = ( C fresh Croom) + Vroom S c

23 Model Variables State Variables: Room temperature (T room ) Solid material temperature (T solid ) Room contaminant concentration (C room ) Disturbances: Outside temperature (heat leakage, T out ) Rate of contaminant generation (S c ) Manipulated Variables: Recycled air flow (F rcy ) Fresh air flow (F fresh )

24 HVAC Control for IAQ Case 1: One Manipulated Variable (F rcy ) with constant fresh air flow (F fresh ) Case 2: Two Manipulated Variables (F rcy and F fresh ) Process Constraints: 0 3 F fresh 0.3 m / 3 0 F rcy 2 m / s s C room 400 ppm 22 C Troom 26 C

25 HVAC Control F fresh (m 3 /s) F ryc (m 3 /s) C room (ppm) T room ( o C)

26 HVAC Control F fresh (m 3 /s) F ryc (m 3 /s) C room (ppm) T room ( o C) Energy Usage of Traditional Controller: 3.16 kw Energy Usage of Energy Efficient Controller: 2.55 kw (a reduction of almost 20%).

27 Outline Introduction (Economic Based Tuning) HVAC / Indoor Air Quality HVAC / Thermal Energy Storage Minimum Levelized Costs

28 Energy Prices and Weather Cents per kw hr Electricity Real Time Pricing July 19-21, 2009 RTP Electricity Forecasted Data Time (days) In summer conditions, electricity prices increase when temperature increases.

29 Thermal Energy Storage (TES)

30 Model Variables State Variables: Room temperature (T room ) TES unit size (Q stg ) Disturbances: Outside temperature (heat leakage, T out ) Cost of electricity (C Elect ) Manipulated Variables (Controller s gain calculated based on State Variables and Disturbances values): Heat to cooler (Q cool ) Heat to TES unit (Q TES )

31 Electric Price Model

32 Energy Prices and Weather Cents per kw hr RTP Electricity Forecasted Data Time (days) White Noise Electricity Real Time Pricing July 19-21, 2009 Model Outside Temperature Electricity Price Cents per k hr Temperature ( C) In summer conditions, electricity prices increase when temperature increases. Electricity Price Outside Temperature Time (days)

33 Model Predictive Control T min Ce( t)* Qcool ( t) dt Qcool ( t) & & 0 where Ce( t) ~ the predicted price (or value) Q& cool ( t) ~ chiller load and Q ( t) ~ amount in storage Stg Constraints include: T min room 0 0 Q& Q T cool Stg room ( t) Q ( t) T ( t) Q& max cool max Stg max room

34 Model Predictive Control T min Ce( t)* Qcool ( t) dt E[ Ce * Qcool ] Qcool ( t) & & = & 0 where Ce( t) ~ the predicted price (or value) Q& cool ( t) ~ chiller load and Q ( t) ~ amount in storage Stg Constraints include: T min room 0 0 Q& Q T cool Stg room ( t) Q ( t) T ( t) Q& max cool max Stg max room R

35 Expected Cost (Re-Scaling of Price) α w(t) Shaping Filter C Elect (t) E [C Elect * Q cool ] Manipulated Variables Process Model Q cool (t) (Controller is u = Lx) where C' α Elect C Elect

36 Expected Cost If E [ ] 2 ( ' ) < ε 0 C Elect Q cool and C' Elect α C Elect then Q cool ( t) α C Elect ( t)

37 Expected Cost If E [ ] 2 ( ' ) < ε 0 C Elect Q cool and C' Elect α C Elect then Q cool ( t) α C Elect ( t) Also, 2 E[ α C 2 Elect ] 2E[ α C Elect Q cool ] + E[ Q 2 cool ] α E [ C ] = α E[ C Q ] = Elect Elect cool E[ Q 2 cool ] 2 α E[ C ] = E[ C Q ] Elect Elect cool R

38 Minimum Expected Costs R = min L, α { c α} R ( c = E[ 2 R C Elect ]) E [ ] 2 ( ' ) < ε 0 C Elect Q cool [ ] 2 max 2 Q cool Q ) E < [ ] 2 max 2 Q Stg Q ) E < ( cool ( Stg [ ] 2 max 2 T room ( T room ) E <

39 Thermal Energy Storage (Small Storage Unit) Heat Leakage T outside Volume of Air (the Room) T room Heat from Room Heat to Cooler Heat to TES Unit Cooling Unit TES Unit Energy Usage Heat from Room Heat to Cooler Heat to TES Unit kw hr / day Time (days)

40 Thermal Energy Storage (Medium Storage Unit) Heat Leakage T outside Volume of Air (the Room) T room Heat from Room Heat to Cooler Heat to TES Unit Cooling Unit TES Unit Energy Usage Heat from Room Heat to Cooler Heat to TES Unit kw hr / day Time (days)

41 Thermal Energy Storage (Large Storage Unit) Heat Leakage T outside Volume of Air (the Room) T room Heat from Room Heat to Cooler Heat to TES Unit Cooling Unit TES Unit Energy Usage Heat from Room Heat to Cooler Heat to TES Unit kw hr / day Time (days)

42 Thermal Energy Storage (Comparison of Storage Cases) Heat from Room Heat to Cooler Heat to TES Unit kw hr / day Time (days) Heat from Room Heat to Cooler Heat to TES Unit Heat from Room Heat to Cooler Heat to TES Unit kw hr / day kw hr / day Time (days) Time (days)

43 Thermal Energy Storage (Revenue Comparisons) Electricity Costs ($ / day) One Ton TES Unit Five Tons TES Unit Ten Tons TES Unit Electricity Price $ / kw hr Time (days) Average Cooling Costs: One ton: $8 per day Five ton: $7 per day (14% savings) Ten ton: $6 per day (25% savings) $/day Storage Size (Ton) 5 10

44 Outline Introduction (Economic Based Tuning) HVAC / Indoor Air Quality HVAC / Thermal Energy Storage Minimum Levelized Costs

45 Minimum Levelized Costs L, α, Q maxmin cool, Q max Stg E, T max room { max max c c Q c Q } α R L,1 cool [ ] 2 ( ' ) < ε 0 C Elect Q cool [ ] 2 max 2 Q cool Q ) E < [ ] 2 max 2 Q Stg Q ) E < ( cool ( Stg [ ] 2 max 2 T room ( T room ) E < L,2 Stg

46 Minimum Levelized Costs E L, α, Q maxmin cool, Q max Stg, T max room [ ] 2 ( ' ) < ε 0 C Elect Q cool { max max c c Q c Q } α R L,1 cool L,2 Stg [ ] 2 max 2 Q cool Q ) E < [ ] 2 max 2 Q Stg Q ) E < ( cool ( Stg [ ] 2 max 2 T room ( T room ) E < Non-Convex Problem (but global solution can be found)

47 Conclusions 1. Response to price variations usually requires controller retuning and/or a re-selection of set-points. 2. Direct response to electricity price changes can be implemented with Model Predictive Control. 3. Alternatively, l a linear controller can be designed d for market responsiveness. 4. Convex optimization used for Market Responsive Controller design. 5. Non-convex, but global methods can be used to size and/or select equipment.

48 Acknowledgements Former Students and Collaborators: Amit Manthanwar Dr. Jui-Kun Peng (ANL) Professor Ralph Muehleison (CAEE, IIT) Professor Demetrois Moschandreas (CAEE, IIT) Funding: National Science Foundation (CBET ) Graduate and Armour Colleges, IIT Chemical & Biological Engineering Department, IIT CONACYT