controller and system design for hvac 3 building r c c

Controller and System Design for HVAC Systems with Thermal Energy Storage

David I. Mendoza-Serrano and Donald J. Chmielewski

Illinois Institute of Technology

American Control Conference June 2012 , Montreal Canada

Outside

Environment

(T3)

...

Windows

...

Walls

To T3T21T12 T11T11To To

...

Outside

Environment

(T3)

Room

Room

Room

Room

Room

Room

QcQr

Qs

Building

Thermal

Energy Storage

T3 PeChiller

Department of Chemical and Biological Engineering


Outline

• Motivation and Objective

• Market Responsive Control

• Equipment Design with Embedded MRC

• Case Study



Power System Reliability

Power Produced Equals Power Consumed



Generators Consumer Demand Transmission

Renewable

with Storage

Generator Dispatch

Smart Homes

Commercial Buildings

Smart Manufacturing

Overview of Smart Grid

http://www.google.com/imgres?imgurl=http://www.netl.doe.gov/technologies/coalpower/gasification/pubs/images/nippon_lg.jpg&imgrefurl=http://www.netl.doe.gov/technologies/coalpower/gasification/pubs/photo.html&usg=__jHfd6seyi1QunoX4aIOKfKOONEs=&h=387&w=500&sz=230&hl=en&start=18&zoom=1&itbs=1&tbnid=katIb-VZwTD8rM:&tbnh=101&tbnw=130&prev=/images?q=IGCC&tbnid=EdexGueWvIH62M:&tbnh=0&tbnw=0&hl=en&gbv=2&tbs=isch:1



Cooling Power Consumption

Cooling is mainly required during the hottest times of a day…

Outside Temperature. August 3 - 6, 2001. Pittsburg, PA.

3 4 5 6 760

70

80

90

100

Time (days)T

emp

era

ture

(F

)



Correlation Between Cooling Loads and Energy Prices

3 4 5 6

70

80

90

Time (hours)

Tem

peratu

re (

F)

3 4 5 60

50

100

150

Time (days)

Ele

ctri

city

Pri

ce (

$/M

Wh

r)

August 3 - 6, 2001. Pittsburg, PA.



Traditional HVAC System

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

• Heat is removed from the building by a chiller

• Chiller consumes electric power

• Assume real-time prices for electricity



Thermal Energy Storage

TES helps time

shift electricity

consumption to

periods of low

electricity prices.



HVAC System with TES

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller

• Building heat can be sent to chiller or TES

• Heat must eventually be removed from TES by chiller.



Impact of TES

23 24 25 26

200

300

400

500

600

Chiller Cooling Load (Qc)

Time (days)

Hea

t F

low

(K

We)

Qc

Qr

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

Chiller



Impact of Larger TES

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES


Heat to

Chiller

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr



HVAC Design Questions

• What are the energy expenditures?

• What is the appropriate size of the TES?

• Is there a benefit to changing chiller size?

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES


Heat to

Chiller

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr



Outline

• Motivation



• Case Study



Building Example

Outside

Environment

(T3)

...

Windows

...

Walls


...Outside

Environment

(T3)

Room

Room

Room

Room

Room

Room



Building Model

opo

cooo

VC

QTTAKTTAKT

0

2122111111 )()(

111

121112111111

)()(

xC

TTKTTKT

p

o

111

12111212

)(2

xC

TTKT

p

222

21212132221

)()(

xC

TTKTTKT

p

o

Air Temperature

Wall Layers

Window Layer

Outside

Environment

(T3)

...

Windows

...

Walls


...

Outside

Environment

(T3)

Room

Room

Room

Room

Room

Room



Building Operation

Manipulated Variable )(kW 0 T

max

cc QQ

Comfort Constraints maxmin

ooo TTT

Power Usage )(kW ecc QP

Instantaneous Expenditures ($/hr) cePCR

Energy Cost hr)($/kW eeC

Disturbance CCT 4323



Building Model with TES

opo

scooo

VC

QQTTAKTTAKT

0

2122111111 )()(

111

121112111111

)()(

xC

TTKTTKT

p

o

111

12111212

)(2

xC

TTKT

p

222

21212132221

)()(

xC

TTKTTKT

p

o

ss QE

Air Temperature

Wall Layers

Window Layer

Energy in Storage Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller



Building Operation with TES

Manipulated Variables max

0 cc QQ maxmin

sss QQQ

Equipment Constraints

0 scR QQQ

max0 ss EE

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller



Outside Temperature Model

White

Noise

Input

Shaping

Filter

Sequence with

Outside

Temperature

Characteristics

3Tw



Outside Temperature Spectral Density

White

Noise

Input

Shaping

Filter

Sequence with

Outside

Temperature

Characteristics

3Tw

10-3

10-2

10-1

100

101

10-2

100

102

104

Frequence (rad/hr)

Sp

ectr

al

Den

sity

(($

/MW

)2/h

r)



Outside Temperature Realization

White

Noise

Input

Shaping

Filter

Sequence with

Outside

Temperature

Characteristics

3Tw

550 560 570 580 590 600 610 620 63026

28

30

32

34

36

38

Time (hours)

Ou

tsid

eT

em

peratu

re (

C)



Outside Temperature Model

313 TeT

h

ccc

ewe

eweee

ee

/)(

)(2

33

3

2

21

2

2

21

where:

cc /2

hr 24c

1.0

hr 1h322

22 124T

hc

hchc

c

wS

2)4(3

KT



Deviation Variables

T

ss

oo

eeeEE

TTTTTTTTx

]

[

321

212112121111

T

ccss QQQQu ][

T

RRccssoo QQQQEETTz ][

maxmin zzz

DuDxz

GwBuAxx



Stochastic Analysis

Lxu

uDxDz

GwBuAxx

ux

) row (

)()(

)()(0

th Ij

LDDLDD

GGSBLABLA

j

jj

T

j

T

uxxuxjj

T

w

T

xx



Stochastic Control

Lxu

uDxDz

GwBuAxx

ux

zjjjj

jj

T

j

T

uxxuxjj

T

w

T

xx

njzz

LDDLDD

GGSBLABLA

L

...1,2 and 2

)()(

)()(0

such that Find

minmax



Stochastic Control

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

Heat from

BuildingBuilding

Heat from

Environment

Power

Consumption Chiller

Heat to

TES

Thermal

Energy Storage

Heat to

Chiller



Expenditures

][

1lim

0

ce

T

ceT

PCE

dtPCT

R

Instantaneous Expenditures

cePCR

Average Expenditures



Economic MPC

dtPCT

RT

ce0

1

Minimize Expenditures over Horizon T

• Braun, 1992 • Morris et al., 1994 • Kintner-Meyer and Emery, 1995 • Henze et al., 2003 • Oldewurtel et al, 2010 • Ma et al, 2012



Market Responsive Control

][ cePCER



where:

Enforce the condition:

ccc PPP ~

eee CCC ~ 0]

~~[ eeBCE

eec BCP~~~

21


and

][ cePCER



where:

Enforce the condition:

ccc PPP ~

eee CCC ~ 0]

~~[ eeBCE

eec BCP~~~

21

ceCe

cee

cece

PC

PCCE

PCPCER

1

2

1 ]~

[

]~~

[

Then:


and

][ cePCER



Electricity Price

Shaping

Filter

K

3

~Tw

eC~



Orthogonal to Electricity Cost

Shaping

Filter

K

3

~Tw

eC~

eB~



Disturbance Scaling

SF1

1 SF2

2 SF3

3

~Tw

eC~

eB~

)( 22110 GGGGGwBuAxx




zjjjj

jj

T

j

T

uxxuxjj

T

w

T

xx

njzz

LDDLDD

GGGG

GGSBLABLA

ts

...1,2 and 2

)()(

)()(0

..

minmax

22110

ceCeL

PCjjx

1

,

,,,0,

21

min




zjjjj

jj

T

j

T

uxxuxjj

T

w

T

xx

njzz

LDDLDD

GGGG

GGSBLABLA

ts

...1,2 and 2

)()(

)()(0

..

minmax

22110

ceCeL

PCjjx

1

,

,,,0,

21

min

Convex Optimization Problem



0.0 kWhr

5000 kWhr

1500 kWhr

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr




Instantaneous Expenditure

23 24 25 263

6

9

12


Time (days)

Ex

pen

dit

ure

($

/hr)

Es,max

= 0

Es,max

= 1500

Es,max

= 5000

23 24 25 263

6

9

12


Time (days)

Ex

pen

dit

ure

($

/hr)

Es,max

= 0

Es,max

= 1500

Es,max

= 5000




MRC Results

Ce

($/MWhr)2

Esmax

(MWhr)

($/hr)

52 0.0 7.05

52 0.5 7.01

52 1.5 6.92 52 5.0 6.90

202 0.0 7.15

202 0.5 6.96 202 1.5 6.63 202 5.0 6.56

452 0.0 7.31

452 0.5 6.88 452 1.5 6.14 452 5.0 5.97

*R



Outline

• Motivation and Objective



• Case Study




zjjjj

jj

T

j

T

uxxuxjj

T

w

T

xx

njzz

LDDLDD

GGGG

GGSBLABLA

ts

...1,2 and 2

)()(

)()(0

..

minmax

22110

ceCeL

PCjjx

1

,

,,,0,

21

min

2/maxmax2 sEz cc PPz

maxmax3

2/maxmin2 sEz cPz min

3



MRC Embedded Equipment Design

zjjjj

jj

T

j

T

uxxuxjj

T

w

T

xx

njzz

LDDLDD

GGGG

GGSBLABLA

ts

...1,2 and 2

)()(

)()(0

..

minmax

22110

maxmax

1

,

,

,,,0,

maxmax21

min sscc

EP

LEcPcc

sc

jjx


maxmax3


3

CefPVc



MRC Embedded Equipment Design

zjjjj

jj

T

j

T

uxxuxjj

T

w

T

xx

njzz

LDDLDD

GGGG

GGSBLABLA

ts

...1,2 and 2

)()(

)()(0

..

minmax

22110

maxmax

1

,

,

,,,0,

maxmax21

min sscc

EP

LEcPcc

sc

jjx


maxmax3


3

CefPVc

Non-Convex

But easily solved with branch and

bound



Equipment costs: 500 $/kWe for the chiller 28.4 $/kWThr for the TES

Present value parameters:

ri = 7% n = 30yrs

Required chiller size without TES:

Pc

max = 111kWe

Case Study



ce

($/MWhr)2 Es

max (MWThr)

Pc

max (kWe)

52 0.5 94.5

52 1.5 78.0

52 2.0 78.0

202 0.5 97.9

202 1.5 105.5

202 2.0 127.3

452 0.5 108.6

452 1.5 124.2

452 2.0 141.8

Chiller Sizing with no cost TES



23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

Ce= ($5/MW hr)2

23 24 25 26

200

300

400

500

600


Time (days)

Hea

t F

low

(K

We)

Qc

Qr

Ce= ($20/MW hr)2

Ce= ($45/MW hr)2

Chiller Sizing with no cost TES

Esmax= 1.5 MW hr



ce

($/MWhr)2 Es

max (MWThr)

Pcmax

(kWe)

202 0.05 113.8

452 1.15 106.5

Chiller and TES Sizing



ce

($/MWhr)2 Es

max (MWThr)

Pcmax

(kWe)

202 0.05 113.8

452 1.15 106.5

Chiller and TES Sizing

28.4 $/kWThr for the TES is too expensive



• Market Responsive Control (MRC) an alternative to economic MPC

• MRC enables controller Embedded Equipment Design (MRC-EED)

• MRC-EED can be used to assess the economic viability of TES

• The cost of TES equipment is the current bottleneck

Conclusions

• Acknowledgements:

National Science Foundation (CBET – 0967906)

Wanger Institute for Sustainable Engineering Research (IIT)

controller and system design for hvac 3 building r c c

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