2016 Annual Conference
St. Louis, Missouri
Donald J. ChmielewskiAssociate Professor
Illinois Institute of [email protected]
Seminar 32 – Intermediate HVAC Controls for Smart Grid Applications
Smart Grid Coordination in Building HVAC Systems: Computational Efficiency of Constrained ELOC
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Session Learning Objectives
1. Learn how EMPC can be used to coordinate building HVAC systems with dynamic electricity prices, and why EMPC with thermal energy storage requires a large prediction horizon to yield desired performance
2. Characterize buildings and heating systems in terms of ability for load shifting, and learn about strategies of rule based, predictive and optimal control
3. Understand the role of frequency regulation ancillary service in power grid operation, and the basic infrastructure setup necessary to provide frequency regulation with HVAC equipment
4. Learn about the practical control and operational considerations when retrofitting chillers to provide frequency regulation, and list factors to consider to gauge economic feasibility
ASHRAE is a Registered Provider with The American Institute of Architects Continuing Education Systems. Credit earned on completion of this program will be reported to ASHRAE Records for AIA members. Certificates of Completion for non-AIA members are available on request.
This program is registered with the AIA/ASHRAE for continuing professional education. As such, it does not include content that may be deemed or construed to be an approval or endorsement by the AIA of any material of construction or any method or manner of handling, using, distributing, or dealing in any material or product. Questions related to specific materials, methods, and services will
be addressed at the conclusion of this presentation.
3
Acknowledgements
Former Students:Benjamin Omell (PhD, 2013) Nation Energy Technology LabDavid Mendoza-Serrano (PhD, 2013) NalcoMing-Wei Yang (PhD, 2010) Taiwan ElectricJui-Kun Peng (PhD, 2004) Argonne National LabAmit Manthanwar (MS, 2003) Texas A&M University
Current PhD Students:Oluwasanmi Adeodu Jin Zhang
Funding:National Science Foundation (CBET-0967906 & CBET-1511925)Wanger Institute for Sustainable Engineering Research (IIT)
Outline/Agenda
• Motivation and Background
• Review of Economic Model Predictive Control (EMPC)
• Impact of Horizon Size on EMPC
• Economic Linear Optimal Control (ELOC)
• Constrained ELOC
• Impact of Horizon Size on Constrained ELOC
Generators with Dispatch Consumer DemandTransmission
Renewable Sources
Energy Storage
Smart Homes
Commercial Buildings
Smart Manufacturing
Motivation
A Dispatch Problem for Generators
6
Dispatch Capable
Generation Power Grid
Smart Grid Electric Power Network:
Demand
(Consumers)
Renewable
Generation
Responsive
Demand Energy Storage
Existing
Components
Expected
Future
Components
0 5 10 15 20
0
200
400
600
800
time (days)
Po
wer
Req
uir
ed f
rom
Dis
pa
tch
ab
le G
ener
ato
rs
(MW
)
Baseline
Baseline with Renewable Power
0 5 10 15 20
0
200
400
600
800
time (days)
Baseline with Renewable Power
Impact of Storage and DR
Incentive for Smart Grid Coordination
7
Operate systems to exploit these time-varying electricity prices.
170 171 172 173 174 175 176 177 178 179 180
0
50
100
150
Day of the Year
Ele
ctr
icit
y P
ric
e
($/M
Wh
r)
Historic electricity prices (Chicago, 2008), [PJM, 2013]
Building HVAC Example
8
Heat from
BuildingBuilding
Heat from
Environment
Power
Consumption Chiller
Houston, TX (July, 2012)
Solid – Outside Temperature Dotted – Electricity Price
Building HVAC Example
9
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
Chiller Cooling Load (Qc)
Time (days)
Hea
t F
low
(K
We)
Qc
Qr
23 24 25 26
2000
4000
6000
Time (days)
Hea
t F
low
(K
We)
Heat to Chiller Heat from Room
Thermal Energy Storage
Building HVAC Example
10
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
TES
Thermal Energy Storage
Heat to
Chiller
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
Chiller Cooling Load (Qc)
Time (days)
Hea
t F
low
(K
We)
Qc
Qr
23 24 25 26
2000
4000
6000
Time (days)
Hea
t F
low
(K
We)
Heat to Chiller Heat from Room
23 24 25 26
2000
4000
6000
Time (days)
Hea
t F
low
(K
We)
Heat to Chiller Heat from Room
Outline/Agenda
• Motivation and Background
• Review of Economic Model Predictive Control (EMPC)
• Impact of Horizon Size on EMPC
• Economic Linear Optimal Control (ELOC)
• Constrained ELOC
• Impact of Horizon Size on Constrained ELOC
Model Predictive Control
iii
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At time the current time, i, optimize over model prediction:
Then, the manipulated variable is set as:*
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12
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imis
Process to be Controlled
???
Controller
1
|||,
),,(min||
Ni
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Traditional vs. Economic MPC
13
In traditional MPC the objective is minimize deviations:
1
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)()()()(min||
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ik
ikT
ikikT
ikms
mmRmmssQssikik
In Economic MPC (EMPC) the objective is minimize expenditures:
See Rawlings et al. (2012) or Ellis et al. (2014) for additional information on EMPC
Outside
Environment
(T3)
...
Windows
...
Walls
To T3T21T12 T11T11To To
...
Outside
Environment
(T3)
Room
Room
Room
Room
Room
Room
5 State Building Example
14
1
|,|,|,
minNi
ik
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QQTTAKTTAKT
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111
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12111212
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TTKT
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21212132221
)()(
xC
TTKTTKT
p
o
ss QE
Economic Objective:
Houston, TX (July, 2012)
EMPC Simulation
15
Solid – EMPC with TES Dotted – EMPC without TES
EMPC Simulation with Smaller Storage
16
Solid – EMPC with TES Dotted – EMPC without TES
At time the current time, i, optimize over model prediction:
Predicting Future Disturbances
iii
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ikikikik
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Ni
ik
ikikikms
ss
Niikqqq
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||||
||||1
1
|||,
1
),,(
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),,(min||
Need forecasts of ikp ik for |
17
if Full Future Information (FFI) is not assumed
Disturbance Forecasting
18
Zero Future Information (ZFI) Forecasts
Assume this the present time
Disturbance Forecasting Model
19
Impact of Forecasting Model
20
4th order model
3rd order model
Incorporating a High Fidelity Forecast Model
21
Pseudo Future Measurement
Impact of High Fidelity Forecast Data
22
Pseudo Future Information (PFI) Forecasts
Impact of Forecasting on EMPC
23
All cases for 1.5 MWh of storage over 28 days and with EMPC horizon of 24h
Controller ExpenditurePercent
Reduction
EMPC (FFI) No TES $759 ---
EMPC (FFI) $521 31.4%
EMPC (ZFI) $556 26.7%
EMPC (PFI) $539 29.0%
Outline/Agenda
• Motivation and Background
• Review of Economic Model Predictive Control (EMPC)
• Impact of Horizon Size on EMPC
• Economic Linear Optimal Control (ELOC)
• Constrained ELOC
• Impact of Horizon Size on Constrained ELOC
Prediction Horizon
25
24 hours
Model Predictive Control
iii
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ikikikik
ikikikik
Ni
ik
ikikikms
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pmshq
pmsfsts
pmslikik
|
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min
||||
||||1
1
|||,
1
),,(
),,(..
),,(min||
At time the current time, i, optimize over model prediction:
26
),,(1 iiii pmsfs
imis
Process to be Controlled
???
Controller
Smaller horizon, N, will reduce computational effort!
3 4 5 6
-1500
-1000
-500
0
Time (days)
En
erg
y i
n
Sto
rag
e (k
WT
hr)
Impact of Horizon Size on EMPC
27
Solid – 24 hr horizon Dotted – 2 hr horizon
3 4 5 6
0
200
400
Time (days)
Hea
t to
C
hil
ler
(kW
T)
28
Controller ExpenditurePercent
Reduction
Computational
Effort (sec)
EMPC (FFI) with No TES $827 --- 13
EMPC (ZFI) N = 24 hrs $575 30.5% 13
EMPC (ZFI) N = 2 hrs $673 18.6% 7
Impact of Horizon Size on EMPC
All cases for 1.5 MWh of storage over 28 days
Outline/Agenda
• Motivation and Background
• Review of Economic Model Predictive Control (EMPC)
• Impact of Horizon Size on EMPC
• Economic Linear Optimal Control (ELOC)
• Constrained ELOC
• Impact of Horizon Size on Constrained ELOC
Economic Linear Optimal Control (ELOC)
Steady-State
Operating
Line
Steady-State
Operating
Line
Optimal Steady-State
Operating Point
Expected
Dynamic
Operating
Region
Steady-State
Operating
Line
Optimal Steady-State
Operating Point
Minimally
Baked-off
Operating
Point
Expected
Dynamic
Operating
Regions
Steady-State
Operating
Line
Optimal Steady-State
Operating Point
30
Different Controller
Tuning Values
Expected
Dynamic
Operating
Regions
Steady-State
Operating
Line
Optimal Steady-State
Operating Point
Minimally
Baked-off
Operating
Point
Different Controller
Tuning Values
Expected
Dynamic
Operating
Regions
Steady-State
Operating
Line
Optimal Steady-State
Operating Point
ssx
mmu
xLu
ii
ii
iELOCi
Comparison of EMPC and ELOC
31
3 4 5 6
10
20
30
40
Time (days)
E
lect
rici
ty
O
uts
ide
P
rice
T
emp
eratu
re
($/M
Wh
r)
(
°C)
T3
Ce
3 4 5 6-400
0
400
800
Time (days)
Hea
t to
C
hil
ler
(kW
T)
ELOC EMPC
3 4 5 6
-2000
0
2000
Time (days)
En
ergy i
n
Sto
rage
(kW
hr T
)
ELOC EMPC
Disturbances Simulated by Forecast Model
Both with ZFI
Comparison of EMPC and ELOC
3 4 5 6
10
20
30
40
Time (days)
Ele
ctr
icit
y
O
uts
ide
P
ric
e
Tem
pera
ture
(
$/M
Wh
r)
(°
C)
T3
Ce
3 4 5 6
-400
0
400
Time (days)
Hea
t to
C
hil
ler
(kW
T)
ELOC EMPC
32
Disturbances taken from Historic Data
Both with ZFI
3 4 5 6
-4000
-2000
0
Time (days)
En
erg
y i
n
Sto
rag
e (k
Wh
r T)
ELOC EMPC
Outline/Agenda
• Motivation and Background
• Review of Economic Model Predictive Control (EMPC)
• Impact of Horizon Size on EMPC
• Economic Linear Optimal Control (ELOC)
• Constrained ELOC
• Impact of Horizon Size on Constrained ELOC
iii
ikikik
iNi
T
iNi
Ni
ik
ik
T
ikik
T
ikux
xx
BuAxx
tsPxxRuuQxxikik
|
|||1
||
1
||||,
..)(min||
34
iLQRi xLu
Predictive Form of ELOC
iii
ikikik
iNiELOC
T
iNi
Ni
ik
ikELOC
T
ikikELOC
T
ikux
xx
BuAxx
tsxPxuRuxQxikik
|
|||1
||
1
||||,
..)(min||
iELOCi xLu
* see Chmielewski & Manthanwar (2004) for details
Linear Quadratic Regulator
Predictive Form of ELOC Constrained ELOC
35
max
|
min
|||
zzz
uDxDz
ik
ikuikxik
iii
ikikik
iNiELOC
T
iNi
Ni
ik
ikELOC
T
ikikELOC
T
ikux
xx
BuAxx
tsxPxuRuxQxikik
|
|||1
||
1
||||,
..)(min||
Comparison of EMPC and Constrained ELOC
3 4 5 6
10
20
30
40
Time (days)
Ele
ctr
icit
y
O
uts
ide
P
ric
e
Tem
pera
ture
(
$/M
Wh
r)
(°
C)
T3
Ce
36
Disturbances taken from Historic Data
Both with ZFI
3 4 5 6
0
400
Time (days)
Hea
t to
C
hil
ler
(kW
T)
CELOC EMPC
3 4 5 6
-1500
-1000
-500
0
500
Time (days)
En
erg
y i
n
Sto
rag
e (k
Wh
r T)
CELOC EMPC
Outline/Agenda
• Motivation and Background
• Review of Economic Model Predictive Control (EMPC)
• Impact of Horizon Size on EMPC
• Economic Linear Optimal Control (ELOC)
• Constrained ELOC
• Impact of Horizon Size on Constrained ELOC
Constrained ELOC and Horizon Size
3 4 5 6
10
20
30
40
Time (days)
Ele
ctr
icit
y
O
uts
ide
P
ric
e
Tem
pera
ture
(
$/M
Wh
r)
(°
C)
T3
Ce
38
Disturbances taken from Historic Data
Both with ZFI
3 4 5 6
0
400
Time (days)
Hea
t to
C
hil
ler
(kW
T)
CELOC, N=2 CELOC, N=24
3 4 5 6
-1500
-1000
-500
0
500
Time (days)
En
ergy i
n
Sto
rage
(kW
hr T
)
CELOC, N=2 CELOC, N=24
39
Controller ExpenditurePercent
Reduction
Computational
Effort (sec)
EMPC (FFI) with No TES $827 --- 13
EMPC (FFI) N = 24 hrs $520 37.1% 13
EMPC (ZFI) N = 24 hrs $575 30.5% 13
EMPC (ZFI) N = 2 hrs $673 18.6% 7
Constrained ELOC (ZFI) N = 24 hrs $567 31.4% 13
Constrained ELOC (ZFI) N = 2 hrs $552 33.3% 7
All cases for 1.5 MWh of storage over 28 days
Impact of Horizon Size on Constrained ELOC
Why Does Constrained ELOC Work?
40
iii
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iNiELOC
T
iNi
Ni
ik
ikELOC
T
ikikELOC
T
ikux
xx
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tsxPxuRuxQxikik
|
|||1
||
1
||||,
..)(min||
max
|
min
|||
zzz
uDxDz
ik
ikuikxik
Conclusions
• EMPC with TES can reduce building HVAC expenditures significantly if under dynamic electricity prices.
• EMPC requires a large prediction horizon.
• Constrained ELOC approximates EMPC, but can use a smaller prediction horizon size.
• Disturbance model is central to Constrained ELOC.
Bibliography• D. J. Chmielewski (2014) "Special Section - Energy: Smart Grid: The Basics — What? Why? Who? How?," Chem.
Eng. Prog., vol. 110 (8), August Issue, pp. 28-34.• D. J. Chmielewski and A. M. Manthanwar (2004) "On the tuning of predictive controllers: Inverse optimality and
the minimum variance covariance constrained control problem," Ind. Eng. Chem. Res., vol. 43, pp. 7807-7814.• M. Ellis, H. Durand, and P. D. Christofides (2014) "A tutorial review of economic model predictive control
methods," J. Proc. Contr., vol. 24, pp. 1156-1178.• Ercot (2012) Historic real time data electricity prices for Houston texas. http://www.ercot.com/mktinfo/prices/• R. M. Lima, I. E. Grossmann, and Y. Jiao (2011) "Long-term scheduling of a single-unit multi-product continuous
process to manufacture high performance glass," Comp. Chem. Eng., vol. 35, pp. 554-574.• D. I. Mendoza-Serrano and D. J. Chmielewski (2012) "HVAC control using infinite-horizon economic MPC," in Proc.
of 51st IEEE Conf. Dec. Cont., Hawaii.• D. I Mendoza-Serrano and D. J Chmielewski (2014) "Smart grid coordination in building HVAC systems: EMPC and
the impact of forecasting," J. Proc. Contr., vol. 24, no. 8, pp. 1301-1310.• D. I Mendoza-Serrano and D. J Chmielewski (2015) “Smart grid coordination in building HVAC systems:
Computational efficiency of constrained economic linear optimal control” Science and Technology for the Built Environment vol. 21(6), pp 812-823
• (NCDC) National climatic data center. (2012) Hourly climate data for Houston Texas. http://www.ncdc.noaa.gov/oa/climate/climatedata.html
• B. P. Omell and D. J. Chmielewski (2013) "IGCC power plant dispatch using infinite-horizon economic model predictive control," Ind. Eng. Chem. Res., vol. 52, no. 9, pp. 3151-3164.
• J. K. Peng, A. M. Manthanwar, and D. J. Chmielewski (2005) "On the tuning of predictive controllers: The minimally backed-off operating point selection problem," Ind. Eng. Chem. Res., vol. 44, pp. 7814-7822.
• J. B. Rawlings, D. Angeli, and C. N. Bates (2012) "Fundamentals of economic model predictive control," in Proc. Of 51st IEEE Conf. Dec. Cont., Hawaii.
ELOC Optimization Problem
Primal Problem (SDP solver)
Master Problem (BARON)
Master Problem
Primal Problem
44
0)(
)(
0)(
)(
))((
..
)(min
2
minmax
cos.
,,,,,,
XYDXD
YDXD
XBYAX
BYAXGGX
diagsqrt
qqqq
mDsDqpGmBsAsts
qg
T
ux
uxz
T
T
w
z
zz
ux
top
YXqms
zz
Generalized Benders Decomposition
1YXLELOC
