optimal design of smart grid t u n in g v a lu e s 1...
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Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Optimal Design of Smart Grid Optimal Design of Smart Grid
Coordinated SystemsCoordinated Systems
Donald J. Chmielewski
Department of Chemical and Biological Engineering Illinois Institute of Technology
Minimally
Baked-off
Operating
Point
Different Controller
Tuning Values
Expected
Dynamic
Operating
Regions
Steady-State
Operating
Line
Optimal Steady-State
Operating Point
Es
min (kW
T hr)
Pcm
ax (
kW
e)
0 -500 -1000 -15000
25
50
1
435 2
383 383.5 384 384.5 385 385.5387.5
388
388.5
389
389.5
390
390.5
391
391.5
T(K
)
T0(K)
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
ChicagoChicago
2
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
IIT and ChicagoIIT and Chicago
3
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Presentation OutlinePresentation Outline
Review of Economic Model Predictive
Control (EMPC)
Challenges Associated with the Design of
Smart Grid Systems
ELOC and Constrained ELOC
Computationally Efficient Design of Smart
Grid Systems
4
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
5
AcknowledgementsAcknowledgements
Former Students:
Benjamin Omell (PhD, 2013)
David Mendoza-Serrano (PhD, 2013)
Ming-Wei Yang (PhD, 2010)
Jui-Kun Peng (PhD, 2004)
Amit Manthanwar (MS, 2003)
Current Students:
Oluwasanmi Adeodu
Jin Zhang
Funding:
National Science Foundation (CBET – 0967906)
Wanger Institute for Sustainable Engineering Research (IIT)
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Review of MPCReview of MPC
iii
ik
ikikikik
ikikikik
iNif
Ni
ik
ikikikms
ss
Niikqqq
pmshq
pmsfs
tsslpmslikik
|
max
|
min
||||
||||1
|
1
|||,
1
),,(
),,(
..)(),,(min||
At time the current time, i, solve:
Then, the manipulated variable is set as: *
|iii mm
6
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
1
|||
)(
,),,(max
||
Ni
ik
ikikik
IP
mspmsg
ikik
Traditional vs. Economic Traditional vs. Economic MPCMPC
7
In traditional MPC the objective is regulation:
iNi
T
iNi
Ni
ik
ik
T
ikik
T
ikux
PxxRuuQxxikik
||
1
||||,
)(min||
In EMPC the objective is maximize average profit
(integral of instantaneous profit):
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
EconomicEconomic MPC LiteratureMPC Literature
8
Conceptual Development and Stability Issues: Rawlings and Amrit (2009); Diehl, et al. (2011); Huang and Biegler (2011); Heidarinejad, et al. (2012)
Process Scheduling: Karwana and Keblisb (2007); Baumrucker and Biegler (2010); Lima et al. (2011); Kostina et al. (2011)
Building HVAC Systems: Braun (1992); Morris et al. (1994); Kintner-Meyer and Emery (1995); Henze et al. (2003); Braun (2007); Oldewurtel et al. (2010), Ma et al. (2012); Mendoza and Chmielewski (2012)
Power Scheduling: Zavala et al. (2009); Xie and Ilić (2009), Hovgaard, et al. (2011), Omell and Chmielewski (2013)
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Economic Economic MPC ExampleMPC Example
A non-isothermal CSTR:
n
CA, CB, T
CA0, T0, n
KT
CekC
HTT
Vdt
dT
CekCVdt
dC
CekCCVdt
dC
A
RTE
p
r
A
RTE
BB
A
RTE
AAA
390
)(
)(
00
0
00
n
n
n
Disturbance:
Manipulation:
ss
A
ss
AA CCC 000 15.0
KT 3850
Instantaneous Profit:
BB
IP CCg n10)()(
9
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
EconomicEconomic MPC ExampleMPC Example
8
1385
390
),,(
..10max
|
|,0
|
||,|,||,|,0||1
1
|,, |,0|
N
ss
NiikKT
KT
TCCsCTsfs
tsC
iii
ik
ik
T
ikikBikAikikAoikikik
Ni
ik
ikBTs ikik
n
*Model converted to discrete-time using Euler’s explicit method.
10
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
EconomicEconomic MPC SimulationMPC Simulation
11
383.5 384 384.5 385388
388.5
389
389.5
390
T0 (K)
T (
K)
0 5 10 15
0.8
1
1.2
1.4
time (minutes)
CA
0 (
km
ole
/m3)
0 5 10 15388
388.5
389
389.5
390
390.5
time (minutes)
T (
K)
0 5 10 15383
383.5
384
384.5
385
385.5
time (minutes)
T0 (
K)
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Economic Economic MPC ExampleMPC Example
A non-isothermal CSTR:
12
n
CA, CB, T
CA0, T0, n
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Economic Economic MPC ExampleMPC Example
A non-isothermal CSTR with preheater:
Instantaneous Profit:
4.05)303(005.010 0 nn TCB
13
n
CA, CB, T
CA0, T0, n
Tf = 303K
Q
Manipulation: KTK 385303 0
)303(005.010),( 00
)( TCTCg BB
IP n
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
EconomicEconomic MPC SimulationMPC Simulation
14
0 5 10 15
0.8
1
1.2
1.4
time (minutes)
CA
0 (
km
ole
/m3)
0 5 10 15
386
388
390
time (minutes)
T (
K)
0 5 10 15383
383.5
384
384.5
385
385.5
time (minutes)
T0 (
K)
0 5 10 15300
320
340
360
380
time (minutes)
T (
K)
0 5 10 15300
320
340
360
380
time (minutes)
T0 (
K)
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
EconomicEconomic MPC SimulationMPC Simulation
15
0 5 10 15
0.8
1
1.2
1.4
time (minutes)
CA
0 (
km
ole
/m3)
0 5 10 150.4
0.6
0.8
1
time (minutes)
CA
(k
mo
le/m
3)
0 5 10 150
0.2
0.4
0.6
0.8
time (minutes)
CB
(k
mole
/m3)
0 0.5 10
0.5
1
CB
(kmole/m3)
CA
(k
mole
/m3)
)303(005.010
),(
0
0
)(
TC
TCg
B
B
IP
n
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
EconomicEconomic MPC SimulationMPC Simulation
16
0 5 10 15
0.8
1
1.2
1.4
time (minutes)
CA
0 (
km
ole
/m3)
0 5 10 15388
388.5
389
389.5
390
390.5
time (minutes)
T (
K)
0 5 10 15383
383.5
384
384.5
385
385.5
time (minutes)
T0 (
K)
0 5 10 150.4
0.5
0.6
0.7
0.8
time (minutes)
CA
(k
mo
le/m
3)
0 5 10 15
0.4
0.5
0.6
0.7
time (minutes)
CB
(k
mole
/m3)
Change horizon
from N = 8 to N = 10
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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4) If N=10 and objective ,
4) If N=10 and objective ,
then UNSTABLESTABLE
Stability of EStability of EMPCMPC
1) If N=8 and objective ,
then STABLESTABLE
17
)303(005.010 0 TCBn
BC10n
2) If N=8 and objective ,
then UNSTABLEUNSTABLE
)303(005.010 0 TCBn3) If N=10 and objective ,
then STABLESTABLE
)303(025.010 0 TCBn
)303(025.010 0 TCBn5) If N=25 and objective ,
then STABLESTABLE
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Why the Instability?Why the Instability?
18
n
CA, CB, T
CA0, T0, n
Tf = 303K
Q
Answer: Myopic Behavior
• EMPC tries to lower costs by lowering To
• In the short run T, CB and Profit will remain high
• In the long run T, CB and Profit will drop-off
• If N is small, then EMPC will not know about the drop-off
• Short term gains lead to long term losses
)303(025.010 0 TCBn
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Presentation OutlinePresentation Outline
Review of EMPC
Challenges Associated with the Design
of Smart Grid Systems
ELOC and Constrained ELOC
Computationally Efficient Design of Smart
Grid Systems
19
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Generators with Dispatch Consumer Demand Transmission
Renewable Sources
Energy Storage
Smart Homes
Commercial Buildings
Smart Manufacturing
Smart Grid OpportunitiesSmart Grid Opportunities
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Motivation for Smart Grid CoordinationMotivation for Smart Grid Coordination
21
Design systems to exploit these time-varying electricity prices.
Applications range from: Building HVAC, Electric Vehicle Charging, Distributed Generation and Storage, Industrial Demand Response
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]
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Building HVAC ExampleBuilding HVAC Example
22
Heat from
BuildingBuilding
Heat from
Environment
Power
Consumption Chiller
Houston, TX (July, 2012)
Solid – Outside Temperature Dotted – Electricity Price
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Building HVAC ExampleBuilding HVAC Example
23
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
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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HVAC Equipment Sizing Problem HVAC Equipment Sizing Problem
24
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
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Outside
Environment
(T3)
...
Windows
...
Walls
To T3T21T12T11T11To To
...
Outside
Environment
(T3)
Room
Room
Room
Room
Room
Room
5 State Building Example 5 State Building Example
25
1
|,|,|,
minNi
ik
ikcikeP
PCikc
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
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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EMPC Simulation EMPC Simulation
26
Solid – EMPC with TES
Dotted – EMPC without TES
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EMPC Simulation with Smaller Storage EMPC Simulation with Smaller Storage
27
Solid – EMPC with TES
Dotted – EMPC without TES
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Smart Grid Equipment Design ProblemSmart Grid Equipment Design Problem
28
Design problem is a Stochastic Program
CapCostOpCostPV fSizeEquip
min
N
k
kEqipSizeOpVar
OpVarInstOpCostN
OpCostk 1
0)(
1min
If no energy storage, then two-stage problem
If energy storage is allow, then a multistage problem
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Simulation Period: 28 days Operating Cost (no TES): $759 Operating Cost Reduction with 1.5MWhr: 31.4% Simulation Time: 1.4 hrs EMPC Horizon Size: 24 hrs Operating Cost Reduction with 1.5MWhr: 13.8% Simulation Time: 6.7 sec EMPC Horizon Size: 3 hr
Possible Solution MethodPossible Solution Method
29
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Inventory CreepInventory Creep
30
Simulation Period: 28 days Operating Cost (no TES): $759 Operating Cost Reduction with 1.5MWhr: 31.4% Simulation Time: 1.4 hrs EMPC Horizon Size: 24 hrs Operating Cost Reduction with 1.5MWhr: 13.8% Simulation Time: 6.7 sec EMPC Horizon Size: 3 hr
Solid – EMPC with 24hr horizon
Dotted – EMPC with 3hr horizon
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Use of Surrogate Controllers Use of Surrogate Controllers
31
ELOC Constrained ELOC
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Presentation OutlinePresentation Outline
Review of EMPC
Challenges Associated with the Design of
Smart Grid Systems
ELOC and Constrained ELOC
Computationally Efficient Design of Smart
Grid Systems
32
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Economic Linear Optimal Control (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
33
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
iELOCi xLu
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Economic Linear Optimal Control Economic Linear Optimal Control
34
min
,
max
,
cos.
,,,,,
)()(
)()(
),,(),,,(..
),(min
jjjzjjjz
T
uxxuxz
T
w
T
xx
zz
ztop
Lqms
qqqq
LDDLDD
GGBLABLA
mshqpmsfsts
qg
zx
Global Solutions can be efficiently determined using GBD
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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35
383 383.5 384 384.5 385 385.5387.5
388
388.5
389
389.5
390
390.5
391
391.5
T(K
)
T0(K)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
CB
(km
ol/
m3)
CA
(kmol/m3)
CSTR CSTR ExampleExample
383 383.5 384 384.5 385 385.5387.5
388
388.5
389
389.5
390
390.5
391
391.5
T(K
)
T0(K)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
CB
(km
ol/
m3)
CA
(kmol/m3)
383 383.5 384 384.5 385 385.5387.5
388
388.5
389
389.5
390
390.5
391
391.5
T(K
)
T0(K)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
CB
(km
ol/
m3)
CA
(kmol/m3)
Statistical constraints are clearly enforced.
What about point-wise-in-time constraints?
Constrained ELOC
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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iii
ikikik
iNi
T
iNi
Ni
ik
ik
T
ikik
T
ikux
xx
BuAxx
tsPxxRuuQxxikik
|
|||1
||
1
||||,
..)(min||
36
iLQRi xLu
Predictive Form of ELOC 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 RegulatorLinear Quadratic Regulator
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Predictive Form of ELOC Predictive Form of ELOC ConstrainedConstrained ELOCELOC
37
max
|
min
|||
zzz
uDxDz
ik
ikuikxik
383 383.5 384 384.5 385 385.5387.5
388
388.5
389
389.5
390
390.5
391
391.5
T(K
)
T0(K)
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
CB
(km
ol/
m3)
CA
(kmol/m3)
iii
ikikik
iNiELOC
T
iNi
Ni
ik
ikELOC
T
ikikELOC
T
ikux
xx
BuAxx
tsxPxuRuxQxikik
|
|||1
||
1
||||,
..)(min||
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Constrained ELOCConstrained ELOC
38
383 383.5 384 384.5 385 385.5387.5
388
388.5
389
389.5
390
390.5
391
391.5
T(K
)
T0(K)
383 383.5 384 384.5 385 385.5387.5
388
388.5
389
389.5
390
390.5
391
391.5
T(K
)
T0(K)
383 384 385 385.5387.5
388.5
389.5
390.5
391.5
Rea
cto
r T
em
pera
ture T
(K
)
Manipulated Variable Tin
(K)
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Constrained ELOCConstrained ELOC
39
0 5 10 15
384
384.5
385
T0(K
)
EMPC
Constrained ELOC
0 5 10 15388.5
389
389.5
390
390.5
T(K
)
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Constrained ELOC and Horizon SizeConstrained ELOC and Horizon Size
40
0 2 4 6 8 10 12 14
384
384.5
385
T0(K
)
EMPC
Constrained ELOC N=1
Constrained ELOC N=10
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Constrained ELOCConstrained ELOC and Nonlinear Plantsand Nonlinear Plants
iiiikikik
iNiELOC
T
iNi
Ni
ik
ikELOC
T
ikikELOC
T
ikux
xxBuAxx
tsxPxuRuxQxikik
||||1
||
1
||||,
..)(min||
41
max
|
min
|||
zzz
uDxDz
ik
ikuikxik
max
|
min
|||
||||1
),(
),(
zzz
uxhz
xxuxfx
ik
ikikik
iiiikikik
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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ELOC in Building HVACELOC in Building HVAC
42
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Constrained ELOC in Building HVACConstrained ELOC in Building HVAC
43
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Horizon Size Insensitivity Horizon Size Insensitivity
44
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Computational EfficiencyComputational Efficiency
45
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Presentation OutlinePresentation Outline
Review of EMPC
Challenges Associated with the Design of
Smart Grid Systems
ELOC and Constrained ELOC
Computationally Efficient Design of
Smart Grid Systems
46
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Where Are We?Where Are We?
47
EMPC
Provides economically optimized performance
Need for large horizons makes it slow
ELOC and Constrained ELOC
Both are good surrogates for EMPC
Both are computationally fast
Objective: Use ELOC to enable computational tractability of Equipment Design problem
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Use of Surrogate Controllers Use of Surrogate Controllers
48
ELOC Constrained ELOC
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
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Possible Search SchemePossible Search Scheme
49
Global Search with ELOC
minimize NPV
over here-and-now variables and ELOC parameters
Statistical Constraint Enforcement
Constrained ELOC
Simulations
Point-wise-in-time
Constraint Enforcement
Gradient Search
minimize NPV
over here-and-now variables
Gradient Search with Constrained ELOCProvide:
here-and-now values
Return: minimum
average operating costs
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Economic Linear Optimal Control Economic Linear Optimal Control ELOC Based DesignELOC Based Design
50
min
,
max
,
cos.
,,,,,
)()(
)()(
),,(),,,(..
),(min
jjjzjjjz
T
uxxuxz
T
w
T
xx
zz
ztop
Lqms
qqqq
LDDLDD
GGBLABLA
mshqpmsfsts
qg
zx
),(),(min minmax
cos.cos.
,
,,,,,,
minmax
jjtcapztop
Lqms
qqgqg
jj
zx
Global Solutions can be determined efficiently using GBD
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
HVAC Equipment Sizing Problem HVAC Equipment Sizing Problem
51
Heat from
BuildingBuilding
Heat from
Environment
Power
Consumption Chiller
Heat to
TES
Thermal
Energy Storage
Heat to
Chiller
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
ELOC Based DesignELOC Based Design
52
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Proposed Search SchemeProposed Search Scheme
53
Global Search with ELOC
minimize NPV
over here-and-now variables and ELOC parameters
Statistical Constraint Enforcement
Constrained ELOC
Simulations
Point-wise-in-time
Constraint Enforcement
Gradient Search
minimize NPV
over here-and-now variables
Gradient Search with Constrained ELOCProvide:
here-and-now values
Return: minimum
average operating costs
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Es
min (kW
T hr)
Pcm
ax (
kW
e)
0 -500 -1000 -15000
25
50
Es
min (kW
T hr)
Pcm
ax (
kW
e)
0 -500 -1000 -15000
25
50
1
435
2
Gradient Search with Constrained ELOCGradient Search with Constrained ELOC
54
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
ConstrainedConstrained ELOCELOC
55
max
|
min
|||
zzz
uDxDz
ik
ikuikxik
iii
ikikik
iNiELOC
T
iNi
Ni
ik
ikELOC
T
ikikELOC
T
ikux
xx
BuAxx
ts
xPxuRuxQxikik
|
|||1
||
1
||||,
..
)(min||
szzsz ik max
|
min
scxPxuRuxQx siNiELOC
T
iNi
Ni
ik
ikELOC
T
ikikELOC
T
ikux ikik
||
1
||||,
)(min||
ConstrainedConstrained ELOC with Soft ConstraintsELOC with Soft Constraints
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Penalty for Infeasible OperationPenalty for Infeasible Operation
56
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
Conclusions Conclusions
57
EMPC
Provides economically optimized performance
Need for large horizons makes it slow
ELOC and Constrained ELOC
Both are good surrogates for EMPC
Both are computationally fast
Equipment Design for Smart Grid Systems
ELOC enables computational tractability
Penalty method developed to address infeasibilities
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
58
Design of Design of DispatchableDispatchable Energy StorageEnergy Storage
max
110 SS EE
max
220 SS EE
max*000,100$ Sjj ECapCost
ELOC Solution:
MWhrEE SS 239max
2
max
1
Department of Chemical and Biological EngineeringDepartment of Chemical and Biological Engineering
Illinois Institute of TechnologyIllinois Institute of Technology
59
ELOC Operating RegionELOC Operating Region with ELOC Optimal Storage Sizing with ELOC Optimal Storage Sizing
0 50 100 150 200 250 300 350200
300
400
500
600
Gas Turbine PG1
(MW)
Co
al
Pla
nt
PG
6(M
W)
0 50 100 150 2000
20
40
60
80
100
Power Flow P23
(MW)
Pow
er F
low
P2
1(M
W)
250 300 350 400 450 500 550 600
-100
-80
-60
-40
-20
0
Power Flow P62
(MW)
Pow
er F
low
P4
2(M
W)
-300 -250 -200 -150-50
0
50
100
Power Flow P46
(MW)
Po
wer F
low
P4
1(M
W)