Post on 27-Jun-2020
Power Coordination Control and Energy Storage Sizing: Application to Hybrid Fuel Cell Vehicles
Donald J. Chmielewski Associate Professor
Department of Chemical and Biological Engineering Illinois Institute of Technology
Chicago, IL
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Research Overview (Chmielewski Lab)
Control Theory
Profit Control
- Chemical Processes
- Inventory Planning
- Smart Grid Operation and
Expansion Planing
- Water Resource Management
- Hybrid Vehicle Control and
System Design
Market Responsive Control
- Dispatchable IGCC
- Building HVAC with Thermal
Energy Storage
Energy Systems
Power Systems
- Dry Gasification Oxy-
Combustion (DGOC) Process
- Oxygen as Energy Carrier
Fuel Cell Systems
- SOFC
- Fuel Processors
- PEMFC
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Outline
• Motivation and Background
• Profit Control
• Controller Embedded System Design:
- Hybrid Vehicle Equipment Sizing
• Utility Scale Power Systems:
- Energy Storage System Sizing
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Motivating Example
time
T(t)
F(t)
F(sp)
T(sp)
time
F
F
CA, T
PI Controller:
)(
)()/(
sp
c
spIcc
TTe
ex
FxeKF
i
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Phase Plane Trajectory
)(tF
)(tT
*
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Expected Dynamic Operating Region (EDOR)
)(tF
)(tT
*
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Expected Dynamic Operating Region (EDOR)
)(tF
)(tT
*
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Selection of Set-Points
)(tF
)(tT
* )(spT
PI Controller:
)(
)()/(
sp
c
spIcc
TTe
ex
FxeKF
)(spF
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(tF
)(tTmaxT
maxF
Available Steady-State Operating Points
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Real-Time Optimization
),,(),,( pmshqpmsfs
Original Nonlinear Process Model:
maxmin
,,
),,(),,(0
s.t. )(max
iii
qms
qqqpmshqpmsf
qg
Real-Time Optimization (maximize profit):
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Optimal Operating Point
)(tF
)(tT
Decrease F
Increase T
Increase conversion
Increase production
maxT
maxF
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Backed-off Operating Point (BOP)
)(tF
)(tT
* maxT
maxF
)(spT
)(spF
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Backed-off Operating Point Selection
Based on Seady-State Models and Flexibility Analysis: Bahri et al. (1995),
Young et al. (1996), Bahri et al. (1996), Figueroa et al. (1996), Contreras-Dordelly
& Marlin, (2000), Zhang & Forbes, (2000), Figueroa & Desages, (2003), Rooney
& Biegler (2003), Arbiza et al. (2003), Young et al. (2004) and Soliman et al.
(2008)
Based on Stochastic Models and Chance Constrained Optimization:
Loeblein & Perkins (1999a, 1999b), van Hessem et al. (2001), Muske (2003),
Peng et al., (2005), Lee et al. (2008), Akande et al. (2009) and Zhao et al. (2009).
Literature Review:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Backed-off Operating Point Selection
Based on Seady-State Models and Flexibility Analysis: Bahri et al. (1995),
Young et al. (1996), Bahri et al. (1996), Figueroa et al. (1996), Contreras-Dordelly
& Marlin, (2000), Zhang & Forbes, (2000), Figueroa & Desages, (2003), Rooney
& Biegler (2003), Arbiza et al. (2003), Young et al. (2004) and Soliman et al.
(2008)
Based on Stochastic Models and Chance Constrained Optimization:
Loeblein & Perkins (1999a, 1999b), van Hessem et al. (2001), Muske (2003),
Peng et al., (2005), Lee et al. (2008), Akande et al. (2009) and Zhao et al. (2009).
Literature Review:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Backed-off Operating Point Selection
Based on Seady-State Models and Flexibility Analysis: Bahri et al. (1995),
Young et al. (1996), Bahri et al. (1996), Figueroa et al. (1996), Contreras-Dordelly
& Marlin, (2000), Zhang & Forbes, (2000), Figueroa & Desages, (2003), Rooney
& Biegler (2003), Arbiza et al. (2003), Young et al. (2004) and Soliman et al.
(2008)
Based on Stochastic Models and Chance Constrained Optimization:
Loeblein & Perkins (1999a, 1999b), van Hessem et al. (2001), Muske (2003),
Peng et al., (2005), Lee et al. (2008), Akande et al. (2009) and Zhao et al. (2009).
Literature Review:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Step 0: Start with Constrained MPC controller:
maxmin
0,
..
min
iii
ux
TT
ux
zzz
uDxDz
GwBuAxxts
dtRuuQxx
Stochastic BOP Selection (Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
PBPBRQPAPA TT 10
PBRL T1
Lxu
uDxDz
GwBuAxxts
dtRuuQxx
ux
TT
ux
..
min
0,
Step 1: Relax constraints and calculate resulting
linear feedback L:
Stochastic BOP Selection (Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
)()( tLxtu
0)()( Tw
Txx GSGBLABLA
Controller:
Step 2: Closed-loop Covariance Analysis:
Plant )(tw
)(tx
L )(tu
)(tz
Stochastic BOP Selection (Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Expected Dynamic Operating Region (EDOR)
EDOR
defined by:
*
1z
2z
22
221
212
21
z
1
2
Department of Chemical and Biological Engineering
Illinois Institute of Technology
q1 max
EDOR BOP
q1 min
q2 min q2 max
q2 - q2min q2
max - q2
The EDOR and the Constraint Set
Department of Chemical and Biological Engineering
Illinois Institute of Technology
q1 max
EDOR BOP
q1 min
q2 min q2 max
q2 - q2min q2
max - q2
Statistical Constraints (AKA: Chance Constraints)
2max22 qq
min222 qq
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Step 3: Solve the following Linear Program:
minmax
maxmin
,,0 s.t. min
iiiiii
iiiux
qqms
qqqq
qqqmDsDq
BmAsqg
Stochastic BOP Selection (Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
i ’s are calculated in Step 2:
Tuxxuxz LDDLDD )()(
0)()( T
w
T
xx GGBLABLA
Step 3: Solve the following Linear Program:
minmax
maxmin
,,0 s.t. min
iiiiii
iiiux
qqms
qqqq
qqqmDsDq
BmAsqg
}{2zi diag
Stochastic BOP Selection (Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( T
w
T
xx GGBLABLA
Step 3: Solve the following Linear Program:
And L is calculated in Step 1:
LxuGwBuAxxts
dtRuuQxx TT
ux
..
min
0,
}{2zi diag
minmax
maxmin
,,0 s.t. min
iiiiii
iiiux
qqms
qqqq
qqqmDsDq
BmAsqg
i ’s are calculated in Step 2:
Stochastic BOP Selection (Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( T
w
T
xx GGBLABLA
Step 3: Solve the following Linear Program:
And L is calculated in Step 1:
PBPBRQPAPA TT 10
PBRL T1
minmax
maxmin
,,0 s.t. min
iiiiii
iiiux
qqms
qqqq
qqqmDsDq
BmAsqg
}{2zi diag
i ’s are calculated in Step 2:
Stochastic BOP Selection (Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(tF
)(tT
*
maxT
maxF
)(spT
)(spF
Minimum Back-off
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(tF
)(tT
*
maxT
maxF
)(spT
)(spF
Minimum Back-off
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(tF
)(tTmaxT
maxF
Increase F
Increase production
What If …. Different Economics
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(tF
)(tT
*
maxT
maxF
)(spT
)(spF
What If …. Different Economics
Increase F
Increase production
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(tF
)(tT
*
maxT
maxF
)(spT
)(spF
Minimum Back-off (not so profitable)
Increase F
Increase production
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(tF
)(tT
*
maxT
maxF
)(spT
)(spF
Increase F
Increase production
Better Operating Point (but infeasible)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(tF
)(tT
*
maxT
maxF
)(spT
)(spF
Requires Different Tuning
Increase F
Increase production
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Less Aggressive Tuning
)(tF
)(tT
*
time
F(t)
F(sp)
T(sp)
time
F(max)
T(max)
T(t)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Automated Tuning?
)(tF
)(tT
*
* PI Controller:
)(
)()/(
sp
c
spIcc
TTe
ex
FxeKF
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Automated Tuning?
)(tF
)(tT
*
* MPC:
maxmin
0,
..
min
iii
ux
TT
ux
zzz
uDxDz
GwBuAxxts
dtRuuQxx
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Outline
• Motivation and Background
• Profit Control
• Controller Embedded System Design:
- Hybrid Vehicle Equipment Sizing
• Utility Scale Power Systems:
- Energy Storage System Sizing
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( T
w
T
xx GGBLABLA
Step 3: Solve the following Linear Program:
And L is calculated in Step 1:
PBPBRQPAPA TT 10
PBRL T1
minmax
maxmin
,,0 s.t. min
iiiiii
iiiux
qqms
qqqq
qqqmDsDq
BmAsqg
}{2zi diag
i ’s are calculated in Step 2:
Fixed Controller BOP Selection (Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( T
w
T
xx GGBLABLA
Free Controller BOP Selection:
Profit Control (Peng, Manthanwar & Chmielewski, 2005)
PBPBRQPAPA TT 10
PBRL T1
minmax
maxmin
,,,,,,
,,,
0 s.t .
min
iiiiii
iiiux
q
RQPL
qms
qqqq
qqqmDsDq
BmAs
qg
izx
}{2zi diag
Department of Chemical and Biological Engineering
Illinois Institute of Technology
*
*
More profit
Less profit
Max
Profit
Different
Tuning
Values
Visualization of Profit Control
Simultaneous BOP Selection and Controller Tuning:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Fluidized Catalytic Cracker
Regenerator and Separator (dynamic):
Riser (pseudo steady state):
(adapted from Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
FCC Constraints and Economics
Process Constraints:
Profit Function:
Fgs Fgl and Fugo are product flows
(gasoline, light gas and unconverted oil).
(adapted from Loeblein & Perkins, 1999)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( T
w
T
xx GGBLABLA
Step 3: Solve the following Linear Program:
Fixed Controller BOP Selection (Loeblein & Perkins, 1999)
And L is calculated in Step 1:
PBPBRQPAPA TT 10
PBRL T1
minmax
maxmin
,,0 s.t. min
iiiiii
iiiux
qqms
qqqq
qqqmDsDq
BmAsqg
}{2zi diag
i ’s are calculated in Step 2:
55xIQ 22xIR
Department of Chemical and Biological Engineering
Illinois Institute of Technology
0 5 10 15 20
x 10-4
25
26
27
28
29
30
31
32
Inle
t A
ir (
kg
/s)
Oxygen Mass Fraction5 5.5 6 6.5 7 7.5 8 8.5
x 10-3
280
300
320
340
360
380
400
Cata
lyst
Flo
w (
kg
/s)
Fraction of Coke in Regenerator
0.0125 0.013 0.0135 0.014 0.0145 0.015
990
992
994
996
998
1000
Reg
en
era
tor
Tem
p (
K)
Coke Fraction in Separator
Fixed Controller Free Controller
785 790 795 800 805 810 815
990
992
994
996
998
1000
Cyclo
ne T
em
pera
ture
(K
)
Separator Temperature (K)
Profit Control vs. Fixed Controller Back-off
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Profit Comparisons
Gross Profit Diff from OSSOP ($/day) ($/day) OSSOP $36,905 $0.0 Fixed Control $34,631 - $2,274 Profit Control $35,416 - $1,489 Improves profit by 2%
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( T
w
T
xx GGBLABLA
Step 3: Solve the following Linear Program:
Fixed Controller BOP Selection (Loeblein & Perkins, 1999)
And L is calculated in Step 1:
PBPBRQPAPA TT 10
PBRL T1
minmax
maxmin
,,0 s.t. min
iiiiii
iiiux
qqms
qqqq
qqqmDsDq
BmAsqg
}{2zi diag
i ’s are calculated in Step 2:
55xIQ 22xIR
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Profit Control Applications
• Mechanical Systems
• Chemical and Reaction Systems
• Hybrid Vehicle Design
• Inventory Control
• Electric Power System Design
• Building HVAC
• Water Resource Management
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
Profit Control Optimization Problem:
Computational Aspects
PBPBRQPAPA TT 10
PBRL T1
minmax
maxmin
,,,,,,
,,,
0 s.t .
min
iiiiii
iiiux
q
RQPL
qms
qqqq
qqqmDsDq
BmAs
qg
izx
}{2zi diag
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
Profit Control Optimization Problem:
Computational Aspects
PBPBRQPAPA TT 10
PBRL T1
minmax
maxmin
,,,,,,
,,,
0 s.t .
min
iiiiii
iiiux
q
RQPL
qms
qqqq
qqqmDsDq
BmAs
qg
izx
}{2zi diag
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
Covariance Equations:
Computational Aspects
PBPBRQPAPA TT 10
PBRL T1
}{2zi diag
LQR Solution:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
Covariance Equations:
Expanded Feasible Region
PBPBRQPAPA TT 10
PBRL T1
}{2zi diag
LQR Solution:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
EDOR Feasible Region
1
2
Region of
Feasible
Controllers
Infeasible
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
}{2zi diag
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Theorem 1 (Chmielewski & Manthanwar, 2004):
MPC Equivalence
All controllers on feasible region boundary
are equal to
some Unconstrained Model Predictive Controller
(aka LQR Control)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Pareto Frontier Interpretation
1
2
LQR Controllers
are on Frontier
Infeasible
Region
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
}{2zi diag
PBPBRQPAPA TT 10
PBRL T1
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
Covariance Equations:
Explicit LQR Constraints Not Needed
PBPBRQPAPA TT 10
PBRL T1
}{2zi diag
LQR Solution:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Inverse Optimality
01 TT MPBRMPBQPAPA TMPBRL 1
Theorem 2 (Chmielewski & Manthanwar, 2004):
If there exists P > 0 and R > 0 such that
0
RPBRL
PBRLPAPARLLTT
TTT
then P and R satisfy
GwBuAxxts
dtRuuMuxQxxLxu TTT
ux
..
2min
0,
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
Nonlinear Covariance Equations:
Computational Aspects
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Tuxxuxz LDDLDD )()(
0)()( Tw
Txx GSGBLABLA
Nonlinear Covariance Equations:
Convexification
0)(
)(
XYDXD
YDXDT
ux
uxz
0)()( Tw
T GSGBYAXBYAX
Equivalent to Convex Linear Matrix Inequalities:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
}{
''
0 s.t . min
2
minmax
maxmin
,,',','
ziii
iiiiii
iiiux
q
YXqms
diag
qqqq
qqqmDsDq
BmAsqg
i
0)(
)(
XYDXD
YDXDT
ux
uxz
0)()( Tw
T GSGBLAXBYAX
Profit Control Optimization Problem
Department of Chemical and Biological Engineering
Illinois Institute of Technology
}{
''
0 s.t . min
2
minmax
maxmin
,,',','
ziii
iiiiii
iiiux
q
YXqms
diag
qqqq
qqqmDsDq
BmAsqg
i
0)(
)(
XYDXD
YDXDT
ux
uxz
0)()( Tw
T GSGBLAXBYAX
Reverse Convex Constraints
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Reverse-Convex Constraints
-2 -1.5 -1 -0.5 00
0.2
0.4
0.6
0.8
1
zss,i
i
(zss,i
+dmin,i
)2 (z
ss,i+d
max,i )
2
Feasible Region
2
1
max
11 )''( qq 2min
111 )''( qq
1'q
1
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Global Solution
-2 -1.5 -1 -0.5 00
0.2
0.4
0.6
0.8
1
zss,i
i
Region 1
Region 2
Region 3
Region 4
Region 5
Based on Branch and Bound algorithm
1'q
1
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Outline
• Motivation and Background
• Profit Control
• Controller Embedded System Design:
- Hybrid Vehicle Equipment Sizing
• Utility Scale Power Systems:
- Energy Storage System Sizing
Department of Chemical and Biological Engineering
Illinois Institute of Technology
q1 max
EDOR BOP
q1 min
q2 min q2 max
q2 - q2min q2
max - q2
Statistical Constraints (AKA: Chance Constraints)
2max22 qq
min222 qq
Department of Chemical and Biological Engineering
Illinois Institute of Technology
q1 max
EDOR BOP
q1 min
q2 min q2 max
q2 - q2min q2
max - q2
Variable Constraint Bounds
2max22 qq
min222 qq
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Hybrid Vehicle Design
iscap
Rscap
Escap
iarm
Rarm
Larm
ibat
Rbat
Ebat
ifc
Efc
Fuel
Cell
Power Bus
warm
Earm
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Hybrid Vehicle Design
iascap
iscap
Rscap
Escap
iarm
Rarm
Larm
DC-DC
Converter
iabatibat
Rbat
Ebat
DC-DC
Converter
iafcifc
EfcDC-DC
Converter
Fuel
Cell
Power Bus
warm
Earm
kfc kbat kscap
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Servo-Loops with PI Controllers
Vehicle
Power
System
+ -Pscap
(sp) Pscap
kscap
+ -Pbat
(sp) Pbat
kbat
+ -Pfc
(sp) Pfc
kfc
PI
PI
PI
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Supervisory Control
Vehicle
Power
System
+ -Pscap
(sp) Pscap
kscap
High
Level
Controller
Pmot(sp)
+ -Pbat
(sp) Pbat
kbat
+ -Pfc
(sp) Pfc
kfc
PI
PI
PI
Department of Chemical and Biological Engineering
Illinois Institute of Technology
High Level Battery Model
)(loss
batbatbat PPE
Department of Chemical and Biological Engineering
Illinois Institute of Technology
)(loss
batbatbat PPE maxmin
batbatbat EEE
0min batE
batbatbat meE ˆmax
High Level Battery Model
Department of Chemical and Biological Engineering
Illinois Institute of Technology
High Level Battery Model
)(loss
batbatbat PPE maxmin
batbatbat EEE
maxmin
batbatbat PPP
0min batE
batbatbat meE ˆmax
batbat
drate
batbat meCP ˆˆ ,min
batbat
crate
batbat meCP ˆˆ ,min
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Ebat
Pbat
max ,c maxrate
bat bat batP C E
min 0batE
max ˆbat bat batE e m
min ,d maxrate
bat bat batP C E
Power and Energy Constraints of the Battery
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Ebat
Pbat
max ,c maxrate
bat bat batP C E
max ˆbat bat batE e m
Constraints a Function of the Mass
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Ebat
Pbat
max ,c maxrate
bat bat batP C E
max ˆbat bat batE e m
Aspect Ratio a Function of C-Rate
Department of Chemical and Biological Engineering
Illinois Institute of Technology
High Level Battery Model
)(loss
batbatbat PPE maxmin
batbatbat EEE
maxmin
batbatbat PPP
0min batE
batbatbat meE ˆmax
batbat
drate
batbat meCP ˆˆ ,min
batbat
crate
batbat meCP ˆˆ ,min
batbat
batloss
batml
PP
ˆ
2)(
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Operating Region with Power Losses
Ebat
Pbat
Department of Chemical and Biological Engineering
Illinois Institute of Technology
High Level Super Cap Model
)(loss
scscsc PPE maxmin
scscsc EEE
maxmin
scscsc PPP
0min scE
scscsc meE ˆmax
scsc
drate
scsc meCP ˆˆ ,min
scsc
crate
scsc meCP ˆˆ ,min
scsc
scloss
scml
PP
ˆ
2)(
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Fuel Cell Model
MEA
Anode
In
(H2, H
2O) H
2
Cathode
Air in
Cathode
Exhaust
O2
H2O
N2
Solid Material Current Collector
H+
H+
H+
H+
H+
H+
H+
H+
Anode
Exhaust
H2O
Department of Chemical and Biological Engineering
Illinois Institute of Technology
High Level Fuel Cell Model
fcfc PP maxmin
fcfcfc PPP
maxmin
fcfcfc PPP
0min fcP
fcfcfc mpP ˆmax
fcfc
drate
batfc mpCP ˆ,min
fcfc
crate
batfc mpCP ˆ,max
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Supervisory Control
Vehicle
Power
System
+ -Pscap
(sp) Pscap
kscap
High
Level
Controller
Pmot(sp)
+ -Pbat
(sp) Pbat
kbat
+ -Pfc
(sp) Pfc
kfc
PI
PI
PI
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Power Demand Disturbance
0 200 400 600 800 1000 1200 14000
20
40
60
time (sec)
Sp
eed
(m
ph
)
0 200 400 600 800 1000 1200 1400-40
-20
0
20
40
time (sec)
Po
wer
to M
oto
r (k
W)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
`
Pfc
Δ Pfc
Optimal Steady-State Operating Point
Ebat
Pbat
Department of Chemical and Biological Engineering
Illinois Institute of Technology
`
Pfc
Δ Pfc
Controller, EDOR and Back-off all Functions of Equipment Sizes
Ebat
Pbat
Department of Chemical and Biological Engineering
Illinois Institute of Technology
min
1
min
2
min
3
min
4
min
5
min
6
0 1...6i
fc fc
bat bat
sc sc
fc fc
bat bat
sc sc
i
P P
E E
E E
P P
P P
P P
Design Problem Formulation
0 0
0
0 0
0
fc o bat sc
v o fc bat sc
bat bat bat
bat bat bat
bat bat bat
sc sc sc
sc sc sc
sc sc sc
P P P P
m m m m m
P P
l m
P l m
P P
l m
P l m
1
1
1
0
0
1...6
T
o v
o v w
i i x u
T T
x u i
AX BY AX BY G m G
G m G
D X D Y
D X D Y X
i
2
max
1
max
2
max
3
max
4
max
5
max
6
i i
fc fc
bat bat
sc sc
fc fc
bat bat
sc sc
P P
E E
E E
P P
P P
P P
. .ˆ ˆ ˆmin{ }fc fc bat bat sc sc
s tc m c m c m
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Case Study
Technology Lithium Battery Super-Capacitor PEM Fuel Cell
Cost $59/kg $93/kg $300/kg
C-Rate 0.5 hr-1 360 hr-1 10 hr-1
Power Density 100 W/kg 110,000 W/kg 1 W/kg
Appetecchi & Prosini (2005) ;
Portet et al., (2005);
Murphy et al., (1998)
Parametric Data:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Case Study
Technology Lithium Battery Super-Capacitor PEM Fuel Cell
Cost $59/kg $93/kg $300/kg
C-Rate 0.5 hr-1 360 hr-1 10 hr-1
Power Density 100 W/kg 110,000 W/kg 1 W/kg
Appetecchi & Prosini (2005) ;
Portet et al., (2005);
Murphy et al., (1998)
Parametric Data:
Technology Lithium Battery Super-Capacitor PEM Fuel Cell Total Capital Cost
Mass 30 kg 2.8 kg 3.5 kg
Nominal Power 0.1 kW 1.5 kW 1.8 kW
Cost $1770 $260 $1050 $3,080
Case Study Solution:
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Case Study Solution: EDOR, Back-off and Time Plots
-1 -0.5 0 0.5 1
x 10-5
0
0.5
1
1.5
2
2.5
3
3.5
Pfc
(
kW
)
Pfc
(kW/s)
Fuel Cell
20 25 30 35 40 451.9
1.95
2
2.05
2.1Fuel Cell Power(kW)
time(hr)
-10 -2 0 2 10
0
100
200
300
400
500
600
700
Esc
(k
J)
Psc
(kW)
Super Capacitor
20 20.02 20.04 20.06 20.08 20.1-15
-10
-5
0
5
10
15SuperCap Power, kW
time(hr)
-1.5 -1 -0.5 0 0.5 1 1.5
0
2000
4000
6000
8000
10000
Eb
at
(kJ)
Pbat
(kW)
Battery
20 20.2 20.4 20.6 20.8 21-2
-1.5
-1
-0.5
0
0.5
1
1.5
2Battery Power, kW
time(hr)
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Outline
• Motivation and Background
• Profit Control
• Controller Embedded System Design:
- Hybrid Vehicle Equipment Sizing
• Utility Scale Power Systems:
- Energy Storage System Sizing
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Electric Power System Design
Gas Turbine
PC Boiler
Renewable Transmission
Grid
Consumer Demand
Energy Storage
Department of Chemical and Biological Engineering
Illinois Institute of Technology
System Disturbances
0 5 10 15 20 25 30 35 400
100
200
300
400
500
600
700
Pr (
MW
)
Days
Consumer Demand
1.5 2 2.5 3 3.5 4 4.5 5
10
12
14
16
Pow
er
Load (
GW
)
Forcasted Data
Simulated Data
Renewable Power
Generated
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Electric Power System Model
min max
min max
max
0.8
1200
C C C
C C
C
P P P
P P
P
min max
max max0.05
C C C
C C
r r r
r P
min max
min max
max
0.2
1000
T T T
T T
T
P P P
P P
P
min max
max max6
T T T
T T
r r r
r P
Power Limits Power Limits
Rate Limits Rate Limits
max0 S SE E
min max
S S SP P P
Energy Limits
Power Limits
PC Boiler
CC rP Gas Turbine
TT rP
Pumped Hydro
SS PE
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Manipulated Variables
min max
min max
max
0.8
1200
C C C
C C
C
P P P
P P
P
min max
max max0.05
C C C
C C
r r r
r P
min max
min max
max
0.2
1000
T T T
T T
T
P P P
P P
P
min max
max max6
T T T
T T
r r r
r P
Power Limits Power Limits
Rate Limits Rate Limits
max0 S SE E
min max
S S SP P P
Energy Limits
Power Limits
PC Boiler
CC rP Gas Turbine
TT rP
Pumped Hydro
SS PE
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Defined by Power Balance
min max
min max
max
0.8
1200
C C C
C C
C
P P P
P P
P
min max
max max0.05
C C C
C C
r r r
r P
min max
min max
max
0.2
1000
T T T
T T
T
P P P
P P
P
min max
max max6
T T T
T T
r r r
r P
Power Limits Power Limits
Rate Limits Rate Limits
max0 S SE E
min max
S S SP P P
Energy Limits
Power Limits
PC Boiler
CC rP Gas Turbine
TT rP
Pumped Hydro
SS PE
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Equipment Costs
min max
min max
max
0.8
1200
C C C
C C
C
P P P
P P
P
min max
max max0.05
C C C
C C
r r r
r P
min max
min max
max
0.2
1000
T T T
T T
T
P P P
P P
P
min max
max max6
T T T
T T
r r r
r P
Power Limits Power Limits
Rate Limits Rate Limits
max0 S SE E
min max
S S SP P P
Energy Limits
Power Limits
PC Boiler
CC rP Gas Turbine
TT rP
Pumped Hydro
SS PE
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Case Study
Average of Power Generators
32% Gas Turbine
48% PC Boiler
20% Renewable
Pumped Hydro Equipment Costs
Energy Storage: $55/kWh
Power Rating: $1300/kW
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Case Study Results
200 400 600 800 1000
-5000
0
5000
Rate
(M
W/h
r)
Power (MW)
Gas Turbine
700 800 900 1000 1100 1200-40
-20
0
20
40
Rate
(M
W/h
r)
Power (MW)
Coal
0 2000 4000 6000 8000 10000 12000 14000
-1000
-500
0
500
1000
Po
wer
(MW
)
Energy (MWh)
Storage
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Other Cases
Case
Coal
Power
Gas
Turbine Renewable
Storage
Size
Storage
Power
1 48% 32% 20% 12.9 GWh 948 MW
2 18% 32% 50% 26.8 GWh 1398 MW
3 75% 5% 20% 61.1 GWh 1188 MW
Department of Chemical and Biological Engineering
Illinois Institute of Technology
New Directions
Gas Turbine
PC Boiler
Renewable Transmission
Grid
Consumer Demand
Energy Storage
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Acknowledgements
• Current Students: Ben Omell David Mendoza-Serrano Ming-Wei Yang Syed Amed
• 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 – 0967906) Graduate and Armour Colleges, IIT Chemical & Biological Engineering Department, IIT
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Conclusions
• Relationship between control system performance
and plant profit quantified.
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Conclusions
• Relationship between control system performance
and plant profit quantified.
• Enables profit guided controller design.
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Conclusions
• Relationship between control system performance
and plant profit quantified.
• Enables profit guided controller design.
• Allows for controller embedded system design
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Conclusions
• Relationship between control system performance
and plant profit quantified.
• Enables profit guided controller design.
• Allows for controller embedded system design
• Broad set of applications from a variety of
disciplines.
Department of Chemical and Biological Engineering
Illinois Institute of Technology
Conclusions
• Relationship between control system performance
and plant profit quantified.
• Enables profit guided controller design.
• Allows for controller embedded system design
• Broad set of applications from a variety of
disciplines.
• Non-convex, but global methods can be used to
size and/or select equipment.